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(→‎Probabilities from Luck: Colored Luck Scalars)
(→‎Move Speed: Note about adding the base 300 Move Speed to the chart value for actual Move Speed)
 
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<metadesc>Dark and Darker Wiki Stats Guide</metadesc>
<metadesc>Dark and Darker Wiki Stats Guide</metadesc>
{{UpdateStatus|Stats Data}}
{{MechanicsBar}}


<p style="width: 100%;border: 1px solid #DD952A;text-align: center;font-size: 24px;padding: 3px;font-weight: bold;margin: 9px;border-radius: 10px;">Stats are currently up to date for: {{:TODO|Stats}}</p>
=Stats=
Stats are primarily modified through the gear your character has equipped. [[Weapons]]/[[utilities]] only modify your character while held. For example, holding a Main-Hand and Off-Hand weapon in the first weapon slot will give each other weapon their stats, but neither will benefit from the stats of the weapon(s) in the second slot. Similarly, the bonuses from a [[Flute]] are only granted while wielding the Flute. Stats from these sources will not be reflected in the Lobby.
 
Stats may also be modified by perks, [[buffs]], and [[debuffs]]. Stats from perks will be reflected in the Lobby only if those stats are applied unconditionally. Stats from conditional perks (as well as buffs and debuffs) will not be viewable from the Lobby.


==Charts==
==Charts==
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=Attributes=
=Attributes=
Stats that come from character's attributes.
Main stats that affect multiple other stats. Each [[class]] has varying base attributes, but they sum up to 105 for each class. Can be found as primary stats (stats which are always present on an item of the same name regardless of rarity or instance such as Strength on a [[Padded Tunic]]) as well as [[enchantments]].
 
==Strength==
==Strength==
===Physical Power===
===Physical Power===
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===Physical Power Bonus===
===Physical Power Bonus===
- More recently known as Physical Damage Bonus,
<span id="Physical Damage Bonus">
Physical Power Bonus governs the potency of your physical damage dealing weapons, utility items, and abilities.
Also known as Physical Damage Bonus, Physical Power Bonus governs the potency of your physical damage dealing weapons, utility items, and abilities.
{{Stats Data|physicalpowerbonus}}
{{Stats Data|physicalpowerbonus}}</span>


Capped to -100%
Lower limit of -100%.


===Max Health from Strength===
===Base Health from Strength===
Max Health determines your characters maximum [[Health]].
Base Health determines your characters maximum [[Health]].


Strength increases Max Health with 25% Scaling. See the Hybrid stat [[Stats#Max_Health|Max Health]] for more.
See the Hybrid stat [[Stats#Base_Health|Base Health]] for more.




==Vigor==
==Vigor==
===Max Health from Vigor===
===Base Health from Vigor===
Max Health determines your characters maximum [[Health]].
Base Health determines your characters maximum [[Health]].


Vigor increases Max Health with 75% Scaling. See the Hybrid stat [[Stats#Max_Health|Max Health]] for more.
See the Hybrid stat [[Stats#Base_Health|Base Health]] for more.




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<code>Health Recovered every 2s = 1 * (1 + .95) = 1.95 Health</code>
<code>Health Recovered every 2s = 1 * (1 + .95) = 1.95 Health</code>
Can't be found on gear aside from in the form of its governing attribute.


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


Agility increases Action Speed with 25% Scaling. See the Hybrid stat [[Stats#Action_Speed|Action Speed]] for more.
See the Hybrid stat [[Stats#Action_Speed|Action Speed]] for more.


===Move Speed===
===Move Speed===
Move Speed governs the speed at which your character moves. This stat is also directly influenced by wearing gear. Every 1 point in Move Speed is equal to 0.3333...% Move Speed. The default Move Speed for each class is 300, which translates to 100% Move Speed, with penalties or bonuses provided based on Agility. Performing certain actions, such as attacking, or moving in certain directions will also affect Move Speed. Backwards = 60%, Crouch = 60%, Walk = 60%.  
Move Speed governs the speed at which your character runs or walks. Every 3 points in Move Speed is equal to 1% movement speed. There are many factors which can affect Move Speed, see [[Movement Speed]] for details.
 
To calculate total Move Speed, add the baseline 300 Move Speed to the appropriate value below.
{{Stats Data|movespeed}}
{{Stats Data|movespeed}}


'''Hard capped to 350 Movement speed'''
'''Hard capped to 330 Move Speed'''


===Regular Interaction Speed from Agility===
===Regular Interaction Speed from Agility===
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
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 [[Stats#Regular_Interaction_Speed|Regular Interaction Speed]] for more.
See the Hybrid stat [[Stats#Regular_Interaction_Speed|Regular Interaction Speed]] for more.


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


Dexterity increases Action Speed with 75% Scaling. See the Hybrid stat [[Stats#Action_Speed|Action Speed]] for more.
See the Hybrid stat [[Stats#Action_Speed|Action Speed]] for more.


===Manual Dexterity===
===Manual Dexterity===
Manual Dexterity determines how quickly Bard plays an instrument.
Manual Dexterity determines how quickly Bard plays an instrument.
Can't be found on gear aside from in the form of its governing attribute.
{{Stats Data|manualdexterity}}
{{Stats Data|manualdexterity}}
Capped to 50%.


===Item Equip Speed===
===Item Equip Speed===
Item Equip Speed exclusively governs the speed at which you equip armors, as equipping weapons, jewelry and utility items is instant.
Item Equip Speed adjusts the speed at which you equip all Armors, Ranged Weapons, and Throwable/Percussion/"explosive Light Source" Utility items.
 
All other items such as Jewelry, Melee Weapons, Shields, and Consumable/Drink/"non-exploding Light Source" Utility items are instantly equipped.
 
Can't be found on gear aside from in the form of its governing attribute.
 
{{Stats Data|itemequipspeed}}
{{Stats Data|itemequipspeed}}


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


===Magic Power Bonus===
===Magic Power Bonus===
<span id="Magical Damage Bonus">
Also known as Magical Damage Bonus, though contrary to this alternative name, it affects [[Healing]] too.</span>
<span id="Magical Power Bonus">
Magic Power bonus governs the potency of your magical spells, magical damage dealing abilities and magical healing abilities.
Magic Power bonus governs the potency of your magical spells, magical damage dealing abilities and magical healing abilities.
{{Stats Data|magicalpowerbonus}}
{{Stats Data|magicalpowerbonus}}</span>
 


===Magic Resistance===
===Magical Resistance===
<span id="Magic Resistance">
Magic Resistance governs your Magical Damage Reduction.
Magic Resistance governs your Magical Damage Reduction.
{{Stats Data|magicresistance}}
{{Stats Data|magicresistance}}</span>


===Magical Damage Reduction===
===Magical Damage Reduction===
Magical Damage Reduction governs your resistance to magical damage dealing weapons, spells and projectiles. Please note that there is currently a bug where Magical Damage Reduction is additively 10% lower than the following expected amounts.
<span id="Magic Damage Reduction">Magical Damage Reduction governs your resistance to magical damage dealing weapons, spells and projectiles.
{{Stats Data|magicaldamagereduction}}
{{Stats Data|magicaldamagereduction}}


Magical Damage Reduction is capped to 85%
Magical Damage Reduction is capped to 65%</span>
 
=== Buff Duration ===
Buff Duration modifies the duration of any temporary beneficial status effects you have.


===Buff Duration===
Buff Duration does not modify buffs you apply to others.
Buff Duration governs the duration of temporary beneficial status effects.
{{Stats Data|buffduration}}
{{Stats Data|buffduration}}


===Debuff Duration===
===Debuff Duration===
Debuff Duration governs the duration of temporary negative status effects. A negative Debuff Duration is beneficial to have, as it will shorten the duration of debuffs. A positive Debuff Duration stat means debuffs last longer, which is detrimental to the player.
Debuff Duration modifies the duration of temporary negative status effects; a negative value will shorten the duration, which is beneficial, and vise versa.  
 
Debuff Duration does not modify debuffs you apply to others.
{{Stats Data|debuffduration}}
{{Stats Data|debuffduration}}


===Magical Interaction Speed===
Debuff Duration has a lower cap of -95%, meaning at minimum a debuff can last 1/20th of its base 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.
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}}
{{Stats Data|magicalinteractionspeed}}
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Note that the Debuff Duration Bonus enchant converts into a negative Debuff Duration, decreasing the duration of debuffs on you.
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 [[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.  
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>


==Knowledge==
==Knowledge ==
===Spell Casting Speed===
===Spell Casting Speed===
Spell Casting Speed governs the speed at which you cast magical spells. See [[Action/Interaction/Cast_Speed]] for more.
Spell Casting Speed governs the speed at which you cast magical spells. See [[Action/Interaction/Cast_Speed]] for more.
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<code>Spell Casting Time = (Base Casting Time)/(1 + Spell Casting Speed)</code>
<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 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.
* A Spell Casting Speed of 100% results in the casting time lasting for only 50% of the base casting time.




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


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


<code> ceil(12 * 1.077) + 8 = 21 Memory Capacity</code>
<code> ceil(12 * 1.077) + 8 = 21 Memory Capacity</code>
<!-- class="nowrap" will not work for me no matter what I attempt -->
{| class="wikitable mw-collapsible mw-collapsed" style="text-align: center;"
|+ class="nowrap" |Knowledge vs Memory Capacity Bonus<!--Formula = RoundUP( ((0.5 + n-1) / Knowledge (-6))*1000) /1000 -->
!Classes!!Knowledge (-6)!!(+1)!!(+2) !! (+3)!!(+4)!!(+5)!! (+6)!!(+7)!!(+8)!! (+9)!!(+10)!!(+11)!!(+12)
|-
| Warlock || <small>15</small> <big>(9)</big>|| 5.6%||16.7%||27.8%||38.9%||50.0%||61.2%|| || || || || ||
|-
| || <small>16</small> <big>(10)</big>||5.0%||15.0%||25.0%||35.0%||45.0%||55.0%||65.0%|| || || ||N/A||
|-
| ||<small>17</small> <big>(11)</big>||4.6%|| 13.7%|| 22.8%|| 31.9%|| 41.0% || 50.0%
|59.1%||68.2%|| || || ||
|-
| ||<small>18</small> <big>(12)</big>||4.2%|| 12.5%|| 20.9%|| 29.2%|| 37.5%|| 45.9% ||54.2%||62.5%|| || || ||
|-
| ||<small>19</small> <big>(13)</big>||3.9% || 11.6% || 19.3% || 27.0% || 34.7% || 42.4% || 50.0% || 57.7% || 65.4% || || ||
|-
|Bard/Cleric/Druid||<small>20</small> <big>(14)</big>||3.6%||10.8%||17.9%||25.0%||32.2%||39.3%||46.5%||53.6%||60.8%||67.9%|| ||
|-
| ||<small>21</small> <big>(15)</big>||3.4%|| 10.0%|| 16.7%|| 23.4%|| 30.0%|| 36.7%|| 43.4%|| 50.0%|| 56.7%|| 63.4%|| 70.0%||
|-
| ||<small>22</small> <big>(16)</big>||3.2%||9.4%|| 15.7%|| 21.9%|| 28.2%|| 34.4%|| 40.7%|| 46.9%|| 53.2%|| 59.4%||65.7%||
|-
| ||<small>23</small> <big>(17)</big>||3.0%||8.9%||14.8%||20.6%||26.5%||32.4%||38.3%||44.2%||50.0%||55.9%||61.8%||67.7%
|-
| ||<small>24</small> <big>(18)</big>||2.8% ||8.4% ||13.9% ||19.5% ||25.0% ||30.6% ||36.2% ||41.7% ||47.3% ||52.8% ||58.4% ||63.9%
|-
| Wizard||<small>25</small> <big>(19)</big>||2.7%||7.9%||13.2%||18.5%||23.7%||29.0%||34.3%||39.5%||44.8%||50.0%||55.3%||60.6%
|-
| ||<small>26</small> <big>(20)</big>||2.5%||7.5%||12.5%||17.5%||22.5%||27.5%||32.5%||37.5%||42.5%||47.5%||52.5%||57.5%
|-
| ||<small>27</small> <big>(21)</big>||2.4%||7.2%||12.0%||16.7%||21.5%||26.2%||31.0%||35.8%||40.5%||45.3%||50.0%||54.8%
|-
| ||<small>28</small> <big>(22)</big>||2.3%||6.9%||12.5%||16.0%||20.5%||25.0%||29.6%||34.1%||38.7%||43.2%||47.8%||52.3%
|-
| ||<small>29</small> <big>(23)</big>||2.2%||6.6%||10.9%||15.3%||19.6%||24.0%||28.3%||32.7%||37.0%||41.4%||45.7%||50.0%
|-
| ||<small>30</small> <big>(24)</big>||2.1%||6.3%||10.5%||14.6%||18.8%||23.0%||27.1%||31.3%||35.5%||39.6%||43.8%||48.0%
|-
| ||<small>31</small> <big>(25)</big>||2.0%||6.0%||10.0%||14.0%||18.0%||22.0%||26.0%||30.0%||34.0%||38.0%||42.0%||46.0%
|-
| ||<small>32</small> <big>(26)</big>||2.0%||5.8%||9.7%||13.5%||17.4%||21.2%||25.0%||28.9%||32.7%||36.6%||40.4%||44.3%
|-
| ||<small>33</small> <big>(27)</big>||1.9% ||5.6% ||9.3%||13.0%||16.7%||20.4%||24.1%||27.8%||31.5%||35.2%||38.9%|| 42.6%
|-
| ||<small>34</small> <big>(28)</big>||1.8% ||5.4% ||9.0%||12.5%||16.1%||19.7%||23.3%||26.8%||30.4%||34.0%||37.5%|| 41.1%
|-
| ||<small>35</small> <big>(29)</big>||1.8% ||5.2% ||8.7%||12.1%||15.6%||19.0%||22.5%||25.9%||29.4%||32.8%||36.3%||39.7%
|-
| ||<small>36</small> <big>(30)</big>||1.7%||5.0%||8.4%||11.7%||15.0%||18.4%||21.7%||25.0%
|28.4% ||31.7%||35.0%||38.4%
|}


===Memory Recovery===
===Memory Recovery===
Increases the amount of [[Spell_Restoration|Spell/(Skill?) Points]] (SP) you restore per tick.  
Increases the amount of [[Spell_Restoration|Spell/(Skill?) Points]] (SP) you restore per tick.  
Despite also being referred to as Spell Recovery Bonus, this also applies to Bard songs.
Can't be found on gear aside from in the form of its governing attribute.


{{Stats Data|memoryrecovery}}
{{Stats Data|memoryrecovery}}
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Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
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 [[Stats#Regular_Interaction_Speed|Regular Interaction Speed]] for more.
See the Hybrid stat [[Stats#Regular_Interaction_Speed|Regular Interaction Speed]] for more.
 
===Cooldown Reduction===
Cooldown Reduction reduces the cooldowns of skills/perks.
 
<code>Reduced cooldown length = Base Cooldown * (1 - Cooldown Reduction)</code><br><br>
 
Note that perk cooldowns are in the form of a debuff and are additionally affected by [[Stats#Buff_Duration|Buff]]/[[Stats#Debuff_Duration|Debuff Duration]].<br>
 
<code>Reduced cooldown length = Post buff/debuff duration cooldown * (1 - Cooldown Reduction)</code>
 
Can't be found on gear aside from in the form of its governing attribute.
 
{{Stats_Data|cooldownreduction}}


===Persuasiveness===
===Persuasiveness===
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Base buff duration formula:
Base buff duration formula:


<code>Scaling x Persuasiveness</code>
<code>Base Duration x (Persuasiveness/Base Persuasiveness) x Persuasiveness Scaling</code>
 
<br>Base Persuasiveness is currently 15 due to [[Bard]]'s 15 Resourcefulness.
 
Each point in Persuasiveness over the base of 15 grants a 6.66% longer base duration.<br>
 
The duration listed both in game and in a song's description at [[Bard]] represent the duration of the song at the base of 15 Persuasiveness. Some songs are noted as 0% Persuasiveness Scaling, meaning they always last the listed amount, before Buff/Debuff duration. Some songs technically apply no duration or their affect lasts only while Channeling, like Peacemaking and Chaotic Discord.
 
For example, Perfectly played Rousing Rhythms has a 90s duration (as of writing this) there if Bard has 20 Persuasiveness, outgoing base buff duration will be:
 
<code>90 x 20/15 x 100% = 120 seconds</code>
 
This will also then get multiplied by the receiver's [[Stats#Buff_Duration|Buff Duration]]/[[Stats#Debuff_Duration|Debuff Duration]]
 
Can't be found on gear aside from in the form of its governing attribute.
 
[https://www.desmos.com/calculator/ouiuljvzua Buff Duration Calculator]
 
==Attribute Bonus==
Attributes can be multiplied by sources such as [[Warlock]]'s Curse of Weakness, or [[Wizard]]'s Sage perk. These multipliers are applied after all other sources of additional attributes.


Each point in Persuasiveness over the base of 15 grants a 6.66% longer base duration.
<code>Final Attribute = Attribute * (1 + Attribute Bonus)</code>


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


<code>4.5 x 20 = 90</code> seconds
<code>Final Strength = 30 * (1 + 0.15) = 34.5 Strength</code>


This will also get multiplied by the receiver's [[Stats#Buff_Duration|Buff Duration]]/[[Stats#Debuff_Duration|Debuff Duration]]
Note that attributes can have decimals, though in the in game details page they will be rounded.


[https://www.desmos.com/calculator/sihhlsxqnt Buff Duration Calculator]
<br>''Not to be confused with Attribute Bonus Ratio ([[Scaling]])''


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


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


{{Stats Data|maxhealth}}
==Base Health==
<span id="Max Health">Base Health partially determines your characters maximum [[Health]].<span> <!--Hyperlink redirect from Stats#Max Health]]-->


Final Max Health formula with examples can be found on the [[Health]] page.
{{Stats Data|basehealth}}


==Action Speed==
Final Health formula with examples can be found on the [[Health#Formula|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.
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.


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For example, an Interaction Speed of 100% results in the interaction time lasting for only 50% of the base interaction length.
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
[[Surgical Kit|Surgical Kits]] and [[Bandage|Bandages]] have 50% [[Scaling]] on regular interaction speed, therefore, their formula looks like


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


==Physical Damage Reduction==
==Armor Rating==
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 (AR) is determined from the armor your wearing, but can also be increased in some ways such as [[Fighter]]'s Barricade (Armor Rating) or [[Fighter]]'s Defense Mastery (Armor Rating Bonus).
{{Stats Data|physicaldamagereduction}}
<br><br>
 
Physical Damage Reduction is capped to 75%
 
==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.
 
==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.<br>
(It is not confirmed if Bard's Unchained Harmony rolls the loot table when it opens the containers.)
 
Luck is capped at 500.<br>
It is possible to get maximum of 450 Luck in the game currently:
*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]]
*200 from [[Enchantments#Table_of_Enchantment_Values|max enchantment rolls]] on other gear
 
===Luck Scalar===
Luck Scalars are one piece of information needed to calculate drop probability at X Luck.<br>
The calculation is not a simple multiplication, so do not expect Uniques to be 4.382 times more common at 500 Luck.<br>
The true effect of Luck varies depending on Drop Rate tables and Loot Drop tables.
 
<div style="display:inline-block; width:740px; vertical-align:top;">
Luck Scalar Table
{| cellspacing="0" class="wikitable" style="text-align:center; text-shadow:0px 0px 4px #000;"
|- style="font-weight:bold; background-color:#FFF3;"
|Luck || 0 || 50 || 100 || 150 || 200 || 250 || 300 || 350 || 400 || 450 || 500
|- style="background-color:#FFF1;"
| style="font-weight:bold; background-color:#FFF2;" | <span class="colorrarity0">Junk</span> || 1.000 || 0.950 || 0.900 || 0.850 || 0.800 || 0.750 || 0.700 || 0.650 || 0.600 || 0.550 || 0.500
|-
| style="font-weight:bold; background-color:#FFF3;" | <span class="colorrarity1">Poor</span> || 1.000 || 0.950 || 0.900 || 0.850 || 0.800 || 0.750 || 0.700 || 0.650 || 0.600 || 0.550 || 0.500
|- style="background-color:#FFF1;"
| style="font-weight:bold; background-color:#FFF2;" | <span class="colorrarity2">Common</span> || 1.000 || 0.975 || 0.950 || 0.925 || 0.900 || 0.875 || 0.850 || 0.825 || 0.800 || 0.775 || 0.750
|-
| style="font-weight:bold; background-color:#FFF3;" | <span class="colorrarity3">Uncommon</span> || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000
|- style="background-color:#FFF1;"
| style="font-weight:bold; background-color:#FFF2;" | <span class="colorrarity4">Rare</span> || 1.000 || 1.476 || 1.901 || 2.277 || 2.602 || 2.878 || 3.103 || 3.279 || 3.404 || 3.480 || 3.505
|-
| style="font-weight:bold; background-color:#FFF3;" | <span class="colorrarity5">Epic</span> || 1.000 || 1.547 || 2.036 || 2.468 || 2.842 || 3.159 || 3.418 || 3.620 || 3.765 || 3.751 || 3.881
|- style="background-color:#FFF1;"
| style="font-weight:bold; background-color:#FFF2;" | <span class="colorrarity6">Legendary</span> || 1.000 || 1.618 || 2.171 || 2.659 || 3.083 || 3.441 || 3.734 || 3.962 || 4.125 || 4.223 || 4.257
|-
| style="font-weight:bold; background-color:#FFF3;" | <span class="colorrarity7">Unique</span> || 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 [https://www.desmos.com/calculator/bjmdlsym5d desmos graph].
The desmos graph displays the LaTeX equations which are continuous curves, but keep in mind that fractional values of Luck do not exist.
</div><div style="display:inline-block; width:500px; height:410px; border-left:20px solid #0000;">
Luck Scalar Graph
<tabber>
|-|0=
{{Stats_Data|luckgrade00}}
 
|-|1=
{{Stats_Data|luckgrade01}}
 
|-|2=
{{Stats_Data|luckgrade02}}
 
|-|3=
{{Stats_Data|luckgrade03}}
 
|-|4=
{{Stats_Data|luckgrade04}}
 
|-|5=
{{Stats_Data|luckgrade05}}
 
|-|6=
{{Stats_Data|luckgrade06}}
 
|-|7=
{{Stats_Data|luckgrade07}}
</tabber>
</div>
 
===Loot Drop Tables and Drop Rate Tables===
 
Each drop instance makes use of three pieces of information: the Loot Drop table, the Drop Rate table, and the player's luck.
 
Loot Drop tables list all possible items for a specific drop instance, and for each item therein it associates a Luck Grade.<br>
Drop Rate tables assign a "rate" to each Luck Grade; when normalized, these rates represent the probability of getting a drop of that Luck Grade.
 
Each Luck Grade's drop rate is split evenly between items that share that Luck Grade. This means that items sharing a Loot Drop table and Luck Grade, will always have the same probability of dropping.<br>
However, be aware that Monsters and Containers can have multiple Loot Drop Tables, each with their own Drop Rate table.  See [[Lich#Loot_Tables|Lich]] for example.
 
A Drop can be rolled more than once, but each roll is independent of the others.<br>
Lich rolls their gear Loot and Drop tables twice, theoretically making it possible (though extremely unlikely) to get two Artifacts from a single HR Lich kill.


===Probabilities from Luck===
Formula can be simplified as:<br>
To calculate the drop rate at X Luck there are three steps.<br>
<code>Final Armor Rating = Armor Rating * (1 + Armor Rating Bonus)</code>
# For each Luck Grade's Drop Rate apply the corresponding Luck Scalar.<br>
# Find the dot product between the Luck Scalar vector at X Luck and the Base Rate.<br>(This is the same as adding up each term from the first step.)<br>
# For each term in the first step divide by the dot product from the second step to get the new drop rate at X Luck.
<tabber>
|-|Quest Drop Example=
The table below is the Drop Rate table of Quest Drops.


Every monster with a quest drop uses the Drop Rate table.<br>
However, depending on the monster's Loot Drop Table, many of the Luck Grade rates will be associated with dropping nothing.


And in other instances, like [[Demon_Centaur#250-1|Demon Centaur]], a Luck Grade's rate may be split between two Loot Drops.<br>
Note that [[Fighter]]'s Defense Mastery and [[Rogue]]'s Weakpoint Attack are specifically Item Armor Rating Bonus, meaning they only affect the AR from Items (excluding enchants), where the following formula should be applied.<br>
This will not affect the calculations below, but they will determine an individual item's probability.


{| cellspacing="0" class="wikitable" style="text-align:center; text-shadow:0px 0px 4px #0008;"
<code>Final Armor Rating = Armor Rating from armor * (1 + Item Armor Rating Bonus) + other Armor Rating * (1 + Armor Rating Bonus)</code>
|- style="font-weight:bold; background-color:#FFF4;"
|Luck Grade ||Drop Rate
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||220
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||250
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||200
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||150
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||100
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||50
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||20
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||10
|}


Drop Rate tables generally sum to a power of ten.  Since the Luck Scalars are simply 1 at 0 Luck, the probability calculation is trivial.


At 0 Luck, the dot product is
Note that only Item Armor Rating Bonus exists currently, and not Armor Rating Bonus. Therefore, the shortest form of this expanded formula can be written as:


{{#tag:math|\color{White}
<code>Final Armor Rating = Armor Rating from armor * (1 + Item Armor Rating bonus) + other Armor Rating</code>
{\color[RGB]{50, 50, 50}1.000} \cdot 220 +
{\color[RGB]{100, 100, 100}1.000} \cdot 250 +
{\color[RGB]{222, 222, 222}1.000} \cdot 200 +
{\color[RGB]{98, 190, 11}1.000} \cdot 150 +
{\color[RGB]{74, 155, 209}1.000} \cdot 100 +  
{\color[RGB]{173, 90, 255}1.000} \cdot 50 +  
{\color[RGB]{247, 162, 45}1.000} \cdot 20 +
{\color[RGB]{227, 216, 140}1.000} \cdot 10 = 1000}}


{| cellspacing="0" class="wikitable" style="text-align:center; text-shadow:0px 0px 4px #0008;"
|- style="font-weight:bold; background-color:#FFF4;"
|Luck Grade ||Drop Probability at 0 Luck
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}1.000} \cdot 220}{1000}=22\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}1.000} \cdot 250}{1000}=25\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}1.000} \cdot 200}{1000}=20\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000} \cdot 150}{1000}=15\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}1.000} \cdot 100}{1000}=10\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}1.000} \cdot 50}{1000}=5\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}1.000} \cdot 20}{1000}=2\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}1.000} \cdot 10}{1000}=1\%}}
|}


<p style="font-size:18px; width:fit-content; border:1px solid #DD952A; border-radius:15px; padding:7px;">Click expand to see the calculations for 250 and 500 Luck.<p>
Example using the last formula:<br>
With 100 AR from equipped Items, 20 from [[Enchantments]], and -40% Item Armor Rating Bonus, the player would result in<br>


<div class="mw-collapsible mw-collapsed" style="width: fit-content">
<code>100 * (1 + -0.4) + 20 = 80 Armor Rating</code>
<div class="mw-collapsible-content">
<br>
<br>
At 250 Luck, the dot product is


{{#tag:math|\color{White}
== Physical Damage Reduction==
{\color[RGB]{50, 50, 50}0.750} \cdot 220 +
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.
{\color[RGB]{100, 100, 100}0.750} \cdot 250 +
{{Stats Data|physicaldamagereduction}}
{\color[RGB]{222, 222, 222}0.875} \cdot 200 +
{\color[RGB]{98, 190, 11}1.000} \cdot 150 +
{\color[RGB]{74, 155, 209}2.878} \cdot 100 +
{\color[RGB]{173, 90, 255}3.125} \cdot 50 +
{\color[RGB]{247, 162, 45}3.441} \cdot 20 +
{\color[RGB]{227, 216, 140}3.535} \cdot 10 = 1227.42}}
 
{| cellspacing="0" class="wikitable" style="text-align:center; text-shadow:0px 0px 4px #0008;"
|- style="font-weight:bold; background-color:#FFF4;"
|Luck Grade ||Drop Probability at 250 Luck
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.750} \cdot 220}{1000}=13.443\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.750} \cdot 250}{1000}=15.276\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.875} \cdot 200}{1000}=14.258\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000} \cdot 150}{1000}=12.221\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}2.878} \cdot 100}{1000}=23.448\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.125} \cdot 50}{1000}=12.868\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}3.441} \cdot 20}{1000}=5.607\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}3.535} \cdot 10}{1000}=2.880\%}}
|}
<br>
At 500 Luck, the dot product is


{{#tag:math|\color{White}
Physical Damage Reduction is capped to 65%
{\color[RGB]{50, 50, 50}0.500} \cdot 220 +
{\color[RGB]{100, 100, 100}0.500} \cdot 250 +
{\color[RGB]{222, 222, 222}0.750} \cdot 200 +
{\color[RGB]{98, 190, 11}1.000} \cdot 150 +
{\color[RGB]{74, 155, 209}3.505} \cdot 100 +
{\color[RGB]{173, 90, 255}3.881} \cdot 50 +
{\color[RGB]{247, 162, 45}4.257} \cdot 20 +
{\color[RGB]{227, 216, 140}4.382} \cdot 10 = 1208.51}}


{| cellspacing="0" class="wikitable" style="text-align:center; text-shadow:0px 0px 4px #0008;"
==Impact Power==
|- style="font-weight:bold; background-color:#FFF4;"
[[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 Grade ||Drop Probability at 500 Luck
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.500} \cdot 220}{1000}=9.102\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.500} \cdot 250}{1000}=10.343\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.750} \cdot 200}{1000}=12.412\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000} \cdot 150}{1000}=12.412\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}3.505} \cdot 100}{1000}=29.003\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.881} \cdot 50}{1000}=16.057\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}4.257} \cdot 20}{1000}=7.045\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382} \cdot 10}{1000}=3.626\%}}
|}
</div></div>


|-|Gold Coin Chest Example=
Can't be found on gear (aside from the base values for each weapon) and is not affected by other stats.


The table below is the Drop Rate table of the Gold Coin Chest.
==Item Swap Speed==
Speed at which items are swapped as the current active item. Note that this is separate from Wearing Time Speed.


The Loot Drop table is rather simple. At Luck Grade 0, "Junk", you get nothing.  At Luck Grade 2, "Common", you get 1x Gold Coin Chest.
Affected by [[#Action Speed|Action Speed]].


Notice that despite the [[Gold Coin Chest]]'s item rarity being unique, its Luck Grade is actually Common.<br>
==Wearing Time Speed==
Item Rarity does not equal Luck Grade, despite the two being equal for most items.
Speed at which items are worn by equipping them from the inventory. Note that this is separate from Item Swap Speed.
{| cellspacing="0" class="wikitable" style="text-align:center; text-shadow:0px 0px 4px #0008;"
|- style="font-weight:bold; background-color:#FFF4;"
|Luck Grade ||Drop Rate
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||99900
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||0
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||100
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||0
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||0
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||0
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||0
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||0
|}


At 0 Luck, the dot product is
Affected by [[#Item Equip Speed|Item Equip Speed]].


{{#tag:math|\color{White}
==Luck==
{\color[RGB]{50, 50, 50}1.000} \cdot 99900 +
Luck affects the Loot that is rolled when you open a [[Containers|container]] or kill a [[monster]].
{\color[RGB]{100, 100, 100}1.000} \cdot 0 +
{\color[RGB]{222, 222, 222}1.000} \cdot 100 +
{\color[RGB]{98, 190, 11}1.000} \cdot 0 +
{\color[RGB]{74, 155, 209}1.000} \cdot 0 +
{\color[RGB]{173, 90, 255}1.000} \cdot 0 +
{\color[RGB]{247, 162, 45}1.000} \cdot 0 +
{\color[RGB]{227, 216, 140}1.000} \cdot 0 = 100000}}


{| cellspacing="0" class="wikitable" style="text-align:center; text-shadow:0px 0px 4px #0008;"
Whoever opens the container first or lands the killing blow on the monster is the character whose Luck is used to calculate the drops.
|- style="font-weight:bold; background-color:#FFF4;"
|Luck Grade ||Drop Probability at 0 Luck
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}1.000} \cdot 99900}{100000}=99.9\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}1.000} \cdot 0}{100000}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}1.000} \cdot 100}{100000}=0.1\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000} \cdot 0}{100000}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}1.000} \cdot 0}{100000}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}1.000} \cdot 0}{100000}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}1.000} \cdot 0}{100000}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}1.000} \cdot 0}{100000}=0\%}}
|}


<p style="font-size:18px; width:fit-content; border:1px solid #DD952A; border-radius:15px; padding:7px;">Click expand to see the calculations for 250 and 500 Luck.<p>
Luck is capped at 500.


<div class="mw-collapsible mw-collapsed" style="width: fit-content">
It is possible to reach the Luck cap:
<div class="mw-collapsible-content">
*50 from [[Bard#Perks-0|Bard's Wanderer's Luck]]
<br>
*150 luck roll from a large [[Potion of Luck]]
At 250 Luck, the dot product is
*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''


{{#tag:math|\color{White}
{{NeedsTesting|It is not confirmed if [[Bard#Songs-0|Bard's Unchained Harmony]] applies the Bard's Luck when it opens containers.}}
{\color[RGB]{50, 50, 50}0.750} \cdot 99900 +
{{NeedsTesting|Which character's Luck is used if a monster or the environment kills a monster? Do monsters/traps have Luck? Is loot instead rolled when the monster is first looted?}}
{\color[RGB]{100, 100, 100}0.750} \cdot 0 +
{\color[RGB]{222, 222, 222}0.875} \cdot 100 +
{\color[RGB]{98, 190, 11}1.000} \cdot 0 +
{\color[RGB]{74, 155, 209}2.878} \cdot 0 +
{\color[RGB]{173, 90, 255}3.159} \cdot 0 +
{\color[RGB]{247, 162, 45}3.441} \cdot 0 +
{\color[RGB]{227, 216, 140}3.535} \cdot 0 = 75012.5}}


{| cellspacing="0" class="wikitable" style="text-align:center; text-shadow:0px 0px 4px #0008;"
===Luck Scalar ===
|- style="font-weight:bold; background-color:#FFF4;"
{{#lsth:Luck|Luck Scalar}}
|Luck Grade ||Drop Probability at 250 Luck
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.750} \cdot 99900}{75012.5}=99.883\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.750} \cdot 0}{75012.5}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.875} \cdot 100}{75012.5}=0.117\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000} \cdot 0}{75012.5}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}2.878} \cdot 0}{75012.5}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.159} \cdot 0}{75012.5}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}3.441} \cdot 0}{75012.5}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}3.535} \cdot 0}{75012.5}=0\%}}
|}
<br>
At 500 Luck, the dot product is


{{#tag:math|\color{White}
==Max Spell Count==
{\color[RGB]{50, 50, 50}0.500} \cdot 99900 +
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
{\color[RGB]{100, 100, 100}0.500} \cdot 0 +
{\color[RGB]{222, 222, 222}0.750} \cdot 100 +
{\color[RGB]{98, 190, 11}1.000} \cdot 0 +
{\color[RGB]{74, 155, 209}3.505} \cdot 0 +
{\color[RGB]{173, 90, 255}3.881} \cdot 0 +
{\color[RGB]{247, 162, 45}4.257} \cdot 0 +
{\color[RGB]{227, 216, 140}4.382} \cdot 0 = 50025}}


{| cellspacing="0" class="wikitable" style="text-align:center; text-shadow:0px 0px 4px #0008;"
Can't be found on gear and is not affected by other stats.
|- style="font-weight:bold; background-color:#FFF4;"
|Luck Grade ||Drop Probability at 500 Luck
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.500} \cdot 99900}{50025}=99.850\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.500} \cdot 0}{50025}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.750} \cdot 100}{50025}=0.150\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000} \cdot 0}{50025}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}3.505} \cdot 0}{50025}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.881} \cdot 0}{50025}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}4.257} \cdot 0}{50025}=0\%}}
|-
| style="font-weight:bold; background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382} \cdot 0}{50025}=0\%}}
|}
</div></div>
</tabber>


=Enchantment Stats=
=Enchantment Stats=
Line 591: Line 411:
=Unimplemented Stats=
=Unimplemented Stats=
These stats are not yet implemented.
These stats are not yet implemented.
==Utility Effectiveness==
==Utility Effectiveness Bonus==
Determines the bonus effectiveness of your utility items
Determines the bonus effectiveness of your utility items

Latest revision as of 17:45, 14 November 2024

Information is up to date! Hover for more details.Stats Data last updated on: Patch:6.6#Hotfix 72.
Dark and Darker is currently on update: Patch:6.6#Hotfix 73.

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

Stats

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

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

Charts

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

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

Attributes

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

Strength

Physical Power

Physical Power governs your Physical Power Bonus.

Strength governs your Physical Power.

0 Strength starts at 0 Physical Power.

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

LaTeX Formula

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

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

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

See Example for how to use.


Physical Power Bonus

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

Physical Power governs your Physical Power Bonus.

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

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

LaTeX Formula

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

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

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

See Example for how to use.

Lower limit of -100%.

Base Health from Strength

Base Health determines your characters maximum Health.

See the Hybrid stat Base Health for more.


Vigor

Base Health from Vigor

Base Health determines your characters maximum Health.

See the Hybrid stat Base Health for more.


Health Recovery

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

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

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

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

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

Vigor governs your Health Recovery.

0 Vigor starts at -55% Health Recovery.

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

LaTeX Formula

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

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

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

See Example for how to use.



Agility

Action Speed from Agility

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

See the Hybrid stat Action Speed for more.

Move Speed

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

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

Agility governs your Move Speed.

0 Agility starts at -10 Move Speed.

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

LaTeX Formula

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

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

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

See Example for how to use.


Hard capped to 330 Move Speed

Regular Interaction Speed from Agility

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

See the Hybrid stat Regular Interaction Speed for more.

Dexterity

Action Speed from Dexterity

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

See the Hybrid stat Action Speed for more.

Manual Dexterity

Manual Dexterity determines how quickly Bard plays an instrument.

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

Dexterity governs your Manual Dexterity.

0 Dexterity starts at -15% Manual Dexterity.

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

LaTeX Formula

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

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

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

See Example for how to use.


Capped to 50%.

Item Equip Speed

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

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

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

Dexterity governs your Item Equip Speed.

0 Dexterity starts at -95% Item Equip Speed.

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

LaTeX Formula

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

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

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

See Example for how to use.


Will

Magical Power

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

Will governs your Magical Power.

0 Will starts at 0 Magical Power.

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

LaTeX Formula

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

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

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

See Example for how to use.


Magic Power Bonus

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

Magical Power governs your Magical Power Bonus.

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

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

LaTeX Formula

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

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

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

See Example for how to use.


Magical Resistance

Magic Resistance governs your Magical Damage Reduction.

Will governs your Magic Resistance.

0 Will starts at -20 Magic Resistance.

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

LaTeX Formula

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

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

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

See Example for how to use.

Magical Damage Reduction

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

Magic Resistance governs your Magical Damage Reduction.

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

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

LaTeX Formula

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

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

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

See Example for how to use.


Magical Damage Reduction is capped to 65%

Buff Duration

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

Buff Duration does not modify buffs you apply to others.

Will governs your Buff Duration.

0 Will starts at -80% Buff Duration.

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

LaTeX Formula

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

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

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

See Example for how to use.


Debuff Duration

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

Debuff Duration does not modify debuffs you apply to others.

Will governs your Debuff Duration.

0 Will starts at 400% Debuff Duration.

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

LaTeX Formula

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

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

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

See Example for how to use.


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

Magical Interaction Speed

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

Will governs your Magical Interaction Speed.

0 Will starts at -75% Magical Interaction Speed.

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

LaTeX Formula

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

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

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

See Example for how to use.


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

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

Knowledge

Spell Casting Speed

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

Knowledge governs your Spell Casting Speed.

0 Knowledge starts at -60% Spell Casting Speed.

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

LaTeX Formula

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

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

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

See Example for how to use.


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

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


Memory Capacity

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

Knowledge governs your Memory Capacity.

0 Knowledge starts at 0 Memory Capacity.

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

LaTeX Formula

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

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

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

See Example for how to use.


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

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

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

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


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

Memory Recovery

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

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

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

Knowledge governs your Memory Recovery.

0 Knowledge starts at 43% Memory Recovery.

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

LaTeX Formula

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

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

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

See Example for how to use.


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

Resourcefulness

Regular Interaction Speed from Resourcefulness

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

See the Hybrid stat Regular Interaction Speed for more.

Cooldown Reduction

Cooldown Reduction reduces the cooldowns of skills/perks.

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

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

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

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

Resourcefulness governs your Cooldown Reduction.

0 Resourcefulness starts at -30% Cooldown Reduction.

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

LaTeX Formula

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

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

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

See Example for how to use.


Persuasiveness

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

Resourcefulness governs your Persuasiveness.

0 Resourcefulness starts at 0 Persuasiveness.

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

LaTeX Formula

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

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

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

See Example for how to use.


Base buff duration formula:

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


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

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

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

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

90 x 20/15 x 100% = 120 seconds

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

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

Buff Duration Calculator

Attribute Bonus

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

Final Attribute = Attribute * (1 + Attribute Bonus)


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

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

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


Not to be confused with Attribute Bonus Ratio (Scaling)

Hybrid Stats

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

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

Base Health

Base Health partially determines your characters maximum Health.

Strength and Vigor governs your Base Health.

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

Base Health Rating = Strength * 0.25 + Vigor * 0.75


0 Base Health Rating starts at 60 Base Health.

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

LaTeX Formula

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

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

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

See Example for how to use.


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

Action Speed

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

Agility and Dexterity governs your Action Speed.

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

Action Speed Rating = Agility * 0.25 + Dexterity * 0.75


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

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

LaTeX Formula

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

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

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

See Example for how to use.



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

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


Regular Interaction Speed

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

Agility and Resourcefulness governs your Regular Interaction Speed.

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

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


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

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

LaTeX Formula

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

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

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

See Example for how to use.



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


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

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

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

Other Stats

Armor Rating

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

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


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

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


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

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


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

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

Physical Damage Reduction

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

Armor Rating governs your Physical Damage Reduction.

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

  • -300 -> -619%
  • -300 to -3 = 2% each, up to -25%
  • -3 to 20 = 1% each, up to -2%
  • 20 to 30 = 0.5% each, up to 3%
  • 30 to 45 = 0.4% each, up to 9%
  • 45 to 65 = 0.3% each, up to 15%
  • 65 to 85 = 0.25% each, up to 20%
  • 85 to 170 = 0.2% each, up to 37%
  • 170 to 300 = 0.15% each, up to 56.5%
  • 300 to 353 = 0.1% each, up to 61.8%
  • 353 to 500 = 0.05% each, up to 69.15%

LaTeX Formula

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

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

P_{hysicalDamageReduction}(A_{rmorRating})=\left\{-300 \le A_{rmorRating}<-3:-6.19+0.02\left|A_{rmorRating}--300\right|,-3 \le A_{rmorRating}<20:-0.25+0.01\left|A_{rmorRating}--3\right|,20 \le A_{rmorRating}<30:-0.02+0.005\left|A_{rmorRating}-20\right|,30 \le A_{rmorRating}<45:0.03+0.004\left|A_{rmorRating}-30\right|,45 \le A_{rmorRating}<65:0.09+0.003\left|A_{rmorRating}-45\right|,65 \le A_{rmorRating}<85:0.15+0.003\left|A_{rmorRating}-65\right|,85 \le A_{rmorRating}<170:0.2+0.002\left|A_{rmorRating}-85\right|,170 \le A_{rmorRating}<300:0.37+0.001\left|A_{rmorRating}-170\right|,300 \le A_{rmorRating}<353:0.565+0.001\left|A_{rmorRating}-300\right|,353 \le A_{rmorRating}<500:0.618+0.001\left|A_{rmorRating}-353\right|\right\}

See Example for how to use.


Physical Damage Reduction is capped to 65%

Impact Power

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

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

Item Swap Speed

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

Affected by Action Speed.

Wearing Time Speed

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

Affected by Item Equip Speed.

Luck

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

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

Luck is capped at 500.

It is possible to reach the Luck cap:


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


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


Luck Scalar

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

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

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

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

Luck Scalar Table

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

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

Luck Scalar Graph

LaTeX Formula

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

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

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

See Example for how to use.


LaTeX Formula

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

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

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

See Example for how to use.


LaTeX Formula

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

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

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

See Example for how to use.


LaTeX Formula

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

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

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

See Example for how to use.


LaTeX Formula

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

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

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

See Example for how to use.


LaTeX Formula

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

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

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

See Example for how to use.


LaTeX Formula

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

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

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

See Example for how to use.


LaTeX Formula

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

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

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

See Example for how to use.


LaTeX Formula

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

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

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

See Example for how to use.



Max Spell Count

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

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

Enchantment Stats

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

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

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

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

Unimplemented Stats

These stats are not yet implemented.

Utility Effectiveness Bonus

Determines the bonus effectiveness of your utility items

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