From Dark and Darker Wiki

m (action speed hybrid stat)
(→‎Move Speed: Note about adding the base 300 Move Speed to the chart value for actual Move Speed)
 
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<metadesc>Dark and Darker Wiki Stats Guide</metadesc>
<metadesc>Dark and Darker Wiki Stats Guide</metadesc>
{{UpdateStatus|Stats Data}}
{{MechanicsBar}}
=Stats=
Stats are primarily modified through the gear your character has equipped. [[Weapons]]/[[utilities]] only modify your character while held. For example, holding a Main-Hand and Off-Hand weapon in the first weapon slot will give each other weapon their stats, but neither will benefit from the stats of the weapon(s) in the second slot. Similarly, the bonuses from a [[Flute]] are only granted while wielding the Flute. Stats from these sources will not be reflected in the Lobby.
Stats may also be modified by perks, [[buffs]], and [[debuffs]]. Stats from perks will be reflected in the Lobby only if those stats are applied unconditionally. Stats from conditional perks (as well as buffs and debuffs) will not be viewable from the Lobby.
==Charts==
==Charts==
Charts are created using the data points directly taken from the game. Therefore, if there is a mismatch between chart and explanation, it is better to look at chart info.  
Charts are created using the data points directly taken from the game. Therefore, if there is a mismatch between chart and the in game display, it is better to look at chart info.  


For example, even though the formula might give 32.5, in game this might get rounded to 33.
For example, even though the formula might give 32.5, in game the display might get [[Damage_Calculation#Rounding|rounded]] to 33.


=Attributes=
=Attributes=
Stats that come from character's attributes.
Main stats that affect multiple other stats. Each [[class]] has varying base attributes, but they sum up to 105 for each class. Can be found as primary stats (stats which are always present on an item of the same name regardless of rarity or instance such as Strength on a [[Padded Tunic]]) as well as [[enchantments]].
 
==Strength==
==Strength==
===Physical Power===
===Physical Power===
Physical Power governs your Physical Power Bonus.
Physical Power governs your Physical Power Bonus.
<div style="display:flex;flex-wrap:wrap;">
{{Stats Data|physicalpower}}
<div style="width:500px;>
0 Strength starts at = 0 Physical Power
 
Every Strength point gives an increase to Physical Power
 
*0 -> 0
*0 to 100 = 1 each, up to 100
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=PhysicalPower|data=[{"x": 0.0,"y": 0.0},{"x": 100.0,"y": 100.0}]|color=orange}}
 
</div>
</div>


===Physical Power Bonus===
===Physical Power Bonus===
- More recently known as Physical Damage Bonus
<span id="Physical Damage Bonus">
Physical Power Bonus governs the potency of your physical damage dealing weapons, utility items and abilities.
Also known as Physical Damage Bonus, Physical Power Bonus governs the potency of your physical damage dealing weapons, utility items, and abilities.
<div style="display:flex;flex-wrap:wrap;">
{{Stats Data|physicalpowerbonus}}</span>
<div style="width:500px;>
0 Physical Power starts at = -80% Physical Power Bonus
 
Every Physical Power point gives a  % increase to overall Physical Power Bonus depending on fixed thresholds
*0 -> -80%
*0 to 5 = 10% each, up to -30%
*5 to 7 = 5% each, up to -20%
*7 to 11 = 3% each, up to -8%
*11 to 15 = 2% each, up to 0%
*15 to 50 = 1% each, up to 35%
*50 to 100 = 0.5% each, up to 60%
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=PhysicalDamageMod|data=[{"x": 0.0,"y": -80.0},{"x": 1.0,"y": -70.0},{"x": 5.0,"y": -30.0},{"x": 7.0,"y": -20.0},{"x": 11.0,"y": -8.0},{"x": 15.0,"y": 0.0},{"x": 19.0,"y": 4.0},{"x": 20.0,"y": 5.0},{"x": 21.0,"y": 6.0},{"x": 27.0,"y": 12.0},{"x": 30.0,"y": 15.0},{"x": 35.0,"y": 20.0},{"x": 36.0,"y": 21.0},{"x": 38.0,"y": 23.0},{"x": 39.0,"y": 24.0},{"x": 44.0,"y": 29.0},{"x": 50.0,"y": 35.0},{"x": 51.0,"y": 35.5},{"x": 58.0,"y": 39.0},{"x": 59.0,"y": 39.5},{"x": 64.0,"y": 42.0},{"x": 70.0,"y": 45.0},{"x": 71.0,"y": 45.5},{"x": 76.0,"y": 48.0},{"x": 86.0,"y": 53.0},{"x": 87.0,"y": 53.5},{"x": 98.0,"y": 59.0},{"x": 100.0,"y": 60.0}]|color=orange}}
 
</div>
</div>
 
===Max Health from Strength===
Max Health governs your character's maximum available health points.
Max Health is comprised of both Strength, which has a weight of 25%, and [[Stats#Vigor|Vigor]], which has a weight of 75%.


Note that your displayed Max Health will be the sum of Strength-sourced Max Health and [[Stats#Vigor|Vigor]]-sourced Max Health.
Lower limit of -100%.


For example, Fighter's 15 strength and 15 vigor results in 25 strength sourced health and 75 vigor sourced health, resulting in 100 Max Health.
===Base Health from Strength===
Base Health determines your characters maximum [[Health]].


<div style="display:flex;flex-wrap:wrap;">
See the Hybrid stat [[Stats#Base_Health|Base Health]] for more.
<div style="width:500px;>
0 Strength starts at = 45 Max Health
 
Every Strength point gives an increase to Max Health depending on fixed thresholds
 
*0 -> 15
*0 to 10 = 0.75 each, up to 22.5
*10 to 50 = 0.5 each, up to 42.5
*50 to 75 = 0.25 each, up to 48.75
*75 to 100 = 0.125 each, up to 51.875
 
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=StrengthSourcedHealth|data=[{"x": 0.0,"y": 15.0},{"x": 10.0,"y": 22.5},{"x": 50.0,"y": 42.5},{"x": 75.0,"y": 48.75},{"x": 100.0,"y": 51.875}]|color=orange}}
 
</div>
</div>




==Vigor==
==Vigor==
===Max Health from Vigor===
===Base Health from Vigor===
Max Health governs your character's maximum available health points.
Base Health determines your characters maximum [[Health]].
Max Health is comprised of both Vigor, which has a weight of 75%, and [[Stats#Strength|Strength]], which has a weight of 25%.  


Note that your displayed Max Health will be the sum of Vigor-sourced Max Health and [[Stats#Strength|Strength]]-sourced Max Health.
See the Hybrid stat [[Stats#Base_Health|Base Health]] for more.


For example, Fighter's 15 strength and 15 vigor results in 25 strength sourced health and 75 vigor sourced health, resulting in 100 Max Health.
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
0 Vigor starts at = 45 Max Health
Every Vigor point gives an increase to Max Health depending on fixed thresholds
*0 -> 45
*0 to 10 = 2.25 each, up to 67.5
*10 to 50 = 1.5 each, up to 127.5
*50 to 75 = 0.75 each, up to 146.25
*75 to 100 = 0.375 each, up to 155.625
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=VigorSourcedHealth|data=[{"x": 0.0,"y": 45.0},{"x": 10.0,"y": 67.5},{"x": 50.0,"y": 127.5},{"x": 75.0,"y": 146.25},{"x": 100.0,"y": 155.625}]|color=orange}}
</div>
</div>


===Health Recovery===
===Health Recovery===
Line 112: Line 50:
<code>Health Recovered every 2s = 1 * (1 + .95) = 1.95 Health</code>
<code>Health Recovered every 2s = 1 * (1 + .95) = 1.95 Health</code>


<div style="display:flex;flex-wrap:wrap;">
Can't be found on gear aside from in the form of its governing attribute.
<div style="width:500px;>
Each point in Vigor increases Health Recovery Bonus
*0 -> -55%
*0 to 5 = 5% each, up to -30%
*5 to 15 = 3% each, up to 0%
*15 to 25 = 7% each, up to 70%
*25 to 35 = 5% each, up to 120%
*35 to 84 = 2% each, up to 218%
*84 to 85 = 1% each, up to 219%
*85 to 86 = 3% each, up to 222%
*86 to 100 = 2% each, up to 250%


</div>
{{Stats Data|healthrecovery}}
<div style="width:400px;">
{{#widget:Chart|uniqueId=HealthRecoveryMod|data=[{"x": 0.0,"y": -0.55},{"x": 5.0,"y": -0.3},{"x": 15.0,"y": 0.0},{"x": 25.0,"y": 0.7},{"x": 35.0,"y": 1.2},{"x": 84.0,"y": 2.18},{"x": 85.0,"y": 2.19},{"x": 86.0,"y": 2.22},{"x": 100.0,"y": 2.5}]|color=orange}}
 
</div>
</div>




==Agility==
==Agility==
===Action Speed===
===Action Speed from Agility===
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;">
0 Agility starts at = -38% Action Speed


Every agility point gives a  % increase to action speed depending on fixed thresholds 
See the Hybrid stat [[Stats#Action_Speed|Action Speed]] for more.
*0 -> -38%
*0 to 10 = 3% each, up to -8%
*10 to 13 = 2% each, up to -2%
*13 to 25 = 1% each, up to 10%
*25 to 41 = 1.5% each, up to 34%
*41 to 50 = 1% each, up to 43%
*50 to 100 = 0.5% each, up to 68%
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=ActionSpeed|data=[{"x": 0.0,"y": -38.0},{"x": 8.0,"y": -14.0},{"x": 10.0,"y": -8.0},{"x": 13.0,"y": -2.0},{"x": 18.0,"y": 3.0},{"x": 20.0,"y": 5.0},{"x": 21.0,"y": 6.0},{"x": 25.0,"y": 10.0},{"x": 26.0,"y": 11.5},{"x": 34.0,"y": 23.5},{"x": 38.0,"y": 29.5},{"x": 41.0,"y": 34.0},{"x": 42.0,"y": 35.0},{"x": 46.0,"y": 39.0},{"x": 47.0,"y": 40.0},{"x": 49.0,"y": 42.0},{"x": 50.0,"y": 43.0},{"x": 54.0,"y": 45.0},{"x": 55.0,"y": 45.5},{"x": 60.0,"y": 48.0},{"x": 70.0,"y": 53.0},{"x": 71.0,"y": 53.5},{"x": 82.0,"y": 59.0},{"x": 95.0,"y": 65.5},{"x": 96.0,"y": 66.0},{"x": 100.0,"y": 68.0}]|color=orange}}
 
</div>
</div>


===Move Speed===
===Move Speed===
Move Speed governs the speed at which your character moves. This stat is also directly influenced by wearing gear. Every 1 point in Move Speed is equal to 0.3333...% Move Speed. The default Move Speed for each class is 300, which translates to 100% Move Speed, with penalties or bonuses provided based on Agility. Performing certain actions, such as attacking, or moving in certain directions will also affect Move Speed. Backwards = 60%, Crouch = 65%, Walk = 65%.
Move Speed governs the speed at which your character runs or walks. Every 3 points in Move Speed is equal to 1% movement speed. There are many factors which can affect Move Speed, see [[Movement Speed]] for details.
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
0 Agility starts at = -30 Move Speed


Every agility point gives a flat increase to Move Speed depending on fixed thresholds
To calculate total Move Speed, add the baseline 300 Move Speed to the appropriate value below.
*0 -> -30 Move Speed
{{Stats Data|movespeed}}
*0 to 15 = 2 each, up to 0
*15 to 45 = 1 each, up to 30
*45 to 65 = 0.5 each, up to 40 (Technically 1 Move Speed every 2 Agility. Agility can not provide decimal Move Speed.)
*65 to 100 = 0.33 each, up to 51 Move Speed (Same as above, 1 Move Speed every 3 Agility.)


'''Hard cap= 350 move speed'''
'''Hard capped to 330 Move Speed'''


</div>
===Regular Interaction Speed from Agility===
<div style="width:400px;">
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
{{#widget:Chart|uniqueId=MoveSpeedBase|data=[{"x": 0.0,"y": -30.0},{"x": 15.0,"y": 0.0},{"x": 45.0,"y": 30.0},{"x": 46.0,"y": 30.0},{"x": 47.0,"y": 31.0},{"x": 48.0,"y": 31.0},{"x": 49.0,"y": 32.0},{"x": 50.0,"y": 32.0},{"x": 51.0,"y": 33.0},{"x": 52.0,"y": 33.0},{"x": 53.0,"y": 34.0},{"x": 54.0,"y": 34.0},{"x": 55.0,"y": 35.0},{"x": 56.0,"y": 35.0},{"x": 57.0,"y": 36.0},{"x": 58.0,"y": 36.0},{"x": 59.0,"y": 37.0},{"x": 60.0,"y": 37.0},{"x": 61.0,"y": 38.0},{"x": 62.0,"y": 38.0},{"x": 63.0,"y": 39.0},{"x": 64.0,"y": 39.0},{"x": 65.0,"y": 40.0},{"x": 67.0,"y": 40.0},{"x": 68.0,"y": 41.0},{"x": 70.0,"y": 41.0},{"x": 71.0,"y": 42.0},{"x": 73.0,"y": 42.0},{"x": 74.0,"y": 43.0},{"x": 76.0,"y": 43.0},{"x": 77.0,"y": 44.0},{"x": 79.0,"y": 44.0},{"x": 80.0,"y": 45.0},{"x": 82.0,"y": 45.0},{"x": 83.0,"y": 46.0},{"x": 85.0,"y": 46.0},{"x": 86.0,"y": 47.0},{"x": 88.0,"y": 47.0},{"x": 89.0,"y": 48.0},{"x": 91.0,"y": 48.0},{"x": 92.0,"y": 49.0},{"x": 94.0,"y": 49.0},{"x": 95.0,"y": 50.0},{"x": 97.0,"y": 50.0},{"x": 98.0,"y": 51.0},{"x": 100.0,"y": 51.0}]|color=orange}}


 
See the Hybrid stat [[Stats#Regular_Interaction_Speed|Regular Interaction Speed]] for more.
 
</div>
</div>
 
===Item Equip Speed===
Item Equip Speed exclusively governs the speed at which you equip armors, as equipping weapons, jewelry and utility items is instant.
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
0 Agility starts at = -95% Item Equip Speed
 
Every agility point gives a  % increase to Item Equip Speed depending on fixed thresholds
 
*0 -> -95%
*0 to 1 = 0% each, up to -95%
*1 to 2 = 4% each, up to -91%
*2 to 15 = 7% each, up to 0%
*15 to 35 = 5% each, up to 100%
*35 to 70 = 2% each, up to 170%
*70 to 100 = 1% each, up to 200%
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=ItemEquipSpeed|data=[{"x": 0.0,"y": -95.0},{"x": 1.0,"y": -95.0},{"x": 2.0,"y": -91.0},{"x": 3.0,"y": -84.0},{"x": 8.0,"y": -49.0},{"x": 9.0,"y": -42.0},{"x": 11.0,"y": -28.0},{"x": 12.0,"y": -21.0},{"x": 14.0,"y": -7.0},{"x": 15.0,"y": 0.0},{"x": 17.0,"y": 10.0},{"x": 19.0,"y": 20.0},{"x": 22.0,"y": 35.0},{"x": 23.0,"y": 40.0},{"x": 27.0,"y": 60.0},{"x": 32.0,"y": 85.0},{"x": 35.0,"y": 100.0},{"x": 38.0,"y": 106.0},{"x": 39.0,"y": 108.0},{"x": 44.0,"y": 118.0},{"x": 50.0,"y": 130.0},{"x": 51.0,"y": 132.0},{"x": 56.0,"y": 142.0},{"x": 63.0,"y": 156.0},{"x": 64.0,"y": 158.0},{"x": 69.0,"y": 168.0},{"x": 70.0,"y": 170.0},{"x": 81.0,"y": 181.0},{"x": 82.0,"y": 182.0},{"x": 93.0,"y": 193.0},{"x": 100.0,"y": 200.0}]|color=orange}}
 
 
</div>
</div>


==Dexterity==
==Dexterity==
===Action Speed===
===Action Speed from Dexterity===
?
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.


===Interaction Speed===
See the Hybrid stat [[Stats#Action_Speed|Action Speed]] for more.
?


===Manual Dexterity===
===Manual Dexterity===
Manual Dexterity determines how quickly Bard plays an instrument.
Manual Dexterity determines how quickly Bard plays an instrument.
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
0 Agility starts at = -15% Manual Dexterity, play speed


Every agility point gives a % increase to Manual Dexterity depending on fixed thresholds
Can't be found on gear aside from in the form of its governing attribute.


*0 -> -15%
{{Stats Data|manualdexterity}}
*0 to 15 = 1% each, up to 0%
*15 to 23 = 3% each, up to 24%
*23 to 31 = 2% each, up to 40%
*31 to 37 = 1% each, up to 46%
*37 to 45 = 0.5% each, up to 50%
*45 to 95 = 0.1% each, up to 55%


Capped to 50%.


</div>
===Item Equip Speed===
<div style="width:400px;">
Item Equip Speed adjusts the speed at which you equip all Armors, Ranged Weapons, and Throwable/Percussion/"explosive Light Source" Utility items.  
{{#widget:Chart|uniqueId=ManualDexterity|data=[{"x": 0.0,"y": -15.0},{"x": 3.0,"y": -12.0},{"x": 6.0,"y": -9.0},{"x": 9.0,"y": -6.0},{"x": 10.0,"y": -5.0},{"x": 13.0,"y": -2.0},{"x": 15.0,"y": 0.0},{"x": 17.0,"y": 6.0},{"x": 18.0,"y": 9.0},{"x": 19.0,"y": 12.0},{"x": 21.0,"y": 18.0},{"x": 22.0,"y": 21.0},{"x": 23.0,"y": 24.0},{"x": 26.0,"y": 30.0},{"x": 31.0,"y": 40.0},{"x": 33.0,"y": 42.0},{"x": 37.0,"y": 46.0},{"x": 41.0,"y": 48.0},{"x": 45.0,"y": 50.0},{"x": 47.0,"y": 50.2},{"x": 51.0,"y": 50.6},{"x": 52.0,"y": 50.7},{"x": 56.0,"y": 51.1},{"x": 57.0,"y": 51.2},{"x": 61.0,"y": 51.6},{"x": 62.0,"y": 51.7},{"x": 65.0,"y": 52.0},{"x": 70.0,"y": 52.5},{"x": 75.0,"y": 53.0},{"x": 79.0,"y": 53.4},{"x": 80.0,"y": 53.5},{"x": 84.0,"y": 53.9},{"x": 85.0,"y": 54.0},{"x": 88.0,"y": 54.3},{"x": 93.0,"y": 54.8},{"x": 95.0,"y": 55.0},{"x": 100.0,"y": 55.0}]|color=orange}}
 


</div>
All other items such as Jewelry, Melee Weapons, Shields, and Consumable/Drink/"non-exploding Light Source" Utility items are instantly equipped.
</div>


===Interaction Speed===
Can't be found on gear aside from in the form of its governing attribute.
Increase Interaction Speed value * 0.4.


Check [[Stats#Interaction_Speed_3|Interaction Speed]] for more
{{Stats Data|itemequipspeed}}


==Will==
==Will==
===Magic Power===
===Magical Power===
Magic Power governs your Magic Power Bonus.
<span id="Magic Power">
<div style="display:flex;flex-wrap:wrap;">
Also known as Magic Power, Magical Power governs your Magic Power Bonus.
<div style="width:500px;>
</span>
0 Will starts at = 0 Magic Power
{{Stats Data|magicalpower}}
 
Every Will point gives an increase to Magic Power
*0 -> 0
*0 to 100 = 1 each, up to 100
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=MagicalPower|data=[{"x": 0.0,"y": 0.0},{"x": 100.0,"y": 100.0}]|color=orange}}
 
</div>
</div>


===Magic Power Bonus===
===Magic Power Bonus===
<span id="Magical Damage Bonus">
Also known as Magical Damage Bonus, though contrary to this alternative name, it affects [[Healing]] too.</span>
<span id="Magical Power Bonus">
Magic Power bonus governs the potency of your magical spells, magical damage dealing abilities and magical healing abilities.
Magic Power bonus governs the potency of your magical spells, magical damage dealing abilities and magical healing abilities.
<div style="display:flex;flex-wrap:wrap;">
{{Stats Data|magicalpowerbonus}}</span>
<div style="width:500px;>
0 Magic Power starts at = -90% Magic Power Bonus


Every Magic Power point gives a  % increase to Magic Power Bonus depending on fixed thresholds


*0 -> -90%
===Magical Resistance===
*0 to 1 = 0% each, up to -90%
<span id="Magic Resistance">
*1 to 5 = 10% each, up to -50%
*5 to 15 = 5% each, up to -0%
*15 to 25 = 3% each, up to 30%
*25 to 40 = 2% each, up to 60%
*40 to 50 = 1% each, up to 70%
*50 to 100 = 0.5% each, up to 95%
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=MagicalDamageMod|data=[{"x": 0.0,"y": -90.0},{"x": 1.0,"y": -90.0},{"x": 2.0,"y": -80.0},{"x": 3.0,"y": -70.0},{"x": 5.0,"y": -50.0},{"x": 7.0,"y": -40.0},{"x": 8.0,"y": -35.0},{"x": 12.0,"y": -15.0},{"x": 14.0,"y": -5.0},{"x": 15.0,"y": 0.0},{"x": 17.0,"y": 6.0},{"x": 18.0,"y": 9.0},{"x": 19.0,"y": 12.0},{"x": 21.0,"y": 18.0},{"x": 22.0,"y": 21.0},{"x": 23.0,"y": 24.0},{"x": 25.0,"y": 30.0},{"x": 30.0,"y": 40.0},{"x": 31.0,"y": 42.0},{"x": 33.0,"y": 46.0},{"x": 34.0,"y": 48.0},{"x": 39.0,"y": 58.0},{"x": 40.0,"y": 60.0},{"x": 45.0,"y": 65.0},{"x": 46.0,"y": 66.0},{"x": 50.0,"y": 70.0},{"x": 53.0,"y": 71.5},{"x": 66.0,"y": 78.0},{"x": 67.0,"y": 78.5},{"x": 78.0,"y": 84.0},{"x": 91.0,"y": 90.5},{"x": 92.0,"y": 91.0},{"x": 100.0,"y": 95.0}]|color=orange}}
 
 
</div>
</div>
 
===Magic Resistance===
Magic Resistance governs your Magical Damage Reduction.
Magic Resistance governs your Magical Damage Reduction.
<div style="display:flex;flex-wrap:wrap;">
{{Stats Data|magicresistance}}</span>
<div style="width:500px;>
0 Will starts at = -20 Magic Resistance
 
Every Will point gives an increase to Magic Resistance depending on fixed thresholds
*0 -> -20
*0 to 5 = 4 each, up to 0
*5 to 35 = 3 each, up to 90
*35 to 55 = 2 each, up to 130
*55 to 65 = 1 each, up to 140
*65 to 91 = 0.5 each, up to 153 (increases by 1 every 2 points)
*91 to 92 = -1 -> 152 (probably a mistake)
*92 to 94 = 1 each, up to 154
*94 to 100 = 0.5 each, up to 157 (increases by 1 every 2 points)
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=MagicResistance|data=[{"x": 0.0,"y": -20.0},{"x": 5.0,"y": 0.0},{"x": 35.0,"y": 90.0},{"x": 55.0,"y": 130.0},{"x": 66.0,"y": 141.0},{"x": 67.0,"y": 141.0},{"x": 68.0,"y": 142.0},{"x": 69.0,"y": 142.0},{"x": 70.0,"y": 143.0},{"x": 71.0,"y": 143.0},{"x": 72.0,"y": 144.0},{"x": 73.0,"y": 144.0},{"x": 74.0,"y": 145.0},{"x": 75.0,"y": 145.0},{"x": 76.0,"y": 146.0},{"x": 77.0,"y": 146.0},{"x": 78.0,"y": 147.0},{"x": 79.0,"y": 147.0},{"x": 80.0,"y": 148.0},{"x": 82.0,"y": 148.0},{"x": 83.0,"y": 149.0},{"x": 84.0,"y": 149.0},{"x": 85.0,"y": 150.0},{"x": 86.0,"y": 150.0},{"x": 87.0,"y": 151.0},{"x": 88.0,"y": 151.0},{"x": 89.0,"y": 152.0},{"x": 90.0,"y": 152.0},{"x": 91.0,"y": 153.0},{"x": 92.0,"y": 152.0},{"x": 94.0,"y": 154.0},{"x": 95.0,"y": 154.0},{"x": 96.0,"y": 155.0},{"x": 97.0,"y": 155.0},{"x": 98.0,"y": 156.0},{"x": 99.0,"y": 156.0},{"x": 100.0,"y": 157.0}]|color=orange}}
 
</div>
</div>


===Magical Damage Reduction===
===Magical Damage Reduction===
Magical Damage Reduction governs your resistance to magical damage dealing weapons, spells and projectiles. Please note that there is currently a bug where Magical Damage Reduction is additively 10% lower than the following expected amounts.
<span id="Magic Damage Reduction">Magical Damage Reduction governs your resistance to magical damage dealing weapons, spells and projectiles.
<div style="display:flex;flex-wrap:wrap;">
{{Stats Data|magicaldamagereduction}}
<div style="width:500px;>
Magic Resistance can go as low as -300 = -595% Magical Damage Reduction


0 Magic Resistance starts at = -10% Magical Damage Reduction  
Magical Damage Reduction is capped to 65%</span>


Magic Resistance gives a  % increase to Magical Damage Reduction depending on fixed thresholds
=== Buff Duration ===
Buff Duration modifies the duration of any temporary beneficial status effects you have.


*-300 -> -595%
Buff Duration does not modify buffs you apply to others.
*-300 to -15 = 2% each, up to -25%
{{Stats Data|buffduration}}
*-15 to 10 = 1% each, up to 0%
*10 to 19 = 0.5% each, up to 4.5%
*19 to 30 = 0.4% each, up to 8.9%
*30 to 40 = 0.3% each, up to 11.9%
*40 to 50 = 0.2% each, up to 13.9%
*50 to 100 = 0.1% each, up to 18.9%
*100 to 150 = 0.2% each, up to 28.9%
*150 to 250 = 0.3% each, up to 58.9%
*250 to 350 = 0.2% each, up to 78.9%
*350 to 500 = 0.1% each, up to 93.9%
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=MagicalReduction|data=[{"x": -49.0,"y": -93.0},{"x": -48.0,"y": -91.0},{"x": -42.0,"y": -79.0},{"x": -36.0,"y": -67.0},{"x": -30.0,"y": -55.0},{"x": -25.0,"y": -45.0},{"x": -20.0,"y": -35.0},{"x": -19.0,"y": -33.0},{"x": -17.0,"y": -29.0},{"x": -16.0,"y": -27.0},{"x": -15.0,"y": -25.0},{"x": -14.0,"y": -24.0},{"x": -13.0,"y": -23.0},{"x": -11.0,"y": -21.0},{"x": -10.0,"y": -20.0},{"x": -1.0,"y": -11.0},{"x": 1.0,"y": -9.0},{"x": 4.0,"y": -6.0},{"x": 5.0,"y": -5.0},{"x": 8.0,"y": -2.0},{"x": 10.0,"y": 0.0},{"x": 14.0,"y": 2.0},{"x": 15.0,"y": 2.5},{"x": 16.0,"y": 3.0},{"x": 19.0,"y": 4.5},{"x": 20.0,"y": 4.9},{"x": 23.0,"y": 6.1},{"x": 30.0,"y": 8.9},{"x": 33.0,"y": 9.8},{"x": 34.0,"y": 10.1},{"x": 39.0,"y": 11.6},{"x": 40.0,"y": 11.9},{"x": 41.0,"y": 12.1},{"x": 42.0,"y": 12.3},{"x": 48.0,"y": 13.5},{"x": 50.0,"y": 13.9},{"x": 54.0,"y": 14.3},{"x": 61.0,"y": 15.0},{"x": 69.0,"y": 15.8},{"x": 70.0,"y": 15.9},{"x": 76.0,"y": 16.5},{"x": 77.0,"y": 16.6},{"x": 83.0,"y": 17.2},{"x": 84.0,"y": 17.3},{"x": 91.0,"y": 18.0},{"x": 98.0,"y": 18.7},{"x": 100.0,"y": 18.9},{"x": 102.0,"y": 19.3},{"x": 106.0,"y": 20.1},{"x": 107.0,"y": 20.3},{"x": 110.0,"y": 20.9},{"x": 117.0,"y": 22.3},{"x": 121.0,"y": 23.1},{"x": 122.0,"y": 23.3},{"x": 124.0,"y": 23.7},{"x": 128.0,"y": 24.5},{"x": 129.0,"y": 24.7},{"x": 130.0,"y": 24.9},{"x": 137.0,"y": 26.3},{"x": 145.0,"y": 27.9},{"x": 146.0,"y": 28.1},{"x": 150.0,"y": 28.9},{"x": 152.0,"y": 29.5},{"x": 153.0,"y": 29.8},{"x": 155.0,"y": 30.4},{"x": 156.0,"y": 30.7},{"x": 158.0,"y": 31.3},{"x": 159.0,"y": 31.6},{"x": 162.0,"y": 32.5},{"x": 169.0,"y": 34.6},{"x": 170.0,"y": 34.9},{"x": 172.0,"y": 35.5},{"x": 173.0,"y": 35.8},{"x": 175.0,"y": 36.4},{"x": 176.0,"y": 36.7},{"x": 179.0,"y": 37.6},{"x": 185.0,"y": 39.4},{"x": 189.0,"y": 40.6},{"x": 190.0,"y": 40.9},{"x": 192.0,"y": 41.5},{"x": 193.0,"y": 41.8},{"x": 196.0,"y": 42.7},{"x": 202.0,"y": 44.5},{"x": 206.0,"y": 45.7},{"x": 207.0,"y": 46.0},{"x": 209.0,"y": 46.6},{"x": 210.0,"y": 46.9},{"x": 213.0,"y": 47.8},{"x": 219.0,"y": 49.6},{"x": 220.0,"y": 49.9},{"x": 226.0,"y": 51.7},{"x": 232.0,"y": 53.5},{"x": 237.0,"y": 55.0},{"x": 243.0,"y": 56.8},{"x": 249.0,"y": 58.6},{"x": 250.0,"y": 58.9},{"x": 251.0,"y": 59.1},{"x": 252.0,"y": 59.3},{"x": 257.0,"y": 60.3},{"x": 260.0,"y": 60.9},{"x": 262.0,"y": 61.3},{"x": 265.0,"y": 61.9},{"x": 266.0,"y": 62.1},{"x": 271.0,"y": 63.1},{"x": 274.0,"y": 63.7},{"x": 276.0,"y": 64.1},{"x": 279.0,"y": 64.7},{"x": 280.0,"y": 64.9},{"x": 285.0,"y": 65.9},{"x": 288.0,"y": 66.5},{"x": 289.0,"y": 66.7},{"x": 294.0,"y": 67.7},{"x": 297.0,"y": 68.3},{"x": 299.0,"y": 68.7},{"x": 302.0,"y": 69.3},{"x": 303.0,"y": 69.5},{"x": 308.0,"y": 70.5},{"x": 311.0,"y": 71.1},{"x": 313.0,"y": 71.5},{"x": 316.0,"y": 72.1},{"x": 317.0,"y": 72.3},{"x": 322.0,"y": 73.3},{"x": 325.0,"y": 73.9},{"x": 327.0,"y": 74.3},{"x": 330.0,"y": 74.9},{"x": 331.0,"y": 75.1},{"x": 334.0,"y": 75.7},{"x": 336.0,"y": 76.1},{"x": 339.0,"y": 76.7},{"x": 340.0,"y": 76.9},{"x": 345.0,"y": 77.9},{"x": 348.0,"y": 78.5},{"x": 350.0,"y": 78.9},{"x": 351.0,"y": 79.0},{"x": 354.0,"y": 79.3},{"x": 359.0,"y": 79.8},{"x": 364.0,"y": 80.3},{"x": 368.0,"y": 80.7},{"x": 369.0,"y": 80.8},{"x": 373.0,"y": 81.2},{"x": 374.0,"y": 81.3},{"x": 378.0,"y": 81.7},{"x": 379.0,"y": 81.8},{"x": 382.0,"y": 82.1},{"x": 387.0,"y": 82.6},{"x": 392.0,"y": 83.1},{"x": 396.0,"y": 83.5},{"x": 397.0,"y": 83.6},{"x": 401.0,"y": 84.0},{"x": 402.0,"y": 84.1},{"x": 405.0,"y": 84.4},{"x": 410.0,"y": 84.9},{"x": 415.0,"y": 85.4},{"x": 419.0,"y": 85.8},{"x": 420.0,"y": 85.9},{"x": 424.0,"y": 86.3},{"x": 425.0,"y": 86.4},{"x": 429.0,"y": 86.8},{"x": 430.0,"y": 86.9},{"x": 433.0,"y": 87.2},{"x": 438.0,"y": 87.7},{"x": 442.0,"y": 88.1},{"x": 443.0,"y": 88.2},{"x": 447.0,"y": 88.6},{"x": 448.0,"y": 88.7},{"x": 452.0,"y": 89.1},{"x": 453.0,"y": 89.2},{"x": 456.0,"y": 89.5},{"x": 461.0,"y": 90.0},{"x": 466.0,"y": 90.5},{"x": 470.0,"y": 90.9},{"x": 471.0,"y": 91.0},{"x": 475.0,"y": 91.4},{"x": 476.0,"y": 91.5},{"x": 479.0,"y": 91.8},{"x": 484.0,"y": 92.3},{"x": 489.0,"y": 92.8},{"x": 493.0,"y": 93.2},{"x": 494.0,"y": 93.3},{"x": 498.0,"y": 93.7},{"x": 499.0,"y": 93.8},{"x": 500.0,"y": 93.9}]|color=orange}}
 
 
*Starts from -50 instead of -300 for better visibility
</div>
</div>
 
 
===Buff Duration===
Buff Duration governs the duration of temporary beneficial status effects.
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
0 Will starts at = -80% Buff Duration
 
Every Will gives point gives a  % increase to Buff Duration depending on fixed thresholds
*0 -> -80%
*0 to 5 = 10% each, up to -30%
*5 to 7 = 5% each, up to -20%
*7 to 11 = 3% each, up to -8%
*11 to 15 = 2% each, up to 0%
*15 to 50 = 1% each, up to 35%
*50 to 100 = 0.5% each, up to 60%
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=BuffDurationMod|data=[{"x": 0.0,"y": -80.0},{"x": 1.0,"y": -70.0},{"x": 5.0,"y": -30.0},{"x": 7.0,"y": -20.0},{"x": 11.0,"y": -8.0},{"x": 15.0,"y": 0.0},{"x": 19.0,"y": 4.0},{"x": 20.0,"y": 5.0},{"x": 21.0,"y": 6.0},{"x": 27.0,"y": 12.0},{"x": 30.0,"y": 15.0},{"x": 35.0,"y": 20.0},{"x": 36.0,"y": 21.0},{"x": 38.0,"y": 23.0},{"x": 39.0,"y": 24.0},{"x": 44.0,"y": 29.0},{"x": 50.0,"y": 35.0},{"x": 51.0,"y": 35.5},{"x": 58.0,"y": 39.0},{"x": 59.0,"y": 39.5},{"x": 64.0,"y": 42.0},{"x": 70.0,"y": 45.0},{"x": 71.0,"y": 45.5},{"x": 76.0,"y": 48.0},{"x": 86.0,"y": 53.0},{"x": 87.0,"y": 53.5},{"x": 98.0,"y": 59.0},{"x": 100.0,"y": 60.0}]|color=orange}}
 
 
</div>
</div>


===Debuff Duration===
===Debuff Duration===
Debuff Duration governs the duration of temporary negative status effects. A negative Debuff Duration is beneficial to have, as it will shorten the duration of debuffs. A positive Debuff Duration stat means debuffs last longer, which is detrimental to the player.
Debuff Duration modifies the duration of temporary negative status effects; a negative value will shorten the duration, which is beneficial, and vise versa.  
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
0 Will starts at = 400% Debuff Duration


Every Will point gives a % decrease to Debuff Duration
Debuff Duration does not modify debuffs you apply to others.
*0 -> 400%
{{Stats Data|debuffduration}}
*0 to 1 = 170%each, up to233%)
*1 to 2 = 83% -> 150%
*2 to 3 = 50% -> 100%
*3 to 4 = 33.3% -> 66.7%
*4 to 5 = 23.8% -> 42.9%
*5 to 6 = 9.6% -> 33.3%
*6 to 7 = 8.3% -> 25%
...
*100 = -37.5%


Use the chart for accurate info.
Debuff Duration has a lower cap of -95%, meaning at minimum a debuff can last 1/20th of its base duration.


The decrease slowly slows down with different reduction amounts that is not logarithmic nor linear.  
===Magical Interaction Speed ===
<span id="Magic Interaction Speed">
Magical Interaction Speed affects the speed with which the player interacts with magical objects, such as Shrines and Portals. See [[Action/Interaction/Cast_Speed]] for more.
{{Stats Data|magicalinteractionspeed}}


Durations are not rounded and last their exact amount. However, actions that are performed in intervals, like Damage/Healing [[https://darkanddarker.wiki.spellsandguns.com/Damage_Calculation#Damage/Healing_over_Time|over time]], are rounded down to the nearest integer, resulting in thresholds that players may want to take advantage of.  
Note that the Debuff Duration Bonus enchant converts into a negative Debuff Duration, decreasing the duration of debuffs on you.
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=DebuffDurationMod|data=[{"x": 0.0,"y": 400.0},{"x": 1.0,"y": 233.3},{"x": 2.0,"y": 150.0},{"x": 3.0,"y": 100.0},{"x": 4.0,"y": 66.7},{"x": 5.0,"y": 42.9},{"x": 6.0,"y": 33.3},{"x": 7.0,"y": 25.0},{"x": 8.0,"y": 20.5},{"x": 9.0,"y": 16.3},{"x": 10.0,"y": 12.4},{"x": 11.0,"y": 8.7},{"x": 12.0,"y": 6.4},{"x": 13.0,"y": 4.2},{"x": 14.0,"y": 2.0},{"x": 15.0,"y": 0.0},{"x": 17.0,"y": -2.0},{"x": 19.0,"y": -3.8},{"x": 20.0,"y": -4.8},{"x": 21.0,"y": -5.7},{"x": 22.0,"y": -6.5},{"x": 24.0,"y": -8.3},{"x": 29.0,"y": -12.3},{"x": 30.0,"y": -13.0},{"x": 31.0,"y": -13.8},{"x": 32.0,"y": -14.5},{"x": 33.0,"y": -15.3},{"x": 36.0,"y": -17.4},{"x": 37.0,"y": -18.0},{"x": 39.0,"y": -19.4},{"x": 41.0,"y": -20.6},{"x": 42.0,"y": -21.3},{"x": 44.0,"y": -22.5},{"x": 46.0,"y": -23.7},{"x": 47.0,"y": -24.2},{"x": 49.0,"y": -25.4},{"x": 50.0,"y": -25.9},{"x": 52.0,"y": -26.5},{"x": 53.0,"y": -26.7},{"x": 54.0,"y": -27.0},{"x": 55.0,"y": -27.3},{"x": 56.0,"y": -27.5},{"x": 58.0,"y": -28.1},{"x": 59.0,"y": -28.3},{"x": 60.0,"y": -28.6},{"x": 61.0,"y": -28.8},{"x": 62.0,"y": -29.1},{"x": 63.0,"y": -29.3},{"x": 64.0,"y": -29.6},{"x": 65.0,"y": -29.8},{"x": 66.0,"y": -30.1},{"x": 67.0,"y": -30.3},{"x": 68.0,"y": -30.6},{"x": 70.0,"y": -31.0},{"x": 71.0,"y": -31.3},{"x": 73.0,"y": -31.7},{"x": 74.0,"y": -32.0},{"x": 76.0,"y": -32.4},{"x": 77.0,"y": -32.7},{"x": 80.0,"y": -33.3},{"x": 81.0,"y": -33.6},{"x": 85.0,"y": -34.4},{"x": 86.0,"y": -34.6},{"x": 87.0,"y": -34.9},{"x": 96.0,"y": -36.7},{"x": 97.0,"y": -36.9},{"x": 100.0,"y": -37.5}]|color=orange}}


</div>
Durations are not rounded and last their exact amount. However, actions that are performed in intervals, like Damage/Healing [[https://darkanddarker.wiki.spellsandguns.com/Damage_Calculation#Damage/Healing_over_Time|over time]], are rounded down to the nearest integer, resulting in thresholds that players may want to take advantage of. </span>
</div>


==Knowledge==
==Knowledge ==
===Spell Casting Speed===
===Spell Casting Speed===
Spell Casting Speed governs the speed at which you cast magical spells.
Spell Casting Speed governs the speed at which you cast magical spells. See [[Action/Interaction/Cast_Speed]] for more.
 
{{Stats Data|spellcastingspeed}}


<code>Spell Casting Time = (Base Casting Time)/(1 + Spell Casting Speed)</code>
<code>Spell Casting Time = (Base Casting Time)/(1 + Spell Casting Speed)</code>
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
0 Knowledge starts at = -95% Spell Casting Speed
Every Knowledge point gives a % increase to Spell Casting speed depending on fixed thresholds
*0 -> -93%
*0 to 1 = 0% per point -> (threshold at -93%)
*1 to 19 = 5% -> -3%
*19 to 30 = 3% -> 30%
*30 to 40 = 4% -> 70%
*40 to 45 = 3% -> 85%
*45 to 100 = 2% -> 195%
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=SpellCastingSpeed|data=[{"x": 0.0,"y": -93.0},{"x": 1.0,"y": -93.0},{"x": 4.0,"y": -78.0},{"x": 15.0,"y": -23.0},{"x": 19.0,"y": -3.0},{"x": 22.0,"y": 6.0},{"x": 23.0,"y": 9.0},{"x": 24.0,"y": 12.0},{"x": 26.0,"y": 18.0},{"x": 27.0,"y": 21.0},{"x": 28.0,"y": 24.0},{"x": 30.0,"y": 30.0},{"x": 33.0,"y": 42.0},{"x": 34.0,"y": 46.0},{"x": 36.0,"y": 54.0},{"x": 37.0,"y": 58.0},{"x": 39.0,"y": 66.0},{"x": 40.0,"y": 70.0},{"x": 43.0,"y": 79.0},{"x": 44.0,"y": 82.0},{"x": 45.0,"y": 85.0},{"x": 47.0,"y": 89.0},{"x": 48.0,"y": 91.0},{"x": 50.0,"y": 95.0},{"x": 55.0,"y": 105.0},{"x": 56.0,"y": 107.0},{"x": 61.0,"y": 117.0},{"x": 68.0,"y": 131.0},{"x": 69.0,"y": 133.0},{"x": 74.0,"y": 143.0},{"x": 80.0,"y": 155.0},{"x": 81.0,"y": 157.0},{"x": 86.0,"y": 167.0},{"x": 93.0,"y": 181.0},{"x": 94.0,"y": 183.0},{"x": 99.0,"y": 193.0},{"x": 100.0,"y": 195.0}]|color=orange}}
</div>
</div>
===Magical Interaction Speed===
Magical Interaction Speed affects the speed with which the player interacts with magical objects, such as Shrines and Portals.
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
0 Knowledge starts at = -75% Magical Interaction Speed
Every Knowledge point gives a  % increase to Magical Interaction Speed depending on fixed thresholds


*0 -> -75%  
*A Spell Casting Speed of 50% results in the casting time lasting for only 67% of the base casting time.
*0 to 15 = 5% each, up to 0%
* A Spell Casting Speed of 100% results in the casting time lasting for only 50% of the base casting time.
*15 to 25 = 7% each, up to 70%
*25 to 35 = 5% each, up to 120%
*35 to 84 = 2% each, up to 218%
*84 to 85 = 1% each, up to 219%
*85 to 86 = 3% each, up to 222%
*86 to 100 = 2% each, up to 250%
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=MagicalInteractionSpeed|data=[{"x": 0.0,"y": -75.0},{"x": 2.0,"y": -65.0},{"x": 7.0,"y": -40.0},{"x": 8.0,"y": -35.0},{"x": 12.0,"y": -15.0},{"x": 14.0,"y": -5.0},{"x": 15.0,"y": 0.0},{"x": 18.0,"y": 21.0},{"x": 21.0,"y": 42.0},{"x": 25.0,"y": 70.0},{"x": 28.0,"y": 85.0},{"x": 32.0,"y": 105.0},{"x": 33.0,"y": 110.0},{"x": 34.0,"y": 115.0},{"x": 35.0,"y": 120.0},{"x": 40.0,"y": 130.0},{"x": 41.0,"y": 132.0},{"x": 46.0,"y": 142.0},{"x": 53.0,"y": 156.0},{"x": 54.0,"y": 158.0},{"x": 59.0,"y": 168.0},{"x": 65.0,"y": 180.0},{"x": 66.0,"y": 182.0},{"x": 71.0,"y": 192.0},{"x": 81.0,"y": 212.0},{"x": 82.0,"y": 214.0},{"x": 84.0,"y": 218.0},{"x": 85.0,"y": 219.0},{"x": 86.0,"y": 222.0},{"x": 93.0,"y": 236.0},{"x": 100.0,"y": 250.0}]|color=orange}}


</div>
</div>


===Memory Capacity===
===Memory Capacity===
Memory Capacity govern your spell cost cap, meaning equipping spells that exceed this cap will not be usable.
Memory Capacity govern your spell/song cost cap, meaning equipping spells/songs that exceed this cap will not be usable.
<div style="display:flex;flex-wrap:wrap;">
{{Stats Data|memorycapacity}}
<div style="width:500px;>
0 Knowledge starts at = 0 Spell Memory/Capacity
 
Every Knowledge point gives an increase to Spell Capacity
 
*0 to 6 -> 0
*6 to 100 = 1 each, up to 94
 


<code> Total Memory Capacity = ceil(Memory Cap from Knowledge * (1 + Memory Cap Bonus%)) + Add Memory Cap </code>
<code> Total Memory Capacity = ceil(Memory Cap from Knowledge * (1 + Memory Cap Bonus%)) + Add Memory Cap </code>
Line 453: Line 167:
Memory Cap Bonus% and Add Memory Cap are two different [[Enchantments]].  
Memory Cap Bonus% and Add Memory Cap are two different [[Enchantments]].  


For example, with 12 Memory Cap from 18 knowledge, +8 Add Memory Cap, and 7.7% Memory Cap Bonus, the final Memory Capacity will be
For example, with 12 Memory Cap from 18 knowledge, 7.7% Memory Cap Bonus, and +8 Add Memory Cap, the final Memory Capacity will be


<code> ceil(12 * 1.077) + 8 = 21 Memory Capacity</code>
<code> ceil(12 * 1.077) + 8 = 21 Memory Capacity</code>


<!-- class="nowrap" will not work for me no matter what I attempt -->


</div>
{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center;"  
<div style="width:400px;">
|+ class="nowrap" |Knowledge vs Memory Capacity Bonus<!--Formula = RoundUP( ((0.5 + n-1) / Knowledge (-6))*1000) /1000 -->
{{#widget:Chart|uniqueId=MemoryCapacity|data=[{"x": 0.0,"y": 0.0},{"x": 6.0,"y": 0.0},{"x": 100.0,"y": 94.0}]|color=orange}}
!Classes!!Knowledge (-6)!!(+1)!!(+2) !! (+3)!!(+4)!!(+5)!! (+6)!!(+7)!!(+8)!! (+9)!!(+10)!!(+11)!!(+12)
 
|-
</div>
| Warlock || <small>15</small> <big>(9)</big>|| 5.6%||16.7%||27.8%||38.9%||50.0%||61.2%|| || || || || ||
</div>
|-
| || <small>16</small> <big>(10)</big>||5.0%||15.0%||25.0%||35.0%||45.0%||55.0%||65.0%|| || || ||N/A||
|-
| ||<small>17</small> <big>(11)</big>||4.6%|| 13.7%|| 22.8%|| 31.9%|| 41.0% || 50.0%
|59.1%||68.2%|| || || ||
|-
| ||<small>18</small> <big>(12)</big>||4.2%|| 12.5%|| 20.9%|| 29.2%|| 37.5%|| 45.9% ||54.2%||62.5%|| || || ||
|-
| ||<small>19</small> <big>(13)</big>||3.9% || 11.6% || 19.3% || 27.0% || 34.7% || 42.4% || 50.0% || 57.7% || 65.4% || || ||
|-
|Bard/Cleric/Druid||<small>20</small> <big>(14)</big>||3.6%||10.8%||17.9%||25.0%||32.2%||39.3%||46.5%||53.6%||60.8%||67.9%|| ||
|-
| ||<small>21</small> <big>(15)</big>||3.4%|| 10.0%|| 16.7%|| 23.4%|| 30.0%|| 36.7%|| 43.4%|| 50.0%|| 56.7%|| 63.4%|| 70.0%||
|-
| ||<small>22</small> <big>(16)</big>||3.2%||9.4%|| 15.7%|| 21.9%|| 28.2%|| 34.4%|| 40.7%|| 46.9%|| 53.2%|| 59.4%||65.7%||
|-
| ||<small>23</small> <big>(17)</big>||3.0%||8.9%||14.8%||20.6%||26.5%||32.4%||38.3%||44.2%||50.0%||55.9%||61.8%||67.7%
|-
| ||<small>24</small> <big>(18)</big>||2.8% ||8.4% ||13.9% ||19.5% ||25.0% ||30.6% ||36.2% ||41.7% ||47.3% ||52.8% ||58.4% ||63.9%
|-
| Wizard||<small>25</small> <big>(19)</big>||2.7%||7.9%||13.2%||18.5%||23.7%||29.0%||34.3%||39.5%||44.8%||50.0%||55.3%||60.6%
|-
| ||<small>26</small> <big>(20)</big>||2.5%||7.5%||12.5%||17.5%||22.5%||27.5%||32.5%||37.5%||42.5%||47.5%||52.5%||57.5%
|-
| ||<small>27</small> <big>(21)</big>||2.4%||7.2%||12.0%||16.7%||21.5%||26.2%||31.0%||35.8%||40.5%||45.3%||50.0%||54.8%
|-
| ||<small>28</small> <big>(22)</big>||2.3%||6.9%||12.5%||16.0%||20.5%||25.0%||29.6%||34.1%||38.7%||43.2%||47.8%||52.3%
|-
| ||<small>29</small> <big>(23)</big>||2.2%||6.6%||10.9%||15.3%||19.6%||24.0%||28.3%||32.7%||37.0%||41.4%||45.7%||50.0%
|-
| ||<small>30</small> <big>(24)</big>||2.1%||6.3%||10.5%||14.6%||18.8%||23.0%||27.1%||31.3%||35.5%||39.6%||43.8%||48.0%
|-
| ||<small>31</small> <big>(25)</big>||2.0%||6.0%||10.0%||14.0%||18.0%||22.0%||26.0%||30.0%||34.0%||38.0%||42.0%||46.0%
|-
| ||<small>32</small> <big>(26)</big>||2.0%||5.8%||9.7%||13.5%||17.4%||21.2%||25.0%||28.9%||32.7%||36.6%||40.4%||44.3%
|-
| ||<small>33</small> <big>(27)</big>||1.9% ||5.6% ||9.3%||13.0%||16.7%||20.4%||24.1%||27.8%||31.5%||35.2%||38.9%|| 42.6%
|-
| ||<small>34</small> <big>(28)</big>||1.8% ||5.4% ||9.0%||12.5%||16.1%||19.7%||23.3%||26.8%||30.4%||34.0%||37.5%|| 41.1%
|-
| ||<small>35</small> <big>(29)</big>||1.8% ||5.2% ||8.7%||12.1%||15.6%||19.0%||22.5%||25.9%||29.4%||32.8%||36.3%||39.7%
|-
| ||<small>36</small> <big>(30)</big>||1.7%||5.0%||8.4%||11.7%||15.0%||18.4%||21.7%||25.0%
|28.4% ||31.7%||35.0%||38.4%
|}


===Spell Recovery===
===Memory Recovery===
Increases the amount of [[Spell_Restoration|Spell/(Skill?) Points]] (SP) you restore per tick.  
Increases the amount of [[Spell_Restoration|Spell/(Skill?) Points]] (SP) you restore per tick.  


<code>''SP Recharge per tick (SP/tick) = Base Recharge * (1 + Spell Recovery Bonus)''</code>
Despite also being referred to as Spell Recovery Bonus, this also applies to Bard songs.


<div style="display:flex;flex-wrap:wrap;">
Can't be found on gear aside from in the form of its governing attribute.
<div style="width:500px;>
Each point in Knowledge increases your Spell Recovery Bonus.
*0 -> 43%
*0 to 28 = 1.5% each, up to 85%
*28 to 35 = 5% each, up to 120%
*35 to 84 = 2% each, up to 218%
*84 to 85 = 1% each, up to 219%
*85 to 86 = 3% each, up to 222%
*86 to 100 = 2% each, up to 250%


</div>
{{Stats Data|memoryrecovery}}
<div style="width:400px;">
{{#widget:Chart|uniqueId=MemoryRecoveryMod|data=[{"x": 0.0,"y": 0.43},{"x": 28.0,"y": 0.85},{"x": 35.0,"y": 1.2},{"x": 84.0,"y": 2.18},{"x": 85.0,"y": 2.19},{"x": 86.0,"y": 2.22},{"x": 100.0,"y": 2.5}]|color=orange}}


</div>
<code>''SP Recharge per tick (SP/tick) = Base Recharge * (1 + Memory Recovery Bonus)''</code>
</div>


==Resourcefulness==
==Resourcefulness==
===Interaction Speed===
===Regular Interaction Speed from Resourcefulness===
Increase Interaction Speed value * 0.6.
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.


Check [[Stats#Interaction_Speed_3|Interaction Speed]] for more
See the Hybrid stat [[Stats#Regular_Interaction_Speed|Regular Interaction Speed]] for more.


===Persuasiveness===
===Cooldown Reduction===
Persuasiveness determines the duration of Bard songs' buffs/debuffs.
Cooldown Reduction reduces the cooldowns of skills/perks.
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
0 Resourcefulness starts at = 0 Persuasiveness


*0 -> 0%
<code>Reduced cooldown length = Base Cooldown * (1 - Cooldown Reduction)</code><br><br>
*0 to 35 -> 1 each, up to 35
*35 to 71 = 0.5 each, up to 53
*71 to 99 = 0.25 each, up to 60


</div>
Note that perk cooldowns are in the form of a debuff and are additionally affected by [[Stats#Buff_Duration|Buff]]/[[Stats#Debuff_Duration|Debuff Duration]].<br>
<div style="width:400px;">
{{#widget:Chart|uniqueId=PersuasivenessStat|data=[{"x": 0.0,"y": 0.0},{"x": 35.0,"y": 35.0},{"x": 71.0,"y": 53.0},{"x": 99.0,"y": 60.0},{"x": 100.0,"y": 60.0}]|color=orange}}


<code>Reduced cooldown length = Post buff/debuff duration cooldown * (1 - Cooldown Reduction)</code>


</div>
Can't be found on gear aside from in the form of its governing attribute.
</div>


Base buff duration formula:
{{Stats_Data|cooldownreduction}}


<code>Scaling x Persuasiveness</code>
===Persuasiveness===
Persuasiveness determines the duration of Bard songs' buffs/debuffs.
{{Stats Data|persuasiveness}}


Note that as of Patch #2 11/22/2023, Bard's base resourcefulness is 15 instead of 20. Each point in Persuasiveness over the base of 15 grants a 6.66% longer base duration.
Base buff duration formula:


For example, Perfectly played Rousing Rhythms have 4.5x scaling and if Bard has 20 Persuasiveness, outgoing buff duration will be:
<code>Base Duration x (Persuasiveness/Base Persuasiveness) x Persuasiveness Scaling</code>


<code>4.5 x 20 = 90</code> seconds
<br>Base Persuasiveness is currently 15 due to [[Bard]]'s 15 Resourcefulness.


This will also get multiplied by the receiver's [[Buff Duration]]
Each point in Persuasiveness over the base of 15 grants a 6.66% longer base duration.<br>


The duration listed both in game and in a song's description at [[Bard]] represent the duration of the song at the base of 15 Persuasiveness. Some songs are noted as 0% Persuasiveness Scaling, meaning they always last the listed amount, before Buff/Debuff duration. Some songs technically apply no duration or their affect lasts only while Channeling, like Peacemaking and Chaotic Discord.


[https://www.desmos.com/calculator/k9kjmyzd3f Buff Duration Calculator]
For example, Perfectly played Rousing Rhythms has a 90s duration (as of writing this) there if Bard has 20 Persuasiveness, outgoing base buff duration will be:


=Hybrid Stats=
<code>90 x 20/15 x 100% = 120 seconds</code>
Hybrid stats are stats which come from a combination of attributes.


==Max Health==
This will also then get multiplied by the receiver's [[Stats#Buff_Duration|Buff Duration]]/[[Stats#Debuff_Duration|Debuff Duration]]
Max Health comes from both Strength and Vigor. Strength has 25% Scaling, and Vigor has 75%, which then get combined into a Sum and translated into Max Health.


<code>Sum = Strength * .25 + Vigor * .75</code>
Can't be found on gear aside from in the form of its governing attribute.


<div style="display:flex;flex-wrap:wrap;">
[https://www.desmos.com/calculator/ouiuljvzua Buff Duration Calculator]
<div style="width:500px;>


Each point in their Sum increases Max Health by different amounts at varying thresholds.
==Attribute Bonus==
Sum of 0 starts at 60 Max Health
Attributes can be multiplied by sources such as [[Warlock]]'s Curse of Weakness, or [[Wizard]]'s Sage perk. These multipliers are applied after all other sources of additional attributes.


*0 -> 60
<code>Final Attribute = Attribute * (1 + Attribute Bonus)</code>
*0 to 10 = 3 each, up to 90
*10 to 50 = 2 each, up to 170
*50 to 75 = 1 each, up to 195
*75 to 100 = 0.5 each, up to 207.5


</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=MaxHealth|data=[{"x": 0.0,"y": 60.0},{"x": 10.0,"y": 90.0},{"x": 50.0,"y": 170.0},{"x": 75.0,"y": 195.0},{"x": 100.0,"y": 207.5}]|color=orange}}


</div>
For example, with 30 Strength, and 15% Strength Bonus, final strength would be
</div>


==Action Speed==
<code>Final Strength = 30 * (1 + 0.15) = 34.5 Strength</code>
Action Speed comes from both Agility and Dexterity. Agility has 25% Scaling, and Dexterity has 75%, which then get combined into a Sum and translated into Action Speed.  


<code>Sum = Agility * .25 + Dexterity * .75</code>
Note that attributes can have decimals, though in the in game details page they will be rounded.


<div style="display:flex;flex-wrap:wrap;">
<br>''Not to be confused with Attribute Bonus Ratio ([[Scaling]])''
<div style="width:500px;>


Each point in their Sum increases Action Speed by different amounts at varying thresholds.
=Hybrid Stats=
Sum of 0 starts at -38% Action Speed
Hybrid stats are stats which come from a combination of attributes. For example, Health is determined by both Strength and Vigor.


*0 -> -38%
Hybrid stats are calculated by first using separate weights to combine the relevant attributes into a Rating (which is not displayed in the Details screen), and then converting that Rating into the value displayed in the Details screen. This intermediate Rating can be fractional and is not rounded before being converted to the appropriate stat.
*0 to 10 = 3% each, up to -8%
*10 to 13 = 2% each, up to -2%
*13 to 25 = 1% each, up to 10%
*25 to 41 = 1.5% each, up to 34%
*41 to 50 = 1% each, up to 43%
*50 to 100 = 0.5% each, up to 68%


</div>
==Base Health==
<div style="width:400px;">
<span id="Max Health">Base Health partially determines your characters maximum [[Health]].<span> <!--Hyperlink redirect from Stats#Max Health]]-->
{{#widget:Chart|uniqueId=ActionSpeed|data=[{"x": 0.0,"y": -0.38},{"x": 10.0,"y": -0.08},{"x": 13.0,"y": -0.02},{"x": 25.0,"y": 0.1},{"x": 41.0,"y": 0.34},{"x": 50.0,"y": 0.43},{"x": 100.0,"y": 0.68}]|color=orange}}


</div>
{{Stats Data|basehealth}}
</div>


=Other Stats=
Final Health formula with examples can be found on the [[Health#Formula|Health page]].
==Interaction Speed==
Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.


Value = Agility * 0.4 + Resourcefulness * 0.6
== Action Speed==
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables. See [[Action/Interaction/Cast_Speed]] for more.


<div style="display:flex;flex-wrap:wrap;">
{{Stats Data|actionspeed}}
<div style="width:500px;">
0 value starts at = -75% Interaction Speed


Every value gives a  % increase to Interaction Speed depending on fixed thresholds


*0 -> -55%
An Action Speed of 50% results in the animation lasting for only 67% of the base animation length.
*0 to 5 = 5% each, up to -30%
*5 to 15 = 3% each, up to 0%
*15 to 25 = 7% each, up to 70%
*25 to 35 = 5% each, up to 120%
*35 to 84 = 2% each, up to 218%
*84 to 85 = 1% each, up to 219%
*85 to 86 = 3% each, up to 222%
*86 to 100 = 2% each, up to 250%


Interaction Speed has 50% [[Attribute Bonus Ratio|Scaling]] for Bandages and Surgical kits, in the same fashion that some damage bonuses scale.
<code> New animation length = Base animation length / (1 + Action Speed) </code>
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=RegularInteractionSpeed|data=[{"x": 0.0,"y": -55.0},{"x": 4.0,"y": -35.0},{"x": 5.0,"y": -30.0},{"x": 8.0,"y": -21.0},{"x": 10.0,"y": -15.0},{"x": 11.0,"y": -12.0},{"x": 12.0,"y": -9.0},{"x": 13.0,"y": -6.0},{"x": 15.0,"y": 0.0},{"x": 18.0,"y": 21.0},{"x": 21.0,"y": 42.0},{"x": 25.0,"y": 70.0},{"x": 28.0,"y": 85.0},{"x": 32.0,"y": 105.0},{"x": 33.0,"y": 110.0},{"x": 34.0,"y": 115.0},{"x": 35.0,"y": 120.0},{"x": 40.0,"y": 130.0},{"x": 41.0,"y": 132.0},{"x": 46.0,"y": 142.0},{"x": 53.0,"y": 156.0},{"x": 54.0,"y": 158.0},{"x": 59.0,"y": 168.0},{"x": 65.0,"y": 180.0},{"x": 66.0,"y": 182.0},{"x": 71.0,"y": 192.0},{"x": 81.0,"y": 212.0},{"x": 82.0,"y": 214.0},{"x": 84.0,"y": 218.0},{"x": 85.0,"y": 219.0},{"x": 86.0,"y": 222.0},{"x": 93.0,"y": 236.0},{"x": 100.0,"y": 250.0}]|color=orange}}




</div>
==Regular Interaction Speed==
</div>
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon. See [[Action/Interaction/Cast_Speed]] for more.


==Physical Damage Reduction==
{{Stats Data|regularinteractionspeed}}
Physical Damage Reduction governs your resistance to physical damage dealing weapons and projectiles. Unlike Magic Resistance that is increased by Will, Armor Rating does not have an attribute stat that it scales off.
<div style="display:flex;flex-wrap:wrap;">
<div style="width:500px;>
Armor Rating can go as low as -300 = -619% Physical Damage Reduction


0 Armor Rating starts at = -22% Physical Damage Reduction


Every Armor Rating point gives a  % increase to Physical Damage Reduction depending on fixed thresholds
<code> New interaction length = Base interaction length / (1 + interaction speed) </code>


*-300 -> -619%
*-300 to -3 = 2% each, up to -25%
*-3 to 22 = 1% each, up to 0%
*22 to 31 = 0.5% each, up to 4.5%
*31 to 42 = 0.4% each, up to 8.9%
*42 to 52 = 0.3% each, up to 11.9%
*52 to 62 = 0.2% each, up to 13.9%
*62 to 112 = 0.1% each, up to 18.9%
*112 to 175 = 0.2% each, up to 31.5%
*175 to 262 = 0.3% each, up to 57.6%
*262 to 317 = 0.2% each, up to 68.6%
*317 to 400 = 0.1% each, up to 76.9%
*400 to 424 = 0.05% each, up to 78.1%
*424 to 450 = 0.025% each, up to 78.75%
*450 to 500 = 0.02% each, up to 79.75%


Armor cap is 85% which can be reached by other perks and shrine buffs.
For example, an Interaction Speed of 100% results in the interaction time lasting for only 50% of the base interaction length.
</div>
<div style="width:400px;">
{{#widget:Chart|uniqueId=PhysicalReduction|data=[{"x": -49.0,"y": -117.0},{"x": -44.0,"y": -107.0},{"x": -37.0,"y": -93.0},{"x": -36.0,"y": -91.0},{"x": -30.0,"y": -79.0},{"x": -24.0,"y": -67.0},{"x": -18.0,"y": -55.0},{"x": -13.0,"y": -45.0},{"x": -8.0,"y": -35.0},{"x": -7.0,"y": -33.0},{"x": -5.0,"y": -29.0},{"x": -4.0,"y": -27.0},{"x": -3.0,"y": -25.0},{"x": -2.0,"y": -24.0},{"x": -1.0,"y": -23.0},{"x": 1.0,"y": -21.0},{"x": 2.0,"y": -20.0},{"x": 11.0,"y": -11.0},{"x": 13.0,"y": -9.0},{"x": 16.0,"y": -6.0},{"x": 17.0,"y": -5.0},{"x": 20.0,"y": -2.0},{"x": 22.0,"y": 0.0},{"x": 26.0,"y": 2.0},{"x": 27.0,"y": 2.5},{"x": 28.0,"y": 3.0},{"x": 31.0,"y": 4.5},{"x": 32.0,"y": 4.9},{"x": 35.0,"y": 6.1},{"x": 42.0,"y": 8.9},{"x": 45.0,"y": 9.8},{"x": 46.0,"y": 10.1},{"x": 51.0,"y": 11.6},{"x": 52.0,"y": 11.9},{"x": 53.0,"y": 12.1},{"x": 54.0,"y": 12.3},{"x": 60.0,"y": 13.5},{"x": 62.0,"y": 13.9},{"x": 66.0,"y": 14.3},{"x": 73.0,"y": 15.0},{"x": 81.0,"y": 15.8},{"x": 82.0,"y": 15.9},{"x": 88.0,"y": 16.5},{"x": 89.0,"y": 16.6},{"x": 95.0,"y": 17.2},{"x": 96.0,"y": 17.3},{"x": 103.0,"y": 18.0},{"x": 110.0,"y": 18.7},{"x": 112.0,"y": 18.9},{"x": 114.0,"y": 19.3},{"x": 118.0,"y": 20.1},{"x": 119.0,"y": 20.3},{"x": 122.0,"y": 20.9},{"x": 129.0,"y": 22.3},{"x": 133.0,"y": 23.1},{"x": 134.0,"y": 23.3},{"x": 136.0,"y": 23.7},{"x": 140.0,"y": 24.5},{"x": 141.0,"y": 24.7},{"x": 142.0,"y": 24.9},{"x": 149.0,"y": 26.3},{"x": 157.0,"y": 27.9},{"x": 158.0,"y": 28.1},{"x": 164.0,"y": 29.3},{"x": 165.0,"y": 29.5},{"x": 171.0,"y": 30.7},{"x": 172.0,"y": 30.9},{"x": 175.0,"y": 31.5},{"x": 176.0,"y": 31.8},{"x": 177.0,"y": 32.1},{"x": 179.0,"y": 32.7},{"x": 180.0,"y": 33.0},{"x": 183.0,"y": 33.9},{"x": 189.0,"y": 35.7},{"x": 193.0,"y": 36.9},{"x": 194.0,"y": 37.2},{"x": 196.0,"y": 37.8},{"x": 197.0,"y": 38.1},{"x": 200.0,"y": 39.0},{"x": 206.0,"y": 40.8},{"x": 210.0,"y": 42.0},{"x": 211.0,"y": 42.3},{"x": 213.0,"y": 42.9},{"x": 214.0,"y": 43.2},{"x": 216.0,"y": 43.8},{"x": 217.0,"y": 44.1},{"x": 220.0,"y": 45.0},{"x": 227.0,"y": 47.1},{"x": 228.0,"y": 47.4},{"x": 230.0,"y": 48.0},{"x": 231.0,"y": 48.3},{"x": 233.0,"y": 48.9},{"x": 234.0,"y": 49.2},{"x": 239.0,"y": 50.7},{"x": 242.0,"y": 51.6},{"x": 244.0,"y": 52.2},{"x": 250.0,"y": 54.0},{"x": 256.0,"y": 55.8},{"x": 259.0,"y": 56.7},{"x": 261.0,"y": 57.3},{"x": 262.0,"y": 57.6},{"x": 263.0,"y": 57.8},{"x": 264.0,"y": 58.0},{"x": 267.0,"y": 58.6},{"x": 269.0,"y": 59.0},{"x": 272.0,"y": 59.6},{"x": 273.0,"y": 59.8},{"x": 278.0,"y": 60.8},{"x": 281.0,"y": 61.4},{"x": 283.0,"y": 61.8},{"x": 286.0,"y": 62.4},{"x": 287.0,"y": 62.6},{"x": 290.0,"y": 63.2},{"x": 292.0,"y": 63.6},{"x": 295.0,"y": 64.2},{"x": 296.0,"y": 64.4},{"x": 301.0,"y": 65.4},{"x": 304.0,"y": 66.0},{"x": 306.0,"y": 66.4},{"x": 309.0,"y": 67.0},{"x": 310.0,"y": 67.2},{"x": 315.0,"y": 68.2},{"x": 317.0,"y": 68.6},{"x": 318.0,"y": 68.7},{"x": 319.0,"y": 68.8},{"x": 323.0,"y": 69.2},{"x": 324.0,"y": 69.3},{"x": 327.0,"y": 69.6},{"x": 332.0,"y": 70.1},{"x": 337.0,"y": 70.6},{"x": 341.0,"y": 71.0},{"x": 342.0,"y": 71.1},{"x": 346.0,"y": 71.5},{"x": 347.0,"y": 71.6},{"x": 350.0,"y": 71.9},{"x": 355.0,"y": 72.4},{"x": 360.0,"y": 72.9},{"x": 364.0,"y": 73.3},{"x": 365.0,"y": 73.4},{"x": 369.0,"y": 73.8},{"x": 370.0,"y": 73.9},{"x": 374.0,"y": 74.3},{"x": 375.0,"y": 74.4},{"x": 378.0,"y": 74.7},{"x": 383.0,"y": 75.2},{"x": 387.0,"y": 75.6},{"x": 388.0,"y": 75.7},{"x": 392.0,"y": 76.1},{"x": 393.0,"y": 76.2},{"x": 397.0,"y": 76.6},{"x": 398.0,"y": 76.7},{"x": 400.0,"y": 76.9},{"x": 404.0,"y": 77.1},{"x": 407.0,"y": 77.25},{"x": 409.0,"y": 77.35},{"x": 410.0,"y": 77.4},{"x": 414.0,"y": 77.6},{"x": 417.0,"y": 77.75},{"x": 419.0,"y": 77.85},{"x": 420.0,"y": 77.9},{"x": 424.0,"y": 78.1},{"x": 426.0,"y": 78.15},{"x": 427.0,"y": 78.17},{"x": 429.0,"y": 78.22},{"x": 433.0,"y": 78.33},{"x": 434.0,"y": 78.35},{"x": 436.0,"y": 78.4},{"x": 443.0,"y": 78.57},{"x": 449.0,"y": 78.72},{"x": 450.0,"y": 78.75},{"x": 452.0,"y": 78.79},{"x": 455.0,"y": 78.85},{"x": 458.0,"y": 78.91},{"x": 459.0,"y": 78.93},{"x": 461.0,"y": 78.97},{"x": 462.0,"y": 78.99},{"x": 465.0,"y": 79.05},{"x": 466.0,"y": 79.07},{"x": 470.0,"y": 79.15},{"x": 473.0,"y": 79.21},{"x": 476.0,"y": 79.27},{"x": 477.0,"y": 79.29},{"x": 479.0,"y": 79.33},{"x": 480.0,"y": 79.35},{"x": 483.0,"y": 79.41},{"x": 484.0,"y": 79.43},{"x": 488.0,"y": 79.51},{"x": 491.0,"y": 79.57},{"x": 494.0,"y": 79.63},{"x": 495.0,"y": 79.65},{"x": 497.0,"y": 79.69},{"x": 498.0,"y": 79.71},{"x": 500.0,"y": 79.75}]|color=orange}}


[[Surgical Kit|Surgical Kits]] and [[Bandage|Bandages]] have 50% [[Scaling]] on regular interaction speed, therefore, their formula looks like


<code> New interaction length = Base interaction length / (1 + interaction speed * .5) </code>


=Other Stats=


*Graph Starts from -49 instead of -300 for better visibility
==Armor Rating==
Armor Rating (AR) is determined from the armor your wearing, but can also be increased in some ways such as [[Fighter]]'s Barricade (Armor Rating) or [[Fighter]]'s Defense Mastery (Armor Rating Bonus).
<br><br>


</div>
Formula can be simplified as:<br>
</div>
<code>Final Armor Rating = Armor Rating * (1 + Armor Rating Bonus)</code>




==Luck==
Note that [[Fighter]]'s Defense Mastery and [[Rogue]]'s Weakpoint Attack are specifically Item Armor Rating Bonus, meaning they only affect the AR from Items (excluding enchants), where the following formula should be applied.<br>
Luck increases chance of getting better loot rarity. Whoever opens the loot first or kills the mob first is the person whos luck is used to calculate the drops.


Luck stat affects each rarity differently. Luck Cap in the game is 500.
<code>Final Armor Rating = Armor Rating from armor * (1 + Item Armor Rating Bonus) + other Armor Rating * (1 + Armor Rating Bonus)</code>




It is only possible to get maximum of 249 Luck in the game currently:
Note that only Item Armor Rating Bonus exists currently, and not Armor Rating Bonus. Therefore, the shortest form of this expanded formula can be written as:
*50 from [[Bard]]'s Wanderer's Luck
*Possible 150 luck roll from a large [[Potion of Luck]]
*25 from a [[Fangs of Death Necklace]]
*24(12 x 2) from two [[Grimsmile Ring| Grimsmile Rings]]


<div style="display:flex;flex-wrap:wrap;">
<code>Final Armor Rating = Armor Rating from armor * (1 + Item Armor Rating bonus) + other Armor Rating</code>
<div style="width:500px;>
<br>
*1-Junk: Each luck decreases chance by 0.1%, 500 Luck: 0.5x Chance
*2-Poor: Each luck decreases chance by 0.1%,  500 Luck: 0.5x Chance
*3-Common: Each luck decreases chance by 0.05%, 500 Luck: 0.75x Chance
*4-Uncommon is not affected by luck
*5-Rare: not linear, diminishing returns, 500 Luck: 3.5x Chance
*6-Epic: not linear, diminishing returns, 500 Luck: 3.88x Chance
*7-Legendary: not linear, diminishing returns, 500 Luck: 4.25x Chance
*8-Unique: not linear, diminishing returns, 500 Luck: 4.38x Chance


</div>


<div style="width:500px;">
Example using the last formula:<br>
<tabber>
With 100 AR from equipped Items, 20 from [[Enchantments]], and -40% Item Armor Rating Bonus, the player would result in<br>
|-|1=
<br>
{{#widget:Chart|uniqueId=LuckGrade00|data=[{"x": 0,"y": 100.0},{"x": 50,"y": 95.0},{"x": 100,"y": 90.0},{"x": 150,"y": 85.0},{"x": 200,"y": 80.0},{"x": 250,"y": 75.0},{"x": 300,"y": 70.0},{"x": 350,"y": 65.0},{"x": 400,"y": 60.0},{"x": 450,"y": 55.0},{"x": 500,"y": 50.0}]|color=orange}}


|-|2=
<code>100 * (1 + -0.4) + 20 = 80 Armor Rating</code>
<br>
<br>
{{#widget:Chart|uniqueId=LuckGrade01|data=[{"x": 0,"y": 100.0},{"x": 50,"y": 95.0},{"x": 100,"y": 90.0},{"x": 150,"y": 85.0},{"x": 200,"y": 80.0},{"x": 250,"y": 75.0},{"x": 300,"y": 70.0},{"x": 350,"y": 65.0},{"x": 400,"y": 60.0},{"x": 450,"y": 55.0},{"x": 500,"y": 50.0}]|color=orange}}


|-|3=
== Physical Damage Reduction==
<br>
Physical Damage Reduction governs your resistance to physical damage dealing weapons and projectiles. Unlike Magic Resistance that is increased by Will, Armor Rating does not have an attribute stat that it scales off.
{{#widget:Chart|uniqueId=LuckGrade02|data=[{"x": 0,"y": 100.0},{"x": 50,"y": 97.5},{"x": 100,"y": 95.0},{"x": 150,"y": 92.5},{"x": 200,"y": 90.0},{"x": 250,"y": 87.5},{"x": 300,"y": 85.0},{"x": 350,"y": 82.5},{"x": 400,"y": 80.0},{"x": 450,"y": 77.5},{"x": 500,"y": 75.0}]|color=orange}}
{{Stats Data|physicaldamagereduction}}
 
|-|4=
<br>
{{#widget:Chart|uniqueId=LuckGrade03|data=[{"x": 0,"y": 1.0},{"x": 500,"y": 1.0}]|color=orange}}
 
|-|5=
{{#widget:Chart|uniqueId=LuckGrade04|data=[{"x": 0,"y": 1.0},{"x": 16,"y": 1.16},{"x": 23,"y": 1.23},{"x": 31,"y": 1.3},{"x": 38,"y": 1.37},{"x": 50,"y": 1.48},{"x": 61,"y": 1.57},{"x": 69,"y": 1.64},{"x": 75,"y": 1.7},{"x": 81,"y": 1.75},{"x": 90,"y": 1.82},{"x": 107,"y": 1.96},{"x": 117,"y": 2.03},{"x": 123,"y": 2.08},{"x": 129,"y": 2.12},{"x": 136,"y": 2.18},{"x": 150,"y": 2.28},{"x": 161,"y": 2.35},{"x": 170,"y": 2.41},{"x": 176,"y": 2.45},{"x": 182,"y": 2.49},{"x": 194,"y": 2.57},{"x": 212,"y": 2.67},{"x": 221,"y": 2.72},{"x": 229,"y": 2.77},{"x": 236,"y": 2.81},{"x": 246,"y": 2.86},{"x": 254,"y": 2.9},{"x": 263,"y": 2.94},{"x": 270,"y": 2.97},{"x": 278,"y": 3.01},{"x": 285,"y": 3.04},{"x": 296,"y": 3.09},{"x": 308,"y": 3.13},{"x": 319,"y": 3.18},{"x": 326,"y": 3.2},{"x": 334,"y": 3.23},{"x": 350,"y": 3.28},{"x": 365,"y": 3.32},{"x": 373,"y": 3.34},{"x": 381,"y": 3.36},{"x": 393,"y": 3.39},{"x": 408,"y": 3.42},{"x": 415,"y": 3.43},{"x": 421,"y": 3.44},{"x": 429,"y": 3.45},{"x": 436,"y": 3.46},{"x": 447,"y": 3.48},{"x": 459,"y": 3.49},{"x": 467,"y": 3.49},{"x": 473,"y": 3.5},{"x": 480,"y": 3.5},{"x": 493,"y": 3.5},{"x": 500,"y": 3.5}]|color=orange}}
 
 
<br>
|-|6=
{{#widget:Chart|uniqueId=LuckGrade05|data=[{"x": 0,"y": 1.0},{"x": 8,"y": 1.09},{"x": 15,"y": 1.17},{"x": 23,"y": 1.26},{"x": 36,"y": 1.4},{"x": 43,"y": 1.47},{"x": 50,"y": 1.55},{"x": 59,"y": 1.64},{"x": 70,"y": 1.75},{"x": 83,"y": 1.88},{"x": 89,"y": 1.93},{"x": 97,"y": 2.01},{"x": 107,"y": 2.1},{"x": 120,"y": 2.22},{"x": 127,"y": 2.28},{"x": 133,"y": 2.33},{"x": 140,"y": 2.39},{"x": 148,"y": 2.45},{"x": 160,"y": 2.55},{"x": 167,"y": 2.6},{"x": 174,"y": 2.65},{"x": 181,"y": 2.71},{"x": 204,"y": 2.87},{"x": 212,"y": 2.92},{"x": 218,"y": 2.96},{"x": 224,"y": 3.0},{"x": 234,"y": 3.06},{"x": 252,"y": 3.17},{"x": 258,"y": 3.2},{"x": 266,"y": 3.25},{"x": 273,"y": 3.29},{"x": 288,"y": 3.36},{"x": 298,"y": 3.41},{"x": 304,"y": 3.44},{"x": 311,"y": 3.47},{"x": 318,"y": 3.5},{"x": 329,"y": 3.54},{"x": 339,"y": 3.58},{"x": 346,"y": 3.61},{"x": 352,"y": 3.63},{"x": 363,"y": 3.66},{"x": 381,"y": 3.72},{"x": 388,"y": 3.73},{"x": 394,"y": 3.75},{"x": 401,"y": 3.77},{"x": 408,"y": 3.78},{"x": 418,"y": 3.8},{"x": 426,"y": 3.82},{"x": 433,"y": 3.83},{"x": 438,"y": 3.84},{"x": 447,"y": 3.85},{"x": 458,"y": 3.86},{"x": 466,"y": 3.87},{"x": 475,"y": 3.87},{"x": 480,"y": 3.88},{"x": 490,"y": 3.88},{"x": 500,"y": 3.88}]|color=orange}}
 
<br>
|-|7=
{{#widget:Chart|uniqueId=LuckGrade06|data=[{"x": 0,"y": 1.0},{"x": 12,"y": 1.15},{"x": 19,"y": 1.24},{"x": 26,"y": 1.33},{"x": 34,"y": 1.43},{"x": 43,"y": 1.54},{"x": 53,"y": 1.65},{"x": 60,"y": 1.73},{"x": 67,"y": 1.81},{"x": 87,"y": 2.03},{"x": 94,"y": 2.11},{"x": 100,"y": 2.17},{"x": 112,"y": 2.3},{"x": 128,"y": 2.45},{"x": 134,"y": 2.51},{"x": 141,"y": 2.58},{"x": 150,"y": 2.66},{"x": 164,"y": 2.78},{"x": 173,"y": 2.86},{"x": 181,"y": 2.93},{"x": 199,"y": 3.08},{"x": 206,"y": 3.14},{"x": 213,"y": 3.18},{"x": 219,"y": 3.23},{"x": 229,"y": 3.3},{"x": 244,"y": 3.4},{"x": 250,"y": 3.45},{"x": 259,"y": 3.5},{"x": 273,"y": 3.58},{"x": 283,"y": 3.64},{"x": 289,"y": 3.67},{"x": 295,"y": 3.71},{"x": 303,"y": 3.75},{"x": 312,"y": 3.79},{"x": 320,"y": 3.83},{"x": 326,"y": 3.86},{"x": 333,"y": 3.89},{"x": 350,"y": 3.96},{"x": 359,"y": 4.0},{"x": 366,"y": 4.02},{"x": 374,"y": 4.05},{"x": 382,"y": 4.07},{"x": 391,"y": 4.1},{"x": 401,"y": 4.13},{"x": 407,"y": 4.14},{"x": 415,"y": 4.16},{"x": 424,"y": 4.18},{"x": 436,"y": 4.2},{"x": 443,"y": 4.21},{"x": 451,"y": 4.22},{"x": 469,"y": 4.24},{"x": 476,"y": 4.25},{"x": 484,"y": 4.25},{"x": 499,"y": 4.26},{"x": 500,"y": 4.26}]|color=orange}}
 
<br>
|-|8=
{{#widget:Chart|uniqueId=LuckGrade07|data=[{"x": 0,"y": 1.0},{"x": 8,"y": 1.11},{"x": 17,"y": 1.23},{"x": 33,"y": 1.43},{"x": 41,"y": 1.53},{"x": 50,"y": 1.64},{"x": 65,"y": 1.82},{"x": 73,"y": 1.92},{"x": 80,"y": 2.0},{"x": 90,"y": 2.11},{"x": 99,"y": 2.21},{"x": 107,"y": 2.29},{"x": 113,"y": 2.37},{"x": 127,"y": 2.5},{"x": 142,"y": 2.65},{"x": 148,"y": 2.7},{"x": 154,"y": 2.76},{"x": 163,"y": 2.84},{"x": 178,"y": 2.98},{"x": 185,"y": 3.04},{"x": 191,"y": 3.09},{"x": 199,"y": 3.15},{"x": 215,"y": 3.28},{"x": 222,"y": 3.33},{"x": 229,"y": 3.39},{"x": 245,"y": 3.5},{"x": 252,"y": 3.56},{"x": 260,"y": 3.6},{"x": 267,"y": 3.65},{"x": 285,"y": 3.75},{"x": 293,"y": 3.8},{"x": 300,"y": 3.84},{"x": 308,"y": 3.88},{"x": 318,"y": 3.93},{"x": 329,"y": 3.98},{"x": 337,"y": 4.02},{"x": 345,"y": 4.05},{"x": 358,"y": 4.11},{"x": 367,"y": 4.14},{"x": 373,"y": 4.16},{"x": 380,"y": 4.19},{"x": 391,"y": 4.22},{"x": 401,"y": 4.25},{"x": 408,"y": 4.27},{"x": 416,"y": 4.29},{"x": 428,"y": 4.31},{"x": 436,"y": 4.33},{"x": 443,"y": 4.34},{"x": 449,"y": 4.35},{"x": 459,"y": 4.36},{"x": 473,"y": 4.37},{"x": 480,"y": 4.38},{"x": 488,"y": 4.38},{"x": 500,"y": 4.38}]|color=orange}}
 
 
 
<br>
</tabber>
</div>
</div>
 
 
===Luck Value Table===
{| cellspacing="0" class="wikitable"
! Luck !! <span class="colorrarity0">Junk</span> !! <span class="colorrarity1">Poor</span> !! <span class="colorrarity2">Common</span> !! <span class="colorrarity3">Uncommon</span> !! <span class="colorrarity4">Rare</span> !! <span class="colorrarity5">Epic</span> !! <span class="colorrarity6">Legendary</span> !! <span class="colorrarity7">Unique</span>
|-
| 50 || x0.95 || x0.95 || x0.975 || x1.0 || x1.48 || x1.54 || x1.62 || x1.64
|-
| 100 || x0.90 || x0.90 || x0.95 || x1.0 || x1.90 || x2.04 || x2.17 || x2.22
|-
| 150 || x0.85 || x0.85 || x0.925 || x1.0 || x2.28 || x2.47 || x2.66 || x2.72
|-
| 200 || x0.80 || x0.80 || x0.90 || x1.0 || x2.60 || x2.84 || x3.08 || x3.17
|-
| 250 || x0.75 || x0.75 || x0.875 || x1.0 || x2.88 || x3.16 || x3.45 || x3.54
|-
| 300 || x0.70 || x0.70 || x0.85 || x1.0 || x3.11 || x3.42 || x3.73 || x3.84
|}
 
It is important to note that Luck only increases chance of finding a high tier loot only if looted container/corpse has a chance of dropping high tier loot.
So if loot table has no "Epic" drop chance, high luck won't make it drop "Epic" even if you have 250 luck as 0% chance multiplied by 3.16 is still 0.
 
Check [[Lootables]] to see which lootables drop high tier loot.


Loot is rolled when you open the container or kill the mob. (It is not confirmed if Bard's Unchained Harmony rolls the loot table when it opens the containers.)
Physical Damage Reduction is capped to 65%
 
=Enchantment Stats=
Stats that come from weapons, armors or jewelry imbued with item enchantments.
 
==Additional Magical Damage==
Increases Magical Damage dealt (not affected by Magical Power Bonus).
 
==Additional Physical Damage==
Increases Physical Damage dealt (not affected by Physical Power Bonus).
 
==All Attributes/Primitive==
Increases all Attributes (Strength, Agility, Will, Knowledge, Resourcefulness).
 
==Armor Penetration==
''Armor Penetration governs the amount of physical damage you do that will completely bypass your enemy's armor rating.''
 
Unlike in game description, armor pen decreases [[Stats#Physical Damage Reduction|Physical Damage Reduction]] instead of Armor Rating. It has no affect on negative [[Stats#Physical Damage Reduction|Physical Damage Reduction]].
 
<code>
% Physical Damage Reduced = (100 - ''Attacker's Armor Pen'') * ''Target's Physical Damage Reduction''
</code>
 
100 Armor Penetration would decrease Damage reduced to 0.
 
This modifier cannot bring Damage Reduction below 0%. There is no functional difference between 105% Penetration and 100% Penetration. This modifier also does nothing if the target's Damage Reduction % is 0% or less.
 
==Headshot Reduction==
Headshot  Reduction governs the amount of mitigated damage conferred by wearing protective head gear.
 
Decreases the headshot multiplier by '''flat''' amount. For example, normal headshot deals 150%, if the enemy has [[Armet]] which has 18% Headshot Reduction, instead it deals <code>150-18 = 132%</code> damage


==Impact Power==
==Impact Power==
Impact Power governs the strength of your weapon strikes against a target, it determines if you can break objects and stagger blocking enemies.
[[Impact_Power|Impact Power]] governs the strength of your weapon strikes against a target, it determines if you can break objects and stagger blocking enemies.


==Magic Penetration==
Can't be found on gear (aside from the base values for each weapon) and is not affected by other stats.
Magic Penetration governs the amount of magical damage you do that will completely bypass your enemy's magic resistance rating.


<code>
==Item Swap Speed==
% Magical Damage Reduced = (100 - ''Attacker's Magic Pen'') * ''Target's Magical Damage Reduction''
Speed at which items are swapped as the current active item. Note that this is separate from Wearing Time Speed.
</code>


100 Magical Penetration would decrease Damage reduced to 0.  
Affected by [[#Action Speed|Action Speed]].


This modifier cannot bring Damage Reduction below 0%. There is no functional difference between 105% Penetration and 100% Penetration. This modifier also does nothing if the target's Damage Reduction % is 0% or less.
==Wearing Time Speed==
Speed at which items are worn by equipping them from the inventory. Note that this is separate from Item Swap Speed.


==Magical Healing==
Affected by [[#Item Equip Speed|Item Equip Speed]].
Increases total healing done by magic (Cleric's heal spells and Warlock's Torture Mastery)


This specifically affects your spells, not heals received from others.
==Luck==
Luck affects the Loot that is rolled when you open a [[Containers|container]] or kill a [[monster]].


<code>(Base Heal Amount + (Magical Healing * Scaling of Spell)) * (1 + Magic Power Bonus * Scaling of Spell)</code>
Whoever opens the container first or lands the killing blow on the monster is the character whose Luck is used to calculate the drops.


[[Damage_Calculation#Attribute_Bonus_Ratio|Scaling]] info:
Luck is capped at 500.
*Lesser Heal = 100%
*Holy Light = 100%
*Sanctuary = 50% per second (250% total)
*Torture Mastery = 25%


It is possible to reach the Luck cap:
*50 from [[Bard#Perks-0|Bard's Wanderer's Luck]]
*150 luck roll from a large [[Potion of Luck]]
*10 from craftable [[Hands#Craftable_Hands_Armors-0|golden hands]] armor piece
*40 from [[Golden Cloak]]
*250 from [[Enchantments#Table_of_Enchantment_Values|max enchantment rolls]] ''on other gear''


Check [[Healing]] page to learn more about the mechanic.
{{NeedsTesting|It is not confirmed if [[Bard#Songs-0|Bard's Unchained Harmony]] applies the Bard's Luck when it opens containers.}}
{{NeedsTesting|Which character's Luck is used if a monster or the environment kills a monster? Do monsters/traps have Luck? Is loot instead rolled when the monster is first looted?}}


==Physical Healing==
===Luck Scalar ===
Increases total healing done by [[Healing Potion|Healing Potions]], [[Troll%27s_Blood|Troll's Blood]], [[Ranger]]'s Field Ration, and [[Campfire Kit|Campfires]].
{{#lsth:Luck|Luck Scalar}}


==Max Spell Count==
Determines the number of spells that can be stored at once. For example, at base, [[Wizard]] can store up to 5 Fireballs. This can be increased with Max Spell Count Bonus multiplicatively


Check [[Healing]] page to learn more about the mechanic.
Can't be found on gear and is not affected by other stats.


==Projectile Reduction==
=Enchantment Stats=
Projectile Reduction governs the amount of mitigated damage from projectiles.
Stats that come from weapons, armors or jewelry imbued with item [[Enchantments]].
 
==True Magical Damage==
Increases Magical Damage dealt that is not influenced by enemy defences or headshot/limb multipliers.
 
==True Physical Damage==
Increases Physical Damage dealt that is not influenced by enemy defences or headshot/limb multipliers.


==Weapon Damage==
{{Transclude|Enchantments#Enchantment Exclusive Stats}}
Increases Weapon damage. Does not increase damage not dealt by the weapon, like from Rogue's Rupture, or Barbarian's Achilles Strike's movement ticks.
- Now listed as +Physical Damage as an enchantment


For the possible values of Enchantments and their historical rolls, see [[Enchantments#Enchantment_Values|Enchantment Values]]


=Unimplemented Stats=
=Unimplemented Stats=
These stats are not yet implemented.
These stats are not yet implemented.
==Utility Effectiveness==
==Utility Effectiveness Bonus==
Determines the bonus effectiveness of your utility items
Determines the bonus effectiveness of your utility items

Latest revision as of 17:45, 14 November 2024

Information is up to date! Hover for more details.Stats Data last updated on: Patch:6.6#Hotfix 69-2.
Dark and Darker is currently on update: Patch:6.6#Hotfix 70.

Stats Damage Spell Restoration Luck
Enchantments Health Impact Power Footstep Sound
Healing Action/Interaction/Cast Speed Silence
Shield Looted Handled Supplied Experience
Spells

Stats

Stats are primarily modified through the gear your character has equipped. Weapons/utilities only modify your character while held. For example, holding a Main-Hand and Off-Hand weapon in the first weapon slot will give each other weapon their stats, but neither will benefit from the stats of the weapon(s) in the second slot. Similarly, the bonuses from a Flute are only granted while wielding the Flute. Stats from these sources will not be reflected in the Lobby.

Stats may also be modified by perks, buffs, and debuffs. Stats from perks will be reflected in the Lobby only if those stats are applied unconditionally. Stats from conditional perks (as well as buffs and debuffs) will not be viewable from the Lobby.

Charts

Charts are created using the data points directly taken from the game. Therefore, if there is a mismatch between chart and the in game display, it is better to look at chart info.

For example, even though the formula might give 32.5, in game the display might get rounded to 33.

Attributes

Main stats that affect multiple other stats. Each class has varying base attributes, but they sum up to 105 for each class. Can be found as primary stats (stats which are always present on an item of the same name regardless of rarity or instance such as Strength on a Padded Tunic) as well as enchantments.

Strength

Physical Power

Physical Power governs your Physical Power Bonus.

Strength governs your Physical Power.

0 Strength starts at 0 Physical Power.

  • 0 -> 0
  • 0 to 100 = 1 each, up to 100

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

P_{hysicalPower}(S_{trength})=\left\{0 \le S_{trength}<100:0+1\left|S_{trength}-0\right|\right\}

See Example for how to use.


Physical Power Bonus

Also known as Physical Damage Bonus, Physical Power Bonus governs the potency of your physical damage dealing weapons, utility items, and abilities.

Physical Power governs your Physical Power Bonus.

0 Physical Power starts at -80% Physical Power Bonus.

  • 0 -> -80%
  • 0 to 5 = 10% each, up to -30%
  • 5 to 7 = 5% each, up to -20%
  • 7 to 11 = 3% each, up to -8%
  • 11 to 15 = 2% each, up to 0%
  • 15 to 50 = 1% each, up to 35%
  • 50 to 100 = 0.5% each, up to 60%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

P_{hysicalPowerBonus}(P_{hysicalPower})=\left\{0 \le P_{hysicalPower}<5:-0.8+0.1\left|P_{hysicalPower}-0\right|,5 \le P_{hysicalPower}<7:-0.3+0.05\left|P_{hysicalPower}-5\right|,7 \le P_{hysicalPower}<11:-0.2+0.03\left|P_{hysicalPower}-7\right|,11 \le P_{hysicalPower}<15:-0.08+0.02\left|P_{hysicalPower}-11\right|,15 \le P_{hysicalPower}<50:0+0.01\left|P_{hysicalPower}-15\right|,50 \le P_{hysicalPower}<100:0.35+0.005\left|P_{hysicalPower}-50\right|\right\}

See Example for how to use.

Lower limit of -100%.

Base Health from Strength

Base Health determines your characters maximum Health.

See the Hybrid stat Base Health for more.


Vigor

Base Health from Vigor

Base Health determines your characters maximum Health.

See the Hybrid stat Base Health for more.


Health Recovery

Affects the rate at which you restore health when Resting, but not when using Bandages.

Health Recovered per tick = Base Recovery * (1 + Health Recovery Bonus)

For example, a Barbarian resting with 95% Health Recovery Bonus will recover

Health Recovered every 2s = 1 * (1 + .95) = 1.95 Health

Can't be found on gear aside from in the form of its governing attribute.

Vigor governs your Health Recovery.

0 Vigor starts at -55% Health Recovery.

  • 0 -> -55%
  • 0 to 5 = 5% each, up to -30%
  • 5 to 15 = 3% each, up to 0%
  • 15 to 25 = 7% each, up to 70%
  • 25 to 35 = 5% each, up to 120%
  • 35 to 84 = 2% each, up to 218%
  • 84 to 85 = 1% each, up to 219%
  • 85 to 86 = 3% each, up to 222%
  • 86 to 100 = 2% each, up to 250%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

H_{ealthRecovery}(V_{igor})=\left\{0 \le V_{igor}<5:-0.55+0.05\left|V_{igor}-0\right|,5 \le V_{igor}<15:-0.3+0.03\left|V_{igor}-5\right|,15 \le V_{igor}<25:0+0.07\left|V_{igor}-15\right|,25 \le V_{igor}<35:0.7+0.05\left|V_{igor}-25\right|,35 \le V_{igor}<84:1.2+0.02\left|V_{igor}-35\right|,84 \le V_{igor}<85:2.18+0.01\left|V_{igor}-84\right|,85 \le V_{igor}<86:2.19+0.03\left|V_{igor}-85\right|,86 \le V_{igor}<100:2.22+0.02\left|V_{igor}-86\right|\right\}

See Example for how to use.



Agility

Action Speed from Agility

Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.

See the Hybrid stat Action Speed for more.

Move Speed

Move Speed governs the speed at which your character runs or walks. Every 3 points in Move Speed is equal to 1% movement speed. There are many factors which can affect Move Speed, see Movement Speed for details.

To calculate total Move Speed, add the baseline 300 Move Speed to the appropriate value below.

Agility governs your Move Speed.

0 Agility starts at -10 Move Speed.

  • 0 -> -10
  • 0 to 10 = 0.5 each, up to -5
  • 10 to 15 = 1 each, up to 0
  • 15 to 75 = 0.75 each, up to 45
  • 75 to 100 = 0.5 each, up to 57.5

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

M_{oveSpeed}(A_{gility})=\left\{0 \le A_{gility}<10:-10+0.5\left|A_{gility}-0\right|,10 \le A_{gility}<15:-5+1\left|A_{gility}-10\right|,15 \le A_{gility}<75:0+0.75\left|A_{gility}-15\right|,75 \le A_{gility}<100:45+0.5\left|A_{gility}-75\right|\right\}

See Example for how to use.


Hard capped to 330 Move Speed

Regular Interaction Speed from Agility

Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.

See the Hybrid stat Regular Interaction Speed for more.

Dexterity

Action Speed from Dexterity

Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.

See the Hybrid stat Action Speed for more.

Manual Dexterity

Manual Dexterity determines how quickly Bard plays an instrument.

Can't be found on gear aside from in the form of its governing attribute.

Dexterity governs your Manual Dexterity.

0 Dexterity starts at -15% Manual Dexterity.

  • 0 -> -15%
  • 0 to 15 = 1% each, up to 0%
  • 15 to 23 = 3% each, up to 24%
  • 23 to 31 = 2% each, up to 40%
  • 31 to 37 = 1% each, up to 46%
  • 37 to 45 = 0.5% each, up to 50%
  • 45 to 95 = 0.1% each, up to 55%
  • 95 to 100 = 0% each, up to 55%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

M_{anualDexterity}(D_{exterity})=\left\{0 \le D_{exterity}<15:-0.15+0.01\left|D_{exterity}-0\right|,15 \le D_{exterity}<23:0+0.03\left|D_{exterity}-15\right|,23 \le D_{exterity}<31:0.24+0.02\left|D_{exterity}-23\right|,31 \le D_{exterity}<37:0.4+0.01\left|D_{exterity}-31\right|,37 \le D_{exterity}<45:0.46+0.005\left|D_{exterity}-37\right|,45 \le D_{exterity}<95:0.5+0.001\left|D_{exterity}-45\right|,95 \le D_{exterity}<100:0.55+0\left|D_{exterity}-95\right|\right\}

See Example for how to use.


Capped to 50%.

Item Equip Speed

Item Equip Speed adjusts the speed at which you equip all Armors, Ranged Weapons, and Throwable/Percussion/"explosive Light Source" Utility items.

All other items such as Jewelry, Melee Weapons, Shields, and Consumable/Drink/"non-exploding Light Source" Utility items are instantly equipped.

Can't be found on gear aside from in the form of its governing attribute.

Dexterity governs your Item Equip Speed.

0 Dexterity starts at -95% Item Equip Speed.

  • 0 -> -95%
  • 0 to 1 = 0% each, up to -95%
  • 1 to 2 = 4% each, up to -91%
  • 2 to 15 = 7% each, up to 0%
  • 15 to 35 = 5% each, up to 100%
  • 35 to 70 = 2% each, up to 170%
  • 70 to 100 = 1% each, up to 200%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

I_{temEquipSpeed}(D_{exterity})=\left\{0 \le D_{exterity}<1:-0.95+0\left|D_{exterity}-0\right|,1 \le D_{exterity}<2:-0.95+0.04\left|D_{exterity}-1\right|,2 \le D_{exterity}<15:-0.91+0.07\left|D_{exterity}-2\right|,15 \le D_{exterity}<35:0+0.05\left|D_{exterity}-15\right|,35 \le D_{exterity}<70:1+0.02\left|D_{exterity}-35\right|,70 \le D_{exterity}<100:1.7+0.01\left|D_{exterity}-70\right|\right\}

See Example for how to use.


Will

Magical Power

Also known as Magic Power, Magical Power governs your Magic Power Bonus.

Will governs your Magical Power.

0 Will starts at 0 Magical Power.

  • 0 -> 0
  • 0 to 100 = 1 each, up to 100

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

M_{agicalPower}(W_{ill})=\left\{0 \le W_{ill}<100:0+1\left|W_{ill}-0\right|\right\}

See Example for how to use.


Magic Power Bonus

Also known as Magical Damage Bonus, though contrary to this alternative name, it affects Healing too. Magic Power bonus governs the potency of your magical spells, magical damage dealing abilities and magical healing abilities.

Magical Power governs your Magical Power Bonus.

0 Magical Power starts at -90% Magical Power Bonus.

  • 0 -> -90%
  • 0 to 1 = 0% each, up to -90%
  • 1 to 5 = 10% each, up to -50%
  • 5 to 15 = 5% each, up to 0%
  • 15 to 21 = 2.5% each, up to 15%
  • 21 to 40 = 2% each, up to 53%
  • 40 to 50 = 1% each, up to 63%
  • 50 to 100 = 0.5% each, up to 88%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

M_{agicalPowerBonus}(M_{agicalPower})=\left\{0 \le M_{agicalPower}<1:-0.9+0\left|M_{agicalPower}-0\right|,1 \le M_{agicalPower}<5:-0.9+0.1\left|M_{agicalPower}-1\right|,5 \le M_{agicalPower}<15:-0.5+0.05\left|M_{agicalPower}-5\right|,15 \le M_{agicalPower}<21:0+0.025\left|M_{agicalPower}-15\right|,21 \le M_{agicalPower}<40:0.15+0.02\left|M_{agicalPower}-21\right|,40 \le M_{agicalPower}<50:0.53+0.01\left|M_{agicalPower}-40\right|,50 \le M_{agicalPower}<100:0.63+0.005\left|M_{agicalPower}-50\right|\right\}

See Example for how to use.


Magical Resistance

Magic Resistance governs your Magical Damage Reduction.

Will governs your Magic Resistance.

0 Will starts at -20 Magic Resistance.

  • 0 -> -20
  • 0 to 5 = 4 each, up to 0
  • 5 to 15 = 3 each, up to 30
  • 15 to 33 = 4 each, up to 102
  • 33 to 48 = 3 each, up to 147
  • 48 to 58 = 2 each, up to 167
  • 58 to 100 = 1 each, up to 209

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

M_{agicResistance}(W_{ill})=\left\{0 \le W_{ill}<5:-20+4\left|W_{ill}-0\right|,5 \le W_{ill}<15:0+3\left|W_{ill}-5\right|,15 \le W_{ill}<33:30+4\left|W_{ill}-15\right|,33 \le W_{ill}<48:102+3\left|W_{ill}-33\right|,48 \le W_{ill}<58:147+2\left|W_{ill}-48\right|,58 \le W_{ill}<100:167+1\left|W_{ill}-58\right|\right\}

See Example for how to use.

Magical Damage Reduction

Magical Damage Reduction governs your resistance to magical damage dealing weapons, spells and projectiles.

Magic Resistance governs your Magical Damage Reduction.

-300 Magic Resistance starts at -595% Magical Damage Reduction.

  • -300 -> -595%
  • -300 to -15 = 2% each, up to -25%
  • -15 to 10 = 1% each, up to 0%
  • 10 to 250 = 0.25% each, up to 60%
  • 250 to 350 = 0.2% each, up to 80%
  • 350 to 500 = 0.1% each, up to 95%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

M_{agicalDamageReduction}(M_{agicResistance})=\left\{-300 \le M_{agicResistance}<-15:-5.95+0.02\left|M_{agicResistance}--300\right|,-15 \le M_{agicResistance}<10:-0.25+0.01\left|M_{agicResistance}--15\right|,10 \le M_{agicResistance}<250:0+0.003\left|M_{agicResistance}-10\right|,250 \le M_{agicResistance}<350:0.6+0.002\left|M_{agicResistance}-250\right|,350 \le M_{agicResistance}<500:0.8+0.001\left|M_{agicResistance}-350\right|\right\}

See Example for how to use.


Magical Damage Reduction is capped to 65%

Buff Duration

Buff Duration modifies the duration of any temporary beneficial status effects you have.

Buff Duration does not modify buffs you apply to others.

Will governs your Buff Duration.

0 Will starts at -80% Buff Duration.

  • 0 -> -80%
  • 0 to 5 = 10% each, up to -30%
  • 5 to 7 = 5% each, up to -20%
  • 7 to 11 = 3% each, up to -8%
  • 11 to 15 = 2% each, up to 0%
  • 15 to 50 = 1% each, up to 35%
  • 50 to 100 = 0.5% each, up to 60%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

B_{uffDuration}(W_{ill})=\left\{0 \le W_{ill}<5:-0.8+0.1\left|W_{ill}-0\right|,5 \le W_{ill}<7:-0.3+0.05\left|W_{ill}-5\right|,7 \le W_{ill}<11:-0.2+0.03\left|W_{ill}-7\right|,11 \le W_{ill}<15:-0.08+0.02\left|W_{ill}-11\right|,15 \le W_{ill}<50:0+0.01\left|W_{ill}-15\right|,50 \le W_{ill}<100:0.35+0.005\left|W_{ill}-50\right|\right\}

See Example for how to use.


Debuff Duration

Debuff Duration modifies the duration of temporary negative status effects; a negative value will shorten the duration, which is beneficial, and vise versa.

Debuff Duration does not modify debuffs you apply to others.

Will governs your Debuff Duration.

0 Will starts at 400% Debuff Duration.

  • 0 -> 400%
  • 0 to 1 = -166.7% each, up to 233.3%
  • 1 to 2 = -83.3% each, up to 150%
  • 2 to 3 = -50% each, up to 100%
  • 3 to 4 = -33.3% each, up to 66.7%
  • 4 to 5 = -23.8% each, up to 42.9%
  • 5 to 6 = -9.6% each, up to 33.3%
  • 6 to 7 = -8.3% each, up to 25%
  • 7 to 8 = -4.5% each, up to 20.5%
  • 8 to 9 = -4.2% each, up to 16.3%
  • 9 to 10 = -3.9% each, up to 12.4%
  • 10 to 11 = -3.7% each, up to 8.7%
  • 11 to 12 = -2.3% each, up to 6.4%
  • 12 to 14 = -2.2% each, up to 2%
  • 14 to 15 = -2% each, up to 0%
  • 15 to 17 = -1% each, up to -2%
  • 17 to 19 = -0.9% each, up to -3.8%
  • 19 to 20 = -1% each, up to -4.8%
  • 20 to 21 = -0.9% each, up to -5.7%
  • 21 to 22 = -0.8% each, up to -6.5%
  • 22 to 24 = -0.9% each, up to -8.3%
  • 24 to 29 = -0.8% each, up to -12.3%
  • 29 to 30 = -0.7% each, up to -13%
  • 30 to 31 = -0.8% each, up to -13.8%
  • 31 to 32 = -0.7% each, up to -14.5%
  • 32 to 33 = -0.8% each, up to -15.3%
  • 33 to 36 = -0.7% each, up to -17.4%
  • 36 to 37 = -0.6% each, up to -18%
  • 37 to 39 = -0.7% each, up to -19.4%
  • 39 to 41 = -0.6% each, up to -20.6%
  • 41 to 42 = -0.7% each, up to -21.3%
  • 42 to 46 = -0.6% each, up to -23.7%
  • 46 to 47 = -0.5% each, up to -24.2%
  • 47 to 49 = -0.6% each, up to -25.4%
  • 49 to 50 = -0.5% each, up to -25.9%
  • 50 to 52 = -0.3% each, up to -26.5%
  • 52 to 53 = -0.2% each, up to -26.7%
  • 53 to 55 = -0.3% each, up to -27.3%
  • 55 to 56 = -0.2% each, up to -27.5%
  • 56 to 58 = -0.3% each, up to -28.1%
  • 58 to 59 = -0.2% each, up to -28.3%
  • 59 to 60 = -0.3% each, up to -28.6%
  • 60 to 61 = -0.2% each, up to -28.8%
  • 61 to 62 = -0.3% each, up to -29.1%
  • 62 to 63 = -0.2% each, up to -29.3%
  • 63 to 64 = -0.3% each, up to -29.6%
  • 64 to 65 = -0.2% each, up to -29.8%
  • 65 to 66 = -0.3% each, up to -30.1%
  • 66 to 67 = -0.2% each, up to -30.3%
  • 67 to 68 = -0.3% each, up to -30.6%
  • 68 to 70 = -0.2% each, up to -31%
  • 70 to 71 = -0.3% each, up to -31.3%
  • 71 to 73 = -0.2% each, up to -31.7%
  • 73 to 74 = -0.3% each, up to -32%
  • 74 to 76 = -0.2% each, up to -32.4%
  • 76 to 77 = -0.3% each, up to -32.7%
  • 77 to 80 = -0.2% each, up to -33.3%
  • 80 to 81 = -0.3% each, up to -33.6%
  • 81 to 86 = -0.2% each, up to -34.6%
  • 86 to 87 = -0.3% each, up to -34.9%
  • 87 to 100 = -0.2% each, up to -37.5%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

D_{ebuffDuration}(W_{ill})=\left\{0 \le W_{ill}<1:4+-1.667\left|W_{ill}-0\right|,1 \le W_{ill}<2:2.333+-0.833\left|W_{ill}-1\right|,2 \le W_{ill}<3:1.5+-0.5\left|W_{ill}-2\right|,3 \le W_{ill}<4:1+-0.333\left|W_{ill}-3\right|,4 \le W_{ill}<5:0.667+-0.238\left|W_{ill}-4\right|,5 \le W_{ill}<6:0.429+-0.096\left|W_{ill}-5\right|,6 \le W_{ill}<7:0.333+-0.083\left|W_{ill}-6\right|,7 \le W_{ill}<8:0.25+-0.045\left|W_{ill}-7\right|,8 \le W_{ill}<9:0.205+-0.042\left|W_{ill}-8\right|,9 \le W_{ill}<10:0.163+-0.039\left|W_{ill}-9\right|,10 \le W_{ill}<11:0.124+-0.037\left|W_{ill}-10\right|,11 \le W_{ill}<12:0.087+-0.023\left|W_{ill}-11\right|,12 \le W_{ill}<14:0.064+-0.022\left|W_{ill}-12\right|,14 \le W_{ill}<15:0.02+-0.02\left|W_{ill}-14\right|,15 \le W_{ill}<17:0+-0.01\left|W_{ill}-15\right|,17 \le W_{ill}<19:-0.02+-0.009\left|W_{ill}-17\right|,19 \le W_{ill}<20:-0.038+-0.01\left|W_{ill}-19\right|,20 \le W_{ill}<21:-0.048+-0.009\left|W_{ill}-20\right|,21 \le W_{ill}<22:-0.057+-0.008\left|W_{ill}-21\right|,22 \le W_{ill}<24:-0.065+-0.009\left|W_{ill}-22\right|,24 \le W_{ill}<29:-0.083+-0.008\left|W_{ill}-24\right|,29 \le W_{ill}<30:-0.123+-0.007\left|W_{ill}-29\right|,30 \le W_{ill}<31:-0.13+-0.008\left|W_{ill}-30\right|,31 \le W_{ill}<32:-0.138+-0.007\left|W_{ill}-31\right|,32 \le W_{ill}<33:-0.145+-0.008\left|W_{ill}-32\right|,33 \le W_{ill}<36:-0.153+-0.007\left|W_{ill}-33\right|,36 \le W_{ill}<37:-0.174+-0.006\left|W_{ill}-36\right|,37 \le W_{ill}<39:-0.18+-0.007\left|W_{ill}-37\right|,39 \le W_{ill}<41:-0.194+-0.006\left|W_{ill}-39\right|,41 \le W_{ill}<42:-0.206+-0.007\left|W_{ill}-41\right|,42 \le W_{ill}<46:-0.213+-0.006\left|W_{ill}-42\right|,46 \le W_{ill}<47:-0.237+-0.005\left|W_{ill}-46\right|,47 \le W_{ill}<49:-0.242+-0.006\left|W_{ill}-47\right|,49 \le W_{ill}<50:-0.254+-0.005\left|W_{ill}-49\right|,50 \le W_{ill}<52:-0.259+-0.003\left|W_{ill}-50\right|,52 \le W_{ill}<53:-0.265+-0.002\left|W_{ill}-52\right|,53 \le W_{ill}<55:-0.267+-0.003\left|W_{ill}-53\right|,55 \le W_{ill}<56:-0.273+-0.002\left|W_{ill}-55\right|,56 \le W_{ill}<58:-0.275+-0.003\left|W_{ill}-56\right|,58 \le W_{ill}<59:-0.281+-0.002\left|W_{ill}-58\right|,59 \le W_{ill}<60:-0.283+-0.003\left|W_{ill}-59\right|,60 \le W_{ill}<61:-0.286+-0.002\left|W_{ill}-60\right|,61 \le W_{ill}<62:-0.288+-0.003\left|W_{ill}-61\right|,62 \le W_{ill}<63:-0.291+-0.002\left|W_{ill}-62\right|,63 \le W_{ill}<64:-0.293+-0.003\left|W_{ill}-63\right|,64 \le W_{ill}<65:-0.296+-0.002\left|W_{ill}-64\right|,65 \le W_{ill}<66:-0.298+-0.003\left|W_{ill}-65\right|,66 \le W_{ill}<67:-0.301+-0.002\left|W_{ill}-66\right|,67 \le W_{ill}<68:-0.303+-0.003\left|W_{ill}-67\right|,68 \le W_{ill}<70:-0.306+-0.002\left|W_{ill}-68\right|,70 \le W_{ill}<71:-0.31+-0.003\left|W_{ill}-70\right|,71 \le W_{ill}<73:-0.313+-0.002\left|W_{ill}-71\right|,73 \le W_{ill}<74:-0.317+-0.003\left|W_{ill}-73\right|,74 \le W_{ill}<76:-0.32+-0.002\left|W_{ill}-74\right|,76 \le W_{ill}<77:-0.324+-0.003\left|W_{ill}-76\right|,77 \le W_{ill}<80:-0.327+-0.002\left|W_{ill}-77\right|,80 \le W_{ill}<81:-0.333+-0.003\left|W_{ill}-80\right|,81 \le W_{ill}<86:-0.336+-0.002\left|W_{ill}-81\right|,86 \le W_{ill}<87:-0.346+-0.003\left|W_{ill}-86\right|,87 \le W_{ill}<100:-0.349+-0.002\left|W_{ill}-87\right|\right\}

See Example for how to use.


Debuff Duration has a lower cap of -95%, meaning at minimum a debuff can last 1/20th of its base duration.

Magical Interaction Speed

Magical Interaction Speed affects the speed with which the player interacts with magical objects, such as Shrines and Portals. See Action/Interaction/Cast_Speed for more.

Will governs your Magical Interaction Speed.

0 Will starts at -75% Magical Interaction Speed.

  • 0 -> -75%
  • 0 to 15 = 5% each, up to 0%
  • 15 to 25 = 7% each, up to 70%
  • 25 to 35 = 5% each, up to 120%
  • 35 to 84 = 2% each, up to 218%
  • 84 to 85 = 1% each, up to 219%
  • 85 to 86 = 3% each, up to 222%
  • 86 to 100 = 2% each, up to 250%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

M_{agicalInteractionSpeed}(W_{ill})=\left\{0 \le W_{ill}<15:-0.75+0.05\left|W_{ill}-0\right|,15 \le W_{ill}<25:0+0.07\left|W_{ill}-15\right|,25 \le W_{ill}<35:0.7+0.05\left|W_{ill}-25\right|,35 \le W_{ill}<84:1.2+0.02\left|W_{ill}-35\right|,84 \le W_{ill}<85:2.18+0.01\left|W_{ill}-84\right|,85 \le W_{ill}<86:2.19+0.03\left|W_{ill}-85\right|,86 \le W_{ill}<100:2.22+0.02\left|W_{ill}-86\right|\right\}

See Example for how to use.


Note that the Debuff Duration Bonus enchant converts into a negative Debuff Duration, decreasing the duration of debuffs on you.

Durations are not rounded and last their exact amount. However, actions that are performed in intervals, like Damage/Healing [time], are rounded down to the nearest integer, resulting in thresholds that players may want to take advantage of.

Knowledge

Spell Casting Speed

Spell Casting Speed governs the speed at which you cast magical spells. See Action/Interaction/Cast_Speed for more.

Knowledge governs your Spell Casting Speed.

0 Knowledge starts at -60% Spell Casting Speed.

  • 0 -> -60%
  • 0 to 5 = 5% each, up to -35%
  • 5 to 10 = 4% each, up to -15%
  • 10 to 20 = 3% each, up to 15%
  • 20 to 50 = 2.5% each, up to 90%
  • 50 to 80 = 2% each, up to 150%
  • 80 to 100 = 1.5% each, up to 180%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

S_{pellCastingSpeed}(K_{nowledge})=\left\{0 \le K_{nowledge}<5:-0.6+0.05\left|K_{nowledge}-0\right|,5 \le K_{nowledge}<10:-0.35+0.04\left|K_{nowledge}-5\right|,10 \le K_{nowledge}<20:-0.15+0.03\left|K_{nowledge}-10\right|,20 \le K_{nowledge}<50:0.15+0.025\left|K_{nowledge}-20\right|,50 \le K_{nowledge}<80:0.9+0.02\left|K_{nowledge}-50\right|,80 \le K_{nowledge}<100:1.5+0.015\left|K_{nowledge}-80\right|\right\}

See Example for how to use.


Spell Casting Time = (Base Casting Time)/(1 + Spell Casting Speed)

  • A Spell Casting Speed of 50% results in the casting time lasting for only 67% of the base casting time.
  • A Spell Casting Speed of 100% results in the casting time lasting for only 50% of the base casting time.


Memory Capacity

Memory Capacity govern your spell/song cost cap, meaning equipping spells/songs that exceed this cap will not be usable.

Knowledge governs your Memory Capacity.

0 Knowledge starts at 0 Memory Capacity.

  • 0 -> 0
  • 0 to 6 = 0 each, up to 0
  • 6 to 100 = 1 each, up to 94

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

M_{emoryCapacity}(K_{nowledge})=\left\{0 \le K_{nowledge}<6:0+0\left|K_{nowledge}-0\right|,6 \le K_{nowledge}<100:0+1\left|K_{nowledge}-6\right|\right\}

See Example for how to use.


Total Memory Capacity = ceil(Memory Cap from Knowledge * (1 + Memory Cap Bonus%)) + Add Memory Cap

Memory Cap Bonus% and Add Memory Cap are two different Enchantments.

For example, with 12 Memory Cap from 18 knowledge, 7.7% Memory Cap Bonus, and +8 Add Memory Cap, the final Memory Capacity will be

ceil(12 * 1.077) + 8 = 21 Memory Capacity


Knowledge vs Memory Capacity Bonus
Classes Knowledge (-6) (+1) (+2) (+3) (+4) (+5) (+6) (+7) (+8) (+9) (+10) (+11) (+12)
Warlock 15 (9) 5.6% 16.7% 27.8% 38.9% 50.0% 61.2%
16 (10) 5.0% 15.0% 25.0% 35.0% 45.0% 55.0% 65.0% N/A
17 (11) 4.6% 13.7% 22.8% 31.9% 41.0% 50.0% 59.1% 68.2%
18 (12) 4.2% 12.5% 20.9% 29.2% 37.5% 45.9% 54.2% 62.5%
19 (13) 3.9% 11.6% 19.3% 27.0% 34.7% 42.4% 50.0% 57.7% 65.4%
Bard/Cleric/Druid 20 (14) 3.6% 10.8% 17.9% 25.0% 32.2% 39.3% 46.5% 53.6% 60.8% 67.9%
21 (15) 3.4% 10.0% 16.7% 23.4% 30.0% 36.7% 43.4% 50.0% 56.7% 63.4% 70.0%
22 (16) 3.2% 9.4% 15.7% 21.9% 28.2% 34.4% 40.7% 46.9% 53.2% 59.4% 65.7%
23 (17) 3.0% 8.9% 14.8% 20.6% 26.5% 32.4% 38.3% 44.2% 50.0% 55.9% 61.8% 67.7%
24 (18) 2.8% 8.4% 13.9% 19.5% 25.0% 30.6% 36.2% 41.7% 47.3% 52.8% 58.4% 63.9%
Wizard 25 (19) 2.7% 7.9% 13.2% 18.5% 23.7% 29.0% 34.3% 39.5% 44.8% 50.0% 55.3% 60.6%
26 (20) 2.5% 7.5% 12.5% 17.5% 22.5% 27.5% 32.5% 37.5% 42.5% 47.5% 52.5% 57.5%
27 (21) 2.4% 7.2% 12.0% 16.7% 21.5% 26.2% 31.0% 35.8% 40.5% 45.3% 50.0% 54.8%
28 (22) 2.3% 6.9% 12.5% 16.0% 20.5% 25.0% 29.6% 34.1% 38.7% 43.2% 47.8% 52.3%
29 (23) 2.2% 6.6% 10.9% 15.3% 19.6% 24.0% 28.3% 32.7% 37.0% 41.4% 45.7% 50.0%
30 (24) 2.1% 6.3% 10.5% 14.6% 18.8% 23.0% 27.1% 31.3% 35.5% 39.6% 43.8% 48.0%
31 (25) 2.0% 6.0% 10.0% 14.0% 18.0% 22.0% 26.0% 30.0% 34.0% 38.0% 42.0% 46.0%
32 (26) 2.0% 5.8% 9.7% 13.5% 17.4% 21.2% 25.0% 28.9% 32.7% 36.6% 40.4% 44.3%
33 (27) 1.9% 5.6% 9.3% 13.0% 16.7% 20.4% 24.1% 27.8% 31.5% 35.2% 38.9% 42.6%
34 (28) 1.8% 5.4% 9.0% 12.5% 16.1% 19.7% 23.3% 26.8% 30.4% 34.0% 37.5% 41.1%
35 (29) 1.8% 5.2% 8.7% 12.1% 15.6% 19.0% 22.5% 25.9% 29.4% 32.8% 36.3% 39.7%
36 (30) 1.7% 5.0% 8.4% 11.7% 15.0% 18.4% 21.7% 25.0% 28.4% 31.7% 35.0% 38.4%

Memory Recovery

Increases the amount of Spell/(Skill?) Points (SP) you restore per tick.

Despite also being referred to as Spell Recovery Bonus, this also applies to Bard songs.

Can't be found on gear aside from in the form of its governing attribute.

Knowledge governs your Memory Recovery.

0 Knowledge starts at 43% Memory Recovery.

  • 0 -> 43%
  • 0 to 28 = 1.5% each, up to 85%
  • 28 to 35 = 5% each, up to 120%
  • 35 to 84 = 2% each, up to 218%
  • 84 to 85 = 1% each, up to 219%
  • 85 to 86 = 3% each, up to 222%
  • 86 to 100 = 2% each, up to 250%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

M_{emoryRecovery}(K_{nowledge})=\left\{0 \le K_{nowledge}<28:0.43+0.015\left|K_{nowledge}-0\right|,28 \le K_{nowledge}<35:0.85+0.05\left|K_{nowledge}-28\right|,35 \le K_{nowledge}<84:1.2+0.02\left|K_{nowledge}-35\right|,84 \le K_{nowledge}<85:2.18+0.01\left|K_{nowledge}-84\right|,85 \le K_{nowledge}<86:2.19+0.03\left|K_{nowledge}-85\right|,86 \le K_{nowledge}<100:2.22+0.02\left|K_{nowledge}-86\right|\right\}

See Example for how to use.


SP Recharge per tick (SP/tick) = Base Recharge * (1 + Memory Recovery Bonus)

Resourcefulness

Regular Interaction Speed from Resourcefulness

Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.

See the Hybrid stat Regular Interaction Speed for more.

Cooldown Reduction

Cooldown Reduction reduces the cooldowns of skills/perks.

Reduced cooldown length = Base Cooldown * (1 - Cooldown Reduction)

Note that perk cooldowns are in the form of a debuff and are additionally affected by Buff/Debuff Duration.

Reduced cooldown length = Post buff/debuff duration cooldown * (1 - Cooldown Reduction)

Can't be found on gear aside from in the form of its governing attribute.

Resourcefulness governs your Cooldown Reduction.

0 Resourcefulness starts at -30% Cooldown Reduction.

  • 0 -> -30%
  • 0 to 20 = 2% each, up to 10%
  • 20 to 50 = 1% each, up to 40%
  • 50 to 100 = 0.5% each, up to 65%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

C_{ooldownReduction}(R_{esourcefulness})=\left\{0 \le R_{esourcefulness}<20:-0.3+0.02\left|R_{esourcefulness}-0\right|,20 \le R_{esourcefulness}<50:0.1+0.01\left|R_{esourcefulness}-20\right|,50 \le R_{esourcefulness}<100:0.4+0.005\left|R_{esourcefulness}-50\right|\right\}

See Example for how to use.


Persuasiveness

Persuasiveness determines the duration of Bard songs' buffs/debuffs.

Resourcefulness governs your Persuasiveness.

0 Resourcefulness starts at 0 Persuasiveness.

  • 0 -> 0
  • 0 to 35 = 1 each, up to 35
  • 35 to 71 = 0.5 each, up to 53
  • 71 to 99 = 0.25 each, up to 60
  • 99 to 100 = 0 each, up to 60

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

P_{ersuasiveness}(R_{esourcefulness})=\left\{0 \le R_{esourcefulness}<35:0+1\left|R_{esourcefulness}-0\right|,35 \le R_{esourcefulness}<71:35+0.5\left|R_{esourcefulness}-35\right|,71 \le R_{esourcefulness}<99:53+0.25\left|R_{esourcefulness}-71\right|,99 \le R_{esourcefulness}<100:60+0\left|R_{esourcefulness}-99\right|\right\}

See Example for how to use.


Base buff duration formula:

Base Duration x (Persuasiveness/Base Persuasiveness) x Persuasiveness Scaling


Base Persuasiveness is currently 15 due to Bard's 15 Resourcefulness.

Each point in Persuasiveness over the base of 15 grants a 6.66% longer base duration.

The duration listed both in game and in a song's description at Bard represent the duration of the song at the base of 15 Persuasiveness. Some songs are noted as 0% Persuasiveness Scaling, meaning they always last the listed amount, before Buff/Debuff duration. Some songs technically apply no duration or their affect lasts only while Channeling, like Peacemaking and Chaotic Discord.

For example, Perfectly played Rousing Rhythms has a 90s duration (as of writing this) there if Bard has 20 Persuasiveness, outgoing base buff duration will be:

90 x 20/15 x 100% = 120 seconds

This will also then get multiplied by the receiver's Buff Duration/Debuff Duration

Can't be found on gear aside from in the form of its governing attribute.

Buff Duration Calculator

Attribute Bonus

Attributes can be multiplied by sources such as Warlock's Curse of Weakness, or Wizard's Sage perk. These multipliers are applied after all other sources of additional attributes.

Final Attribute = Attribute * (1 + Attribute Bonus)


For example, with 30 Strength, and 15% Strength Bonus, final strength would be

Final Strength = 30 * (1 + 0.15) = 34.5 Strength

Note that attributes can have decimals, though in the in game details page they will be rounded.


Not to be confused with Attribute Bonus Ratio (Scaling)

Hybrid Stats

Hybrid stats are stats which come from a combination of attributes. For example, Health is determined by both Strength and Vigor.

Hybrid stats are calculated by first using separate weights to combine the relevant attributes into a Rating (which is not displayed in the Details screen), and then converting that Rating into the value displayed in the Details screen. This intermediate Rating can be fractional and is not rounded before being converted to the appropriate stat.

Base Health

Base Health partially determines your characters maximum Health.

Strength and Vigor governs your Base Health.

Strength gives 0.25 Base Health Rating, and Vigor gives 0.75 Base Health Rating, which then get summed into a total Base Health Rating and finally converted into Base Health using the graph.

Base Health Rating = Strength * 0.25 + Vigor * 0.75


0 Base Health Rating starts at 60 Base Health.

  • 0 -> 60
  • 0 to 10 = 3 each, up to 90
  • 10 to 50 = 2 each, up to 170
  • 50 to 75 = 1 each, up to 195
  • 75 to 100 = 0.5 each, up to 207.5

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

B_{aseHealth}(S_{um})=\left\{0 \le S_{um}<10:60+3\left|S_{um}-0\right|,10 \le S_{um}<50:90+2\left|S_{um}-10\right|,50 \le S_{um}<75:170+1\left|S_{um}-50\right|,75 \le S_{um}<100:195+0.5\left|S_{um}-75\right|\right\}

See Example for how to use.


Final Health formula with examples can be found on the Health page.

Action Speed

Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables. See Action/Interaction/Cast_Speed for more.

Agility and Dexterity governs your Action Speed.

Agility gives 0.25 Action Speed Rating, and Dexterity gives 0.75 Action Speed Rating, which then get summed into a total Action Speed Rating and finally converted into Action Speed using the graph.

Action Speed Rating = Agility * 0.25 + Dexterity * 0.75


0 Action Speed Rating starts at -38% Action Speed.

  • 0 -> -38%
  • 0 to 10 = 3% each, up to -8%
  • 10 to 13 = 2% each, up to -2%
  • 13 to 25 = 1% each, up to 10%
  • 25 to 41 = 1.5% each, up to 34%
  • 41 to 50 = 1% each, up to 43%
  • 50 to 100 = 0.5% each, up to 68%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

A_{ctionSpeed}(S_{um})=\left\{0 \le S_{um}<10:-0.38+0.03\left|S_{um}-0\right|,10 \le S_{um}<13:-0.08+0.02\left|S_{um}-10\right|,13 \le S_{um}<25:-0.02+0.01\left|S_{um}-13\right|,25 \le S_{um}<41:0.1+0.015\left|S_{um}-25\right|,41 \le S_{um}<50:0.34+0.01\left|S_{um}-41\right|,50 \le S_{um}<100:0.43+0.005\left|S_{um}-50\right|\right\}

See Example for how to use.



An Action Speed of 50% results in the animation lasting for only 67% of the base animation length.

New animation length = Base animation length / (1 + Action Speed)


Regular Interaction Speed

Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon. See Action/Interaction/Cast_Speed for more.

Agility and Resourcefulness governs your Regular Interaction Speed.

Agility gives 0.4 Regular Interaction Speed Rating, and Resourcefulness gives 0.6 Regular Interaction Speed Rating, which then get summed into a total Regular Interaction Speed Rating and finally converted into Regular Interaction Speed using the graph.

Regular Interaction Speed Rating = Agility * 0.4 + Resourcefulness * 0.6


0 Regular Interaction Speed Rating starts at -26% Regular Interaction Speed.

  • 0 -> -26%
  • 0 to 7 = 2% each, up to -12%
  • 7 to 15 = 1.5% each, up to 0%
  • 15 to 20 = 7% each, up to 35%
  • 20 to 25 = 6% each, up to 65%
  • 25 to 30 = 5% each, up to 90%
  • 30 to 35 = 4% each, up to 110%
  • 35 to 40 = 3% each, up to 125%
  • 40 to 45 = 2% each, up to 135%
  • 45 to 100 = 1% each, up to 190%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

R_{egularInteractionSpeed}(S_{um})=\left\{0 \le S_{um}<7:-0.26+0.02\left|S_{um}-0\right|,7 \le S_{um}<15:-0.12+0.015\left|S_{um}-7\right|,15 \le S_{um}<20:0+0.07\left|S_{um}-15\right|,20 \le S_{um}<25:0.35+0.06\left|S_{um}-20\right|,25 \le S_{um}<30:0.65+0.05\left|S_{um}-25\right|,30 \le S_{um}<35:0.9+0.04\left|S_{um}-30\right|,35 \le S_{um}<40:1.1+0.03\left|S_{um}-35\right|,40 \le S_{um}<45:1.25+0.02\left|S_{um}-40\right|,45 \le S_{um}<100:1.35+0.01\left|S_{um}-45\right|\right\}

See Example for how to use.



New interaction length = Base interaction length / (1 + interaction speed)


For example, an Interaction Speed of 100% results in the interaction time lasting for only 50% of the base interaction length.

Surgical Kits and Bandages have 50% Scaling on regular interaction speed, therefore, their formula looks like

New interaction length = Base interaction length / (1 + interaction speed * .5)

Other Stats

Armor Rating

Armor Rating (AR) is determined from the armor your wearing, but can also be increased in some ways such as Fighter's Barricade (Armor Rating) or Fighter's Defense Mastery (Armor Rating Bonus).

Formula can be simplified as:
Final Armor Rating = Armor Rating * (1 + Armor Rating Bonus)


Note that Fighter's Defense Mastery and Rogue's Weakpoint Attack are specifically Item Armor Rating Bonus, meaning they only affect the AR from Items (excluding enchants), where the following formula should be applied.

Final Armor Rating = Armor Rating from armor * (1 + Item Armor Rating Bonus) + other Armor Rating * (1 + Armor Rating Bonus)


Note that only Item Armor Rating Bonus exists currently, and not Armor Rating Bonus. Therefore, the shortest form of this expanded formula can be written as:

Final Armor Rating = Armor Rating from armor * (1 + Item Armor Rating bonus) + other Armor Rating


Example using the last formula:
With 100 AR from equipped Items, 20 from Enchantments, and -40% Item Armor Rating Bonus, the player would result in

100 * (1 + -0.4) + 20 = 80 Armor Rating

Physical Damage Reduction

Physical Damage Reduction governs your resistance to physical damage dealing weapons and projectiles. Unlike Magic Resistance that is increased by Will, Armor Rating does not have an attribute stat that it scales off.

Armor Rating governs your Physical Damage Reduction.

-300 Armor Rating starts at -619% Physical Damage Reduction.

  • -300 -> -619%
  • -300 to -3 = 2% each, up to -25%
  • -3 to 22 = 1% each, up to 0%
  • 22 to 31 = 0.5% each, up to 4.5%
  • 31 to 42 = 0.4% each, up to 8.9%
  • 42 to 52 = 0.3% each, up to 11.9%
  • 52 to 62 = 0.2% each, up to 13.9%
  • 62 to 112 = 0.1% each, up to 18.9%
  • 112 to 175 = 0.2% each, up to 31.5%
  • 175 to 230 = 0.25% each, up to 45.25%
  • 230 to 317 = 0.2% each, up to 62.65%
  • 317 to 353 = 0.1% each, up to 66.25%
  • 353 to 368 = 0.05% each, up to 67%
  • 368 to 369 = 0.03% each, up to 67.03%
  • 369 to 370 = 0.07% each, up to 67.1%
  • 370 to 428 = 0.05% each, up to 70%
  • 428 to 429 = -0.075% each, up to 69.925%
  • 429 to 450 = 0.025% each, up to 70.45%
  • 450 to 500 = 0.02% each, up to 71.45%

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

P_{hysicalDamageReduction}(A_{rmorRating})=\left\{-300 \le A_{rmorRating}<-3:-6.19+0.02\left|A_{rmorRating}--300\right|,-3 \le A_{rmorRating}<22:-0.25+0.01\left|A_{rmorRating}--3\right|,22 \le A_{rmorRating}<31:0+0.005\left|A_{rmorRating}-22\right|,31 \le A_{rmorRating}<42:0.045+0.004\left|A_{rmorRating}-31\right|,42 \le A_{rmorRating}<52:0.089+0.003\left|A_{rmorRating}-42\right|,52 \le A_{rmorRating}<62:0.119+0.002\left|A_{rmorRating}-52\right|,62 \le A_{rmorRating}<112:0.139+0.001\left|A_{rmorRating}-62\right|,112 \le A_{rmorRating}<175:0.189+0.002\left|A_{rmorRating}-112\right|,175 \le A_{rmorRating}<230:0.315+0.003\left|A_{rmorRating}-175\right|,230 \le A_{rmorRating}<317:0.453+0.002\left|A_{rmorRating}-230\right|,317 \le A_{rmorRating}<353:0.626+0.001\left|A_{rmorRating}-317\right|,353 \le A_{rmorRating}<368:0.662+0.001\left|A_{rmorRating}-353\right|,368 \le A_{rmorRating}<369:0.67+0\left|A_{rmorRating}-368\right|,369 \le A_{rmorRating}<370:0.67+0.001\left|A_{rmorRating}-369\right|,370 \le A_{rmorRating}<428:0.671+0\left|A_{rmorRating}-370\right|,428 \le A_{rmorRating}<429:0.7+-0.001\left|A_{rmorRating}-428\right|,429 \le A_{rmorRating}<450:0.699+0\left|A_{rmorRating}-429\right|,450 \le A_{rmorRating}<500:0.705+0\left|A_{rmorRating}-450\right|\right\}

See Example for how to use.


Physical Damage Reduction is capped to 65%

Impact Power

Impact Power governs the strength of your weapon strikes against a target, it determines if you can break objects and stagger blocking enemies.

Can't be found on gear (aside from the base values for each weapon) and is not affected by other stats.

Item Swap Speed

Speed at which items are swapped as the current active item. Note that this is separate from Wearing Time Speed.

Affected by Action Speed.

Wearing Time Speed

Speed at which items are worn by equipping them from the inventory. Note that this is separate from Item Swap Speed.

Affected by Item Equip Speed.

Luck

Luck affects the Loot that is rolled when you open a container or kill a monster.

Whoever opens the container first or lands the killing blow on the monster is the character whose Luck is used to calculate the drops.

Luck is capped at 500.

It is possible to reach the Luck cap:


Icon Caution.pngNeeds further testing!
It is not confirmed if Bard's Unchained Harmony applies the Bard's Luck when it opens containers.
Contribute by joining the Spells & Guns discord!


Icon Caution.pngNeeds further testing!
Which character's Luck is used if a monster or the environment kills a monster? Do monsters/traps have Luck? Is loot instead rolled when the monster is first looted?
Contribute by joining the Spells & Guns discord!


Luck Scalar

Luck Scalars are but one piece of information needed to calculate drop probability at X Luck.

The calculation is not a simple multiplication, so do not expect Uniques to be 4.382 times more common at 500 Luck.

The true effect of Luck varies depending on Drop Rate tables. See the Luck subsection Probabilities from Luck for an in-depth explanation of how Luck Scalars affect probabilities of drops.

Additionally, luck works with a hidden property called Luck Grade. While the table below has luck grade colored similar to item rarities, the two properties are not equivalent.
Many loot tables will match Item Rarity one to one with item Luck Grade, but there are exceptions. Don't fall into the trap of thinking luck makes higher rarities more common; see the Cave Troll's quest drops for a counterexample.

Luck Scalar Table

Luck Grade Luck
0 50 100 150 200 250 300 350 400 450 500
0 1.000 0.950 0.900 0.850 0.800 0.750 0.700 0.650 0.600 0.550 0.500
1 1.000 0.950 0.900 0.850 0.800 0.750 0.700 0.650 0.600 0.550 0.500
2 1.000 0.975 0.950 0.925 0.900 0.875 0.850 0.825 0.800 0.775 0.750
3 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
4 1.000 1.476 1.901 2.277 2.602 2.878 3.103 3.279 3.404 3.480 3.505
5 1.000 1.547 2.036 2.468 2.842 3.159 3.418 3.620 3.765 3.851 3.881
6 1.000 1.618 2.171 2.659 3.083 3.441 3.734 3.962 4.125 4.223 4.257
7 1.000 1.642 2.216 2.723 3.163 3.535 3.839 4.076 4.245 4.347 4.382
8 1.000 1.642 2.216 2.723 3.163 3.535 3.839 4.076 4.245 4.347 4.382

If the Luck Scalar Table and Graph don't cover a Scalar value you wish to see, use the desmos graph. The desmos graph displays the LaTeX equations. While the curves are continuous, keep in mind that fractional values of Luck do not exist.

Luck Scalar Graph

LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade00}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<500:1+-0.001\left|L_{uckGrade}-0\right|\right\}

See Example for how to use.


LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade01}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<500:1+-0.001\left|L_{uckGrade}-0\right|\right\}

See Example for how to use.


LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade02}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<1:1+0\left|L_{uckGrade}-0\right|,1 \le L_{uckGrade}<2:1+-0.001\left|L_{uckGrade}-1\right|,2 \le L_{uckGrade}<3:0.999+0\left|L_{uckGrade}-2\right|,3 \le L_{uckGrade}<4:0.999+-0.001\left|L_{uckGrade}-3\right|,4 \le L_{uckGrade}<5:0.998+0\left|L_{uckGrade}-4\right|,5 \le L_{uckGrade}<6:0.998+-0.001\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<7:0.997+0\left|L_{uckGrade}-6\right|,7 \le L_{uckGrade}<8:0.997+-0.001\left|L_{uckGrade}-7\right|,8 \le L_{uckGrade}<9:0.996+0\left|L_{uckGrade}-8\right|,9 \le L_{uckGrade}<10:0.996+-0.001\left|L_{uckGrade}-9\right|,10 \le L_{uckGrade}<11:0.995+0\left|L_{uckGrade}-10\right|,11 \le L_{uckGrade}<12:0.995+-0.001\left|L_{uckGrade}-11\right|,12 \le L_{uckGrade}<13:0.994+0\left|L_{uckGrade}-12\right|,13 \le L_{uckGrade}<14:0.994+-0.001\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<15:0.993+0\left|L_{uckGrade}-14\right|,15 \le L_{uckGrade}<16:0.993+-0.001\left|L_{uckGrade}-15\right|,16 \le L_{uckGrade}<17:0.992+0\left|L_{uckGrade}-16\right|,17 \le L_{uckGrade}<18:0.992+-0.001\left|L_{uckGrade}-17\right|,18 \le L_{uckGrade}<19:0.991+0\left|L_{uckGrade}-18\right|,19 \le L_{uckGrade}<20:0.991+-0.001\left|L_{uckGrade}-19\right|,20 \le L_{uckGrade}<21:0.99+0\left|L_{uckGrade}-20\right|,21 \le L_{uckGrade}<22:0.99+-0.001\left|L_{uckGrade}-21\right|,22 \le L_{uckGrade}<23:0.989+0\left|L_{uckGrade}-22\right|,23 \le L_{uckGrade}<24:0.989+-0.001\left|L_{uckGrade}-23\right|,24 \le L_{uckGrade}<25:0.988+0\left|L_{uckGrade}-24\right|,25 \le L_{uckGrade}<26:0.988+-0.001\left|L_{uckGrade}-25\right|,26 \le L_{uckGrade}<27:0.987+0\left|L_{uckGrade}-26\right|,27 \le L_{uckGrade}<28:0.987+-0.001\left|L_{uckGrade}-27\right|,28 \le L_{uckGrade}<29:0.986+0\left|L_{uckGrade}-28\right|,29 \le L_{uckGrade}<30:0.986+-0.001\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<31:0.985+0\left|L_{uckGrade}-30\right|,31 \le L_{uckGrade}<32:0.985+-0.001\left|L_{uckGrade}-31\right|,32 \le L_{uckGrade}<33:0.984+0\left|L_{uckGrade}-32\right|,33 \le L_{uckGrade}<34:0.984+-0.001\left|L_{uckGrade}-33\right|,34 \le L_{uckGrade}<35:0.983+0\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<36:0.983+-0.001\left|L_{uckGrade}-35\right|,36 \le L_{uckGrade}<37:0.982+0\left|L_{uckGrade}-36\right|,37 \le L_{uckGrade}<38:0.982+-0.001\left|L_{uckGrade}-37\right|,38 \le L_{uckGrade}<39:0.981+0\left|L_{uckGrade}-38\right|,39 \le L_{uckGrade}<40:0.981+-0.001\left|L_{uckGrade}-39\right|,40 \le L_{uckGrade}<41:0.98+0\left|L_{uckGrade}-40\right|,41 \le L_{uckGrade}<42:0.98+-0.001\left|L_{uckGrade}-41\right|,42 \le L_{uckGrade}<43:0.979+0\left|L_{uckGrade}-42\right|,43 \le L_{uckGrade}<44:0.979+-0.001\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<45:0.978+0\left|L_{uckGrade}-44\right|,45 \le L_{uckGrade}<46:0.978+-0.001\left|L_{uckGrade}-45\right|,46 \le L_{uckGrade}<47:0.977+0\left|L_{uckGrade}-46\right|,47 \le L_{uckGrade}<48:0.977+-0.001\left|L_{uckGrade}-47\right|,48 \le L_{uckGrade}<49:0.976+0\left|L_{uckGrade}-48\right|,49 \le L_{uckGrade}<50:0.976+-0.001\left|L_{uckGrade}-49\right|,50 \le L_{uckGrade}<51:0.975+0\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<52:0.975+-0.001\left|L_{uckGrade}-51\right|,52 \le L_{uckGrade}<53:0.974+0\left|L_{uckGrade}-52\right|,53 \le L_{uckGrade}<54:0.974+-0.001\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<55:0.973+0\left|L_{uckGrade}-54\right|,55 \le L_{uckGrade}<56:0.973+-0.001\left|L_{uckGrade}-55\right|,56 \le L_{uckGrade}<57:0.972+0\left|L_{uckGrade}-56\right|,57 \le L_{uckGrade}<58:0.972+-0.001\left|L_{uckGrade}-57\right|,58 \le L_{uckGrade}<59:0.971+0\left|L_{uckGrade}-58\right|,59 \le L_{uckGrade}<60:0.971+-0.001\left|L_{uckGrade}-59\right|,60 \le L_{uckGrade}<61:0.97+0\left|L_{uckGrade}-60\right|,61 \le L_{uckGrade}<62:0.97+-0.001\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<63:0.969+0\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<64:0.969+-0.001\left|L_{uckGrade}-63\right|,64 \le L_{uckGrade}<65:0.968+0\left|L_{uckGrade}-64\right|,65 \le L_{uckGrade}<66:0.968+-0.001\left|L_{uckGrade}-65\right|,66 \le L_{uckGrade}<67:0.967+0\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<68:0.967+-0.001\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<69:0.966+0\left|L_{uckGrade}-68\right|,69 \le L_{uckGrade}<70:0.966+-0.001\left|L_{uckGrade}-69\right|,70 \le L_{uckGrade}<71:0.965+0\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<72:0.965+-0.001\left|L_{uckGrade}-71\right|,72 \le L_{uckGrade}<73:0.964+0\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<74:0.964+-0.001\left|L_{uckGrade}-73\right|,74 \le L_{uckGrade}<75:0.963+0\left|L_{uckGrade}-74\right|,75 \le L_{uckGrade}<76:0.963+-0.001\left|L_{uckGrade}-75\right|,76 \le L_{uckGrade}<77:0.962+0\left|L_{uckGrade}-76\right|,77 \le L_{uckGrade}<78:0.962+-0.001\left|L_{uckGrade}-77\right|,78 \le L_{uckGrade}<79:0.961+0\left|L_{uckGrade}-78\right|,79 \le L_{uckGrade}<80:0.961+-0.001\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<81:0.96+0\left|L_{uckGrade}-80\right|,81 \le L_{uckGrade}<82:0.96+-0.001\left|L_{uckGrade}-81\right|,82 \le L_{uckGrade}<83:0.959+0\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<84:0.959+-0.001\left|L_{uckGrade}-83\right|,84 \le L_{uckGrade}<85:0.958+0\left|L_{uckGrade}-84\right|,85 \le L_{uckGrade}<86:0.958+-0.001\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<87:0.957+0\left|L_{uckGrade}-86\right|,87 \le L_{uckGrade}<88:0.957+-0.001\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<89:0.956+0\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<90:0.956+-0.001\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<91:0.955+0\left|L_{uckGrade}-90\right|,91 \le L_{uckGrade}<92:0.955+-0.001\left|L_{uckGrade}-91\right|,92 \le L_{uckGrade}<93:0.954+0\left|L_{uckGrade}-92\right|,93 \le L_{uckGrade}<94:0.954+-0.001\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<95:0.953+0\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<96:0.953+-0.001\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<97:0.952+0\left|L_{uckGrade}-96\right|,97 \le L_{uckGrade}<98:0.952+-0.001\left|L_{uckGrade}-97\right|,98 \le L_{uckGrade}<99:0.951+0\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<100:0.951+-0.001\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<101:0.95+0\left|L_{uckGrade}-100\right|,101 \le L_{uckGrade}<102:0.95+-0.001\left|L_{uckGrade}-101\right|,102 \le L_{uckGrade}<103:0.949+0\left|L_{uckGrade}-102\right|,103 \le L_{uckGrade}<104:0.949+-0.001\left|L_{uckGrade}-103\right|,104 \le L_{uckGrade}<105:0.948+0\left|L_{uckGrade}-104\right|,105 \le L_{uckGrade}<106:0.948+-0.001\left|L_{uckGrade}-105\right|,106 \le L_{uckGrade}<107:0.947+0\left|L_{uckGrade}-106\right|,107 \le L_{uckGrade}<108:0.947+-0.001\left|L_{uckGrade}-107\right|,108 \le L_{uckGrade}<109:0.946+0\left|L_{uckGrade}-108\right|,109 \le L_{uckGrade}<110:0.946+-0.001\left|L_{uckGrade}-109\right|,110 \le L_{uckGrade}<111:0.945+0\left|L_{uckGrade}-110\right|,111 \le L_{uckGrade}<112:0.945+-0.001\left|L_{uckGrade}-111\right|,112 \le L_{uckGrade}<113:0.944+0\left|L_{uckGrade}-112\right|,113 \le L_{uckGrade}<114:0.944+-0.001\left|L_{uckGrade}-113\right|,114 \le L_{uckGrade}<115:0.943+0\left|L_{uckGrade}-114\right|,115 \le L_{uckGrade}<116:0.943+-0.001\left|L_{uckGrade}-115\right|,116 \le L_{uckGrade}<117:0.942+0\left|L_{uckGrade}-116\right|,117 \le L_{uckGrade}<118:0.942+-0.001\left|L_{uckGrade}-117\right|,118 \le L_{uckGrade}<119:0.941+0\left|L_{uckGrade}-118\right|,119 \le L_{uckGrade}<120:0.941+-0.001\left|L_{uckGrade}-119\right|,120 \le L_{uckGrade}<121:0.94+0\left|L_{uckGrade}-120\right|,121 \le L_{uckGrade}<122:0.94+-0.001\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<123:0.939+0\left|L_{uckGrade}-122\right|,123 \le L_{uckGrade}<124:0.939+-0.001\left|L_{uckGrade}-123\right|,124 \le L_{uckGrade}<125:0.938+0\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<126:0.938+-0.001\left|L_{uckGrade}-125\right|,126 \le L_{uckGrade}<127:0.937+0\left|L_{uckGrade}-126\right|,127 \le L_{uckGrade}<128:0.937+-0.001\left|L_{uckGrade}-127\right|,128 \le L_{uckGrade}<129:0.936+0\left|L_{uckGrade}-128\right|,129 \le L_{uckGrade}<130:0.936+-0.001\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<131:0.935+0\left|L_{uckGrade}-130\right|,131 \le L_{uckGrade}<132:0.935+-0.001\left|L_{uckGrade}-131\right|,132 \le L_{uckGrade}<133:0.934+0\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<134:0.934+-0.001\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<135:0.933+0\left|L_{uckGrade}-134\right|,135 \le L_{uckGrade}<136:0.933+-0.001\left|L_{uckGrade}-135\right|,136 \le L_{uckGrade}<137:0.932+0\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<138:0.932+-0.001\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<139:0.931+0\left|L_{uckGrade}-138\right|,139 \le L_{uckGrade}<140:0.931+-0.001\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<141:0.93+0\left|L_{uckGrade}-140\right|,141 \le L_{uckGrade}<142:0.93+-0.001\left|L_{uckGrade}-141\right|,142 \le L_{uckGrade}<143:0.929+0\left|L_{uckGrade}-142\right|,143 \le L_{uckGrade}<144:0.929+-0.001\left|L_{uckGrade}-143\right|,144 \le L_{uckGrade}<145:0.928+0\left|L_{uckGrade}-144\right|,145 \le L_{uckGrade}<146:0.928+-0.001\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<147:0.927+0\left|L_{uckGrade}-146\right|,147 \le L_{uckGrade}<148:0.927+-0.001\left|L_{uckGrade}-147\right|,148 \le L_{uckGrade}<149:0.926+0\left|L_{uckGrade}-148\right|,149 \le L_{uckGrade}<150:0.926+-0.001\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<151:0.925+0\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:0.925+-0.001\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<153:0.924+0\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<154:0.924+-0.001\left|L_{uckGrade}-153\right|,154 \le L_{uckGrade}<155:0.923+0\left|L_{uckGrade}-154\right|,155 \le L_{uckGrade}<156:0.923+-0.001\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<157:0.922+0\left|L_{uckGrade}-156\right|,157 \le L_{uckGrade}<158:0.922+-0.001\left|L_{uckGrade}-157\right|,158 \le L_{uckGrade}<159:0.921+0\left|L_{uckGrade}-158\right|,159 \le L_{uckGrade}<160:0.921+-0.001\left|L_{uckGrade}-159\right|,160 \le L_{uckGrade}<161:0.92+0\left|L_{uckGrade}-160\right|,161 \le L_{uckGrade}<162:0.92+-0.001\left|L_{uckGrade}-161\right|,162 \le L_{uckGrade}<163:0.919+0\left|L_{uckGrade}-162\right|,163 \le L_{uckGrade}<164:0.919+-0.001\left|L_{uckGrade}-163\right|,164 \le L_{uckGrade}<165:0.918+0\left|L_{uckGrade}-164\right|,165 \le L_{uckGrade}<166:0.918+-0.001\left|L_{uckGrade}-165\right|,166 \le L_{uckGrade}<167:0.917+0\left|L_{uckGrade}-166\right|,167 \le L_{uckGrade}<168:0.917+-0.001\left|L_{uckGrade}-167\right|,168 \le L_{uckGrade}<169:0.916+0\left|L_{uckGrade}-168\right|,169 \le L_{uckGrade}<170:0.916+-0.001\left|L_{uckGrade}-169\right|,170 \le L_{uckGrade}<171:0.915+0\left|L_{uckGrade}-170\right|,171 \le L_{uckGrade}<172:0.915+-0.001\left|L_{uckGrade}-171\right|,172 \le L_{uckGrade}<173:0.914+0\left|L_{uckGrade}-172\right|,173 \le L_{uckGrade}<174:0.914+-0.001\left|L_{uckGrade}-173\right|,174 \le L_{uckGrade}<175:0.913+0\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<176:0.913+-0.001\left|L_{uckGrade}-175\right|,176 \le L_{uckGrade}<177:0.912+0\left|L_{uckGrade}-176\right|,177 \le L_{uckGrade}<178:0.912+-0.001\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<179:0.911+0\left|L_{uckGrade}-178\right|,179 \le L_{uckGrade}<180:0.911+-0.001\left|L_{uckGrade}-179\right|,180 \le L_{uckGrade}<181:0.91+0\left|L_{uckGrade}-180\right|,181 \le L_{uckGrade}<182:0.91+-0.001\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<183:0.909+0\left|L_{uckGrade}-182\right|,183 \le L_{uckGrade}<184:0.909+-0.001\left|L_{uckGrade}-183\right|,184 \le L_{uckGrade}<185:0.908+0\left|L_{uckGrade}-184\right|,185 \le L_{uckGrade}<186:0.908+-0.001\left|L_{uckGrade}-185\right|,186 \le L_{uckGrade}<187:0.907+0\left|L_{uckGrade}-186\right|,187 \le L_{uckGrade}<188:0.907+-0.001\left|L_{uckGrade}-187\right|,188 \le L_{uckGrade}<189:0.906+0\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<190:0.906+-0.001\left|L_{uckGrade}-189\right|,190 \le L_{uckGrade}<191:0.905+0\left|L_{uckGrade}-190\right|,191 \le L_{uckGrade}<192:0.905+-0.001\left|L_{uckGrade}-191\right|,192 \le L_{uckGrade}<193:0.904+0\left|L_{uckGrade}-192\right|,193 \le L_{uckGrade}<194:0.904+-0.001\left|L_{uckGrade}-193\right|,194 \le L_{uckGrade}<195:0.903+0\left|L_{uckGrade}-194\right|,195 \le L_{uckGrade}<196:0.903+-0.001\left|L_{uckGrade}-195\right|,196 \le L_{uckGrade}<197:0.902+0\left|L_{uckGrade}-196\right|,197 \le L_{uckGrade}<198:0.902+-0.001\left|L_{uckGrade}-197\right|,198 \le L_{uckGrade}<199:0.901+0\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<200:0.901+-0.001\left|L_{uckGrade}-199\right|,200 \le L_{uckGrade}<201:0.9+0\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<202:0.9+-0.001\left|L_{uckGrade}-201\right|,202 \le L_{uckGrade}<203:0.899+0\left|L_{uckGrade}-202\right|,203 \le L_{uckGrade}<204:0.899+-0.001\left|L_{uckGrade}-203\right|,204 \le L_{uckGrade}<205:0.898+0\left|L_{uckGrade}-204\right|,205 \le L_{uckGrade}<206:0.898+-0.001\left|L_{uckGrade}-205\right|,206 \le L_{uckGrade}<207:0.897+0\left|L_{uckGrade}-206\right|,207 \le L_{uckGrade}<208:0.897+-0.001\left|L_{uckGrade}-207\right|,208 \le L_{uckGrade}<209:0.896+0\left|L_{uckGrade}-208\right|,209 \le L_{uckGrade}<210:0.896+-0.001\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<211:0.895+0\left|L_{uckGrade}-210\right|,211 \le L_{uckGrade}<212:0.895+-0.001\left|L_{uckGrade}-211\right|,212 \le L_{uckGrade}<213:0.894+0\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<214:0.894+-0.001\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<215:0.893+0\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<216:0.893+-0.001\left|L_{uckGrade}-215\right|,216 \le L_{uckGrade}<217:0.892+0\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<218:0.892+-0.001\left|L_{uckGrade}-217\right|,218 \le L_{uckGrade}<219:0.891+0\left|L_{uckGrade}-218\right|,219 \le L_{uckGrade}<220:0.891+-0.001\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<221:0.89+0\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:0.89+-0.001\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:0.889+0\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:0.889+-0.001\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<225:0.888+0\left|L_{uckGrade}-224\right|,225 \le L_{uckGrade}<226:0.888+-0.001\left|L_{uckGrade}-225\right|,226 \le L_{uckGrade}<227:0.887+0\left|L_{uckGrade}-226\right|,227 \le L_{uckGrade}<228:0.887+-0.001\left|L_{uckGrade}-227\right|,228 \le L_{uckGrade}<229:0.886+0\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<230:0.886+-0.001\left|L_{uckGrade}-229\right|,230 \le L_{uckGrade}<231:0.885+0\left|L_{uckGrade}-230\right|,231 \le L_{uckGrade}<232:0.885+-0.001\left|L_{uckGrade}-231\right|,232 \le L_{uckGrade}<233:0.884+0\left|L_{uckGrade}-232\right|,233 \le L_{uckGrade}<234:0.884+-0.001\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<235:0.883+0\left|L_{uckGrade}-234\right|,235 \le L_{uckGrade}<236:0.883+-0.001\left|L_{uckGrade}-235\right|,236 \le L_{uckGrade}<237:0.882+0\left|L_{uckGrade}-236\right|,237 \le L_{uckGrade}<238:0.882+-0.001\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<239:0.881+0\left|L_{uckGrade}-238\right|,239 \le L_{uckGrade}<240:0.881+-0.001\left|L_{uckGrade}-239\right|,240 \le L_{uckGrade}<241:0.88+0\left|L_{uckGrade}-240\right|,241 \le L_{uckGrade}<242:0.88+-0.001\left|L_{uckGrade}-241\right|,242 \le L_{uckGrade}<243:0.879+0\left|L_{uckGrade}-242\right|,243 \le L_{uckGrade}<244:0.879+-0.001\left|L_{uckGrade}-243\right|,244 \le L_{uckGrade}<245:0.878+0\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<246:0.878+-0.001\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<247:0.877+0\left|L_{uckGrade}-246\right|,247 \le L_{uckGrade}<248:0.877+-0.001\left|L_{uckGrade}-247\right|,248 \le L_{uckGrade}<249:0.876+0\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<250:0.876+-0.001\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<251:0.875+0\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:0.875+-0.001\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<253:0.874+0\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<254:0.874+-0.001\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<255:0.873+0\left|L_{uckGrade}-254\right|,255 \le L_{uckGrade}<256:0.873+-0.001\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<257:0.872+0\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<258:0.872+-0.001\left|L_{uckGrade}-257\right|,258 \le L_{uckGrade}<259:0.871+0\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<260:0.871+-0.001\left|L_{uckGrade}-259\right|,260 \le L_{uckGrade}<261:0.87+0\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<262:0.87+-0.001\left|L_{uckGrade}-261\right|,262 \le L_{uckGrade}<263:0.869+0\left|L_{uckGrade}-262\right|,263 \le L_{uckGrade}<264:0.869+-0.001\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<265:0.868+0\left|L_{uckGrade}-264\right|,265 \le L_{uckGrade}<266:0.868+-0.001\left|L_{uckGrade}-265\right|,266 \le L_{uckGrade}<267:0.867+0\left|L_{uckGrade}-266\right|,267 \le L_{uckGrade}<268:0.867+-0.001\left|L_{uckGrade}-267\right|,268 \le L_{uckGrade}<269:0.866+0\left|L_{uckGrade}-268\right|,269 \le L_{uckGrade}<270:0.866+-0.001\left|L_{uckGrade}-269\right|,270 \le L_{uckGrade}<271:0.865+0\left|L_{uckGrade}-270\right|,271 \le L_{uckGrade}<272:0.865+-0.001\left|L_{uckGrade}-271\right|,272 \le L_{uckGrade}<273:0.864+0\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<274:0.864+-0.001\left|L_{uckGrade}-273\right|,274 \le L_{uckGrade}<275:0.863+0\left|L_{uckGrade}-274\right|,275 \le L_{uckGrade}<276:0.863+-0.001\left|L_{uckGrade}-275\right|,276 \le L_{uckGrade}<277:0.862+0\left|L_{uckGrade}-276\right|,277 \le L_{uckGrade}<278:0.862+-0.001\left|L_{uckGrade}-277\right|,278 \le L_{uckGrade}<279:0.861+0\left|L_{uckGrade}-278\right|,279 \le L_{uckGrade}<280:0.861+-0.001\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<281:0.86+0\left|L_{uckGrade}-280\right|,281 \le L_{uckGrade}<282:0.86+-0.001\left|L_{uckGrade}-281\right|,282 \le L_{uckGrade}<283:0.859+0\left|L_{uckGrade}-282\right|,283 \le L_{uckGrade}<284:0.859+-0.001\left|L_{uckGrade}-283\right|,284 \le L_{uckGrade}<285:0.858+0\left|L_{uckGrade}-284\right|,285 \le L_{uckGrade}<286:0.858+-0.001\left|L_{uckGrade}-285\right|,286 \le L_{uckGrade}<287:0.857+0\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<288:0.857+-0.001\left|L_{uckGrade}-287\right|,288 \le L_{uckGrade}<289:0.856+0\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<290:0.856+-0.001\left|L_{uckGrade}-289\right|,290 \le L_{uckGrade}<291:0.855+0\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<292:0.855+-0.001\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<293:0.854+0\left|L_{uckGrade}-292\right|,293 \le L_{uckGrade}<294:0.854+-0.001\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<295:0.853+0\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<296:0.853+-0.001\left|L_{uckGrade}-295\right|,296 \le L_{uckGrade}<297:0.852+0\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<298:0.852+-0.001\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<299:0.851+0\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<300:0.851+-0.001\left|L_{uckGrade}-299\right|,300 \le L_{uckGrade}<301:0.85+0\left|L_{uckGrade}-300\right|,301 \le L_{uckGrade}<302:0.85+-0.001\left|L_{uckGrade}-301\right|,302 \le L_{uckGrade}<303:0.849+0\left|L_{uckGrade}-302\right|,303 \le L_{uckGrade}<304:0.849+-0.001\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<305:0.848+0\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<306:0.848+-0.001\left|L_{uckGrade}-305\right|,306 \le L_{uckGrade}<307:0.847+0\left|L_{uckGrade}-306\right|,307 \le L_{uckGrade}<308:0.847+-0.001\left|L_{uckGrade}-307\right|,308 \le L_{uckGrade}<309:0.846+0\left|L_{uckGrade}-308\right|,309 \le L_{uckGrade}<310:0.846+-0.001\left|L_{uckGrade}-309\right|,310 \le L_{uckGrade}<311:0.845+0\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<312:0.845+-0.001\left|L_{uckGrade}-311\right|,312 \le L_{uckGrade}<313:0.844+0\left|L_{uckGrade}-312\right|,313 \le L_{uckGrade}<314:0.844+-0.001\left|L_{uckGrade}-313\right|,314 \le L_{uckGrade}<315:0.843+0\left|L_{uckGrade}-314\right|,315 \le L_{uckGrade}<316:0.843+-0.001\left|L_{uckGrade}-315\right|,316 \le L_{uckGrade}<317:0.842+0\left|L_{uckGrade}-316\right|,317 \le L_{uckGrade}<318:0.842+-0.001\left|L_{uckGrade}-317\right|,318 \le L_{uckGrade}<319:0.841+0\left|L_{uckGrade}-318\right|,319 \le L_{uckGrade}<320:0.841+-0.001\left|L_{uckGrade}-319\right|,320 \le L_{uckGrade}<321:0.84+0\left|L_{uckGrade}-320\right|,321 \le L_{uckGrade}<322:0.84+-0.001\left|L_{uckGrade}-321\right|,322 \le L_{uckGrade}<323:0.839+0\left|L_{uckGrade}-322\right|,323 \le L_{uckGrade}<324:0.839+-0.001\left|L_{uckGrade}-323\right|,324 \le L_{uckGrade}<325:0.838+0\left|L_{uckGrade}-324\right|,325 \le L_{uckGrade}<326:0.838+-0.001\left|L_{uckGrade}-325\right|,326 \le L_{uckGrade}<327:0.837+0\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<328:0.837+-0.001\left|L_{uckGrade}-327\right|,328 \le L_{uckGrade}<329:0.836+0\left|L_{uckGrade}-328\right|,329 \le L_{uckGrade}<330:0.836+-0.001\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<331:0.835+0\left|L_{uckGrade}-330\right|,331 \le L_{uckGrade}<332:0.835+-0.001\left|L_{uckGrade}-331\right|,332 \le L_{uckGrade}<333:0.834+0\left|L_{uckGrade}-332\right|,333 \le L_{uckGrade}<334:0.834+-0.001\left|L_{uckGrade}-333\right|,334 \le L_{uckGrade}<335:0.833+0\left|L_{uckGrade}-334\right|,335 \le L_{uckGrade}<336:0.833+-0.001\left|L_{uckGrade}-335\right|,336 \le L_{uckGrade}<337:0.832+0\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<338:0.832+-0.001\left|L_{uckGrade}-337\right|,338 \le L_{uckGrade}<339:0.831+0\left|L_{uckGrade}-338\right|,339 \le L_{uckGrade}<340:0.831+-0.001\left|L_{uckGrade}-339\right|,340 \le L_{uckGrade}<341:0.83+0\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<342:0.83+-0.001\left|L_{uckGrade}-341\right|,342 \le L_{uckGrade}<343:0.829+0\left|L_{uckGrade}-342\right|,343 \le L_{uckGrade}<344:0.829+-0.001\left|L_{uckGrade}-343\right|,344 \le L_{uckGrade}<345:0.828+0\left|L_{uckGrade}-344\right|,345 \le L_{uckGrade}<346:0.828+-0.001\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<347:0.827+0\left|L_{uckGrade}-346\right|,347 \le L_{uckGrade}<348:0.827+-0.001\left|L_{uckGrade}-347\right|,348 \le L_{uckGrade}<349:0.826+0\left|L_{uckGrade}-348\right|,349 \le L_{uckGrade}<350:0.826+-0.001\left|L_{uckGrade}-349\right|,350 \le L_{uckGrade}<351:0.825+0\left|L_{uckGrade}-350\right|,351 \le L_{uckGrade}<352:0.825+-0.001\left|L_{uckGrade}-351\right|,352 \le L_{uckGrade}<353:0.824+0\left|L_{uckGrade}-352\right|,353 \le L_{uckGrade}<354:0.824+-0.001\left|L_{uckGrade}-353\right|,354 \le L_{uckGrade}<355:0.823+0\left|L_{uckGrade}-354\right|,355 \le L_{uckGrade}<356:0.823+-0.001\left|L_{uckGrade}-355\right|,356 \le L_{uckGrade}<357:0.822+0\left|L_{uckGrade}-356\right|,357 \le L_{uckGrade}<358:0.822+-0.001\left|L_{uckGrade}-357\right|,358 \le L_{uckGrade}<359:0.821+0\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<360:0.821+-0.001\left|L_{uckGrade}-359\right|,360 \le L_{uckGrade}<361:0.82+0\left|L_{uckGrade}-360\right|,361 \le L_{uckGrade}<362:0.82+-0.001\left|L_{uckGrade}-361\right|,362 \le L_{uckGrade}<363:0.819+0\left|L_{uckGrade}-362\right|,363 \le L_{uckGrade}<364:0.819+-0.001\left|L_{uckGrade}-363\right|,364 \le L_{uckGrade}<365:0.818+0\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<366:0.818+-0.001\left|L_{uckGrade}-365\right|,366 \le L_{uckGrade}<367:0.817+0\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:0.817+-0.001\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<369:0.816+0\left|L_{uckGrade}-368\right|,369 \le L_{uckGrade}<370:0.816+-0.001\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<371:0.815+0\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<372:0.815+-0.001\left|L_{uckGrade}-371\right|,372 \le L_{uckGrade}<373:0.814+0\left|L_{uckGrade}-372\right|,373 \le L_{uckGrade}<374:0.814+-0.001\left|L_{uckGrade}-373\right|,374 \le L_{uckGrade}<375:0.813+0\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<376:0.813+-0.001\left|L_{uckGrade}-375\right|,376 \le L_{uckGrade}<377:0.812+0\left|L_{uckGrade}-376\right|,377 \le L_{uckGrade}<378:0.812+-0.001\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<379:0.811+0\left|L_{uckGrade}-378\right|,379 \le L_{uckGrade}<380:0.811+-0.001\left|L_{uckGrade}-379\right|,380 \le L_{uckGrade}<381:0.81+0\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<382:0.81+-0.001\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<383:0.809+0\left|L_{uckGrade}-382\right|,383 \le L_{uckGrade}<384:0.809+-0.001\left|L_{uckGrade}-383\right|,384 \le L_{uckGrade}<385:0.808+0\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<386:0.808+-0.001\left|L_{uckGrade}-385\right|,386 \le L_{uckGrade}<387:0.807+0\left|L_{uckGrade}-386\right|,387 \le L_{uckGrade}<388:0.807+-0.001\left|L_{uckGrade}-387\right|,388 \le L_{uckGrade}<389:0.806+0\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<390:0.806+-0.001\left|L_{uckGrade}-389\right|,390 \le L_{uckGrade}<391:0.805+0\left|L_{uckGrade}-390\right|,391 \le L_{uckGrade}<392:0.805+-0.001\left|L_{uckGrade}-391\right|,392 \le L_{uckGrade}<393:0.804+0\left|L_{uckGrade}-392\right|,393 \le L_{uckGrade}<394:0.804+-0.001\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<395:0.803+0\left|L_{uckGrade}-394\right|,395 \le L_{uckGrade}<396:0.803+-0.001\left|L_{uckGrade}-395\right|,396 \le L_{uckGrade}<397:0.802+0\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<398:0.802+-0.001\left|L_{uckGrade}-397\right|,398 \le L_{uckGrade}<399:0.801+0\left|L_{uckGrade}-398\right|,399 \le L_{uckGrade}<400:0.801+-0.001\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<401:0.8+0\left|L_{uckGrade}-400\right|,401 \le L_{uckGrade}<402:0.8+-0.001\left|L_{uckGrade}-401\right|,402 \le L_{uckGrade}<403:0.799+0\left|L_{uckGrade}-402\right|,403 \le L_{uckGrade}<404:0.799+-0.001\left|L_{uckGrade}-403\right|,404 \le L_{uckGrade}<405:0.798+0\left|L_{uckGrade}-404\right|,405 \le L_{uckGrade}<406:0.798+-0.001\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:0.797+0\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<408:0.797+-0.001\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<409:0.796+0\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<410:0.796+-0.001\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<411:0.795+0\left|L_{uckGrade}-410\right|,411 \le L_{uckGrade}<412:0.795+-0.001\left|L_{uckGrade}-411\right|,412 \le L_{uckGrade}<413:0.794+0\left|L_{uckGrade}-412\right|,413 \le L_{uckGrade}<414:0.794+-0.001\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<415:0.793+0\left|L_{uckGrade}-414\right|,415 \le L_{uckGrade}<416:0.793+-0.001\left|L_{uckGrade}-415\right|,416 \le L_{uckGrade}<417:0.792+0\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<418:0.792+-0.001\left|L_{uckGrade}-417\right|,418 \le L_{uckGrade}<419:0.791+0\left|L_{uckGrade}-418\right|,419 \le L_{uckGrade}<420:0.791+-0.001\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<421:0.79+0\left|L_{uckGrade}-420\right|,421 \le L_{uckGrade}<422:0.79+-0.001\left|L_{uckGrade}-421\right|,422 \le L_{uckGrade}<423:0.789+0\left|L_{uckGrade}-422\right|,423 \le L_{uckGrade}<424:0.789+-0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<425:0.788+0\left|L_{uckGrade}-424\right|,425 \le L_{uckGrade}<426:0.788+-0.001\left|L_{uckGrade}-425\right|,426 \le L_{uckGrade}<427:0.787+0\left|L_{uckGrade}-426\right|,427 \le L_{uckGrade}<428:0.787+-0.001\left|L_{uckGrade}-427\right|,428 \le L_{uckGrade}<429:0.786+0\left|L_{uckGrade}-428\right|,429 \le L_{uckGrade}<430:0.786+-0.001\left|L_{uckGrade}-429\right|,430 \le L_{uckGrade}<431:0.785+0\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<432:0.785+-0.001\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<433:0.784+0\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<434:0.784+-0.001\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<435:0.783+0\left|L_{uckGrade}-434\right|,435 \le L_{uckGrade}<436:0.783+-0.001\left|L_{uckGrade}-435\right|,436 \le L_{uckGrade}<437:0.782+0\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<438:0.782+-0.001\left|L_{uckGrade}-437\right|,438 \le L_{uckGrade}<439:0.781+0\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<440:0.781+-0.001\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<441:0.78+0\left|L_{uckGrade}-440\right|,441 \le L_{uckGrade}<442:0.78+-0.001\left|L_{uckGrade}-441\right|,442 \le L_{uckGrade}<443:0.779+0\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<444:0.779+-0.001\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<445:0.778+0\left|L_{uckGrade}-444\right|,445 \le L_{uckGrade}<446:0.778+-0.001\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<447:0.777+0\left|L_{uckGrade}-446\right|,447 \le L_{uckGrade}<448:0.777+-0.001\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<449:0.776+0\left|L_{uckGrade}-448\right|,449 \le L_{uckGrade}<450:0.776+-0.001\left|L_{uckGrade}-449\right|,450 \le L_{uckGrade}<451:0.775+0\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<452:0.775+-0.001\left|L_{uckGrade}-451\right|,452 \le L_{uckGrade}<453:0.774+0\left|L_{uckGrade}-452\right|,453 \le L_{uckGrade}<454:0.774+-0.001\left|L_{uckGrade}-453\right|,454 \le L_{uckGrade}<455:0.773+0\left|L_{uckGrade}-454\right|,455 \le L_{uckGrade}<456:0.773+-0.001\left|L_{uckGrade}-455\right|,456 \le L_{uckGrade}<457:0.772+0\left|L_{uckGrade}-456\right|,457 \le L_{uckGrade}<458:0.772+-0.001\left|L_{uckGrade}-457\right|,458 \le L_{uckGrade}<459:0.771+0\left|L_{uckGrade}-458\right|,459 \le L_{uckGrade}<460:0.771+-0.001\left|L_{uckGrade}-459\right|,460 \le L_{uckGrade}<461:0.77+0\left|L_{uckGrade}-460\right|,461 \le L_{uckGrade}<462:0.77+-0.001\left|L_{uckGrade}-461\right|,462 \le L_{uckGrade}<463:0.769+0\left|L_{uckGrade}-462\right|,463 \le L_{uckGrade}<464:0.769+-0.001\left|L_{uckGrade}-463\right|,464 \le L_{uckGrade}<465:0.768+0\left|L_{uckGrade}-464\right|,465 \le L_{uckGrade}<466:0.768+-0.001\left|L_{uckGrade}-465\right|,466 \le L_{uckGrade}<467:0.767+0\left|L_{uckGrade}-466\right|,467 \le L_{uckGrade}<468:0.767+-0.001\left|L_{uckGrade}-467\right|,468 \le L_{uckGrade}<469:0.766+0\left|L_{uckGrade}-468\right|,469 \le L_{uckGrade}<470:0.766+-0.001\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<471:0.765+0\left|L_{uckGrade}-470\right|,471 \le L_{uckGrade}<472:0.765+-0.001\left|L_{uckGrade}-471\right|,472 \le L_{uckGrade}<473:0.764+0\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<474:0.764+-0.001\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<475:0.763+0\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<476:0.763+-0.001\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<477:0.762+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<478:0.762+-0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:0.761+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<480:0.761+-0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:0.76+0\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:0.76+-0.001\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:0.759+0\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<484:0.759+-0.001\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<485:0.758+0\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<486:0.758+-0.001\left|L_{uckGrade}-485\right|,486 \le L_{uckGrade}<487:0.757+0\left|L_{uckGrade}-486\right|,487 \le L_{uckGrade}<488:0.757+-0.001\left|L_{uckGrade}-487\right|,488 \le L_{uckGrade}<489:0.756+0\left|L_{uckGrade}-488\right|,489 \le L_{uckGrade}<490:0.756+-0.001\left|L_{uckGrade}-489\right|,490 \le L_{uckGrade}<491:0.755+0\left|L_{uckGrade}-490\right|,491 \le L_{uckGrade}<492:0.755+-0.001\left|L_{uckGrade}-491\right|,492 \le L_{uckGrade}<493:0.754+0\left|L_{uckGrade}-492\right|,493 \le L_{uckGrade}<494:0.754+-0.001\left|L_{uckGrade}-493\right|,494 \le L_{uckGrade}<495:0.753+0\left|L_{uckGrade}-494\right|,495 \le L_{uckGrade}<496:0.753+-0.001\left|L_{uckGrade}-495\right|,496 \le L_{uckGrade}<497:0.752+0\left|L_{uckGrade}-496\right|,497 \le L_{uckGrade}<498:0.752+-0.001\left|L_{uckGrade}-497\right|,498 \le L_{uckGrade}<499:0.751+0\left|L_{uckGrade}-498\right|,499 \le L_{uckGrade}<500:0.751+-0.001\left|L_{uckGrade}-499\right|\right\}

See Example for how to use.


LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade03}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<500:1+0\left|L_{uckGrade}-0\right|\right\}

See Example for how to use.


LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade04}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<7:1+0.01\left|L_{uckGrade}-0\right|,7 \le L_{uckGrade}<8:1.07+0.009\left|L_{uckGrade}-7\right|,8 \le L_{uckGrade}<12:1.079+0.01\left|L_{uckGrade}-8\right|,12 \le L_{uckGrade}<13:1.119+0.009\left|L_{uckGrade}-12\right|,13 \le L_{uckGrade}<16:1.128+0.01\left|L_{uckGrade}-13\right|,16 \le L_{uckGrade}<17:1.158+0.009\left|L_{uckGrade}-16\right|,17 \le L_{uckGrade}<19:1.167+0.01\left|L_{uckGrade}-17\right|,19 \le L_{uckGrade}<20:1.187+0.009\left|L_{uckGrade}-19\right|,20 \le L_{uckGrade}<21:1.196+0.01\left|L_{uckGrade}-20\right|,21 \le L_{uckGrade}<22:1.206+0.009\left|L_{uckGrade}-21\right|,22 \le L_{uckGrade}<23:1.215+0.01\left|L_{uckGrade}-22\right|,23 \le L_{uckGrade}<24:1.225+0.009\left|L_{uckGrade}-23\right|,24 \le L_{uckGrade}<26:1.234+0.01\left|L_{uckGrade}-24\right|,26 \le L_{uckGrade}<28:1.254+0.009\left|L_{uckGrade}-26\right|,28 \le L_{uckGrade}<29:1.272+0.01\left|L_{uckGrade}-28\right|,29 \le L_{uckGrade}<30:1.282+0.009\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<31:1.291+0.01\left|L_{uckGrade}-30\right|,31 \le L_{uckGrade}<33:1.301+0.009\left|L_{uckGrade}-31\right|,33 \le L_{uckGrade}<34:1.319+0.01\left|L_{uckGrade}-33\right|,34 \le L_{uckGrade}<36:1.329+0.009\left|L_{uckGrade}-34\right|,36 \le L_{uckGrade}<37:1.347+0.01\left|L_{uckGrade}-36\right|,37 \le L_{uckGrade}<40:1.357+0.009\left|L_{uckGrade}-37\right|,40 \le L_{uckGrade}<41:1.384+0.01\left|L_{uckGrade}-40\right|,41 \le L_{uckGrade}<49:1.394+0.009\left|L_{uckGrade}-41\right|,49 \le L_{uckGrade}<50:1.466+0.01\left|L_{uckGrade}-49\right|,50 \le L_{uckGrade}<51:1.476+0.009\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<52:1.485+0.008\left|L_{uckGrade}-51\right|,52 \le L_{uckGrade}<60:1.493+0.009\left|L_{uckGrade}-52\right|,60 \le L_{uckGrade}<61:1.565+0.008\left|L_{uckGrade}-60\right|,61 \le L_{uckGrade}<64:1.573+0.009\left|L_{uckGrade}-61\right|,64 \le L_{uckGrade}<65:1.6+0.008\left|L_{uckGrade}-64\right|,65 \le L_{uckGrade}<67:1.608+0.009\left|L_{uckGrade}-65\right|,67 \le L_{uckGrade}<68:1.626+0.008\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<70:1.634+0.009\left|L_{uckGrade}-68\right|,70 \le L_{uckGrade}<71:1.652+0.008\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<72:1.66+0.009\left|L_{uckGrade}-71\right|,72 \le L_{uckGrade}<73:1.669+0.008\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<75:1.677+0.009\left|L_{uckGrade}-73\right|,75 \le L_{uckGrade}<77:1.695+0.008\left|L_{uckGrade}-75\right|,77 \le L_{uckGrade}<78:1.711+0.009\left|L_{uckGrade}-77\right|,78 \le L_{uckGrade}<79:1.72+0.008\left|L_{uckGrade}-78\right|,79 \le L_{uckGrade}<80:1.728+0.009\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<81:1.737+0.008\left|L_{uckGrade}-80\right|,81 \le L_{uckGrade}<82:1.745+0.009\left|L_{uckGrade}-81\right|,82 \le L_{uckGrade}<84:1.754+0.008\left|L_{uckGrade}-82\right|,84 \le L_{uckGrade}<85:1.77+0.009\left|L_{uckGrade}-84\right|,85 \le L_{uckGrade}<88:1.779+0.008\left|L_{uckGrade}-85\right|,88 \le L_{uckGrade}<89:1.803+0.009\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<93:1.812+0.008\left|L_{uckGrade}-89\right|,93 \le L_{uckGrade}<94:1.844+0.009\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<107:1.853+0.008\left|L_{uckGrade}-94\right|,107 \le L_{uckGrade}<108:1.957+0.007\left|L_{uckGrade}-107\right|,108 \le L_{uckGrade}<112:1.964+0.008\left|L_{uckGrade}-108\right|,112 \le L_{uckGrade}<113:1.996+0.007\left|L_{uckGrade}-112\right|,113 \le L_{uckGrade}<116:2.003+0.008\left|L_{uckGrade}-113\right|,116 \le L_{uckGrade}<117:2.027+0.007\left|L_{uckGrade}-116\right|,117 \le L_{uckGrade}<119:2.034+0.008\left|L_{uckGrade}-117\right|,119 \le L_{uckGrade}<120:2.05+0.007\left|L_{uckGrade}-119\right|,120 \le L_{uckGrade}<121:2.057+0.008\left|L_{uckGrade}-120\right|,121 \le L_{uckGrade}<122:2.065+0.007\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<123:2.072+0.008\left|L_{uckGrade}-122\right|,123 \le L_{uckGrade}<124:2.08+0.007\left|L_{uckGrade}-123\right|,124 \le L_{uckGrade}<126:2.087+0.008\left|L_{uckGrade}-124\right|,126 \le L_{uckGrade}<128:2.103+0.007\left|L_{uckGrade}-126\right|,128 \le L_{uckGrade}<129:2.117+0.008\left|L_{uckGrade}-128\right|,129 \le L_{uckGrade}<130:2.125+0.007\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<131:2.132+0.008\left|L_{uckGrade}-130\right|,131 \le L_{uckGrade}<133:2.14+0.007\left|L_{uckGrade}-131\right|,133 \le L_{uckGrade}<134:2.154+0.008\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<136:2.162+0.007\left|L_{uckGrade}-134\right|,136 \le L_{uckGrade}<137:2.176+0.008\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<140:2.184+0.007\left|L_{uckGrade}-137\right|,140 \le L_{uckGrade}<141:2.205+0.008\left|L_{uckGrade}-140\right|,141 \le L_{uckGrade}<149:2.213+0.007\left|L_{uckGrade}-141\right|,149 \le L_{uckGrade}<150:2.269+0.008\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<151:2.277+0.007\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:2.284+0.006\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<160:2.29+0.007\left|L_{uckGrade}-152\right|,160 \le L_{uckGrade}<161:2.346+0.006\left|L_{uckGrade}-160\right|,161 \le L_{uckGrade}<164:2.352+0.007\left|L_{uckGrade}-161\right|,164 \le L_{uckGrade}<165:2.373+0.006\left|L_{uckGrade}-164\right|,165 \le L_{uckGrade}<167:2.379+0.007\left|L_{uckGrade}-165\right|,167 \le L_{uckGrade}<168:2.393+0.006\left|L_{uckGrade}-167\right|,168 \le L_{uckGrade}<170:2.399+0.007\left|L_{uckGrade}-168\right|,170 \le L_{uckGrade}<171:2.413+0.006\left|L_{uckGrade}-170\right|,171 \le L_{uckGrade}<172:2.419+0.007\left|L_{uckGrade}-171\right|,172 \le L_{uckGrade}<173:2.426+0.006\left|L_{uckGrade}-172\right|,173 \le L_{uckGrade}<175:2.432+0.007\left|L_{uckGrade}-173\right|,175 \le L_{uckGrade}<177:2.446+0.006\left|L_{uckGrade}-175\right|,177 \le L_{uckGrade}<178:2.458+0.007\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<179:2.465+0.006\left|L_{uckGrade}-178\right|,179 \le L_{uckGrade}<180:2.471+0.007\left|L_{uckGrade}-179\right|,180 \le L_{uckGrade}<181:2.478+0.006\left|L_{uckGrade}-180\right|,181 \le L_{uckGrade}<182:2.484+0.007\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<184:2.491+0.006\left|L_{uckGrade}-182\right|,184 \le L_{uckGrade}<185:2.503+0.007\left|L_{uckGrade}-184\right|,185 \le L_{uckGrade}<188:2.51+0.006\left|L_{uckGrade}-185\right|,188 \le L_{uckGrade}<189:2.528+0.007\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<193:2.535+0.006\left|L_{uckGrade}-189\right|,193 \le L_{uckGrade}<194:2.559+0.007\left|L_{uckGrade}-193\right|,194 \le L_{uckGrade}<207:2.566+0.006\left|L_{uckGrade}-194\right|,207 \le L_{uckGrade}<208:2.644+0.005\left|L_{uckGrade}-207\right|,208 \le L_{uckGrade}<212:2.649+0.006\left|L_{uckGrade}-208\right|,212 \le L_{uckGrade}<213:2.673+0.005\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<216:2.678+0.006\left|L_{uckGrade}-213\right|,216 \le L_{uckGrade}<217:2.696+0.005\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<219:2.701+0.006\left|L_{uckGrade}-217\right|,219 \le L_{uckGrade}<220:2.713+0.005\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<221:2.718+0.006\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:2.724+0.005\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:2.729+0.006\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:2.735+0.005\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<226:2.74+0.006\left|L_{uckGrade}-224\right|,226 \le L_{uckGrade}<228:2.752+0.005\left|L_{uckGrade}-226\right|,228 \le L_{uckGrade}<229:2.762+0.006\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<230:2.768+0.005\left|L_{uckGrade}-229\right|,230 \le L_{uckGrade}<231:2.773+0.006\left|L_{uckGrade}-230\right|,231 \le L_{uckGrade}<233:2.779+0.005\left|L_{uckGrade}-231\right|,233 \le L_{uckGrade}<234:2.789+0.006\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<236:2.795+0.005\left|L_{uckGrade}-234\right|,236 \le L_{uckGrade}<237:2.805+0.006\left|L_{uckGrade}-236\right|,237 \le L_{uckGrade}<240:2.811+0.005\left|L_{uckGrade}-237\right|,240 \le L_{uckGrade}<241:2.826+0.006\left|L_{uckGrade}-240\right|,241 \le L_{uckGrade}<249:2.832+0.005\left|L_{uckGrade}-241\right|,249 \le L_{uckGrade}<250:2.872+0.006\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<251:2.878+0.005\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:2.883+0.004\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<260:2.887+0.005\left|L_{uckGrade}-252\right|,260 \le L_{uckGrade}<261:2.927+0.004\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<264:2.931+0.005\left|L_{uckGrade}-261\right|,264 \le L_{uckGrade}<265:2.946+0.004\left|L_{uckGrade}-264\right|,265 \le L_{uckGrade}<267:2.95+0.005\left|L_{uckGrade}-265\right|,267 \le L_{uckGrade}<268:2.96+0.004\left|L_{uckGrade}-267\right|,268 \le L_{uckGrade}<270:2.964+0.005\left|L_{uckGrade}-268\right|,270 \le L_{uckGrade}<271:2.974+0.004\left|L_{uckGrade}-270\right|,271 \le L_{uckGrade}<272:2.978+0.005\left|L_{uckGrade}-271\right|,272 \le L_{uckGrade}<273:2.983+0.004\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<275:2.987+0.005\left|L_{uckGrade}-273\right|,275 \le L_{uckGrade}<277:2.997+0.004\left|L_{uckGrade}-275\right|,277 \le L_{uckGrade}<278:3.005+0.005\left|L_{uckGrade}-277\right|,278 \le L_{uckGrade}<279:3.01+0.004\left|L_{uckGrade}-278\right|,279 \le L_{uckGrade}<280:3.014+0.005\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<281:3.019+0.004\left|L_{uckGrade}-280\right|,281 \le L_{uckGrade}<282:3.023+0.005\left|L_{uckGrade}-281\right|,282 \le L_{uckGrade}<284:3.028+0.004\left|L_{uckGrade}-282\right|,284 \le L_{uckGrade}<285:3.036+0.005\left|L_{uckGrade}-284\right|,285 \le L_{uckGrade}<288:3.041+0.004\left|L_{uckGrade}-285\right|,288 \le L_{uckGrade}<289:3.053+0.005\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<293:3.058+0.004\left|L_{uckGrade}-289\right|,293 \le L_{uckGrade}<294:3.074+0.005\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<307:3.079+0.004\left|L_{uckGrade}-294\right|,307 \le L_{uckGrade}<308:3.131+0.003\left|L_{uckGrade}-307\right|,308 \le L_{uckGrade}<312:3.134+0.004\left|L_{uckGrade}-308\right|,312 \le L_{uckGrade}<313:3.15+0.003\left|L_{uckGrade}-312\right|,313 \le L_{uckGrade}<316:3.153+0.004\left|L_{uckGrade}-313\right|,316 \le L_{uckGrade}<317:3.165+0.003\left|L_{uckGrade}-316\right|,317 \le L_{uckGrade}<319:3.168+0.004\left|L_{uckGrade}-317\right|,319 \le L_{uckGrade}<320:3.176+0.003\left|L_{uckGrade}-319\right|,320 \le L_{uckGrade}<321:3.179+0.004\left|L_{uckGrade}-320\right|,321 \le L_{uckGrade}<322:3.183+0.003\left|L_{uckGrade}-321\right|,322 \le L_{uckGrade}<323:3.186+0.004\left|L_{uckGrade}-322\right|,323 \le L_{uckGrade}<324:3.19+0.003\left|L_{uckGrade}-323\right|,324 \le L_{uckGrade}<326:3.193+0.004\left|L_{uckGrade}-324\right|,326 \le L_{uckGrade}<328:3.201+0.003\left|L_{uckGrade}-326\right|,328 \le L_{uckGrade}<329:3.207+0.004\left|L_{uckGrade}-328\right|,329 \le L_{uckGrade}<330:3.211+0.003\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<331:3.214+0.004\left|L_{uckGrade}-330\right|,331 \le L_{uckGrade}<333:3.218+0.003\left|L_{uckGrade}-331\right|,333 \le L_{uckGrade}<334:3.224+0.004\left|L_{uckGrade}-333\right|,334 \le L_{uckGrade}<336:3.228+0.003\left|L_{uckGrade}-334\right|,336 \le L_{uckGrade}<337:3.234+0.004\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<340:3.238+0.003\left|L_{uckGrade}-337\right|,340 \le L_{uckGrade}<341:3.247+0.004\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<349:3.251+0.003\left|L_{uckGrade}-341\right|,349 \le L_{uckGrade}<350:3.275+0.004\left|L_{uckGrade}-349\right|,350 \le L_{uckGrade}<351:3.279+0.003\left|L_{uckGrade}-350\right|,351 \le L_{uckGrade}<352:3.282+0.002\left|L_{uckGrade}-351\right|,352 \le L_{uckGrade}<360:3.284+0.003\left|L_{uckGrade}-352\right|,360 \le L_{uckGrade}<361:3.308+0.002\left|L_{uckGrade}-360\right|,361 \le L_{uckGrade}<364:3.31+0.003\left|L_{uckGrade}-361\right|,364 \le L_{uckGrade}<365:3.319+0.002\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<367:3.321+0.003\left|L_{uckGrade}-365\right|,367 \le L_{uckGrade}<368:3.327+0.002\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<370:3.329+0.003\left|L_{uckGrade}-368\right|,370 \le L_{uckGrade}<371:3.335+0.002\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<372:3.337+0.003\left|L_{uckGrade}-371\right|,372 \le L_{uckGrade}<373:3.34+0.002\left|L_{uckGrade}-372\right|,373 \le L_{uckGrade}<375:3.342+0.003\left|L_{uckGrade}-373\right|,375 \le L_{uckGrade}<377:3.348+0.002\left|L_{uckGrade}-375\right|,377 \le L_{uckGrade}<378:3.352+0.003\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<379:3.355+0.002\left|L_{uckGrade}-378\right|,379 \le L_{uckGrade}<380:3.357+0.003\left|L_{uckGrade}-379\right|,380 \le L_{uckGrade}<381:3.36+0.002\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<382:3.362+0.003\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<384:3.365+0.002\left|L_{uckGrade}-382\right|,384 \le L_{uckGrade}<385:3.369+0.003\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<388:3.372+0.002\left|L_{uckGrade}-385\right|,388 \le L_{uckGrade}<389:3.378+0.003\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<393:3.381+0.002\left|L_{uckGrade}-389\right|,393 \le L_{uckGrade}<394:3.389+0.003\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<407:3.392+0.002\left|L_{uckGrade}-394\right|,407 \le L_{uckGrade}<408:3.418+0.001\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<412:3.419+0.002\left|L_{uckGrade}-408\right|,412 \le L_{uckGrade}<413:3.427+0.001\left|L_{uckGrade}-412\right|,413 \le L_{uckGrade}<416:3.428+0.002\left|L_{uckGrade}-413\right|,416 \le L_{uckGrade}<417:3.434+0.001\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<419:3.435+0.002\left|L_{uckGrade}-417\right|,419 \le L_{uckGrade}<420:3.439+0.001\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<421:3.44+0.002\left|L_{uckGrade}-420\right|,421 \le L_{uckGrade}<422:3.442+0.001\left|L_{uckGrade}-421\right|,422 \le L_{uckGrade}<423:3.443+0.002\left|L_{uckGrade}-422\right|,423 \le L_{uckGrade}<424:3.445+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<426:3.446+0.002\left|L_{uckGrade}-424\right|,426 \le L_{uckGrade}<428:3.45+0.001\left|L_{uckGrade}-426\right|,428 \le L_{uckGrade}<429:3.452+0.002\left|L_{uckGrade}-428\right|,429 \le L_{uckGrade}<430:3.454+0.001\left|L_{uckGrade}-429\right|,430 \le L_{uckGrade}<431:3.455+0.002\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<433:3.457+0.001\left|L_{uckGrade}-431\right|,433 \le L_{uckGrade}<434:3.459+0.002\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<436:3.461+0.001\left|L_{uckGrade}-434\right|,436 \le L_{uckGrade}<437:3.463+0.002\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<440:3.465+0.001\left|L_{uckGrade}-437\right|,440 \le L_{uckGrade}<441:3.468+0.002\left|L_{uckGrade}-440\right|,441 \le L_{uckGrade}<449:3.47+0.001\left|L_{uckGrade}-441\right|,449 \le L_{uckGrade}<450:3.478+0.002\left|L_{uckGrade}-449\right|,450 \le L_{uckGrade}<451:3.48+0.001\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<452:3.481+0\left|L_{uckGrade}-451\right|,452 \le L_{uckGrade}<460:3.481+0.001\left|L_{uckGrade}-452\right|,460 \le L_{uckGrade}<461:3.489+0\left|L_{uckGrade}-460\right|,461 \le L_{uckGrade}<464:3.489+0.001\left|L_{uckGrade}-461\right|,464 \le L_{uckGrade}<465:3.492+0\left|L_{uckGrade}-464\right|,465 \le L_{uckGrade}<467:3.492+0.001\left|L_{uckGrade}-465\right|,467 \le L_{uckGrade}<468:3.494+0\left|L_{uckGrade}-467\right|,468 \le L_{uckGrade}<470:3.494+0.001\left|L_{uckGrade}-468\right|,470 \le L_{uckGrade}<471:3.496+0\left|L_{uckGrade}-470\right|,471 \le L_{uckGrade}<472:3.496+0.001\left|L_{uckGrade}-471\right|,472 \le L_{uckGrade}<473:3.497+0\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<475:3.497+0.001\left|L_{uckGrade}-473\right|,475 \le L_{uckGrade}<477:3.499+0\left|L_{uckGrade}-475\right|,477 \le L_{uckGrade}<478:3.499+0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:3.5+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<480:3.5+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:3.501+0\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:3.501+0.001\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<484:3.502+0\left|L_{uckGrade}-482\right|,484 \le L_{uckGrade}<485:3.502+0.001\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<488:3.503+0\left|L_{uckGrade}-485\right|,488 \le L_{uckGrade}<489:3.503+0.001\left|L_{uckGrade}-488\right|,489 \le L_{uckGrade}<493:3.504+0\left|L_{uckGrade}-489\right|,493 \le L_{uckGrade}<494:3.504+0.001\left|L_{uckGrade}-493\right|,494 \le L_{uckGrade}<500:3.505+0\left|L_{uckGrade}-494\right|\right\}

See Example for how to use.


LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade05}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<1:1+0.012\left|L_{uckGrade}-0\right|,1 \le L_{uckGrade}<3:1.012+0.011\left|L_{uckGrade}-1\right|,3 \le L_{uckGrade}<4:1.034+0.012\left|L_{uckGrade}-3\right|,4 \le L_{uckGrade}<5:1.046+0.011\left|L_{uckGrade}-4\right|,5 \le L_{uckGrade}<6:1.057+0.012\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<8:1.069+0.011\left|L_{uckGrade}-6\right|,8 \le L_{uckGrade}<9:1.091+0.012\left|L_{uckGrade}-8\right|,9 \le L_{uckGrade}<12:1.103+0.011\left|L_{uckGrade}-9\right|,12 \le L_{uckGrade}<13:1.136+0.012\left|L_{uckGrade}-12\right|,13 \le L_{uckGrade}<18:1.148+0.011\left|L_{uckGrade}-13\right|,18 \le L_{uckGrade}<19:1.203+0.012\left|L_{uckGrade}-18\right|,19 \le L_{uckGrade}<26:1.215+0.011\left|L_{uckGrade}-19\right|,26 \le L_{uckGrade}<27:1.292+0.01\left|L_{uckGrade}-26\right|,27 \le L_{uckGrade}<32:1.302+0.011\left|L_{uckGrade}-27\right|,32 \le L_{uckGrade}<33:1.357+0.01\left|L_{uckGrade}-32\right|,33 \le L_{uckGrade}<36:1.367+0.011\left|L_{uckGrade}-33\right|,36 \le L_{uckGrade}<37:1.4+0.01\left|L_{uckGrade}-36\right|,37 \le L_{uckGrade}<38:1.41+0.011\left|L_{uckGrade}-37\right|,38 \le L_{uckGrade}<39:1.421+0.01\left|L_{uckGrade}-38\right|,39 \le L_{uckGrade}<41:1.431+0.011\left|L_{uckGrade}-39\right|,41 \le L_{uckGrade}<42:1.453+0.01\left|L_{uckGrade}-41\right|,42 \le L_{uckGrade}<43:1.463+0.011\left|L_{uckGrade}-42\right|,43 \le L_{uckGrade}<44:1.474+0.01\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<45:1.484+0.011\left|L_{uckGrade}-44\right|,45 \le L_{uckGrade}<46:1.495+0.01\left|L_{uckGrade}-45\right|,46 \le L_{uckGrade}<47:1.505+0.011\left|L_{uckGrade}-46\right|,47 \le L_{uckGrade}<49:1.516+0.01\left|L_{uckGrade}-47\right|,49 \le L_{uckGrade}<50:1.536+0.011\left|L_{uckGrade}-49\right|,50 \le L_{uckGrade}<51:1.547+0.01\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<52:1.557+0.011\left|L_{uckGrade}-51\right|,52 \le L_{uckGrade}<55:1.568+0.01\left|L_{uckGrade}-52\right|,55 \le L_{uckGrade}<56:1.598+0.011\left|L_{uckGrade}-55\right|,56 \le L_{uckGrade}<61:1.609+0.01\left|L_{uckGrade}-56\right|,61 \le L_{uckGrade}<62:1.659+0.011\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<69:1.67+0.01\left|L_{uckGrade}-62\right|,69 \le L_{uckGrade}<70:1.74+0.009\left|L_{uckGrade}-69\right|,70 \le L_{uckGrade}<75:1.749+0.01\left|L_{uckGrade}-70\right|,75 \le L_{uckGrade}<76:1.799+0.009\left|L_{uckGrade}-75\right|,76 \le L_{uckGrade}<79:1.808+0.01\left|L_{uckGrade}-76\right|,79 \le L_{uckGrade}<80:1.838+0.009\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<82:1.847+0.01\left|L_{uckGrade}-80\right|,82 \le L_{uckGrade}<83:1.867+0.009\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<84:1.876+0.01\left|L_{uckGrade}-83\right|,84 \le L_{uckGrade}<85:1.886+0.009\left|L_{uckGrade}-84\right|,85 \le L_{uckGrade}<86:1.895+0.01\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<87:1.905+0.009\left|L_{uckGrade}-86\right|,87 \le L_{uckGrade}<88:1.914+0.01\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<89:1.924+0.009\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<90:1.933+0.01\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<91:1.943+0.009\left|L_{uckGrade}-90\right|,91 \le L_{uckGrade}<92:1.952+0.01\left|L_{uckGrade}-91\right|,92 \le L_{uckGrade}<94:1.962+0.009\left|L_{uckGrade}-92\right|,94 \le L_{uckGrade}<95:1.98+0.01\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<97:1.99+0.009\left|L_{uckGrade}-95\right|,97 \le L_{uckGrade}<98:2.008+0.01\left|L_{uckGrade}-97\right|,98 \le L_{uckGrade}<101:2.018+0.009\left|L_{uckGrade}-98\right|,101 \le L_{uckGrade}<102:2.045+0.01\left|L_{uckGrade}-101\right|,102 \le L_{uckGrade}<116:2.055+0.009\left|L_{uckGrade}-102\right|,116 \le L_{uckGrade}<117:2.181+0.008\left|L_{uckGrade}-116\right|,117 \le L_{uckGrade}<121:2.189+0.009\left|L_{uckGrade}-117\right|,121 \le L_{uckGrade}<122:2.225+0.008\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<124:2.233+0.009\left|L_{uckGrade}-122\right|,124 \le L_{uckGrade}<125:2.251+0.008\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<126:2.259+0.009\left|L_{uckGrade}-125\right|,126 \le L_{uckGrade}<127:2.268+0.008\left|L_{uckGrade}-126\right|,127 \le L_{uckGrade}<129:2.276+0.009\left|L_{uckGrade}-127\right|,129 \le L_{uckGrade}<130:2.294+0.008\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<131:2.302+0.009\left|L_{uckGrade}-130\right|,131 \le L_{uckGrade}<132:2.311+0.008\left|L_{uckGrade}-131\right|,132 \le L_{uckGrade}<133:2.319+0.009\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<135:2.328+0.008\left|L_{uckGrade}-133\right|,135 \le L_{uckGrade}<136:2.344+0.009\left|L_{uckGrade}-135\right|,136 \le L_{uckGrade}<137:2.353+0.008\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<138:2.361+0.009\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<141:2.37+0.008\left|L_{uckGrade}-138\right|,141 \le L_{uckGrade}<142:2.394+0.009\left|L_{uckGrade}-141\right|,142 \le L_{uckGrade}<145:2.403+0.008\left|L_{uckGrade}-142\right|,145 \le L_{uckGrade}<146:2.427+0.009\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<159:2.436+0.008\left|L_{uckGrade}-146\right|,159 \le L_{uckGrade}<160:2.54+0.007\left|L_{uckGrade}-159\right|,160 \le L_{uckGrade}<164:2.547+0.008\left|L_{uckGrade}-160\right|,164 \le L_{uckGrade}<165:2.579+0.007\left|L_{uckGrade}-164\right|,165 \le L_{uckGrade}<167:2.586+0.008\left|L_{uckGrade}-165\right|,167 \le L_{uckGrade}<168:2.602+0.007\left|L_{uckGrade}-167\right|,168 \le L_{uckGrade}<170:2.609+0.008\left|L_{uckGrade}-168\right|,170 \le L_{uckGrade}<171:2.625+0.007\left|L_{uckGrade}-170\right|,171 \le L_{uckGrade}<172:2.632+0.008\left|L_{uckGrade}-171\right|,172 \le L_{uckGrade}<173:2.64+0.007\left|L_{uckGrade}-172\right|,173 \le L_{uckGrade}<174:2.647+0.008\left|L_{uckGrade}-173\right|,174 \le L_{uckGrade}<175:2.655+0.007\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<176:2.662+0.008\left|L_{uckGrade}-175\right|,176 \le L_{uckGrade}<177:2.67+0.007\left|L_{uckGrade}-176\right|,177 \le L_{uckGrade}<178:2.677+0.008\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<180:2.685+0.007\left|L_{uckGrade}-178\right|,180 \le L_{uckGrade}<181:2.699+0.008\left|L_{uckGrade}-180\right|,181 \le L_{uckGrade}<183:2.707+0.007\left|L_{uckGrade}-181\right|,183 \le L_{uckGrade}<184:2.721+0.008\left|L_{uckGrade}-183\right|,184 \le L_{uckGrade}<186:2.729+0.007\left|L_{uckGrade}-184\right|,186 \le L_{uckGrade}<187:2.743+0.008\left|L_{uckGrade}-186\right|,187 \le L_{uckGrade}<205:2.751+0.007\left|L_{uckGrade}-187\right|,205 \le L_{uckGrade}<206:2.877+0.006\left|L_{uckGrade}-205\right|,206 \le L_{uckGrade}<209:2.883+0.007\left|L_{uckGrade}-206\right|,209 \le L_{uckGrade}<210:2.904+0.006\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<212:2.91+0.007\left|L_{uckGrade}-210\right|,212 \le L_{uckGrade}<213:2.924+0.006\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<214:2.93+0.007\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<215:2.937+0.006\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<216:2.943+0.007\left|L_{uckGrade}-215\right|,216 \le L_{uckGrade}<217:2.95+0.006\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<218:2.956+0.007\left|L_{uckGrade}-217\right|,218 \le L_{uckGrade}<219:2.963+0.006\left|L_{uckGrade}-218\right|,219 \le L_{uckGrade}<220:2.969+0.007\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<221:2.976+0.006\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:2.982+0.007\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:2.989+0.006\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:2.995+0.007\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<226:3.002+0.006\left|L_{uckGrade}-224\right|,226 \le L_{uckGrade}<227:3.014+0.007\left|L_{uckGrade}-226\right|,227 \le L_{uckGrade}<230:3.021+0.006\left|L_{uckGrade}-227\right|,230 \le L_{uckGrade}<231:3.039+0.007\left|L_{uckGrade}-230\right|,231 \le L_{uckGrade}<248:3.046+0.006\left|L_{uckGrade}-231\right|,248 \le L_{uckGrade}<249:3.148+0.005\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<252:3.153+0.006\left|L_{uckGrade}-249\right|,252 \le L_{uckGrade}<253:3.171+0.005\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<255:3.176+0.006\left|L_{uckGrade}-253\right|,255 \le L_{uckGrade}<256:3.188+0.005\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<257:3.193+0.006\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<258:3.199+0.005\left|L_{uckGrade}-257\right|,258 \le L_{uckGrade}<260:3.204+0.006\left|L_{uckGrade}-258\right|,260 \le L_{uckGrade}<261:3.216+0.005\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<262:3.221+0.006\left|L_{uckGrade}-261\right|,262 \le L_{uckGrade}<263:3.227+0.005\left|L_{uckGrade}-262\right|,263 \le L_{uckGrade}<264:3.232+0.006\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<266:3.238+0.005\left|L_{uckGrade}-264\right|,266 \le L_{uckGrade}<267:3.248+0.006\left|L_{uckGrade}-266\right|,267 \le L_{uckGrade}<269:3.254+0.005\left|L_{uckGrade}-267\right|,269 \le L_{uckGrade}<270:3.264+0.006\left|L_{uckGrade}-269\right|,270 \le L_{uckGrade}<272:3.27+0.005\left|L_{uckGrade}-270\right|,272 \le L_{uckGrade}<273:3.28+0.006\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<278:3.286+0.005\left|L_{uckGrade}-273\right|,278 \le L_{uckGrade}<279:3.311+0.006\left|L_{uckGrade}-278\right|,279 \le L_{uckGrade}<287:3.317+0.005\left|L_{uckGrade}-279\right|,287 \le L_{uckGrade}<288:3.357+0.004\left|L_{uckGrade}-287\right|,288 \le L_{uckGrade}<293:3.361+0.005\left|L_{uckGrade}-288\right|,293 \le L_{uckGrade}<294:3.386+0.004\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<297:3.39+0.005\left|L_{uckGrade}-294\right|,297 \le L_{uckGrade}<298:3.405+0.004\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<299:3.409+0.005\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<300:3.414+0.004\left|L_{uckGrade}-299\right|,300 \le L_{uckGrade}<302:3.418+0.005\left|L_{uckGrade}-300\right|,302 \le L_{uckGrade}<303:3.428+0.004\left|L_{uckGrade}-302\right|,303 \le L_{uckGrade}<304:3.432+0.005\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<305:3.437+0.004\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<306:3.441+0.005\left|L_{uckGrade}-305\right|,306 \le L_{uckGrade}<307:3.446+0.004\left|L_{uckGrade}-306\right|,307 \le L_{uckGrade}<308:3.45+0.005\left|L_{uckGrade}-307\right|,308 \le L_{uckGrade}<310:3.455+0.004\left|L_{uckGrade}-308\right|,310 \le L_{uckGrade}<311:3.463+0.005\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<313:3.468+0.004\left|L_{uckGrade}-311\right|,313 \le L_{uckGrade}<314:3.476+0.005\left|L_{uckGrade}-313\right|,314 \le L_{uckGrade}<316:3.481+0.004\left|L_{uckGrade}-314\right|,316 \le L_{uckGrade}<317:3.489+0.005\left|L_{uckGrade}-316\right|,317 \le L_{uckGrade}<323:3.494+0.004\left|L_{uckGrade}-317\right|,323 \le L_{uckGrade}<324:3.518+0.005\left|L_{uckGrade}-323\right|,324 \le L_{uckGrade}<329:3.523+0.004\left|L_{uckGrade}-324\right|,329 \le L_{uckGrade}<330:3.543+0.003\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<336:3.546+0.004\left|L_{uckGrade}-330\right|,336 \le L_{uckGrade}<337:3.57+0.003\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<340:3.573+0.004\left|L_{uckGrade}-337\right|,340 \le L_{uckGrade}<341:3.585+0.003\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<342:3.588+0.004\left|L_{uckGrade}-341\right|,342 \le L_{uckGrade}<343:3.592+0.003\left|L_{uckGrade}-342\right|,343 \le L_{uckGrade}<345:3.595+0.004\left|L_{uckGrade}-343\right|,345 \le L_{uckGrade}<346:3.603+0.003\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<347:3.606+0.004\left|L_{uckGrade}-346\right|,347 \le L_{uckGrade}<348:3.61+0.003\left|L_{uckGrade}-347\right|,348 \le L_{uckGrade}<349:3.613+0.004\left|L_{uckGrade}-348\right|,349 \le L_{uckGrade}<350:3.617+0.003\left|L_{uckGrade}-349\right|,350 \le L_{uckGrade}<351:3.62+0.004\left|L_{uckGrade}-350\right|,351 \le L_{uckGrade}<352:3.624+0.003\left|L_{uckGrade}-351\right|,352 \le L_{uckGrade}<353:3.627+0.004\left|L_{uckGrade}-352\right|,353 \le L_{uckGrade}<355:3.631+0.003\left|L_{uckGrade}-353\right|,355 \le L_{uckGrade}<356:3.637+0.004\left|L_{uckGrade}-355\right|,356 \le L_{uckGrade}<359:3.641+0.003\left|L_{uckGrade}-356\right|,359 \le L_{uckGrade}<360:3.65+0.004\left|L_{uckGrade}-359\right|,360 \le L_{uckGrade}<364:3.654+0.003\left|L_{uckGrade}-360\right|,364 \le L_{uckGrade}<365:3.666+0.004\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<376:3.67+0.003\left|L_{uckGrade}-365\right|,376 \le L_{uckGrade}<377:3.703+0.002\left|L_{uckGrade}-376\right|,377 \le L_{uckGrade}<381:3.705+0.003\left|L_{uckGrade}-377\right|,381 \le L_{uckGrade}<382:3.717+0.002\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<384:3.719+0.003\left|L_{uckGrade}-382\right|,384 \le L_{uckGrade}<385:3.725+0.002\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<387:3.727+0.003\left|L_{uckGrade}-385\right|,387 \le L_{uckGrade}<388:3.733+0.002\left|L_{uckGrade}-387\right|,388 \le L_{uckGrade}<389:3.735+0.003\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<390:3.738+0.002\left|L_{uckGrade}-389\right|,390 \le L_{uckGrade}<391:3.74+0.003\left|L_{uckGrade}-390\right|,391 \le L_{uckGrade}<392:3.743+0.002\left|L_{uckGrade}-391\right|,392 \le L_{uckGrade}<393:3.745+0.003\left|L_{uckGrade}-392\right|,393 \le L_{uckGrade}<394:3.748+0.002\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<395:3.75+0.003\left|L_{uckGrade}-394\right|,395 \le L_{uckGrade}<396:3.753+0.002\left|L_{uckGrade}-395\right|,396 \le L_{uckGrade}<397:3.755+0.003\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<399:3.758+0.002\left|L_{uckGrade}-397\right|,399 \le L_{uckGrade}<400:3.762+0.003\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<403:3.765+0.002\left|L_{uckGrade}-400\right|,403 \le L_{uckGrade}<404:3.771+0.003\left|L_{uckGrade}-403\right|,404 \le L_{uckGrade}<409:3.774+0.002\left|L_{uckGrade}-404\right|,409 \le L_{uckGrade}<410:3.784+0.003\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<417:3.787+0.002\left|L_{uckGrade}-410\right|,417 \le L_{uckGrade}<418:3.801+0.001\left|L_{uckGrade}-417\right|,418 \le L_{uckGrade}<423:3.802+0.002\left|L_{uckGrade}-418\right|,423 \le L_{uckGrade}<424:3.812+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<427:3.813+0.002\left|L_{uckGrade}-424\right|,427 \le L_{uckGrade}<428:3.819+0.001\left|L_{uckGrade}-427\right|,428 \le L_{uckGrade}<430:3.82+0.002\left|L_{uckGrade}-428\right|,430 \le L_{uckGrade}<431:3.824+0.001\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<432:3.825+0.002\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<433:3.827+0.001\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<434:3.828+0.002\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<435:3.83+0.001\left|L_{uckGrade}-434\right|,435 \le L_{uckGrade}<436:3.831+0.002\left|L_{uckGrade}-435\right|,436 \le L_{uckGrade}<437:3.833+0.001\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<438:3.834+0.002\left|L_{uckGrade}-437\right|,438 \le L_{uckGrade}<439:3.836+0.001\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<440:3.837+0.002\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<442:3.839+0.001\left|L_{uckGrade}-440\right|,442 \le L_{uckGrade}<443:3.841+0.002\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<445:3.843+0.001\left|L_{uckGrade}-443\right|,445 \le L_{uckGrade}<446:3.845+0.002\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<450:3.847+0.001\left|L_{uckGrade}-446\right|,450 \le L_{uckGrade}<451:3.851+0.002\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<463:3.853+0.001\left|L_{uckGrade}-451\right|,463 \le L_{uckGrade}<464:3.865+0\left|L_{uckGrade}-463\right|,464 \le L_{uckGrade}<468:3.865+0.001\left|L_{uckGrade}-464\right|,468 \le L_{uckGrade}<469:3.869+0\left|L_{uckGrade}-468\right|,469 \le L_{uckGrade}<471:3.869+0.001\left|L_{uckGrade}-469\right|,471 \le L_{uckGrade}<472:3.871+0\left|L_{uckGrade}-471\right|,472 \le L_{uckGrade}<474:3.871+0.001\left|L_{uckGrade}-472\right|,474 \le L_{uckGrade}<475:3.873+0\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<476:3.873+0.001\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<477:3.874+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<478:3.874+0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:3.875+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<480:3.875+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:3.876+0\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:3.876+0.001\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:3.877+0\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<484:3.877+0.001\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<486:3.878+0\left|L_{uckGrade}-484\right|,486 \le L_{uckGrade}<487:3.878+0.001\left|L_{uckGrade}-486\right|,487 \le L_{uckGrade}<490:3.879+0\left|L_{uckGrade}-487\right|,490 \le L_{uckGrade}<491:3.879+0.001\left|L_{uckGrade}-490\right|,491 \le L_{uckGrade}<495:3.88+0\left|L_{uckGrade}-491\right|,495 \le L_{uckGrade}<496:3.88+0.001\left|L_{uckGrade}-495\right|,496 \le L_{uckGrade}<500:3.881+0\left|L_{uckGrade}-496\right|\right\}

See Example for how to use.


LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade06}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<6:1+0.013\left|L_{uckGrade}-0\right|,6 \le L_{uckGrade}<7:1.078+0.012\left|L_{uckGrade}-6\right|,7 \le L_{uckGrade}<11:1.09+0.013\left|L_{uckGrade}-7\right|,11 \le L_{uckGrade}<12:1.142+0.012\left|L_{uckGrade}-11\right|,12 \le L_{uckGrade}<14:1.154+0.013\left|L_{uckGrade}-12\right|,14 \le L_{uckGrade}<15:1.18+0.012\left|L_{uckGrade}-14\right|,15 \le L_{uckGrade}<16:1.192+0.013\left|L_{uckGrade}-15\right|,16 \le L_{uckGrade}<17:1.205+0.012\left|L_{uckGrade}-16\right|,17 \le L_{uckGrade}<19:1.217+0.013\left|L_{uckGrade}-17\right|,19 \le L_{uckGrade}<20:1.243+0.012\left|L_{uckGrade}-19\right|,20 \le L_{uckGrade}<21:1.255+0.013\left|L_{uckGrade}-20\right|,21 \le L_{uckGrade}<23:1.268+0.012\left|L_{uckGrade}-21\right|,23 \le L_{uckGrade}<24:1.292+0.013\left|L_{uckGrade}-23\right|,24 \le L_{uckGrade}<25:1.305+0.012\left|L_{uckGrade}-24\right|,25 \le L_{uckGrade}<26:1.317+0.013\left|L_{uckGrade}-25\right|,26 \le L_{uckGrade}<29:1.33+0.012\left|L_{uckGrade}-26\right|,29 \le L_{uckGrade}<30:1.366+0.013\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<34:1.379+0.012\left|L_{uckGrade}-30\right|,34 \le L_{uckGrade}<35:1.427+0.013\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<43:1.44+0.012\left|L_{uckGrade}-35\right|,43 \le L_{uckGrade}<44:1.536+0.011\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<48:1.547+0.012\left|L_{uckGrade}-44\right|,48 \le L_{uckGrade}<49:1.595+0.011\left|L_{uckGrade}-48\right|,49 \le L_{uckGrade}<52:1.606+0.012\left|L_{uckGrade}-49\right|,52 \le L_{uckGrade}<53:1.642+0.011\left|L_{uckGrade}-52\right|,53 \le L_{uckGrade}<54:1.653+0.012\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<55:1.665+0.011\left|L_{uckGrade}-54\right|,55 \le L_{uckGrade}<57:1.676+0.012\left|L_{uckGrade}-55\right|,57 \le L_{uckGrade}<58:1.7+0.011\left|L_{uckGrade}-57\right|,58 \le L_{uckGrade}<59:1.711+0.012\left|L_{uckGrade}-58\right|,59 \le L_{uckGrade}<61:1.723+0.011\left|L_{uckGrade}-59\right|,61 \le L_{uckGrade}<62:1.745+0.012\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<63:1.757+0.011\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<64:1.768+0.012\left|L_{uckGrade}-63\right|,64 \le L_{uckGrade}<66:1.78+0.011\left|L_{uckGrade}-64\right|,66 \le L_{uckGrade}<67:1.802+0.012\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<71:1.814+0.011\left|L_{uckGrade}-67\right|,71 \le L_{uckGrade}<72:1.858+0.012\left|L_{uckGrade}-71\right|,72 \le L_{uckGrade}<83:1.87+0.011\left|L_{uckGrade}-72\right|,83 \le L_{uckGrade}<84:1.991+0.01\left|L_{uckGrade}-83\right|,84 \le L_{uckGrade}<87:2.001+0.011\left|L_{uckGrade}-84\right|,87 \le L_{uckGrade}<88:2.034+0.01\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<91:2.044+0.011\left|L_{uckGrade}-88\right|,91 \le L_{uckGrade}<92:2.077+0.01\left|L_{uckGrade}-91\right|,92 \le L_{uckGrade}<93:2.087+0.011\left|L_{uckGrade}-92\right|,93 \le L_{uckGrade}<94:2.098+0.01\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<95:2.108+0.011\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<96:2.119+0.01\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<97:2.129+0.011\left|L_{uckGrade}-96\right|,97 \le L_{uckGrade}<98:2.14+0.01\left|L_{uckGrade}-97\right|,98 \le L_{uckGrade}<99:2.15+0.011\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<100:2.161+0.01\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<101:2.171+0.011\left|L_{uckGrade}-100\right|,101 \le L_{uckGrade}<103:2.182+0.01\left|L_{uckGrade}-101\right|,103 \le L_{uckGrade}<104:2.202+0.011\left|L_{uckGrade}-103\right|,104 \le L_{uckGrade}<106:2.213+0.01\left|L_{uckGrade}-104\right|,106 \le L_{uckGrade}<107:2.233+0.011\left|L_{uckGrade}-106\right|,107 \le L_{uckGrade}<113:2.244+0.01\left|L_{uckGrade}-107\right|,113 \le L_{uckGrade}<114:2.304+0.011\left|L_{uckGrade}-113\right|,114 \le L_{uckGrade}<118:2.315+0.01\left|L_{uckGrade}-114\right|,118 \le L_{uckGrade}<119:2.355+0.009\left|L_{uckGrade}-118\right|,119 \le L_{uckGrade}<125:2.364+0.01\left|L_{uckGrade}-119\right|,125 \le L_{uckGrade}<126:2.424+0.009\left|L_{uckGrade}-125\right|,126 \le L_{uckGrade}<128:2.433+0.01\left|L_{uckGrade}-126\right|,128 \le L_{uckGrade}<129:2.453+0.009\left|L_{uckGrade}-128\right|,129 \le L_{uckGrade}<131:2.462+0.01\left|L_{uckGrade}-129\right|,131 \le L_{uckGrade}<132:2.482+0.009\left|L_{uckGrade}-131\right|,132 \le L_{uckGrade}<133:2.491+0.01\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<134:2.501+0.009\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<135:2.51+0.01\left|L_{uckGrade}-134\right|,135 \le L_{uckGrade}<136:2.52+0.009\left|L_{uckGrade}-135\right|,136 \le L_{uckGrade}<137:2.529+0.01\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<138:2.539+0.009\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<139:2.548+0.01\left|L_{uckGrade}-138\right|,139 \le L_{uckGrade}<141:2.558+0.009\left|L_{uckGrade}-139\right|,141 \le L_{uckGrade}<142:2.576+0.01\left|L_{uckGrade}-141\right|,142 \le L_{uckGrade}<144:2.586+0.009\left|L_{uckGrade}-142\right|,144 \le L_{uckGrade}<145:2.604+0.01\left|L_{uckGrade}-144\right|,145 \le L_{uckGrade}<150:2.614+0.009\left|L_{uckGrade}-145\right|,150 \le L_{uckGrade}<151:2.659+0.01\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<158:2.669+0.009\left|L_{uckGrade}-151\right|,158 \le L_{uckGrade}<159:2.732+0.008\left|L_{uckGrade}-158\right|,159 \le L_{uckGrade}<163:2.74+0.009\left|L_{uckGrade}-159\right|,163 \le L_{uckGrade}<164:2.776+0.008\left|L_{uckGrade}-163\right|,164 \le L_{uckGrade}<167:2.784+0.009\left|L_{uckGrade}-164\right|,167 \le L_{uckGrade}<168:2.811+0.008\left|L_{uckGrade}-167\right|,168 \le L_{uckGrade}<170:2.819+0.009\left|L_{uckGrade}-168\right|,170 \le L_{uckGrade}<171:2.837+0.008\left|L_{uckGrade}-170\right|,171 \le L_{uckGrade}<172:2.845+0.009\left|L_{uckGrade}-171\right|,172 \le L_{uckGrade}<173:2.854+0.008\left|L_{uckGrade}-172\right|,173 \le L_{uckGrade}<174:2.862+0.009\left|L_{uckGrade}-173\right|,174 \le L_{uckGrade}<175:2.871+0.008\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<176:2.879+0.009\left|L_{uckGrade}-175\right|,176 \le L_{uckGrade}<178:2.888+0.008\left|L_{uckGrade}-176\right|,178 \le L_{uckGrade}<179:2.904+0.009\left|L_{uckGrade}-178\right|,179 \le L_{uckGrade}<181:2.913+0.008\left|L_{uckGrade}-179\right|,181 \le L_{uckGrade}<182:2.929+0.009\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<185:2.938+0.008\left|L_{uckGrade}-182\right|,185 \le L_{uckGrade}<186:2.962+0.009\left|L_{uckGrade}-185\right|,186 \le L_{uckGrade}<200:2.971+0.008\left|L_{uckGrade}-186\right|,200 \le L_{uckGrade}<201:3.083+0.007\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<204:3.09+0.008\left|L_{uckGrade}-201\right|,204 \le L_{uckGrade}<205:3.114+0.007\left|L_{uckGrade}-204\right|,205 \le L_{uckGrade}<207:3.121+0.008\left|L_{uckGrade}-205\right|,207 \le L_{uckGrade}<208:3.137+0.007\left|L_{uckGrade}-207\right|,208 \le L_{uckGrade}<209:3.144+0.008\left|L_{uckGrade}-208\right|,209 \le L_{uckGrade}<210:3.152+0.007\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<211:3.159+0.008\left|L_{uckGrade}-210\right|,211 \le L_{uckGrade}<212:3.167+0.007\left|L_{uckGrade}-211\right|,212 \le L_{uckGrade}<213:3.174+0.008\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<214:3.182+0.007\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<215:3.189+0.008\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<216:3.197+0.007\left|L_{uckGrade}-215\right|,216 \le L_{uckGrade}<217:3.204+0.008\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<219:3.212+0.007\left|L_{uckGrade}-217\right|,219 \le L_{uckGrade}<220:3.226+0.008\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<223:3.234+0.007\left|L_{uckGrade}-220\right|,223 \le L_{uckGrade}<224:3.255+0.008\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<239:3.263+0.007\left|L_{uckGrade}-224\right|,239 \le L_{uckGrade}<240:3.368+0.006\left|L_{uckGrade}-239\right|,240 \le L_{uckGrade}<243:3.374+0.007\left|L_{uckGrade}-240\right|,243 \le L_{uckGrade}<244:3.395+0.006\left|L_{uckGrade}-243\right|,244 \le L_{uckGrade}<245:3.401+0.007\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<246:3.408+0.006\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<248:3.414+0.007\left|L_{uckGrade}-246\right|,248 \le L_{uckGrade}<249:3.428+0.006\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<250:3.434+0.007\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<251:3.441+0.006\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:3.447+0.007\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<253:3.454+0.006\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<254:3.46+0.007\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<256:3.467+0.006\left|L_{uckGrade}-254\right|,256 \le L_{uckGrade}<257:3.479+0.007\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<259:3.486+0.006\left|L_{uckGrade}-257\right|,259 \le L_{uckGrade}<260:3.498+0.007\left|L_{uckGrade}-259\right|,260 \le L_{uckGrade}<264:3.505+0.006\left|L_{uckGrade}-260\right|,264 \le L_{uckGrade}<265:3.529+0.007\left|L_{uckGrade}-264\right|,265 \le L_{uckGrade}<274:3.536+0.006\left|L_{uckGrade}-265\right|,274 \le L_{uckGrade}<275:3.59+0.005\left|L_{uckGrade}-274\right|,275 \le L_{uckGrade}<279:3.595+0.006\left|L_{uckGrade}-275\right|,279 \le L_{uckGrade}<280:3.619+0.005\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<283:3.624+0.006\left|L_{uckGrade}-280\right|,283 \le L_{uckGrade}<284:3.642+0.005\left|L_{uckGrade}-283\right|,284 \le L_{uckGrade}<285:3.647+0.006\left|L_{uckGrade}-284\right|,285 \le L_{uckGrade}<286:3.653+0.005\left|L_{uckGrade}-285\right|,286 \le L_{uckGrade}<287:3.658+0.006\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<288:3.664+0.005\left|L_{uckGrade}-287\right|,288 \le L_{uckGrade}<289:3.669+0.006\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<290:3.675+0.005\left|L_{uckGrade}-289\right|,290 \le L_{uckGrade}<291:3.68+0.006\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<292:3.686+0.005\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<293:3.691+0.006\left|L_{uckGrade}-292\right|,293 \le L_{uckGrade}<294:3.697+0.005\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<295:3.702+0.006\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<298:3.708+0.005\left|L_{uckGrade}-295\right|,298 \le L_{uckGrade}<299:3.723+0.006\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<303:3.729+0.005\left|L_{uckGrade}-299\right|,303 \le L_{uckGrade}<304:3.749+0.006\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<312:3.755+0.005\left|L_{uckGrade}-304\right|,312 \le L_{uckGrade}<313:3.795+0.004\left|L_{uckGrade}-312\right|,313 \le L_{uckGrade}<318:3.799+0.005\left|L_{uckGrade}-313\right|,318 \le L_{uckGrade}<319:3.824+0.004\left|L_{uckGrade}-318\right|,319 \le L_{uckGrade}<321:3.828+0.005\left|L_{uckGrade}-319\right|,321 \le L_{uckGrade}<322:3.838+0.004\left|L_{uckGrade}-321\right|,322 \le L_{uckGrade}<324:3.842+0.005\left|L_{uckGrade}-322\right|,324 \le L_{uckGrade}<325:3.852+0.004\left|L_{uckGrade}-324\right|,325 \le L_{uckGrade}<326:3.856+0.005\left|L_{uckGrade}-325\right|,326 \le L_{uckGrade}<327:3.861+0.004\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<328:3.865+0.005\left|L_{uckGrade}-327\right|,328 \le L_{uckGrade}<329:3.87+0.004\left|L_{uckGrade}-328\right|,329 \le L_{uckGrade}<330:3.874+0.005\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<332:3.879+0.004\left|L_{uckGrade}-330\right|,332 \le L_{uckGrade}<333:3.887+0.005\left|L_{uckGrade}-332\right|,333 \le L_{uckGrade}<335:3.892+0.004\left|L_{uckGrade}-333\right|,335 \le L_{uckGrade}<336:3.9+0.005\left|L_{uckGrade}-335\right|,336 \le L_{uckGrade}<339:3.905+0.004\left|L_{uckGrade}-336\right|,339 \le L_{uckGrade}<340:3.917+0.005\left|L_{uckGrade}-339\right|,340 \le L_{uckGrade}<353:3.922+0.004\left|L_{uckGrade}-340\right|,353 \le L_{uckGrade}<354:3.974+0.003\left|L_{uckGrade}-353\right|,354 \le L_{uckGrade}<358:3.977+0.004\left|L_{uckGrade}-354\right|,358 \le L_{uckGrade}<359:3.993+0.003\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<361:3.996+0.004\left|L_{uckGrade}-359\right|,361 \le L_{uckGrade}<362:4.004+0.003\left|L_{uckGrade}-361\right|,362 \le L_{uckGrade}<363:4.007+0.004\left|L_{uckGrade}-362\right|,363 \le L_{uckGrade}<364:4.011+0.003\left|L_{uckGrade}-363\right|,364 \le L_{uckGrade}<365:4.014+0.004\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<366:4.018+0.003\left|L_{uckGrade}-365\right|,366 \le L_{uckGrade}<367:4.021+0.004\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:4.025+0.003\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<369:4.028+0.004\left|L_{uckGrade}-368\right|,369 \le L_{uckGrade}<371:4.032+0.003\left|L_{uckGrade}-369\right|,371 \le L_{uckGrade}<372:4.038+0.004\left|L_{uckGrade}-371\right|,372 \le L_{uckGrade}<374:4.042+0.003\left|L_{uckGrade}-372\right|,374 \le L_{uckGrade}<375:4.048+0.004\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<378:4.052+0.003\left|L_{uckGrade}-375\right|,378 \le L_{uckGrade}<379:4.061+0.004\left|L_{uckGrade}-378\right|,379 \le L_{uckGrade}<391:4.065+0.003\left|L_{uckGrade}-379\right|,391 \le L_{uckGrade}<392:4.101+0.002\left|L_{uckGrade}-391\right|,392 \le L_{uckGrade}<396:4.103+0.003\left|L_{uckGrade}-392\right|,396 \le L_{uckGrade}<397:4.115+0.002\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<399:4.117+0.003\left|L_{uckGrade}-397\right|,399 \le L_{uckGrade}<400:4.123+0.002\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<401:4.125+0.003\left|L_{uckGrade}-400\right|,401 \le L_{uckGrade}<402:4.128+0.002\left|L_{uckGrade}-401\right|,402 \le L_{uckGrade}<403:4.13+0.003\left|L_{uckGrade}-402\right|,403 \le L_{uckGrade}<404:4.133+0.002\left|L_{uckGrade}-403\right|,404 \le L_{uckGrade}<405:4.135+0.003\left|L_{uckGrade}-404\right|,405 \le L_{uckGrade}<406:4.138+0.002\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:4.14+0.003\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<408:4.143+0.002\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<409:4.145+0.003\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<411:4.148+0.002\left|L_{uckGrade}-409\right|,411 \le L_{uckGrade}<412:4.152+0.003\left|L_{uckGrade}-411\right|,412 \le L_{uckGrade}<415:4.155+0.002\left|L_{uckGrade}-412\right|,415 \le L_{uckGrade}<416:4.161+0.003\left|L_{uckGrade}-415\right|,416 \le L_{uckGrade}<432:4.164+0.002\left|L_{uckGrade}-416\right|,432 \le L_{uckGrade}<433:4.196+0.001\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<435:4.197+0.002\left|L_{uckGrade}-433\right|,435 \le L_{uckGrade}<436:4.201+0.001\left|L_{uckGrade}-435\right|,436 \le L_{uckGrade}<438:4.202+0.002\left|L_{uckGrade}-436\right|,438 \le L_{uckGrade}<439:4.206+0.001\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<440:4.207+0.002\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<441:4.209+0.001\left|L_{uckGrade}-440\right|,441 \le L_{uckGrade}<443:4.21+0.002\left|L_{uckGrade}-441\right|,443 \le L_{uckGrade}<445:4.214+0.001\left|L_{uckGrade}-443\right|,445 \le L_{uckGrade}<446:4.216+0.002\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<447:4.218+0.001\left|L_{uckGrade}-446\right|,447 \le L_{uckGrade}<448:4.219+0.002\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<450:4.221+0.001\left|L_{uckGrade}-448\right|,450 \le L_{uckGrade}<451:4.223+0.002\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<454:4.225+0.001\left|L_{uckGrade}-451\right|,454 \le L_{uckGrade}<455:4.228+0.002\left|L_{uckGrade}-454\right|,455 \le L_{uckGrade}<469:4.23+0.001\left|L_{uckGrade}-455\right|,469 \le L_{uckGrade}<470:4.244+0\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<473:4.244+0.001\left|L_{uckGrade}-470\right|,473 \le L_{uckGrade}<474:4.247+0\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<476:4.247+0.001\left|L_{uckGrade}-474\right|,476 \le L_{uckGrade}<477:4.249+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<478:4.249+0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:4.25+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<481:4.25+0.001\left|L_{uckGrade}-479\right|,481 \le L_{uckGrade}<482:4.252+0\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:4.252+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<485:4.253+0\left|L_{uckGrade}-483\right|,485 \le L_{uckGrade}<486:4.253+0.001\left|L_{uckGrade}-485\right|,486 \le L_{uckGrade}<488:4.254+0\left|L_{uckGrade}-486\right|,488 \le L_{uckGrade}<489:4.254+0.001\left|L_{uckGrade}-488\right|,489 \le L_{uckGrade}<491:4.255+0\left|L_{uckGrade}-489\right|,491 \le L_{uckGrade}<492:4.255+0.001\left|L_{uckGrade}-491\right|,492 \le L_{uckGrade}<499:4.256+0\left|L_{uckGrade}-492\right|,499 \le L_{uckGrade}<500:4.256+0.001\left|L_{uckGrade}-499\right|\right\}

See Example for how to use.


LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade07}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<1:1+0.014\left|L_{uckGrade}-0\right|,1 \le L_{uckGrade}<3:1.014+0.013\left|L_{uckGrade}-1\right|,3 \le L_{uckGrade}<4:1.04+0.014\left|L_{uckGrade}-3\right|,4 \le L_{uckGrade}<5:1.054+0.013\left|L_{uckGrade}-4\right|,5 \le L_{uckGrade}<6:1.067+0.014\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<8:1.081+0.013\left|L_{uckGrade}-6\right|,8 \le L_{uckGrade}<9:1.107+0.014\left|L_{uckGrade}-8\right|,9 \le L_{uckGrade}<13:1.121+0.013\left|L_{uckGrade}-9\right|,13 \le L_{uckGrade}<14:1.173+0.014\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<24:1.187+0.013\left|L_{uckGrade}-14\right|,24 \le L_{uckGrade}<25:1.317+0.012\left|L_{uckGrade}-24\right|,25 \le L_{uckGrade}<29:1.329+0.013\left|L_{uckGrade}-25\right|,29 \le L_{uckGrade}<30:1.381+0.012\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<32:1.393+0.013\left|L_{uckGrade}-30\right|,32 \le L_{uckGrade}<33:1.419+0.012\left|L_{uckGrade}-32\right|,33 \le L_{uckGrade}<34:1.431+0.013\left|L_{uckGrade}-33\right|,34 \le L_{uckGrade}<35:1.444+0.012\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<37:1.456+0.013\left|L_{uckGrade}-35\right|,37 \le L_{uckGrade}<39:1.482+0.012\left|L_{uckGrade}-37\right|,39 \le L_{uckGrade}<40:1.506+0.013\left|L_{uckGrade}-39\right|,40 \le L_{uckGrade}<41:1.519+0.012\left|L_{uckGrade}-40\right|,41 \le L_{uckGrade}<42:1.531+0.013\left|L_{uckGrade}-41\right|,42 \le L_{uckGrade}<44:1.544+0.012\left|L_{uckGrade}-42\right|,44 \le L_{uckGrade}<45:1.568+0.013\left|L_{uckGrade}-44\right|,45 \le L_{uckGrade}<47:1.581+0.012\left|L_{uckGrade}-45\right|,47 \le L_{uckGrade}<48:1.605+0.013\left|L_{uckGrade}-47\right|,48 \le L_{uckGrade}<64:1.618+0.012\left|L_{uckGrade}-48\right|,64 \le L_{uckGrade}<65:1.81+0.011\left|L_{uckGrade}-64\right|,65 \le L_{uckGrade}<67:1.821+0.012\left|L_{uckGrade}-65\right|,67 \le L_{uckGrade}<68:1.845+0.011\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<70:1.856+0.012\left|L_{uckGrade}-68\right|,70 \le L_{uckGrade}<71:1.88+0.011\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<73:1.891+0.012\left|L_{uckGrade}-71\right|,73 \le L_{uckGrade}<74:1.915+0.011\left|L_{uckGrade}-73\right|,74 \le L_{uckGrade}<75:1.926+0.012\left|L_{uckGrade}-74\right|,75 \le L_{uckGrade}<77:1.938+0.011\left|L_{uckGrade}-75\right|,77 \le L_{uckGrade}<78:1.96+0.012\left|L_{uckGrade}-77\right|,78 \le L_{uckGrade}<79:1.972+0.011\left|L_{uckGrade}-78\right|,79 \le L_{uckGrade}<80:1.983+0.012\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<82:1.995+0.011\left|L_{uckGrade}-80\right|,82 \le L_{uckGrade}<83:2.017+0.012\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<87:2.029+0.011\left|L_{uckGrade}-83\right|,87 \le L_{uckGrade}<88:2.073+0.012\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<99:2.085+0.011\left|L_{uckGrade}-88\right|,99 \le L_{uckGrade}<100:2.206+0.01\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<103:2.216+0.011\left|L_{uckGrade}-100\right|,103 \le L_{uckGrade}<104:2.249+0.01\left|L_{uckGrade}-103\right|,104 \le L_{uckGrade}<106:2.259+0.011\left|L_{uckGrade}-104\right|,106 \le L_{uckGrade}<107:2.281+0.01\left|L_{uckGrade}-106\right|,107 \le L_{uckGrade}<109:2.291+0.011\left|L_{uckGrade}-107\right|,109 \le L_{uckGrade}<110:2.313+0.01\left|L_{uckGrade}-109\right|,110 \le L_{uckGrade}<111:2.323+0.011\left|L_{uckGrade}-110\right|,111 \le L_{uckGrade}<112:2.334+0.01\left|L_{uckGrade}-111\right|,112 \le L_{uckGrade}<113:2.344+0.011\left|L_{uckGrade}-112\right|,113 \le L_{uckGrade}<114:2.355+0.01\left|L_{uckGrade}-113\right|,114 \le L_{uckGrade}<115:2.365+0.011\left|L_{uckGrade}-114\right|,115 \le L_{uckGrade}<117:2.376+0.01\left|L_{uckGrade}-115\right|,117 \le L_{uckGrade}<118:2.396+0.011\left|L_{uckGrade}-117\right|,118 \le L_{uckGrade}<121:2.407+0.01\left|L_{uckGrade}-118\right|,121 \le L_{uckGrade}<122:2.437+0.011\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<127:2.448+0.01\left|L_{uckGrade}-122\right|,127 \le L_{uckGrade}<128:2.498+0.011\left|L_{uckGrade}-127\right|,128 \le L_{uckGrade}<132:2.509+0.01\left|L_{uckGrade}-128\right|,132 \le L_{uckGrade}<133:2.549+0.009\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<139:2.558+0.01\left|L_{uckGrade}-133\right|,139 \le L_{uckGrade}<140:2.618+0.009\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<142:2.627+0.01\left|L_{uckGrade}-140\right|,142 \le L_{uckGrade}<143:2.647+0.009\left|L_{uckGrade}-142\right|,143 \le L_{uckGrade}<145:2.656+0.01\left|L_{uckGrade}-143\right|,145 \le L_{uckGrade}<146:2.676+0.009\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<147:2.685+0.01\left|L_{uckGrade}-146\right|,147 \le L_{uckGrade}<148:2.695+0.009\left|L_{uckGrade}-147\right|,148 \le L_{uckGrade}<149:2.704+0.01\left|L_{uckGrade}-148\right|,149 \le L_{uckGrade}<150:2.714+0.009\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<151:2.723+0.01\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:2.733+0.009\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<153:2.742+0.01\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<155:2.752+0.009\left|L_{uckGrade}-153\right|,155 \le L_{uckGrade}<156:2.77+0.01\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<159:2.78+0.009\left|L_{uckGrade}-156\right|,159 \le L_{uckGrade}<160:2.807+0.01\left|L_{uckGrade}-159\right|,160 \le L_{uckGrade}<174:2.817+0.009\left|L_{uckGrade}-160\right|,174 \le L_{uckGrade}<175:2.943+0.008\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<178:2.951+0.009\left|L_{uckGrade}-175\right|,178 \le L_{uckGrade}<179:2.978+0.008\left|L_{uckGrade}-178\right|,179 \le L_{uckGrade}<181:2.986+0.009\left|L_{uckGrade}-179\right|,181 \le L_{uckGrade}<182:3.004+0.008\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<183:3.012+0.009\left|L_{uckGrade}-182\right|,183 \le L_{uckGrade}<184:3.021+0.008\left|L_{uckGrade}-183\right|,184 \le L_{uckGrade}<185:3.029+0.009\left|L_{uckGrade}-184\right|,185 \le L_{uckGrade}<186:3.038+0.008\left|L_{uckGrade}-185\right|,186 \le L_{uckGrade}<187:3.046+0.009\left|L_{uckGrade}-186\right|,187 \le L_{uckGrade}<188:3.055+0.008\left|L_{uckGrade}-187\right|,188 \le L_{uckGrade}<189:3.063+0.009\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<190:3.072+0.008\left|L_{uckGrade}-189\right|,190 \le L_{uckGrade}<191:3.08+0.009\left|L_{uckGrade}-190\right|,191 \le L_{uckGrade}<193:3.089+0.008\left|L_{uckGrade}-191\right|,193 \le L_{uckGrade}<194:3.105+0.009\left|L_{uckGrade}-193\right|,194 \le L_{uckGrade}<198:3.114+0.008\left|L_{uckGrade}-194\right|,198 \le L_{uckGrade}<199:3.146+0.009\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<209:3.155+0.008\left|L_{uckGrade}-199\right|,209 \le L_{uckGrade}<210:3.235+0.007\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<214:3.242+0.008\left|L_{uckGrade}-210\right|,214 \le L_{uckGrade}<215:3.274+0.007\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<217:3.281+0.008\left|L_{uckGrade}-215\right|,217 \le L_{uckGrade}<218:3.297+0.007\left|L_{uckGrade}-217\right|,218 \le L_{uckGrade}<220:3.304+0.008\left|L_{uckGrade}-218\right|,220 \le L_{uckGrade}<221:3.32+0.007\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:3.327+0.008\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:3.335+0.007\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:3.342+0.008\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<225:3.35+0.007\left|L_{uckGrade}-224\right|,225 \le L_{uckGrade}<226:3.357+0.008\left|L_{uckGrade}-225\right|,226 \le L_{uckGrade}<228:3.365+0.007\left|L_{uckGrade}-226\right|,228 \le L_{uckGrade}<229:3.379+0.008\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<231:3.387+0.007\left|L_{uckGrade}-229\right|,231 \le L_{uckGrade}<232:3.401+0.008\left|L_{uckGrade}-231\right|,232 \le L_{uckGrade}<237:3.409+0.007\left|L_{uckGrade}-232\right|,237 \le L_{uckGrade}<238:3.444+0.008\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<244:3.452+0.007\left|L_{uckGrade}-238\right|,244 \le L_{uckGrade}<245:3.494+0.006\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<250:3.5+0.007\left|L_{uckGrade}-245\right|,250 \le L_{uckGrade}<251:3.535+0.006\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<253:3.541+0.007\left|L_{uckGrade}-251\right|,253 \le L_{uckGrade}<254:3.555+0.006\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<256:3.561+0.007\left|L_{uckGrade}-254\right|,256 \le L_{uckGrade}<257:3.575+0.006\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<258:3.581+0.007\left|L_{uckGrade}-257\right|,258 \le L_{uckGrade}<259:3.588+0.006\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<260:3.594+0.007\left|L_{uckGrade}-259\right|,260 \le L_{uckGrade}<261:3.601+0.006\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<262:3.607+0.007\left|L_{uckGrade}-261\right|,262 \le L_{uckGrade}<263:3.614+0.006\left|L_{uckGrade}-262\right|,263 \le L_{uckGrade}<264:3.62+0.007\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<266:3.627+0.006\left|L_{uckGrade}-264\right|,266 \le L_{uckGrade}<267:3.639+0.007\left|L_{uckGrade}-266\right|,267 \le L_{uckGrade}<270:3.646+0.006\left|L_{uckGrade}-267\right|,270 \le L_{uckGrade}<271:3.664+0.007\left|L_{uckGrade}-270\right|,271 \le L_{uckGrade}<286:3.671+0.006\left|L_{uckGrade}-271\right|,286 \le L_{uckGrade}<287:3.761+0.005\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<290:3.766+0.006\left|L_{uckGrade}-287\right|,290 \le L_{uckGrade}<291:3.784+0.005\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<292:3.789+0.006\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<293:3.795+0.005\left|L_{uckGrade}-292\right|,293 \le L_{uckGrade}<295:3.8+0.006\left|L_{uckGrade}-293\right|,295 \le L_{uckGrade}<296:3.812+0.005\left|L_{uckGrade}-295\right|,296 \le L_{uckGrade}<297:3.817+0.006\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<298:3.823+0.005\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<299:3.828+0.006\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<301:3.834+0.005\left|L_{uckGrade}-299\right|,301 \le L_{uckGrade}<302:3.844+0.006\left|L_{uckGrade}-301\right|,302 \le L_{uckGrade}<304:3.85+0.005\left|L_{uckGrade}-302\right|,304 \le L_{uckGrade}<305:3.86+0.006\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<308:3.866+0.005\left|L_{uckGrade}-305\right|,308 \le L_{uckGrade}<309:3.881+0.006\left|L_{uckGrade}-308\right|,309 \le L_{uckGrade}<322:3.887+0.005\left|L_{uckGrade}-309\right|,322 \le L_{uckGrade}<323:3.952+0.004\left|L_{uckGrade}-322\right|,323 \le L_{uckGrade}<326:3.956+0.005\left|L_{uckGrade}-323\right|,326 \le L_{uckGrade}<327:3.971+0.004\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<329:3.975+0.005\left|L_{uckGrade}-327\right|,329 \le L_{uckGrade}<330:3.985+0.004\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<331:3.989+0.005\left|L_{uckGrade}-330\right|,331 \le L_{uckGrade}<332:3.994+0.004\left|L_{uckGrade}-331\right|,332 \le L_{uckGrade}<334:3.998+0.005\left|L_{uckGrade}-332\right|,334 \le L_{uckGrade}<336:4.008+0.004\left|L_{uckGrade}-334\right|,336 \le L_{uckGrade}<337:4.016+0.005\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<338:4.021+0.004\left|L_{uckGrade}-337\right|,338 \le L_{uckGrade}<339:4.025+0.005\left|L_{uckGrade}-338\right|,339 \le L_{uckGrade}<341:4.03+0.004\left|L_{uckGrade}-339\right|,341 \le L_{uckGrade}<342:4.038+0.005\left|L_{uckGrade}-341\right|,342 \le L_{uckGrade}<345:4.043+0.004\left|L_{uckGrade}-342\right|,345 \le L_{uckGrade}<346:4.055+0.005\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<358:4.06+0.004\left|L_{uckGrade}-346\right|,358 \le L_{uckGrade}<359:4.108+0.003\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<363:4.111+0.004\left|L_{uckGrade}-359\right|,363 \le L_{uckGrade}<364:4.127+0.003\left|L_{uckGrade}-363\right|,364 \le L_{uckGrade}<366:4.13+0.004\left|L_{uckGrade}-364\right|,366 \le L_{uckGrade}<367:4.138+0.003\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:4.141+0.004\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<369:4.145+0.003\left|L_{uckGrade}-368\right|,369 \le L_{uckGrade}<370:4.148+0.004\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<371:4.152+0.003\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<372:4.155+0.004\left|L_{uckGrade}-371\right|,372 \le L_{uckGrade}<373:4.159+0.003\left|L_{uckGrade}-372\right|,373 \le L_{uckGrade}<374:4.162+0.004\left|L_{uckGrade}-373\right|,374 \le L_{uckGrade}<375:4.166+0.003\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<376:4.169+0.004\left|L_{uckGrade}-375\right|,376 \le L_{uckGrade}<379:4.173+0.003\left|L_{uckGrade}-376\right|,379 \le L_{uckGrade}<380:4.182+0.004\left|L_{uckGrade}-379\right|,380 \le L_{uckGrade}<383:4.186+0.003\left|L_{uckGrade}-380\right|,383 \le L_{uckGrade}<384:4.195+0.004\left|L_{uckGrade}-383\right|,384 \le L_{uckGrade}<394:4.199+0.003\left|L_{uckGrade}-384\right|,394 \le L_{uckGrade}<395:4.229+0.002\left|L_{uckGrade}-394\right|,395 \le L_{uckGrade}<399:4.231+0.003\left|L_{uckGrade}-395\right|,399 \le L_{uckGrade}<400:4.243+0.002\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<402:4.245+0.003\left|L_{uckGrade}-400\right|,402 \le L_{uckGrade}<403:4.251+0.002\left|L_{uckGrade}-402\right|,403 \le L_{uckGrade}<405:4.253+0.003\left|L_{uckGrade}-403\right|,405 \le L_{uckGrade}<406:4.259+0.002\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:4.261+0.003\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<408:4.264+0.002\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<409:4.266+0.003\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<410:4.269+0.002\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<411:4.271+0.003\left|L_{uckGrade}-410\right|,411 \le L_{uckGrade}<413:4.274+0.002\left|L_{uckGrade}-411\right|,413 \le L_{uckGrade}<414:4.278+0.003\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<416:4.281+0.002\left|L_{uckGrade}-414\right|,416 \le L_{uckGrade}<417:4.285+0.003\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<421:4.288+0.002\left|L_{uckGrade}-417\right|,421 \le L_{uckGrade}<422:4.296+0.003\left|L_{uckGrade}-421\right|,422 \le L_{uckGrade}<431:4.299+0.002\left|L_{uckGrade}-422\right|,431 \le L_{uckGrade}<432:4.317+0.001\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<436:4.318+0.002\left|L_{uckGrade}-432\right|,436 \le L_{uckGrade}<437:4.326+0.001\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<439:4.327+0.002\left|L_{uckGrade}-437\right|,439 \le L_{uckGrade}<440:4.331+0.001\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<442:4.332+0.002\left|L_{uckGrade}-440\right|,442 \le L_{uckGrade}<443:4.336+0.001\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<444:4.337+0.002\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<445:4.339+0.001\left|L_{uckGrade}-444\right|,445 \le L_{uckGrade}<446:4.34+0.002\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<447:4.342+0.001\left|L_{uckGrade}-446\right|,447 \le L_{uckGrade}<448:4.343+0.002\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<450:4.345+0.001\left|L_{uckGrade}-448\right|,450 \le L_{uckGrade}<451:4.347+0.002\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<453:4.349+0.001\left|L_{uckGrade}-451\right|,453 \le L_{uckGrade}<454:4.351+0.002\left|L_{uckGrade}-453\right|,454 \le L_{uckGrade}<458:4.353+0.001\left|L_{uckGrade}-454\right|,458 \le L_{uckGrade}<459:4.357+0.002\left|L_{uckGrade}-458\right|,459 \le L_{uckGrade}<467:4.359+0.001\left|L_{uckGrade}-459\right|,467 \le L_{uckGrade}<468:4.367+0\left|L_{uckGrade}-467\right|,468 \le L_{uckGrade}<473:4.367+0.001\left|L_{uckGrade}-468\right|,473 \le L_{uckGrade}<474:4.372+0\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<476:4.372+0.001\left|L_{uckGrade}-474\right|,476 \le L_{uckGrade}<477:4.374+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<479:4.374+0.001\left|L_{uckGrade}-477\right|,479 \le L_{uckGrade}<480:4.376+0\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:4.376+0.001\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:4.377+0\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:4.377+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<484:4.378+0\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<485:4.378+0.001\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<487:4.379+0\left|L_{uckGrade}-485\right|,487 \le L_{uckGrade}<488:4.379+0.001\left|L_{uckGrade}-487\right|,488 \le L_{uckGrade}<490:4.38+0\left|L_{uckGrade}-488\right|,490 \le L_{uckGrade}<491:4.38+0.001\left|L_{uckGrade}-490\right|,491 \le L_{uckGrade}<496:4.381+0\left|L_{uckGrade}-491\right|,496 \le L_{uckGrade}<497:4.381+0.001\left|L_{uckGrade}-496\right|,497 \le L_{uckGrade}<500:4.382+0\left|L_{uckGrade}-497\right|\right\}

See Example for how to use.


LaTeX Formula

Can be pasted into Desmos or other LaTeX editors for quick use of the equation.

Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results. 

L_{uckGrade08}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<1:1+0.014\left|L_{uckGrade}-0\right|,1 \le L_{uckGrade}<3:1.014+0.013\left|L_{uckGrade}-1\right|,3 \le L_{uckGrade}<4:1.04+0.014\left|L_{uckGrade}-3\right|,4 \le L_{uckGrade}<5:1.054+0.013\left|L_{uckGrade}-4\right|,5 \le L_{uckGrade}<6:1.067+0.014\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<8:1.081+0.013\left|L_{uckGrade}-6\right|,8 \le L_{uckGrade}<9:1.107+0.014\left|L_{uckGrade}-8\right|,9 \le L_{uckGrade}<13:1.121+0.013\left|L_{uckGrade}-9\right|,13 \le L_{uckGrade}<14:1.173+0.014\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<24:1.187+0.013\left|L_{uckGrade}-14\right|,24 \le L_{uckGrade}<25:1.317+0.012\left|L_{uckGrade}-24\right|,25 \le L_{uckGrade}<29:1.329+0.013\left|L_{uckGrade}-25\right|,29 \le L_{uckGrade}<30:1.381+0.012\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<32:1.393+0.013\left|L_{uckGrade}-30\right|,32 \le L_{uckGrade}<33:1.419+0.012\left|L_{uckGrade}-32\right|,33 \le L_{uckGrade}<34:1.431+0.013\left|L_{uckGrade}-33\right|,34 \le L_{uckGrade}<35:1.444+0.012\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<37:1.456+0.013\left|L_{uckGrade}-35\right|,37 \le L_{uckGrade}<39:1.482+0.012\left|L_{uckGrade}-37\right|,39 \le L_{uckGrade}<40:1.506+0.013\left|L_{uckGrade}-39\right|,40 \le L_{uckGrade}<41:1.519+0.012\left|L_{uckGrade}-40\right|,41 \le L_{uckGrade}<42:1.531+0.013\left|L_{uckGrade}-41\right|,42 \le L_{uckGrade}<44:1.544+0.012\left|L_{uckGrade}-42\right|,44 \le L_{uckGrade}<45:1.568+0.013\left|L_{uckGrade}-44\right|,45 \le L_{uckGrade}<47:1.581+0.012\left|L_{uckGrade}-45\right|,47 \le L_{uckGrade}<48:1.605+0.013\left|L_{uckGrade}-47\right|,48 \le L_{uckGrade}<64:1.618+0.012\left|L_{uckGrade}-48\right|,64 \le L_{uckGrade}<65:1.81+0.011\left|L_{uckGrade}-64\right|,65 \le L_{uckGrade}<67:1.821+0.012\left|L_{uckGrade}-65\right|,67 \le L_{uckGrade}<68:1.845+0.011\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<70:1.856+0.012\left|L_{uckGrade}-68\right|,70 \le L_{uckGrade}<71:1.88+0.011\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<73:1.891+0.012\left|L_{uckGrade}-71\right|,73 \le L_{uckGrade}<74:1.915+0.011\left|L_{uckGrade}-73\right|,74 \le L_{uckGrade}<75:1.926+0.012\left|L_{uckGrade}-74\right|,75 \le L_{uckGrade}<77:1.938+0.011\left|L_{uckGrade}-75\right|,77 \le L_{uckGrade}<78:1.96+0.012\left|L_{uckGrade}-77\right|,78 \le L_{uckGrade}<79:1.972+0.011\left|L_{uckGrade}-78\right|,79 \le L_{uckGrade}<80:1.983+0.012\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<82:1.995+0.011\left|L_{uckGrade}-80\right|,82 \le L_{uckGrade}<83:2.017+0.012\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<87:2.029+0.011\left|L_{uckGrade}-83\right|,87 \le L_{uckGrade}<88:2.073+0.012\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<99:2.085+0.011\left|L_{uckGrade}-88\right|,99 \le L_{uckGrade}<100:2.206+0.01\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<103:2.216+0.011\left|L_{uckGrade}-100\right|,103 \le L_{uckGrade}<104:2.249+0.01\left|L_{uckGrade}-103\right|,104 \le L_{uckGrade}<106:2.259+0.011\left|L_{uckGrade}-104\right|,106 \le L_{uckGrade}<107:2.281+0.01\left|L_{uckGrade}-106\right|,107 \le L_{uckGrade}<109:2.291+0.011\left|L_{uckGrade}-107\right|,109 \le L_{uckGrade}<110:2.313+0.01\left|L_{uckGrade}-109\right|,110 \le L_{uckGrade}<111:2.323+0.011\left|L_{uckGrade}-110\right|,111 \le L_{uckGrade}<112:2.334+0.01\left|L_{uckGrade}-111\right|,112 \le L_{uckGrade}<113:2.344+0.011\left|L_{uckGrade}-112\right|,113 \le L_{uckGrade}<114:2.355+0.01\left|L_{uckGrade}-113\right|,114 \le L_{uckGrade}<115:2.365+0.011\left|L_{uckGrade}-114\right|,115 \le L_{uckGrade}<117:2.376+0.01\left|L_{uckGrade}-115\right|,117 \le L_{uckGrade}<118:2.396+0.011\left|L_{uckGrade}-117\right|,118 \le L_{uckGrade}<121:2.407+0.01\left|L_{uckGrade}-118\right|,121 \le L_{uckGrade}<122:2.437+0.011\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<127:2.448+0.01\left|L_{uckGrade}-122\right|,127 \le L_{uckGrade}<128:2.498+0.011\left|L_{uckGrade}-127\right|,128 \le L_{uckGrade}<132:2.509+0.01\left|L_{uckGrade}-128\right|,132 \le L_{uckGrade}<133:2.549+0.009\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<139:2.558+0.01\left|L_{uckGrade}-133\right|,139 \le L_{uckGrade}<140:2.618+0.009\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<142:2.627+0.01\left|L_{uckGrade}-140\right|,142 \le L_{uckGrade}<143:2.647+0.009\left|L_{uckGrade}-142\right|,143 \le L_{uckGrade}<145:2.656+0.01\left|L_{uckGrade}-143\right|,145 \le L_{uckGrade}<146:2.676+0.009\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<147:2.685+0.01\left|L_{uckGrade}-146\right|,147 \le L_{uckGrade}<148:2.695+0.009\left|L_{uckGrade}-147\right|,148 \le L_{uckGrade}<149:2.704+0.01\left|L_{uckGrade}-148\right|,149 \le L_{uckGrade}<150:2.714+0.009\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<151:2.723+0.01\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:2.733+0.009\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<153:2.742+0.01\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<155:2.752+0.009\left|L_{uckGrade}-153\right|,155 \le L_{uckGrade}<156:2.77+0.01\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<159:2.78+0.009\left|L_{uckGrade}-156\right|,159 \le L_{uckGrade}<160:2.807+0.01\left|L_{uckGrade}-159\right|,160 \le L_{uckGrade}<174:2.817+0.009\left|L_{uckGrade}-160\right|,174 \le L_{uckGrade}<175:2.943+0.008\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<178:2.951+0.009\left|L_{uckGrade}-175\right|,178 \le L_{uckGrade}<179:2.978+0.008\left|L_{uckGrade}-178\right|,179 \le L_{uckGrade}<181:2.986+0.009\left|L_{uckGrade}-179\right|,181 \le L_{uckGrade}<182:3.004+0.008\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<183:3.012+0.009\left|L_{uckGrade}-182\right|,183 \le L_{uckGrade}<184:3.021+0.008\left|L_{uckGrade}-183\right|,184 \le L_{uckGrade}<185:3.029+0.009\left|L_{uckGrade}-184\right|,185 \le L_{uckGrade}<186:3.038+0.008\left|L_{uckGrade}-185\right|,186 \le L_{uckGrade}<187:3.046+0.009\left|L_{uckGrade}-186\right|,187 \le L_{uckGrade}<188:3.055+0.008\left|L_{uckGrade}-187\right|,188 \le L_{uckGrade}<189:3.063+0.009\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<190:3.072+0.008\left|L_{uckGrade}-189\right|,190 \le L_{uckGrade}<191:3.08+0.009\left|L_{uckGrade}-190\right|,191 \le L_{uckGrade}<193:3.089+0.008\left|L_{uckGrade}-191\right|,193 \le L_{uckGrade}<194:3.105+0.009\left|L_{uckGrade}-193\right|,194 \le L_{uckGrade}<198:3.114+0.008\left|L_{uckGrade}-194\right|,198 \le L_{uckGrade}<199:3.146+0.009\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<209:3.155+0.008\left|L_{uckGrade}-199\right|,209 \le L_{uckGrade}<210:3.235+0.007\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<214:3.242+0.008\left|L_{uckGrade}-210\right|,214 \le L_{uckGrade}<215:3.274+0.007\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<217:3.281+0.008\left|L_{uckGrade}-215\right|,217 \le L_{uckGrade}<218:3.297+0.007\left|L_{uckGrade}-217\right|,218 \le L_{uckGrade}<220:3.304+0.008\left|L_{uckGrade}-218\right|,220 \le L_{uckGrade}<221:3.32+0.007\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:3.327+0.008\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:3.335+0.007\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:3.342+0.008\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<225:3.35+0.007\left|L_{uckGrade}-224\right|,225 \le L_{uckGrade}<226:3.357+0.008\left|L_{uckGrade}-225\right|,226 \le L_{uckGrade}<228:3.365+0.007\left|L_{uckGrade}-226\right|,228 \le L_{uckGrade}<229:3.379+0.008\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<231:3.387+0.007\left|L_{uckGrade}-229\right|,231 \le L_{uckGrade}<232:3.401+0.008\left|L_{uckGrade}-231\right|,232 \le L_{uckGrade}<237:3.409+0.007\left|L_{uckGrade}-232\right|,237 \le L_{uckGrade}<238:3.444+0.008\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<244:3.452+0.007\left|L_{uckGrade}-238\right|,244 \le L_{uckGrade}<245:3.494+0.006\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<250:3.5+0.007\left|L_{uckGrade}-245\right|,250 \le L_{uckGrade}<251:3.535+0.006\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<253:3.541+0.007\left|L_{uckGrade}-251\right|,253 \le L_{uckGrade}<254:3.555+0.006\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<256:3.561+0.007\left|L_{uckGrade}-254\right|,256 \le L_{uckGrade}<257:3.575+0.006\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<258:3.581+0.007\left|L_{uckGrade}-257\right|,258 \le L_{uckGrade}<259:3.588+0.006\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<260:3.594+0.007\left|L_{uckGrade}-259\right|,260 \le L_{uckGrade}<261:3.601+0.006\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<262:3.607+0.007\left|L_{uckGrade}-261\right|,262 \le L_{uckGrade}<263:3.614+0.006\left|L_{uckGrade}-262\right|,263 \le L_{uckGrade}<264:3.62+0.007\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<266:3.627+0.006\left|L_{uckGrade}-264\right|,266 \le L_{uckGrade}<267:3.639+0.007\left|L_{uckGrade}-266\right|,267 \le L_{uckGrade}<270:3.646+0.006\left|L_{uckGrade}-267\right|,270 \le L_{uckGrade}<271:3.664+0.007\left|L_{uckGrade}-270\right|,271 \le L_{uckGrade}<286:3.671+0.006\left|L_{uckGrade}-271\right|,286 \le L_{uckGrade}<287:3.761+0.005\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<290:3.766+0.006\left|L_{uckGrade}-287\right|,290 \le L_{uckGrade}<291:3.784+0.005\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<292:3.789+0.006\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<293:3.795+0.005\left|L_{uckGrade}-292\right|,293 \le L_{uckGrade}<295:3.8+0.006\left|L_{uckGrade}-293\right|,295 \le L_{uckGrade}<296:3.812+0.005\left|L_{uckGrade}-295\right|,296 \le L_{uckGrade}<297:3.817+0.006\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<298:3.823+0.005\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<299:3.828+0.006\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<301:3.834+0.005\left|L_{uckGrade}-299\right|,301 \le L_{uckGrade}<302:3.844+0.006\left|L_{uckGrade}-301\right|,302 \le L_{uckGrade}<304:3.85+0.005\left|L_{uckGrade}-302\right|,304 \le L_{uckGrade}<305:3.86+0.006\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<308:3.866+0.005\left|L_{uckGrade}-305\right|,308 \le L_{uckGrade}<309:3.881+0.006\left|L_{uckGrade}-308\right|,309 \le L_{uckGrade}<322:3.887+0.005\left|L_{uckGrade}-309\right|,322 \le L_{uckGrade}<323:3.952+0.004\left|L_{uckGrade}-322\right|,323 \le L_{uckGrade}<326:3.956+0.005\left|L_{uckGrade}-323\right|,326 \le L_{uckGrade}<327:3.971+0.004\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<329:3.975+0.005\left|L_{uckGrade}-327\right|,329 \le L_{uckGrade}<330:3.985+0.004\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<331:3.989+0.005\left|L_{uckGrade}-330\right|,331 \le L_{uckGrade}<332:3.994+0.004\left|L_{uckGrade}-331\right|,332 \le L_{uckGrade}<334:3.998+0.005\left|L_{uckGrade}-332\right|,334 \le L_{uckGrade}<336:4.008+0.004\left|L_{uckGrade}-334\right|,336 \le L_{uckGrade}<337:4.016+0.005\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<338:4.021+0.004\left|L_{uckGrade}-337\right|,338 \le L_{uckGrade}<339:4.025+0.005\left|L_{uckGrade}-338\right|,339 \le L_{uckGrade}<341:4.03+0.004\left|L_{uckGrade}-339\right|,341 \le L_{uckGrade}<342:4.038+0.005\left|L_{uckGrade}-341\right|,342 \le L_{uckGrade}<345:4.043+0.004\left|L_{uckGrade}-342\right|,345 \le L_{uckGrade}<346:4.055+0.005\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<358:4.06+0.004\left|L_{uckGrade}-346\right|,358 \le L_{uckGrade}<359:4.108+0.003\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<363:4.111+0.004\left|L_{uckGrade}-359\right|,363 \le L_{uckGrade}<364:4.127+0.003\left|L_{uckGrade}-363\right|,364 \le L_{uckGrade}<366:4.13+0.004\left|L_{uckGrade}-364\right|,366 \le L_{uckGrade}<367:4.138+0.003\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:4.141+0.004\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<369:4.145+0.003\left|L_{uckGrade}-368\right|,369 \le L_{uckGrade}<370:4.148+0.004\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<371:4.152+0.003\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<372:4.155+0.004\left|L_{uckGrade}-371\right|,372 \le L_{uckGrade}<373:4.159+0.003\left|L_{uckGrade}-372\right|,373 \le L_{uckGrade}<374:4.162+0.004\left|L_{uckGrade}-373\right|,374 \le L_{uckGrade}<375:4.166+0.003\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<376:4.169+0.004\left|L_{uckGrade}-375\right|,376 \le L_{uckGrade}<379:4.173+0.003\left|L_{uckGrade}-376\right|,379 \le L_{uckGrade}<380:4.182+0.004\left|L_{uckGrade}-379\right|,380 \le L_{uckGrade}<383:4.186+0.003\left|L_{uckGrade}-380\right|,383 \le L_{uckGrade}<384:4.195+0.004\left|L_{uckGrade}-383\right|,384 \le L_{uckGrade}<394:4.199+0.003\left|L_{uckGrade}-384\right|,394 \le L_{uckGrade}<395:4.229+0.002\left|L_{uckGrade}-394\right|,395 \le L_{uckGrade}<399:4.231+0.003\left|L_{uckGrade}-395\right|,399 \le L_{uckGrade}<400:4.243+0.002\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<402:4.245+0.003\left|L_{uckGrade}-400\right|,402 \le L_{uckGrade}<403:4.251+0.002\left|L_{uckGrade}-402\right|,403 \le L_{uckGrade}<405:4.253+0.003\left|L_{uckGrade}-403\right|,405 \le L_{uckGrade}<406:4.259+0.002\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:4.261+0.003\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<408:4.264+0.002\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<409:4.266+0.003\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<410:4.269+0.002\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<411:4.271+0.003\left|L_{uckGrade}-410\right|,411 \le L_{uckGrade}<413:4.274+0.002\left|L_{uckGrade}-411\right|,413 \le L_{uckGrade}<414:4.278+0.003\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<416:4.281+0.002\left|L_{uckGrade}-414\right|,416 \le L_{uckGrade}<417:4.285+0.003\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<421:4.288+0.002\left|L_{uckGrade}-417\right|,421 \le L_{uckGrade}<422:4.296+0.003\left|L_{uckGrade}-421\right|,422 \le L_{uckGrade}<431:4.299+0.002\left|L_{uckGrade}-422\right|,431 \le L_{uckGrade}<432:4.317+0.001\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<436:4.318+0.002\left|L_{uckGrade}-432\right|,436 \le L_{uckGrade}<437:4.326+0.001\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<439:4.327+0.002\left|L_{uckGrade}-437\right|,439 \le L_{uckGrade}<440:4.331+0.001\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<442:4.332+0.002\left|L_{uckGrade}-440\right|,442 \le L_{uckGrade}<443:4.336+0.001\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<444:4.337+0.002\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<445:4.339+0.001\left|L_{uckGrade}-444\right|,445 \le L_{uckGrade}<446:4.34+0.002\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<447:4.342+0.001\left|L_{uckGrade}-446\right|,447 \le L_{uckGrade}<448:4.343+0.002\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<450:4.345+0.001\left|L_{uckGrade}-448\right|,450 \le L_{uckGrade}<451:4.347+0.002\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<453:4.349+0.001\left|L_{uckGrade}-451\right|,453 \le L_{uckGrade}<454:4.351+0.002\left|L_{uckGrade}-453\right|,454 \le L_{uckGrade}<458:4.353+0.001\left|L_{uckGrade}-454\right|,458 \le L_{uckGrade}<459:4.357+0.002\left|L_{uckGrade}-458\right|,459 \le L_{uckGrade}<467:4.359+0.001\left|L_{uckGrade}-459\right|,467 \le L_{uckGrade}<468:4.367+0\left|L_{uckGrade}-467\right|,468 \le L_{uckGrade}<473:4.367+0.001\left|L_{uckGrade}-468\right|,473 \le L_{uckGrade}<474:4.372+0\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<476:4.372+0.001\left|L_{uckGrade}-474\right|,476 \le L_{uckGrade}<477:4.374+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<479:4.374+0.001\left|L_{uckGrade}-477\right|,479 \le L_{uckGrade}<480:4.376+0\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:4.376+0.001\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:4.377+0\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:4.377+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<484:4.378+0\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<485:4.378+0.001\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<487:4.379+0\left|L_{uckGrade}-485\right|,487 \le L_{uckGrade}<488:4.379+0.001\left|L_{uckGrade}-487\right|,488 \le L_{uckGrade}<490:4.38+0\left|L_{uckGrade}-488\right|,490 \le L_{uckGrade}<491:4.38+0.001\left|L_{uckGrade}-490\right|,491 \le L_{uckGrade}<496:4.381+0\left|L_{uckGrade}-491\right|,496 \le L_{uckGrade}<497:4.381+0.001\left|L_{uckGrade}-496\right|,497 \le L_{uckGrade}<500:4.382+0\left|L_{uckGrade}-497\right|\right\}

See Example for how to use.



Max Spell Count

Determines the number of spells that can be stored at once. For example, at base, Wizard can store up to 5 Fireballs. This can be increased with Max Spell Count Bonus multiplicatively

Can't be found on gear and is not affected by other stats.

Enchantment Stats

Stats that come from weapons, armors or jewelry imbued with item Enchantments.

Enchantments that aren't traditional Stats and only exist in a Damage/Healing formula are listed below and can also be found in Damage_Calculation and Healing.

Enchantment Description
Physical Base Healing Increases Physical Base Healing performed
Magical Base Healing Increases Magical Base Healing performed
Armor Penetration Increases the amount of Physical Damage that bypasses enemy's Physical Damage Reduction
Magic Penetration Increases the amount of Magical Damage that bypasses enemy's Magical Damage Reduction
Projectile Reduction Decreases damage taken from projectiles (Arrows, Throwing Knives, etc.)
Headshot Damage Reduction Decreases Hit Location Bonus additively if targeting the head
True Physical Damage Increases Physical Damage dealt that is not influenced by enemy defences
True Magical Damage Increases Magical Damage dealt that is not influenced by enemy defences
Weapon Damage Increases Gear Weapon Damage
Additional Physical Damage Increases Physical Damage dealt (not affected by Physical Power Bonus)
Additional Magical Damage Increases Magical Damage dealt (not affected by Magical Power Bonus)
Luck Increases Luck for obtaining items)

For the possible values of Enchantments and their historical rolls, see Enchantment Values

Unimplemented Stats

These stats are not yet implemented.

Utility Effectiveness Bonus

Determines the bonus effectiveness of your utility items

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