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<metadesc>Dark and Darker Wiki Stats Guide</metadesc>
<metadesc>Dark and Darker Wiki Stats Guide</metadesc>
{{UpdateStatus|Stats Data|Stats}}
{{MechanicsBar}}
=Stats=
Stats modify your character while equipped. [[Weapons]]/[[Utilities|Consumables]] 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.
<p style="center;font-size">See exact changes to Stats here [[Patch:6.4#Stat_Curve_Changes]] </p>
==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 [[Damage_Calculation#Rounding|rounded]] to 33.
=Attributes=
Stats that come from character's attributes.
==Strength==
==Strength==
===Physical Power===
Physical Power governs your Physical Power Bonus.
{{Stats Data|physicalpower}}
===Physical Power Bonus===
<span id="Physical Damage Bonus">
- Also known as Physical Damage Bonus,
Physical Power Bonus governs the potency of your physical damage dealing weapons, utility items, and abilities.
{{Stats Data|physicalpowerbonus}}<span>
Capped to -100%
===Max Health from Strength===
Max Health determines your characters maximum [[Health]].
Strength increases Max Health with 25% Scaling. See the Hybrid stat [[Stats#Max_Health|Max Health]] for more.
==Vigor==
===Max Health from Vigor===
Max Health determines your characters maximum [[Health]].
Vigor increases Max Health with 75% Scaling. See the Hybrid stat [[Stats#Max_Health|Max Health]] for more.


===Physical Power===
0 Strength starts at = 0 Physical Power


Every Strength gives increase to your Physical Power
===Health Recovery===
Affects the rate at which you restore health when Resting, but not when using Bandages.


*0 to 100 = 1 (capped at 100)
<code>Health Recovered per tick = Base Recovery * (1 + Health Recovery Bonus)</code>


===Max Health===
For example, a Barbarian resting with 95% Health Recovery Bonus will recover
0 Strength starts at = 60 Max Health


Every Strength gives increase to Max Health
<code>Health Recovered every 2s = 1 * (1 + .95) = 1.95 Health</code>


*0 to 10 = 3 (capped at 90)
{{Stats Data|healthrecovery}}
*10 to 50 = 2 -> 170
*50 to 75 = 1 -> 195
*75 to 100 = .5 -> 207.5




==Agility==
==Agility==
===Action Speed===
===Action Speed from Agility===
0 Agility starts at = -45% 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.


Every agility point gives % action speed between intervals
Agility increases Action Speed with 25% Scaling. See the Hybrid stat [[Stats#Action_Speed|Action Speed]] for more.
 
*0 to 15 = 3% -> 0%
*15 to 25 = 1% -> 10%
*25 to 40 = 2% -> 40%
*40 to 50 = 1% ->  50%
*50 to 100 = 0.5% -> 75%


===Move Speed===
===Move Speed===
0 Agility starts at = -30% 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 = 40%.
{{Stats Data|movespeed}}


Every agility point gives % Move speed between intervals
'''Hard capped to 330 Movement speed'''


*0 to 15 = 2% - 0%
===Regular Interaction Speed from Agility===
*15 to 45 = 1.0% - 30%
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
*45 to 65 = 0.5% - 40%
*65 to 100 = 0.33% - 51%


Capped at 51% at Agility 98.
Agility increases Regular Interaction Speed with 40% Scaling. See the Hybrid stat [[Stats#Regular_Interaction_Speed|Regular Interaction Speed]] for more.


===Item Equip Speed===
==Dexterity==
0 Agility starts at = -95% Item Equip 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.


Every agility point gives % Item Equip speed between intervals
Dexterity increases Action Speed with 75% Scaling. See the Hybrid stat [[Stats#Action_Speed|Action Speed]] for more.


*0 to 1 = 0% (capped at -95%)
===Manual Dexterity===
*1 to 2 = 4% -> -91%
Manual Dexterity determines how quickly Bard plays an instrument.
*2 to 15 = 7% -> 0%
{{Stats Data|manualdexterity}}
*15 to 35 = 5% -> 100%
*35 to 70 = 2% -> 170%
*70 to 100 = 1% -> 200%


===Item Equip Speed===
Item Equip Speed exclusively governs the speed at which you equip armors, as equipping weapons, jewelry and utility items is instant.
{{Stats Data|itemequipspeed}}


==Will==
==Will==
===Magical Power===
<span id="Magic Power">
Magic Power governs your Magic Power Bonus.
<span>
{{Stats Data|magicalpower}}


===Spell Power===
===Magic Power Bonus===
0 Will starts at = 0 Spell Power
<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.
{{Stats Data|magicalpowerbonus}}<span>


Every Will gives increase to your Spell Power


*0 to 100 = 1 (capped at 100)
===Magical Resistance===
<span id="Magic Resistance">
Magic Resistance governs your Magical Damage Reduction.
{{Stats Data|magicresistance}}<span>


===Magic Resistance===
===Magical Damage Reduction===
0 Will starts at = -20 Magic Resistance
<span id="Magic Damage Reduction">Magical Damage Reduction governs your resistance to magical damage dealing weapons, spells and projectiles.
{{Stats Data|magicaldamagereduction}}


Every Will gives increase to Magic Resistance
Magical Damage Reduction is capped to 75%<span>


*0 to 5 = 4 (capped at 0)
===Buff Duration===
*5 to 35 = 3 -> 90
Buff Duration governs the duration of temporary beneficial status effects.
*35 to 55 = 2 -> 130
{{Stats Data|buffduration}}
*55 to 66 = 1 -> 141
*66 to 100 = .5 -> 158.5


===Buff Duration===
===Debuff Duration===
<div style="display:inline-block; min-width:400px; width:50%">
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.
0 Will starts at = -80% Buff Duration
{{Stats Data|debuffduration}}
 
Debuff Duration has a lower cap of -95%, meaning at minimum a debuff can last 1/20th of its base duration.


Every Will gives % increase to your Buff Duration
===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}}


*0 to 7 = 10% (capped at -20%)
Note that the Debuff Duration Bonus enchant converts into a negative Debuff Duration, decreasing the duration of debuffs on you.
*7 to 11 = 3% -> -8%
*11 to 15 = 2% -> 0%
*15 to 50 = 1% -> 35%
*50 to 100 = .5% -> 60%
</div>
<div style="display:inline-block; min-width:400px; width:50%" id='BuffDurationModGraph'><!-- Plotly chart will be drawn inside this DIV --></div>


===Curse Duration===
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>
0 Will starts at = 400% Curse Duration


Every Will gives % decreases to your Curse Duration
==Knowledge==
===Spell Casting Speed===
Spell Casting Speed governs the speed at which you cast magical spells. See [[Action/Interaction/Cast_Speed]] for more.


*0 to 1 = 170% (capped at 233.333%)
{{Stats Data|spellcastingspeed}}
*1 to 2 = 83.33% -> 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%
The decrease slowly slows down with different reduction amounts that is not logarithmic nor linear. Finally


<code>Spell Casting Time = (Base Casting Time)/(1 + Spell Casting Speed)</code>


* 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.


==Knowledge==
===Spell Casting Speed===
0 Knowledge starts at = -95% Spell Casting Speed


Every Knowledge point gives % Spell Casting speed between intervals


*0 to 1 = 0% (capped at -95%)
===Memory Capacity===
*1 to 30 = 5% -> 50%
Memory Capacity govern your spell/song cost cap, meaning equipping spells/songs that exceed this cap will not be usable.
*30 to 40 = 3% -> 80%
{{Stats Data|memorycapacity}}
*40 to 100 = 2% -> 200%


===Item Identification Speed===
<code> Total Memory Capacity = ceil(Memory Cap from Knowledge * (1 + Memory Cap Bonus%)) + Add Memory Cap </code>
0 Knowledge starts at = -75% Item Identification Speed


Every Knowledge point gives % Item Identification speed between intervals
Memory Cap Bonus% and Add Memory Cap are two different [[Enchantments]].


*0 to 15 = 5% (capped at 0%)
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
*15 to 25 = 7% -> 70%
*25 to 35 = 5% -> 120%
*35 to 84 = 2% -> 218%
*84 to 85 = 1% -> 219%
*85 to 86 = 3% -> 222%
*86 to 100 = 2% -> 250%


===Spell Capacity Speed===
<code> ceil(12 * 1.077) + 8 = 21 Memory Capacity</code>
0 Knowledge starts at = 0% Spell Capacity


Every Knowledge point gives % Spell Capacity between intervals
===Memory Recovery===
Increases the amount of [[Spell_Restoration|Spell/(Skill?) Points]] (SP) you restore per tick.


*0 to 100 = 1% (capped at 100%)
{{Stats Data|memoryrecovery}}


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


==Resourcefulness==
==Resourcefulness==
===Interaction Speed===
===Regular Interaction Speed from Resourcefulness===
0 Resourcefulness starts at = -75% Interaction Speed
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.


Every Resourcefulness gives % increase to your Interaction Speed with objects
Resourcefulness increases Regular Interaction Speed with 60% Scaling. See the Hybrid stat [[Stats#Regular_Interaction_Speed|Regular Interaction Speed]] for more.


*0 to 15 = 5% (capped at 0%)
===Cooldown Reduction===
*15 to 25 = 7% -> 70%
Cooldown Reduction reduces the cooldowns of skills/perks.
*25 to 35 = 5% -> 120%
*35 to 84 = 2% -> 218%
*84 to 85 = 1% -> 219%
*85 to 86 = 3% -> 222%
*86 to 100 = 2% -> 250%


<code>Reduced cooldown length = Base Cooldown * (1 - Cooldown Reduction)</code><br><br>


Note that perk cooldowns are in the form of a buff/debuff and are additionally affected by [[Stats#Buff_Duration|Buff]]/[[Stats#Debuff_Duration|Debuff Duration]].<br>


<code>Reduced cooldown length = Post buff/debuff duration cooldown * (1 - Cooldown Reduction)</code>
{{Stats_Data|cooldownreduction}}


==Magic Power Bonus==
===Persuasiveness===
0 Magic Power Bonus starts at = -90% Magic Power Bonus
Persuasiveness determines the duration of Bard songs' buffs/debuffs.
{{Stats Data|persuasiveness}}


Every Magic Power Bonus gives % increase to your overall spell power
Base buff duration formula:


*0 to 1 = 0% (capped at -90%)
<code>Scaling x Persuasiveness</code>
*1 to 5 = 10% -> -50%
*5 to 15 = 5% -> -0%
*15 to 25 = 3% -> 30%
*25 to 40 = 2% -> 60%
*40 to 50 = 1% -> 70%
*50 to 100 = 0.5% -> 95%


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 there are noted to not scale with Persuasiveness, 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 have 4.5x scaling and if Bard has 20 Persuasiveness, outgoing buff duration will be:
<code>4.5 x 20 = 90</code> seconds
This will also get multiplied by the receiver's [[Stats#Buff_Duration|Buff Duration]]/[[Stats#Debuff_Duration|Debuff Duration]]
[https://www.desmos.com/calculator/sihhlsxqnt Buff Duration Calculator]
=Hybrid Stats=
Hybrid stats are stats which come from a combination of attributes. For example, Health is determined by both Strength and Vigor.
==Max Health==
Max Health determines your characters maximum [[Health]].
{{Stats Data|maxhealth}}
Final Max 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.
{{Stats Data|actionspeed}}
An Action Speed of 50% results in the animation lasting for only 67% of the base animation length.
<code> New animation length = Base animation length / (1 + Action Speed) </code>
==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.
{{Stats Data|regularinteractionspeed}}
<code> New interaction length = Base interaction length / (1 + interaction speed) </code>
For example, an Interaction Speed of 100% results in the interaction time lasting for only 50% of the base interaction length.
[[Surgical Kit]]s 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=


==Armor Rating==
==Armor Rating==
Armor Rating can go as low as -300 starts at = -596% Physical Damage Reduction
Armor Rating 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 (x 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.
{{Stats Data|physicaldamagereduction}}


0 Armor Rating starts at = -10% Physical Damage Reduction  
Physical Damage Reduction is capped to 75%


Every Armor Rating gives % Physical Damage Reduction between intervals
==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.


*-300 to -15 = 2% (capped at -25%)
==Luck==
*-15 to 10 = 1% -> 0%
Loot is rolled when you open the container or kill the mob.
*10 to 19 = 0.5% -> 4.5%
*19 to 40 = 0.3% -> 11.9%
*40 to 50 = 0.2% -> 13.9%
*50 to 100 = 0.1% -> 18.9%
*100 to 150 = 0.2% -> 28.9%
*150 to 250 = 0.3% -> 58.9%
*250 to 350 = 0.4% -> 78.9%
*350 to 500 = 0.1% -> 93.9%


==Magic Resistance==
Whoever opens the loot first or kills the mob first is the person whose luck is used to calculate the drops.<br>
Magic Resistance can go as low as -300 starts at = -596% Magical Damage Reduction
(It is not confirmed if Bard's Unchained Harmony rolls the loot table when it opens the containers.)


0 Magic Resistance starts at = -10% Magical Damage Reduction
Luck is capped at 500.<br>
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''


Magic Resistance gives % Magical Damage Reduction between intervals
===Luck Scalar===
{{#lsth:Luck|Luck Scalar}}


*-300 to -15 = 2% (capped at -25%)
==Max Spell Count==
*-15 to 10 = 1% -> 0%
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
*10 to 19 = 0.5% -> 4.5%
*19 to 40 = 0.3% -> 11.9%
*40 to 50 = 0.2% -> 13.9%
*50 to 100 = 0.1% -> 18.9%
*100 to 150 = 0.2% -> 28.9%
*150 to 250 = 0.3% -> 58.9%
*250 to 350 = 0.2% -> 78.9%
*350 to 500 = 0.1% -> 93.9%


=Enchantment Stats=
Stats that come from weapons, armors or jewelry imbued with item [[Enchantments]].


==Physical Power Bonus==
{{Transclude|Enchantments#Enchantment Exclusive Stats}}
0 Physical Power Bonus starts at = -80% Physical Power Bonus


Every Physical Power Bonus gives % increase to your overall physical power
For the possible values of Enchantments and their historical rolls, see [[Enchantments#Enchantment_Values|Enchantment Values]]


*0 to 5 = 10% (capped at -30%)
=Unimplemented Stats=
*5 to 7 = 5% -> -20%
These stats are not yet implemented.
*7 to 11 = 3% -> -8%
==Utility Effectiveness Bonus==
*11 to 15 = 2% -> 0%
Determines the bonus effectiveness of your utility items
*15 to 50 = 1% -> 35%
*50 to 100 = 0.5% -> 60%

Latest revision as of 02:23, 26 June 2024


Information is up to date! Hover for more details.Stats Data last updated on: Patch:6.5#Hotfix 54-1.
Dark and Darker is currently on update: Patch:6.5#Hotfix 54-1.

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

Stats

Stats modify your character while equipped. Weapons/Consumables 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.

See exact changes to Stats here Patch:6.4#Stat_Curve_Changes

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

Stats that come from character's attributes.

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. 

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. 

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.

Capped to -100%

Max Health from Strength

Max Health determines your characters maximum Health.

Strength increases Max Health with 25% Scaling. See the Hybrid stat Max Health for more.


Vigor

Max Health from Vigor

Max Health determines your characters maximum Health.

Vigor increases Max Health with 75% Scaling. See the Hybrid stat Max 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

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. 

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.

Agility increases Action Speed with 25% Scaling. See the Hybrid stat Action Speed for more.

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 = 40%.

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. 

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 Movement speed

Regular Interaction Speed from Agility

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

Agility increases Regular Interaction Speed with 40% Scaling. 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.

Dexterity increases Action Speed with 75% Scaling. See the Hybrid stat Action Speed for more.

Manual Dexterity

Manual Dexterity determines how quickly Bard plays an instrument.

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. 

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.


Item Equip Speed

Item Equip Speed exclusively governs the speed at which you equip armors, as equipping weapons, jewelry and utility items is instant.

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. 

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

Magic 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. 

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. 

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 20 = 4 each, up to 50
  • 20 to 28 = 5 each, up to 90
  • 28 to 38 = 4 each, up to 130
  • 38 to 48 = 3 each, up to 160
  • 48 to 58 = 2 each, up to 180
  • 58 to 100 = 1 each, up to 222

LaTeX Formula

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

Triple click to select all. 

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}<20:30+4\left|W_{ill}-15\right|,20 \le W_{ill}<28:50+5\left|W_{ill}-20\right|,28 \le W_{ill}<38:90+4\left|W_{ill}-28\right|,38 \le W_{ill}<48:130+3\left|W_{ill}-38\right|,48 \le W_{ill}<58:160+2\left|W_{ill}-48\right|,58 \le W_{ill}<100:180+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. 

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 75%

Buff Duration

Buff Duration governs the duration of temporary beneficial status effects.

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. 

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 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.

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. 

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. 

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. 

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. 

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, +8 Add Memory Cap, and 7.7% Memory Cap Bonus, the final Memory Capacity will be

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

Memory Recovery

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

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. 

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.

Resourcefulness increases Regular Interaction Speed with 60% Scaling. 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 buff/debuff and are additionally affected by Buff/Debuff Duration.

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

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. 

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. 

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:

Scaling x Persuasiveness

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 there are noted to not scale with Persuasiveness, 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 have 4.5x scaling and if Bard has 20 Persuasiveness, outgoing buff duration will be:

4.5 x 20 = 90 seconds

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

Buff Duration Calculator

Hybrid Stats

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

Max Health

Max Health determines your characters maximum Health.

Strength and Vigor governs your Max Health.

Strength has 25% scaling, and Vigor has 75% scaling, which then get combined into a Sum and translated into MaxHealth.

Sum = Strength * 0.25 + Vigor * 0.75


0 Sum starts at 75 Max Health.

  • 0 -> 75
  • 0 to 10 = 3 each, up to 105
  • 10 to 50 = 2 each, up to 185
  • 50 to 75 = 1 each, up to 210
  • 75 to 100 = 0.5 each, up to 222.5

LaTeX Formula

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

Triple click to select all. 

M_{axHealth}(S_{um})=\left\{0 \le S_{um}<10:75+3\left|S_{um}-0\right|,10 \le S_{um}<50:105+2\left|S_{um}-10\right|,50 \le S_{um}<75:185+1\left|S_{um}-50\right|,75 \le S_{um}<100:210+0.5\left|S_{um}-75\right|\right\}

See Example for how to use.


Final Max 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 has 25% scaling, and Dexterity has 75% scaling, which then get combined into a Sum and translated into ActionSpeed.

Sum = Agility * 0.25 + Dexterity * 0.75


0 Sum 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. 

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 has 40% scaling, and Resourcefulness has 60% scaling, which then get combined into a Sum and translated into RegularInteractionSpeed.

Sum = Agility * 0.4 + Resourcefulness * 0.6


0 Sum 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. 

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 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 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 (x 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 = 0.3% each, up to 48%
  • 230 to 317 = 0.2% each, up to 65.4%
  • 317 to 353 = 0.1% each, up to 69%
  • 353 to 368 = 0.05% each, up to 69.75%
  • 368 to 369 = 0.03% each, up to 69.78%
  • 369 to 370 = 0.07% each, up to 69.85%
  • 370 to 428 = 0.05% each, up to 72.75%
  • 428 to 429 = -0.075% each, up to 72.675%
  • 429 to 450 = 0.025% each, up to 73.2%
  • 450 to 500 = 0.02% each, up to 74.2%

LaTeX Formula

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

Triple click to select all. 

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}<317:0.48+0.002\left|A_{rmorRating}-230\right|,317 \le A_{rmorRating}<353:0.654+0.001\left|A_{rmorRating}-317\right|,353 \le A_{rmorRating}<368:0.69+0.001\left|A_{rmorRating}-353\right|,368 \le A_{rmorRating}<369:0.698+0\left|A_{rmorRating}-368\right|,369 \le A_{rmorRating}<370:0.698+0.001\left|A_{rmorRating}-369\right|,370 \le A_{rmorRating}<428:0.699+0.001\left|A_{rmorRating}-370\right|,428 \le A_{rmorRating}<429:0.728+-0.001\left|A_{rmorRating}-428\right|,429 \le A_{rmorRating}<450:0.727+0\left|A_{rmorRating}-429\right|,450 \le A_{rmorRating}<500:0.732+0\left|A_{rmorRating}-450\right|\right\}

See Example for how to use.


Physical Damage Reduction is capped to 75%

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.

Luck

Loot is rolled when you open the container or kill the mob.

Whoever opens the loot first or kills the mob first is the person whose luck is used to calculate the drops.
(It is not confirmed if Bard's Unchained Harmony rolls the loot table when it opens the containers.)

Luck is capped at 500.
It is possible to reach the Luck cap:

Luck Scalar

Luck Scalars are 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/Probabilities from Luck subsection for an in-depth explanation of how Luck Scalars affect probabilities of drops.

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. 

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. 

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. 

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. 

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. 

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. 

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. 

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. 

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.


Could not find stat in Template:Stats_Data

LaTeX Formula

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

Triple click to select all. Could not find stat in Template:Stats_Data 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

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 Healing Increases True Physical Healing performed
Magical Healing Increases True Magical 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 Multiplier 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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