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#redirect [[Stats#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''
 
===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.
 
===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" style="text-align:center; text-shadow:0px 0px 4px #000; border:1px solid #FFF9; border-collapse:collapse;"
|- style="font-weight:bold; background-color:#FFF3; border-bottom:1px solid #FFF9;"
| Luck
| style="width:8%;"| 0
| style="width:8%;"| 50
| style="width:8%;"| 100
| style="width:8%;"| 150
| style="width:8%;"| 200
| style="width:8%;"| 250
| style="width:8%;"| 300
| style="width:8%;"| 350
| style="width:8%;"| 400
| style="width:8%;"| 450
| style="width:8%;"| 500
|- class="colorrarity0"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | Junk || 1.000 || 0.950 || 0.900 || 0.850 || 0.800 || 0.750 || 0.700 || 0.650 || 0.600 || 0.550 || 0.500
|- class="colorrarity1"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | Poor || 1.000 || 0.950 || 0.900 || 0.850 || 0.800 || 0.750 || 0.700 || 0.650 || 0.600 || 0.550 || 0.500
|- class="colorrarity2"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | Common || 1.000 || 0.975 || 0.950 || 0.925 || 0.900 || 0.875 || 0.850 || 0.825 || 0.800 || 0.775 || 0.750
|- class="colorrarity3"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | Uncommon || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000 || 1.000
|- class="colorrarity4"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | Rare || 1.000 || 1.476 || 1.901 || 2.277 || 2.602 || 2.878 || 3.103 || 3.279 || 3.404 || 3.480 || 3.505
|- class="colorrarity5"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | Epic || 1.000 || 1.547 || 2.036 || 2.468 || 2.842 || 3.159 || 3.418 || 3.620 || 3.765 || 3.751 || 3.881
|- class="colorrarity6"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | Legendary || 1.000 || 1.618 || 2.171 || 2.659 || 3.083 || 3.441 || 3.734 || 3.962 || 4.125 || 4.223 || 4.257
|- class="colorrarity7"
| style=" background-color:#FFF3; font-weight:bold; border-right:1px solid #FFF9;" | Unique || 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>
 
===Probabilities from Luck===
To calculate the drop rate at X Luck there are three steps.<br>
# 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>
This will not affect the calculations below, but they will determine an individual item's probability.
 
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Rate
|- style="color:rgb(50,50,50);"
| style="background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||<span class="colorrarity0">220</span>
|- style="color:rgb(100,100,100);"
| style="background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||<span class="colorrarity1">250</span>
|- style="color:rgb(222,222,222);"
| style="background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||<span class="colorrarity2">200</span>
|- style="color:rgb(98,190,11);"
| style="background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||<span class="colorrarity3">150</span>
|- style="color:rgb(74,155,209);"
| style="background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||<span class="colorrarity4">100</span>
|- style="color:rgb(173,90,255);"
| style="background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||<span class="colorrarity5">50</span>
|- style="color:rgb(247,162,45);"
| style="background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||<span class="colorrarity6">20</span>
|- style="color:rgb(227,216,140);"
| style="background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||<span class="colorrarity7">10</span>
|}
<br>
<p style="font-size:18px; width:fit-content; border:1px solid #DD952A; border-radius:15px; padding:7px;">Click expand to see the calculations for 0 and 250 Luck.<p>
 
<div class="mw-collapsible mw-collapsed" style="width: fit-content">
<div class="mw-collapsible-content">
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.
 
Using the Luck Scalars at 0 Luck, the dot product is
 
{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}1.000 \cdot \textbf{220} }  +
{\color[RGB]{100, 100, 100}1.000 \cdot \textbf{250} }  +
{\color[RGB]{222, 222, 222}1.000 \cdot \textbf{200} }  +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} }  +
{\color[RGB]{74, 155, 209}1.000 \cdot \textbf{100} }  +
{\color[RGB]{173, 90, 255}1.000 \cdot \textbf{50} }  +
{\color[RGB]{247, 162, 45}1.000 \cdot \textbf{20} }  +
{\color[RGB]{227, 216, 140}1.000 \cdot \textbf{10} }  = {\color{violet}1000} }}
 
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 0 Luck
|-
| style="background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}1.000 \cdot \textbf{220} } }{ {\color{violet}1000} }=22\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}1.000 \cdot \textbf{250} } }{ {\color{violet}1000} }=25\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}1.000 \cdot \textbf{200} } }{ {\color{violet}1000} }=20\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } }{ {\color{violet}1000} }=15\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}1.000 \cdot \textbf{100} } }{ {\color{violet}1000} }=10\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}1.000 \cdot \textbf{50} } }{ {\color{violet}1000} }=5\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}1.000 \cdot \textbf{20} } }{ {\color{violet}1000} }=2\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}1.000 \cdot \textbf{10} } }{ {\color{violet}1000} }=1\%}}
|}
 
<br>
Using the Luck Scalars at 250 Luck, the dot product is
 
{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}0.750 \cdot \textbf{220} }  +
{\color[RGB]{100, 100, 100}0.750 \cdot \textbf{250} }  +
{\color[RGB]{222, 222, 222}0.875 \cdot \textbf{200} }  +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} }  +
{\color[RGB]{74, 155, 209}2.878 \cdot \textbf{100} }  +
{\color[RGB]{173, 90, 255}3.125 \cdot \textbf{50} }  +
{\color[RGB]{247, 162, 45}3.441 \cdot \textbf{20} }  +
{\color[RGB]{227, 216, 140}3.535 \cdot \textbf{10} }  = {\color{violet}1227.42} }}
 
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 250 Luck
|-
| style="background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.750 \cdot \textbf{220} } }{ {\color{violet}1227.42} }=13.443\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.750 \cdot \textbf{250} } }{ {\color{violet}1227.42} }=15.276\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.875 \cdot \textbf{200} } }{ {\color{violet}1227.42} }=14.258\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } }{ {\color{violet}1227.42} }=12.221\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}2.878 \cdot \textbf{100} } }{ {\color{violet}1227.42} }=23.448\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.125 \cdot \textbf{50} } }{ {\color{violet}1227.42} }=12.868\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}3.441 \cdot \textbf{20} } }{ {\color{violet}1227.42} }=5.607\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{10} } }{ {\color{violet}1227.42} }=2.880\%}}
|}
</div></div>
<br><br>
Using the Luck Scalars at 500 Luck, the dot product is
 
{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}0.500 \cdot \textbf{220} }  +
{\color[RGB]{100, 100, 100}0.500 \cdot \textbf{250} }  +
{\color[RGB]{222, 222, 222}0.750 \cdot \textbf{200} }  +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} }  +
{\color[RGB]{74, 155, 209}3.505 \cdot \textbf{100} }  +
{\color[RGB]{173, 90, 255}3.881 \cdot \textbf{50} }  +
{\color[RGB]{247, 162, 45}4.257 \cdot \textbf{20} }  +
{\color[RGB]{227, 216, 140}4.382 \cdot \textbf{10} }  = {\color{violet}1208.51} }}
 
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 500 Luck
|-
| style="background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.500 \cdot \textbf{220} } }{ {\color{violet}1208.51} }=9.102\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.500 \cdot \textbf{250} } }{ {\color{violet}1208.51} }=10.343\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.750 \cdot \textbf{200} } }{ {\color{violet}1208.51} }=12.412\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } }{ {\color{violet}1208.51} }=12.412\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}3.505 \cdot \textbf{100} } }{ {\color{violet}1208.51} }=29.003\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.881 \cdot \textbf{50} } }{ {\color{violet}1208.51} }=16.057\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}4.257 \cdot \textbf{20} } }{ {\color{violet}1208.51} }=7.045\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{10} } }{ {\color{violet}1208.51} }=3.626\%}}
|}
 
|-|Gold Coin Chest Example=
 
The table below is the Drop Rate table of the Gold Coin Chest.
 
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.
 
Notice that despite the [[Gold Coin Chest]]'s item rarity being unique, its Luck Grade is actually Common.<br>
Item Rarity does not equal Luck Grade, despite the two being equal for most items.
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Rate
|-
| style="background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||<span class="colorrarity0">99900</span>
|-
| style="background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||<span class="colorrarity1">0</span>
|-
| style="background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||<span class="colorrarity2">100</span>
|-
| style="background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||<span class="colorrarity3">0</span>
|-
| style="background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||<span class="colorrarity4">0</span>
|-
| style="background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||<span class="colorrarity5">0</span>
|-
| style="background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||<span class="colorrarity6">0</span>
|-
| style="background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||<span class="colorrarity7">0</span>
|}
<br>
<p style="font-size:18px; width:fit-content; border:1px solid #DD952A; border-radius:15px; padding:7px;">Click expand to see the calculations for 0 and 250 Luck.<p>
 
<div class="mw-collapsible mw-collapsed" style="width: fit-content">
<div class="mw-collapsible-content">
Using the Luck Scalars at 0 Luck, the dot product is
 
{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}1.000 \cdot \textbf{99900} }  +
{\color[RGB]{100, 100, 100}1.000 \cdot \textbf{0} }  +
{\color[RGB]{222, 222, 222}1.000 \cdot \textbf{100} }  +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} }  +
{\color[RGB]{74, 155, 209}1.000 \cdot \textbf{0} }  +
{\color[RGB]{173, 90, 255}1.000 \cdot \textbf{0} }  +
{\color[RGB]{247, 162, 45}1.000 \cdot \textbf{0} }  +
{\color[RGB]{227, 216, 140}1.000 \cdot \textbf{0} }  = {\color{violet}100000} }}
 
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 0 Luck
|-
| style="background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}1.000 \cdot \textbf{99900} } }{ {\color{violet}100000} }=99.9\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}1.000 \cdot \textbf{100} } }{ {\color{violet}100000} }=0.1\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}1.000 \cdot \textbf{0} } }{ {\color{violet}100000} }=0\%}}
|}
 
Using the Luck Scalars at 250 Luck, the dot product is
 
{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}0.750 \cdot \textbf{99900} }  +
{\color[RGB]{100, 100, 100}0.750 \cdot \textbf{0} }  +
{\color[RGB]{222, 222, 222}0.875 \cdot \textbf{100} }  +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} }  +
{\color[RGB]{74, 155, 209}2.878 \cdot \textbf{0} }  +
{\color[RGB]{173, 90, 255}3.159 \cdot \textbf{0} }  +
{\color[RGB]{247, 162, 45}3.441 \cdot \textbf{0} }  +
{\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} }  = {\color{violet}75012.5} }}
 
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 250 Luck
|-
| style="background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.750 \cdot \textbf{99900} } }{ {\color{violet}75012.5} }=99.883\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.750 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.875 \cdot \textbf{100} } }{ {\color{violet}75012.5} }=0.117\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}2.878 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.159 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}3.441 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}}
|}
</div></div>
<br><br>
Using the Luck Scalars at 500 Luck, the dot product is
 
{{#tag:math|\color{White}
{\color[RGB]{50, 50, 50}0.500 \cdot \textbf{99900} }  +
{\color[RGB]{100, 100, 100}0.500 \cdot \textbf{0} }  +
{\color[RGB]{222, 222, 222}0.750 \cdot \textbf{100} }  +
{\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} }  +
{\color[RGB]{74, 155, 209}3.505 \cdot \textbf{0} }  +
{\color[RGB]{173, 90, 255}3.881 \cdot \textbf{0} }  +
{\color[RGB]{247, 162, 45}4.257 \cdot \textbf{0} }  +
{\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} }  = {\color{violet}50025} }}
 
{| cellspacing="0" class="wikitable" style="text-align:center; font-weight:bold; text-shadow:0px 0px 4px #0008;"
|- style="background-color:#FFF4;"
|Luck Grade ||Drop Probability at 500 Luck
|-
| style="background-color:#FFF4;" | <span class="colorrarity0">Junk</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{50, 50, 50}0.500 \cdot \textbf{99900} } }{ {\color{violet}50025} }=99.850\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity1">Poor</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{100, 100, 100}0.500 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity2">Common</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{222, 222, 222}0.750 \cdot \textbf{100} } }{ {\color{violet}50025} }=0.150\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity3">Uncommon</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity4">Rare</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{74, 155, 209}3.505 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity5">Epic</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{173, 90, 255}3.881 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity6">Legendary</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{247, 162, 45}4.257 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|-
| style="background-color:#FFF4;" | <span class="colorrarity7">Unique</span> ||{{#tag:math|\color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}}
|}
</tabber>
 
It's worth noting that you can calculate probability at X Luck from either the Drop Rate table ''or'' the Drop Probability at 0 Luck table.<br>
Using the Drop Probability at 0 Luck table works because the Luck Scalars are all 1 and you have to normalize regardless of using the Drop Rate or the Probability at 0 Luck.
 
The wiki does not display the Drop Rate tables themselves, however it does show the alternative.

Revision as of 02:49, 4 May 2024

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

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

Luck is capped at 500.
It is possible to get maximum of 450 Luck in the game currently:

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.
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.
However, be aware that Monsters and Containers can have multiple Loot Drop Tables, each with their own Drop Rate table. See Lich for example.

A Drop can be rolled more than once, but each roll is independent of the others.
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.

Luck Scalar

Luck Scalars are one piece of information needed to calculate drop probability at X Luck.
The calculation is not a simple multiplication, so do not expect Uniques to be 4.382 times more common at 500 Luck.
The true effect of Luck varies depending on Drop Rate tables and Loot Drop tables.

Luck Scalar Table

Luck 0 50 100 150 200 250 300 350 400 450 500
Junk 1.000 0.950 0.900 0.850 0.800 0.750 0.700 0.650 0.600 0.550 0.500
Poor 1.000 0.950 0.900 0.850 0.800 0.750 0.700 0.650 0.600 0.550 0.500
Common 1.000 0.975 0.950 0.925 0.900 0.875 0.850 0.825 0.800 0.775 0.750
Uncommon 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
Rare 1.000 1.476 1.901 2.277 2.602 2.878 3.103 3.279 3.404 3.480 3.505
Epic 1.000 1.547 2.036 2.468 2.842 3.159 3.418 3.620 3.765 3.751 3.881
Legendary 1.000 1.618 2.171 2.659 3.083 3.441 3.734 3.962 4.125 4.223 4.257
Unique 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 which are continuous curves, but 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}<5000:1+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_{uckGrade01}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+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_{uckGrade02}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+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_{uckGrade03}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+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}<130:1+0\left|L_{uckGrade}-0\right|,130 \le L_{uckGrade}<140:1.039+0\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<220:1.041+0\left|L_{uckGrade}-140\right|,220 \le L_{uckGrade}<230:1.065+0\left|L_{uckGrade}-220\right|,230 \le L_{uckGrade}<290:1.067+0\left|L_{uckGrade}-230\right|,290 \le L_{uckGrade}<300:1.085+0\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<340:1.087+0\left|L_{uckGrade}-300\right|,340 \le L_{uckGrade}<350:1.099+0\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<390:1.101+0\left|L_{uckGrade}-350\right|,390 \le L_{uckGrade}<400:1.113+0\left|L_{uckGrade}-390\right|,400 \le L_{uckGrade}<430:1.115+0\left|L_{uckGrade}-400\right|,430 \le L_{uckGrade}<440:1.124+0\left|L_{uckGrade}-430\right|,440 \le L_{uckGrade}<470:1.126+0\left|L_{uckGrade}-440\right|,470 \le L_{uckGrade}<480:1.135+0\left|L_{uckGrade}-470\right|,480 \le L_{uckGrade}<500:1.137+0\left|L_{uckGrade}-480\right|,500 \le L_{uckGrade}<510:1.143+0\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<530:1.145+0\left|L_{uckGrade}-510\right|,530 \le L_{uckGrade}<540:1.151+0\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<560:1.153+0\left|L_{uckGrade}-540\right|,560 \le L_{uckGrade}<570:1.159+0\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<590:1.161+0\left|L_{uckGrade}-570\right|,590 \le L_{uckGrade}<600:1.167+0\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<620:1.169+0\left|L_{uckGrade}-600\right|,620 \le L_{uckGrade}<630:1.175+0\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<650:1.177+0\left|L_{uckGrade}-630\right|,650 \le L_{uckGrade}<660:1.183+0\left|L_{uckGrade}-650\right|,660 \le L_{uckGrade}<670:1.185+0\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:1.188+0\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<700:1.19+0\left|L_{uckGrade}-680\right|,700 \le L_{uckGrade}<710:1.196+0\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<720:1.198+0\left|L_{uckGrade}-710\right|,720 \le L_{uckGrade}<730:1.201+0\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<740:1.203+0\left|L_{uckGrade}-730\right|,740 \le L_{uckGrade}<750:1.206+0\left|L_{uckGrade}-740\right|,750 \le L_{uckGrade}<760:1.208+0\left|L_{uckGrade}-750\right|,760 \le L_{uckGrade}<770:1.211+0\left|L_{uckGrade}-760\right|,770 \le L_{uckGrade}<790:1.213+0\left|L_{uckGrade}-770\right|,790 \le L_{uckGrade}<800:1.219+0\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<810:1.221+0\left|L_{uckGrade}-800\right|,810 \le L_{uckGrade}<820:1.224+0\left|L_{uckGrade}-810\right|,820 \le L_{uckGrade}<830:1.226+0\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<840:1.229+0\left|L_{uckGrade}-830\right|,840 \le L_{uckGrade}<850:1.231+0\left|L_{uckGrade}-840\right|,850 \le L_{uckGrade}<860:1.234+0\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<870:1.236+0\left|L_{uckGrade}-860\right|,870 \le L_{uckGrade}<880:1.239+0\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<890:1.241+0\left|L_{uckGrade}-880\right|,890 \le L_{uckGrade}<910:1.244+0\left|L_{uckGrade}-890\right|,910 \le L_{uckGrade}<920:1.248+0\left|L_{uckGrade}-910\right|,920 \le L_{uckGrade}<930:1.251+0\left|L_{uckGrade}-920\right|,930 \le L_{uckGrade}<940:1.253+0\left|L_{uckGrade}-930\right|,940 \le L_{uckGrade}<950:1.256+0\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<960:1.258+0\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<980:1.261+0\left|L_{uckGrade}-960\right|,980 \le L_{uckGrade}<990:1.265+0\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1000:1.268+0\left|L_{uckGrade}-990\right|,1000 \le L_{uckGrade}<1010:1.27+0\left|L_{uckGrade}-1000\right|,1010 \le L_{uckGrade}<1030:1.273+0\left|L_{uckGrade}-1010\right|,1030 \le L_{uckGrade}<1040:1.277+0\left|L_{uckGrade}-1030\right|,1040 \le L_{uckGrade}<1050:1.28+0\left|L_{uckGrade}-1040\right|,1050 \le L_{uckGrade}<1060:1.282+0\left|L_{uckGrade}-1050\right|,1060 \le L_{uckGrade}<1080:1.285+0\left|L_{uckGrade}-1060\right|,1080 \le L_{uckGrade}<1090:1.289+0\left|L_{uckGrade}-1080\right|,1090 \le L_{uckGrade}<1110:1.292+0\left|L_{uckGrade}-1090\right|,1110 \le L_{uckGrade}<1120:1.296+0\left|L_{uckGrade}-1110\right|,1120 \le L_{uckGrade}<1140:1.299+0\left|L_{uckGrade}-1120\right|,1140 \le L_{uckGrade}<1150:1.303+0\left|L_{uckGrade}-1140\right|,1150 \le L_{uckGrade}<1170:1.306+0\left|L_{uckGrade}-1150\right|,1170 \le L_{uckGrade}<1180:1.31+0\left|L_{uckGrade}-1170\right|,1180 \le L_{uckGrade}<1210:1.313+0\left|L_{uckGrade}-1180\right|,1210 \le L_{uckGrade}<1220:1.319+0\left|L_{uckGrade}-1210\right|,1220 \le L_{uckGrade}<1240:1.322+0\left|L_{uckGrade}-1220\right|,1240 \le L_{uckGrade}<1250:1.326+0\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1290:1.329+0\left|L_{uckGrade}-1250\right|,1290 \le L_{uckGrade}<1300:1.337+0\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1330:1.34+0\left|L_{uckGrade}-1300\right|,1330 \le L_{uckGrade}<1340:1.346+0\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1390:1.349+0\left|L_{uckGrade}-1340\right|,1390 \le L_{uckGrade}<1400:1.359+0\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1460:1.362+0\left|L_{uckGrade}-1400\right|,1460 \le L_{uckGrade}<1470:1.374+0\left|L_{uckGrade}-1460\right|,1470 \le L_{uckGrade}<1560:1.377+0\left|L_{uckGrade}-1470\right|,1560 \le L_{uckGrade}<1570:1.395+0\left|L_{uckGrade}-1560\right|,1570 \le L_{uckGrade}<1770:1.398+0\left|L_{uckGrade}-1570\right|,1770 \le L_{uckGrade}<1780:1.438+0\left|L_{uckGrade}-1770\right|,1780 \le L_{uckGrade}<1880:1.439+0\left|L_{uckGrade}-1780\right|,1880 \le L_{uckGrade}<1890:1.459+0\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1950:1.46+0\left|L_{uckGrade}-1890\right|,1950 \le L_{uckGrade}<1960:1.472+0\left|L_{uckGrade}-1950\right|,1960 \le L_{uckGrade}<2000:1.473+0\left|L_{uckGrade}-1960\right|,2000 \le L_{uckGrade}<2010:1.481+0\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2050:1.482+0\left|L_{uckGrade}-2010\right|,2050 \le L_{uckGrade}<2060:1.49+0\left|L_{uckGrade}-2050\right|,2060 \le L_{uckGrade}<2090:1.491+0\left|L_{uckGrade}-2060\right|,2090 \le L_{uckGrade}<2100:1.497+0\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2130:1.498+0\left|L_{uckGrade}-2100\right|,2130 \le L_{uckGrade}<2140:1.504+0\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2160:1.505+0\left|L_{uckGrade}-2140\right|,2160 \le L_{uckGrade}<2170:1.509+0\left|L_{uckGrade}-2160\right|,2170 \le L_{uckGrade}<2190:1.51+0\left|L_{uckGrade}-2170\right|,2190 \le L_{uckGrade}<2200:1.514+0\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2220:1.515+0\left|L_{uckGrade}-2200\right|,2220 \le L_{uckGrade}<2230:1.519+0\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2250:1.52+0\left|L_{uckGrade}-2230\right|,2250 \le L_{uckGrade}<2260:1.524+0\left|L_{uckGrade}-2250\right|,2260 \le L_{uckGrade}<2280:1.525+0\left|L_{uckGrade}-2260\right|,2280 \le L_{uckGrade}<2290:1.529+0\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2310:1.53+0\left|L_{uckGrade}-2290\right|,2310 \le L_{uckGrade}<2320:1.534+0\left|L_{uckGrade}-2310\right|,2320 \le L_{uckGrade}<2330:1.535+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2340:1.537+0\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2360:1.538+0\left|L_{uckGrade}-2340\right|,2360 \le L_{uckGrade}<2370:1.542+0\left|L_{uckGrade}-2360\right|,2370 \le L_{uckGrade}<2380:1.543+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2390:1.545+0\left|L_{uckGrade}-2380\right|,2390 \le L_{uckGrade}<2400:1.546+0\left|L_{uckGrade}-2390\right|,2400 \le L_{uckGrade}<2410:1.548+0\left|L_{uckGrade}-2400\right|,2410 \le L_{uckGrade}<2430:1.549+0\left|L_{uckGrade}-2410\right|,2430 \le L_{uckGrade}<2440:1.553+0\left|L_{uckGrade}-2430\right|,2440 \le L_{uckGrade}<2450:1.554+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2460:1.556+0\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:1.557+0\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:1.559+0\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2490:1.56+0\left|L_{uckGrade}-2480\right|,2490 \le L_{uckGrade}<2500:1.562+0\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2510:1.563+0\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:1.565+0\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2530:1.566+0\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2540:1.568+0\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2550:1.569+0\left|L_{uckGrade}-2540\right|,2550 \le L_{uckGrade}<2560:1.571+0\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2570:1.572+0\left|L_{uckGrade}-2560\right|,2570 \le L_{uckGrade}<2580:1.574+0\left|L_{uckGrade}-2570\right|,2580 \le L_{uckGrade}<2590:1.575+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2610:1.577+0\left|L_{uckGrade}-2590\right|,2610 \le L_{uckGrade}<2620:1.579+0\left|L_{uckGrade}-2610\right|,2620 \le L_{uckGrade}<2630:1.581+0\left|L_{uckGrade}-2620\right|,2630 \le L_{uckGrade}<2640:1.582+0\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2650:1.584+0\left|L_{uckGrade}-2640\right|,2650 \le L_{uckGrade}<2660:1.585+0\left|L_{uckGrade}-2650\right|,2660 \le L_{uckGrade}<2680:1.587+0\left|L_{uckGrade}-2660\right|,2680 \le L_{uckGrade}<2690:1.589+0\left|L_{uckGrade}-2680\right|,2690 \le L_{uckGrade}<2710:1.591+0\left|L_{uckGrade}-2690\right|,2710 \le L_{uckGrade}<2720:1.593+0\left|L_{uckGrade}-2710\right|,2720 \le L_{uckGrade}<2730:1.595+0\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2740:1.596+0\left|L_{uckGrade}-2730\right|,2740 \le L_{uckGrade}<2760:1.598+0\left|L_{uckGrade}-2740\right|,2760 \le L_{uckGrade}<2770:1.6+0\left|L_{uckGrade}-2760\right|,2770 \le L_{uckGrade}<2790:1.602+0\left|L_{uckGrade}-2770\right|,2790 \le L_{uckGrade}<2800:1.604+0\left|L_{uckGrade}-2790\right|,2800 \le L_{uckGrade}<2820:1.606+0\left|L_{uckGrade}-2800\right|,2820 \le L_{uckGrade}<2830:1.608+0\left|L_{uckGrade}-2820\right|,2830 \le L_{uckGrade}<2860:1.61+0\left|L_{uckGrade}-2830\right|,2860 \le L_{uckGrade}<2870:1.613+0\left|L_{uckGrade}-2860\right|,2870 \le L_{uckGrade}<2890:1.615+0\left|L_{uckGrade}-2870\right|,2890 \le L_{uckGrade}<2900:1.617+0\left|L_{uckGrade}-2890\right|,2900 \le L_{uckGrade}<2930:1.619+0\left|L_{uckGrade}-2900\right|,2930 \le L_{uckGrade}<2940:1.622+0\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2980:1.624+0\left|L_{uckGrade}-2940\right|,2980 \le L_{uckGrade}<2990:1.628+0\left|L_{uckGrade}-2980\right|,2990 \le L_{uckGrade}<3030:1.63+0\left|L_{uckGrade}-2990\right|,3030 \le L_{uckGrade}<3040:1.634+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3090:1.636+0\left|L_{uckGrade}-3040\right|,3090 \le L_{uckGrade}<3100:1.641+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3170:1.643+0\left|L_{uckGrade}-3100\right|,3170 \le L_{uckGrade}<3180:1.65+0\left|L_{uckGrade}-3170\right|,3180 \le L_{uckGrade}<3500:1.652+0\left|L_{uckGrade}-3180\right|,3500 \le L_{uckGrade}<3510:1.684+0\left|L_{uckGrade}-3500\right|,3510 \le L_{uckGrade}<3580:1.684+0\left|L_{uckGrade}-3510\right|,3580 \le L_{uckGrade}<3590:1.691+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3640:1.691+0\left|L_{uckGrade}-3590\right|,3640 \le L_{uckGrade}<3650:1.696+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3690:1.696+0\left|L_{uckGrade}-3650\right|,3690 \le L_{uckGrade}<3700:1.7+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3730:1.7+0\left|L_{uckGrade}-3700\right|,3730 \le L_{uckGrade}<3740:1.703+0\left|L_{uckGrade}-3730\right|,3740 \le L_{uckGrade}<3770:1.703+0\left|L_{uckGrade}-3740\right|,3770 \le L_{uckGrade}<3780:1.706+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3810:1.706+0\left|L_{uckGrade}-3780\right|,3810 \le L_{uckGrade}<3820:1.709+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3840:1.709+0\left|L_{uckGrade}-3820\right|,3840 \le L_{uckGrade}<3850:1.711+0\left|L_{uckGrade}-3840\right|,3850 \le L_{uckGrade}<3880:1.711+0\left|L_{uckGrade}-3850\right|,3880 \le L_{uckGrade}<3890:1.714+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3910:1.714+0\left|L_{uckGrade}-3890\right|,3910 \le L_{uckGrade}<3920:1.716+0\left|L_{uckGrade}-3910\right|,3920 \le L_{uckGrade}<3930:1.716+0\left|L_{uckGrade}-3920\right|,3930 \le L_{uckGrade}<3940:1.717+0\left|L_{uckGrade}-3930\right|,3940 \le L_{uckGrade}<3960:1.717+0\left|L_{uckGrade}-3940\right|,3960 \le L_{uckGrade}<3970:1.719+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3990:1.719+0\left|L_{uckGrade}-3970\right|,3990 \le L_{uckGrade}<4000:1.721+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4010:1.721+0\left|L_{uckGrade}-4000\right|,4010 \le L_{uckGrade}<4020:1.722+0\left|L_{uckGrade}-4010\right|,4020 \le L_{uckGrade}<4040:1.722+0\left|L_{uckGrade}-4020\right|,4040 \le L_{uckGrade}<4050:1.724+0\left|L_{uckGrade}-4040\right|,4050 \le L_{uckGrade}<4060:1.724+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4070:1.725+0\left|L_{uckGrade}-4060\right|,4070 \le L_{uckGrade}<4080:1.725+0\left|L_{uckGrade}-4070\right|,4080 \le L_{uckGrade}<4090:1.726+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4100:1.726+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4110:1.727+0\left|L_{uckGrade}-4100\right|,4110 \le L_{uckGrade}<4130:1.727+0\left|L_{uckGrade}-4110\right|,4130 \le L_{uckGrade}<4140:1.729+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4150:1.729+0\left|L_{uckGrade}-4140\right|,4150 \le L_{uckGrade}<4160:1.73+0\left|L_{uckGrade}-4150\right|,4160 \le L_{uckGrade}<4170:1.73+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4180:1.731+0\left|L_{uckGrade}-4170\right|,4180 \le L_{uckGrade}<4190:1.731+0\left|L_{uckGrade}-4180\right|,4190 \le L_{uckGrade}<4200:1.732+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4210:1.732+0\left|L_{uckGrade}-4200\right|,4210 \le L_{uckGrade}<4230:1.733+0\left|L_{uckGrade}-4210\right|,4230 \le L_{uckGrade}<4240:1.733+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:1.734+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4260:1.734+0\left|L_{uckGrade}-4250\right|,4260 \le L_{uckGrade}<4270:1.735+0\left|L_{uckGrade}-4260\right|,4270 \le L_{uckGrade}<4280:1.735+0\left|L_{uckGrade}-4270\right|,4280 \le L_{uckGrade}<4290:1.736+0\left|L_{uckGrade}-4280\right|,4290 \le L_{uckGrade}<4300:1.736+0\left|L_{uckGrade}-4290\right|,4300 \le L_{uckGrade}<4320:1.737+0\left|L_{uckGrade}-4300\right|,4320 \le L_{uckGrade}<4330:1.737+0\left|L_{uckGrade}-4320\right|,4330 \le L_{uckGrade}<4340:1.738+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4350:1.738+0\left|L_{uckGrade}-4340\right|,4350 \le L_{uckGrade}<4370:1.739+0\left|L_{uckGrade}-4350\right|,4370 \le L_{uckGrade}<4380:1.739+0\left|L_{uckGrade}-4370\right|,4380 \le L_{uckGrade}<4390:1.74+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4400:1.74+0\left|L_{uckGrade}-4390\right|,4400 \le L_{uckGrade}<4420:1.741+0\left|L_{uckGrade}-4400\right|,4420 \le L_{uckGrade}<4430:1.741+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4450:1.742+0\left|L_{uckGrade}-4430\right|,4450 \le L_{uckGrade}<4460:1.742+0\left|L_{uckGrade}-4450\right|,4460 \le L_{uckGrade}<4480:1.743+0\left|L_{uckGrade}-4460\right|,4480 \le L_{uckGrade}<4490:1.743+0\left|L_{uckGrade}-4480\right|,4490 \le L_{uckGrade}<4520:1.744+0\left|L_{uckGrade}-4490\right|,4520 \le L_{uckGrade}<4530:1.744+0\left|L_{uckGrade}-4520\right|,4530 \le L_{uckGrade}<4550:1.745+0\left|L_{uckGrade}-4530\right|,4550 \le L_{uckGrade}<4560:1.745+0\left|L_{uckGrade}-4550\right|,4560 \le L_{uckGrade}<4590:1.746+0\left|L_{uckGrade}-4560\right|,4590 \le L_{uckGrade}<4600:1.746+0\left|L_{uckGrade}-4590\right|,4600 \le L_{uckGrade}<4630:1.747+0\left|L_{uckGrade}-4600\right|,4630 \le L_{uckGrade}<4640:1.747+0\left|L_{uckGrade}-4630\right|,4640 \le L_{uckGrade}<4680:1.748+0\left|L_{uckGrade}-4640\right|,4680 \le L_{uckGrade}<4690:1.748+0\left|L_{uckGrade}-4680\right|,4690 \le L_{uckGrade}<4740:1.749+0\left|L_{uckGrade}-4690\right|,4740 \le L_{uckGrade}<4750:1.749+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4820:1.75+0\left|L_{uckGrade}-4750\right|,4820 \le L_{uckGrade}<4830:1.75+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4990:1.751+0\left|L_{uckGrade}-4830\right|,4990 \le L_{uckGrade}<5000:1.751+0\left|L_{uckGrade}-4990\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}<10:1+0.001\left|L_{uckGrade}-0\right|,10 \le L_{uckGrade}<20:1.006+0.001\left|L_{uckGrade}-10\right|,20 \le L_{uckGrade}<50:1.013+0.001\left|L_{uckGrade}-20\right|,50 \le L_{uckGrade}<60:1.031+0.001\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<90:1.038+0.001\left|L_{uckGrade}-60\right|,90 \le L_{uckGrade}<100:1.056+0.001\left|L_{uckGrade}-90\right|,100 \le L_{uckGrade}<140:1.063+0.001\left|L_{uckGrade}-100\right|,140 \le L_{uckGrade}<150:1.087+0.001\left|L_{uckGrade}-140\right|,150 \le L_{uckGrade}<370:1.094+0.001\left|L_{uckGrade}-150\right|,370 \le L_{uckGrade}<380:1.226+0.001\left|L_{uckGrade}-370\right|,380 \le L_{uckGrade}<430:1.231+0.001\left|L_{uckGrade}-380\right|,430 \le L_{uckGrade}<440:1.261+0.001\left|L_{uckGrade}-430\right|,440 \le L_{uckGrade}<470:1.266+0.001\left|L_{uckGrade}-440\right|,470 \le L_{uckGrade}<480:1.284+0\left|L_{uckGrade}-470\right|,480 \le L_{uckGrade}<500:1.289+0.001\left|L_{uckGrade}-480\right|,500 \le L_{uckGrade}<510:1.301+0.001\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<530:1.306+0.001\left|L_{uckGrade}-510\right|,530 \le L_{uckGrade}<540:1.318+0\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<560:1.323+0.001\left|L_{uckGrade}-540\right|,560 \le L_{uckGrade}<570:1.335+0.001\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<590:1.34+0.001\left|L_{uckGrade}-570\right|,590 \le L_{uckGrade}<600:1.352+0\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<610:1.357+0.001\left|L_{uckGrade}-600\right|,610 \le L_{uckGrade}<620:1.363+0.001\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<630:1.368+0.001\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<640:1.374+0\left|L_{uckGrade}-630\right|,640 \le L_{uckGrade}<650:1.379+0.001\left|L_{uckGrade}-640\right|,650 \le L_{uckGrade}<660:1.385+0\left|L_{uckGrade}-650\right|,660 \le L_{uckGrade}<670:1.39+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:1.396+0.001\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<690:1.401+0.001\left|L_{uckGrade}-680\right|,690 \le L_{uckGrade}<700:1.407+0\left|L_{uckGrade}-690\right|,700 \le L_{uckGrade}<710:1.412+0.001\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<730:1.418+0.001\left|L_{uckGrade}-710\right|,730 \le L_{uckGrade}<740:1.428+0.001\left|L_{uckGrade}-730\right|,740 \le L_{uckGrade}<750:1.434+0.001\left|L_{uckGrade}-740\right|,750 \le L_{uckGrade}<760:1.439+0.001\left|L_{uckGrade}-750\right|,760 \le L_{uckGrade}<780:1.445+0.001\left|L_{uckGrade}-760\right|,780 \le L_{uckGrade}<790:1.455+0.001\left|L_{uckGrade}-780\right|,790 \le L_{uckGrade}<810:1.461+0.001\left|L_{uckGrade}-790\right|,810 \le L_{uckGrade}<820:1.471+0.001\left|L_{uckGrade}-810\right|,820 \le L_{uckGrade}<850:1.477+0\left|L_{uckGrade}-820\right|,850 \le L_{uckGrade}<860:1.492+0.001\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<890:1.498+0\left|L_{uckGrade}-860\right|,890 \le L_{uckGrade}<900:1.513+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<950:1.519+0.001\left|L_{uckGrade}-900\right|,950 \le L_{uckGrade}<960:1.544+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<1140:1.55+0\left|L_{uckGrade}-960\right|,1140 \le L_{uckGrade}<1150:1.64+0\left|L_{uckGrade}-1140\right|,1150 \le L_{uckGrade}<1200:1.644+0.001\left|L_{uckGrade}-1150\right|,1200 \le L_{uckGrade}<1210:1.669+0\left|L_{uckGrade}-1200\right|,1210 \le L_{uckGrade}<1250:1.673+0.001\left|L_{uckGrade}-1210\right|,1250 \le L_{uckGrade}<1260:1.693+0\left|L_{uckGrade}-1250\right|,1260 \le L_{uckGrade}<1280:1.697+0.001\left|L_{uckGrade}-1260\right|,1280 \le L_{uckGrade}<1290:1.707+0\left|L_{uckGrade}-1280\right|,1290 \le L_{uckGrade}<1320:1.711+0\left|L_{uckGrade}-1290\right|,1320 \le L_{uckGrade}<1330:1.726+0\left|L_{uckGrade}-1320\right|,1330 \le L_{uckGrade}<1340:1.73+0.001\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1350:1.735+0\left|L_{uckGrade}-1340\right|,1350 \le L_{uckGrade}<1370:1.739+0.001\left|L_{uckGrade}-1350\right|,1370 \le L_{uckGrade}<1380:1.749+0\left|L_{uckGrade}-1370\right|,1380 \le L_{uckGrade}<1390:1.753+0.001\left|L_{uckGrade}-1380\right|,1390 \le L_{uckGrade}<1400:1.758+0\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1420:1.762+0.001\left|L_{uckGrade}-1400\right|,1420 \le L_{uckGrade}<1430:1.772+0\left|L_{uckGrade}-1420\right|,1430 \le L_{uckGrade}<1440:1.776+0\left|L_{uckGrade}-1430\right|,1440 \le L_{uckGrade}<1450:1.781+0\left|L_{uckGrade}-1440\right|,1450 \le L_{uckGrade}<1460:1.785+0.001\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1480:1.79+0\left|L_{uckGrade}-1460\right|,1480 \le L_{uckGrade}<1490:1.798+0\left|L_{uckGrade}-1480\right|,1490 \le L_{uckGrade}<1500:1.803+0\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1510:1.807+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:1.812+0\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1530:1.816+0\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1550:1.821+0\left|L_{uckGrade}-1530\right|,1550 \le L_{uckGrade}<1560:1.829+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1580:1.834+0\left|L_{uckGrade}-1560\right|,1580 \le L_{uckGrade}<1590:1.842+0\left|L_{uckGrade}-1580\right|,1590 \le L_{uckGrade}<1610:1.847+0\left|L_{uckGrade}-1590\right|,1610 \le L_{uckGrade}<1620:1.855+0.001\left|L_{uckGrade}-1610\right|,1620 \le L_{uckGrade}<1650:1.86+0\left|L_{uckGrade}-1620\right|,1650 \le L_{uckGrade}<1660:1.872+0\left|L_{uckGrade}-1650\right|,1660 \le L_{uckGrade}<1690:1.877+0\left|L_{uckGrade}-1660\right|,1690 \le L_{uckGrade}<1700:1.889+0\left|L_{uckGrade}-1690\right|,1700 \le L_{uckGrade}<1770:1.894+0\left|L_{uckGrade}-1700\right|,1770 \le L_{uckGrade}<1780:1.922+0.001\left|L_{uckGrade}-1770\right|,1780 \le L_{uckGrade}<1910:1.927+0\left|L_{uckGrade}-1780\right|,1910 \le L_{uckGrade}<1920:1.979+0\left|L_{uckGrade}-1910\right|,1920 \le L_{uckGrade}<1980:1.982+0\left|L_{uckGrade}-1920\right|,1980 \le L_{uckGrade}<1990:2.006+0\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2030:2.009+0\left|L_{uckGrade}-1990\right|,2030 \le L_{uckGrade}<2040:2.025+0\left|L_{uckGrade}-2030\right|,2040 \le L_{uckGrade}<2070:2.028+0\left|L_{uckGrade}-2040\right|,2070 \le L_{uckGrade}<2080:2.04+0\left|L_{uckGrade}-2070\right|,2080 \le L_{uckGrade}<2100:2.043+0\left|L_{uckGrade}-2080\right|,2100 \le L_{uckGrade}<2110:2.051+0\left|L_{uckGrade}-2100\right|,2110 \le L_{uckGrade}<2130:2.054+0\left|L_{uckGrade}-2110\right|,2130 \le L_{uckGrade}<2140:2.062+0\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2150:2.065+0\left|L_{uckGrade}-2140\right|,2150 \le L_{uckGrade}<2160:2.069+0\left|L_{uckGrade}-2150\right|,2160 \le L_{uckGrade}<2180:2.072+0\left|L_{uckGrade}-2160\right|,2180 \le L_{uckGrade}<2190:2.08+0\left|L_{uckGrade}-2180\right|,2190 \le L_{uckGrade}<2200:2.083+0\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2210:2.087+0\left|L_{uckGrade}-2200\right|,2210 \le L_{uckGrade}<2220:2.09+0\left|L_{uckGrade}-2210\right|,2220 \le L_{uckGrade}<2230:2.094+0\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2240:2.097+0\left|L_{uckGrade}-2230\right|,2240 \le L_{uckGrade}<2250:2.101+0\left|L_{uckGrade}-2240\right|,2250 \le L_{uckGrade}<2260:2.104+0\left|L_{uckGrade}-2250\right|,2260 \le L_{uckGrade}<2270:2.108+0\left|L_{uckGrade}-2260\right|,2270 \le L_{uckGrade}<2280:2.111+0\left|L_{uckGrade}-2270\right|,2280 \le L_{uckGrade}<2290:2.115+0\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2300:2.118+0\left|L_{uckGrade}-2290\right|,2300 \le L_{uckGrade}<2320:2.122+0\left|L_{uckGrade}-2300\right|,2320 \le L_{uckGrade}<2330:2.128+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2340:2.132+0\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2350:2.135+0\left|L_{uckGrade}-2340\right|,2350 \le L_{uckGrade}<2370:2.139+0\left|L_{uckGrade}-2350\right|,2370 \le L_{uckGrade}<2380:2.145+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2410:2.149+0\left|L_{uckGrade}-2380\right|,2410 \le L_{uckGrade}<2420:2.158+0\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2440:2.162+0\left|L_{uckGrade}-2420\right|,2440 \le L_{uckGrade}<2450:2.168+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2490:2.172+0\left|L_{uckGrade}-2450\right|,2490 \le L_{uckGrade}<2500:2.184+0\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2580:2.188+0\left|L_{uckGrade}-2500\right|,2580 \le L_{uckGrade}<2590:2.212+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2680:2.216+0\left|L_{uckGrade}-2590\right|,2680 \le L_{uckGrade}<2690:2.243+0\left|L_{uckGrade}-2680\right|,2690 \le L_{uckGrade}<2760:2.245+0\left|L_{uckGrade}-2690\right|,2760 \le L_{uckGrade}<2770:2.266+0\left|L_{uckGrade}-2760\right|,2770 \le L_{uckGrade}<2810:2.268+0\left|L_{uckGrade}-2770\right|,2810 \le L_{uckGrade}<2820:2.28+0\left|L_{uckGrade}-2810\right|,2820 \le L_{uckGrade}<2850:2.282+0\left|L_{uckGrade}-2820\right|,2850 \le L_{uckGrade}<2860:2.291+0\left|L_{uckGrade}-2850\right|,2860 \le L_{uckGrade}<2880:2.293+0\left|L_{uckGrade}-2860\right|,2880 \le L_{uckGrade}<2890:2.299+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2910:2.301+0\left|L_{uckGrade}-2890\right|,2910 \le L_{uckGrade}<2920:2.307+0\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2940:2.309+0\left|L_{uckGrade}-2920\right|,2940 \le L_{uckGrade}<2950:2.315+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2960:2.317+0\left|L_{uckGrade}-2950\right|,2960 \le L_{uckGrade}<2970:2.32+0\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<2990:2.322+0\left|L_{uckGrade}-2970\right|,2990 \le L_{uckGrade}<3000:2.328+0\left|L_{uckGrade}-2990\right|,3000 \le L_{uckGrade}<3010:2.33+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3020:2.333+0\left|L_{uckGrade}-3010\right|,3020 \le L_{uckGrade}<3030:2.335+0\left|L_{uckGrade}-3020\right|,3030 \le L_{uckGrade}<3040:2.338+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3050:2.34+0\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3060:2.343+0\left|L_{uckGrade}-3050\right|,3060 \le L_{uckGrade}<3070:2.345+0\left|L_{uckGrade}-3060\right|,3070 \le L_{uckGrade}<3090:2.348+0\left|L_{uckGrade}-3070\right|,3090 \le L_{uckGrade}<3100:2.352+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3110:2.355+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3120:2.357+0\left|L_{uckGrade}-3110\right|,3120 \le L_{uckGrade}<3140:2.36+0\left|L_{uckGrade}-3120\right|,3140 \le L_{uckGrade}<3150:2.364+0\left|L_{uckGrade}-3140\right|,3150 \le L_{uckGrade}<3170:2.367+0\left|L_{uckGrade}-3150\right|,3170 \le L_{uckGrade}<3180:2.371+0\left|L_{uckGrade}-3170\right|,3180 \le L_{uckGrade}<3200:2.374+0\left|L_{uckGrade}-3180\right|,3200 \le L_{uckGrade}<3210:2.378+0\left|L_{uckGrade}-3200\right|,3210 \le L_{uckGrade}<3240:2.381+0\left|L_{uckGrade}-3210\right|,3240 \le L_{uckGrade}<3250:2.387+0\left|L_{uckGrade}-3240\right|,3250 \le L_{uckGrade}<3290:2.39+0\left|L_{uckGrade}-3250\right|,3290 \le L_{uckGrade}<3300:2.398+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3400:2.401+0\left|L_{uckGrade}-3300\right|,3400 \le L_{uckGrade}<3410:2.421+0\left|L_{uckGrade}-3400\right|,3410 \le L_{uckGrade}<3440:2.424+0\left|L_{uckGrade}-3410\right|,3440 \le L_{uckGrade}<3450:2.43+0\left|L_{uckGrade}-3440\right|,3450 \le L_{uckGrade}<3550:2.431+0\left|L_{uckGrade}-3450\right|,3550 \le L_{uckGrade}<3560:2.451+0\left|L_{uckGrade}-3550\right|,3560 \le L_{uckGrade}<3600:2.452+0\left|L_{uckGrade}-3560\right|,3600 \le L_{uckGrade}<3610:2.46+0\left|L_{uckGrade}-3600\right|,3610 \le L_{uckGrade}<3640:2.461+0\left|L_{uckGrade}-3610\right|,3640 \le L_{uckGrade}<3650:2.467+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3670:2.468+0\left|L_{uckGrade}-3650\right|,3670 \le L_{uckGrade}<3680:2.472+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3700:2.473+0\left|L_{uckGrade}-3680\right|,3700 \le L_{uckGrade}<3710:2.477+0\left|L_{uckGrade}-3700\right|,3710 \le L_{uckGrade}<3730:2.478+0\left|L_{uckGrade}-3710\right|,3730 \le L_{uckGrade}<3740:2.482+0\left|L_{uckGrade}-3730\right|,3740 \le L_{uckGrade}<3750:2.483+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3760:2.485+0\left|L_{uckGrade}-3750\right|,3760 \le L_{uckGrade}<3770:2.486+0\left|L_{uckGrade}-3760\right|,3770 \le L_{uckGrade}<3780:2.488+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3800:2.489+0\left|L_{uckGrade}-3780\right|,3800 \le L_{uckGrade}<3810:2.493+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<3820:2.494+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3830:2.496+0\left|L_{uckGrade}-3820\right|,3830 \le L_{uckGrade}<3840:2.497+0\left|L_{uckGrade}-3830\right|,3840 \le L_{uckGrade}<3860:2.499+0\left|L_{uckGrade}-3840\right|,3860 \le L_{uckGrade}<3870:2.501+0\left|L_{uckGrade}-3860\right|,3870 \le L_{uckGrade}<3880:2.503+0\left|L_{uckGrade}-3870\right|,3880 \le L_{uckGrade}<3890:2.504+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3900:2.506+0\left|L_{uckGrade}-3890\right|,3900 \le L_{uckGrade}<3910:2.507+0\left|L_{uckGrade}-3900\right|,3910 \le L_{uckGrade}<3930:2.509+0\left|L_{uckGrade}-3910\right|,3930 \le L_{uckGrade}<3940:2.511+0\left|L_{uckGrade}-3930\right|,3940 \le L_{uckGrade}<3960:2.513+0\left|L_{uckGrade}-3940\right|,3960 \le L_{uckGrade}<3970:2.515+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3990:2.517+0\left|L_{uckGrade}-3970\right|,3990 \le L_{uckGrade}<4000:2.519+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4030:2.521+0\left|L_{uckGrade}-4000\right|,4030 \le L_{uckGrade}<4040:2.524+0\left|L_{uckGrade}-4030\right|,4040 \le L_{uckGrade}<4090:2.526+0\left|L_{uckGrade}-4040\right|,4090 \le L_{uckGrade}<4100:2.531+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4330:2.533+0\left|L_{uckGrade}-4100\right|,4330 \le L_{uckGrade}<4340:2.556+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4380:2.556+0\left|L_{uckGrade}-4340\right|,4380 \le L_{uckGrade}<4390:2.56+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4430:2.56+0\left|L_{uckGrade}-4390\right|,4430 \le L_{uckGrade}<4440:2.564+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4460:2.564+0\left|L_{uckGrade}-4440\right|,4460 \le L_{uckGrade}<4470:2.566+0\left|L_{uckGrade}-4460\right|,4470 \le L_{uckGrade}<4490:2.566+0\left|L_{uckGrade}-4470\right|,4490 \le L_{uckGrade}<4500:2.568+0\left|L_{uckGrade}-4490\right|,4500 \le L_{uckGrade}<4520:2.568+0\left|L_{uckGrade}-4500\right|,4520 \le L_{uckGrade}<4530:2.57+0\left|L_{uckGrade}-4520\right|,4530 \le L_{uckGrade}<4540:2.57+0\left|L_{uckGrade}-4530\right|,4540 \le L_{uckGrade}<4550:2.571+0\left|L_{uckGrade}-4540\right|,4550 \le L_{uckGrade}<4560:2.571+0\left|L_{uckGrade}-4550\right|,4560 \le L_{uckGrade}<4570:2.572+0\left|L_{uckGrade}-4560\right|,4570 \le L_{uckGrade}<4590:2.572+0\left|L_{uckGrade}-4570\right|,4590 \le L_{uckGrade}<4600:2.574+0\left|L_{uckGrade}-4590\right|,4600 \le L_{uckGrade}<4610:2.574+0\left|L_{uckGrade}-4600\right|,4610 \le L_{uckGrade}<4620:2.575+0\left|L_{uckGrade}-4610\right|,4620 \le L_{uckGrade}<4630:2.575+0\left|L_{uckGrade}-4620\right|,4630 \le L_{uckGrade}<4650:2.576+0\left|L_{uckGrade}-4630\right|,4650 \le L_{uckGrade}<4660:2.576+0\left|L_{uckGrade}-4650\right|,4660 \le L_{uckGrade}<4670:2.577+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4680:2.577+0\left|L_{uckGrade}-4670\right|,4680 \le L_{uckGrade}<4690:2.578+0\left|L_{uckGrade}-4680\right|,4690 \le L_{uckGrade}<4700:2.578+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4720:2.579+0\left|L_{uckGrade}-4700\right|,4720 \le L_{uckGrade}<4730:2.579+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4750:2.58+0\left|L_{uckGrade}-4730\right|,4750 \le L_{uckGrade}<4760:2.58+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4790:2.581+0\left|L_{uckGrade}-4760\right|,4790 \le L_{uckGrade}<4800:2.581+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4830:2.582+0\left|L_{uckGrade}-4800\right|,4830 \le L_{uckGrade}<4840:2.582+0\left|L_{uckGrade}-4830\right|,4840 \le L_{uckGrade}<4880:2.583+0\left|L_{uckGrade}-4840\right|,4880 \le L_{uckGrade}<4890:2.583+0\left|L_{uckGrade}-4880\right|,4890 \le L_{uckGrade}<5000:2.584+0\left|L_{uckGrade}-4890\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}<150:1+0.001\left|L_{uckGrade}-0\right|,150 \le L_{uckGrade}<160:1.135+0.001\left|L_{uckGrade}-150\right|,160 \le L_{uckGrade}<200:1.143+0.001\left|L_{uckGrade}-160\right|,200 \le L_{uckGrade}<210:1.179+0.001\left|L_{uckGrade}-200\right|,210 \le L_{uckGrade}<230:1.187+0.001\left|L_{uckGrade}-210\right|,230 \le L_{uckGrade}<240:1.205+0.001\left|L_{uckGrade}-230\right|,240 \le L_{uckGrade}<260:1.213+0.001\left|L_{uckGrade}-240\right|,260 \le L_{uckGrade}<270:1.231+0.001\left|L_{uckGrade}-260\right|,270 \le L_{uckGrade}<290:1.239+0.001\left|L_{uckGrade}-270\right|,290 \le L_{uckGrade}<300:1.257+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<310:1.265+0.001\left|L_{uckGrade}-300\right|,310 \le L_{uckGrade}<320:1.274+0.001\left|L_{uckGrade}-310\right|,320 \le L_{uckGrade}<330:1.282+0.001\left|L_{uckGrade}-320\right|,330 \le L_{uckGrade}<340:1.291+0.001\left|L_{uckGrade}-330\right|,340 \le L_{uckGrade}<350:1.299+0.001\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<360:1.308+0.001\left|L_{uckGrade}-350\right|,360 \le L_{uckGrade}<370:1.316+0.001\left|L_{uckGrade}-360\right|,370 \le L_{uckGrade}<390:1.325+0.001\left|L_{uckGrade}-370\right|,390 \le L_{uckGrade}<400:1.341+0.001\left|L_{uckGrade}-390\right|,400 \le L_{uckGrade}<410:1.35+0.001\left|L_{uckGrade}-400\right|,410 \le L_{uckGrade}<420:1.358+0.001\left|L_{uckGrade}-410\right|,420 \le L_{uckGrade}<450:1.367+0.001\left|L_{uckGrade}-420\right|,450 \le L_{uckGrade}<460:1.391+0.001\left|L_{uckGrade}-450\right|,460 \le L_{uckGrade}<490:1.4+0.001\left|L_{uckGrade}-460\right|,490 \le L_{uckGrade}<500:1.424+0.001\left|L_{uckGrade}-490\right|,500 \le L_{uckGrade}<550:1.433+0.001\left|L_{uckGrade}-500\right|,550 \le L_{uckGrade}<560:1.473+0.001\left|L_{uckGrade}-550\right|,560 \le L_{uckGrade}<660:1.482+0.001\left|L_{uckGrade}-560\right|,660 \le L_{uckGrade}<670:1.562+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<720:1.569+0.001\left|L_{uckGrade}-670\right|,720 \le L_{uckGrade}<730:1.609+0.001\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<760:1.616+0.001\left|L_{uckGrade}-730\right|,760 \le L_{uckGrade}<770:1.64+0.001\left|L_{uckGrade}-760\right|,770 \le L_{uckGrade}<790:1.647+0.001\left|L_{uckGrade}-770\right|,790 \le L_{uckGrade}<800:1.663+0.001\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<820:1.67+0.001\left|L_{uckGrade}-800\right|,820 \le L_{uckGrade}<830:1.686+0.001\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<850:1.693+0.001\left|L_{uckGrade}-830\right|,850 \le L_{uckGrade}<860:1.709+0.001\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<870:1.716+0.001\left|L_{uckGrade}-860\right|,870 \le L_{uckGrade}<880:1.724+0.001\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<890:1.731+0.001\left|L_{uckGrade}-880\right|,890 \le L_{uckGrade}<900:1.739+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<910:1.746+0.001\left|L_{uckGrade}-900\right|,910 \le L_{uckGrade}<930:1.754+0.001\left|L_{uckGrade}-910\right|,930 \le L_{uckGrade}<940:1.768+0.001\left|L_{uckGrade}-930\right|,940 \le L_{uckGrade}<950:1.776+0.001\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<960:1.783+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<980:1.791+0.001\left|L_{uckGrade}-960\right|,980 \le L_{uckGrade}<990:1.805+0.001\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1020:1.813+0.001\left|L_{uckGrade}-990\right|,1020 \le L_{uckGrade}<1030:1.834+0.001\left|L_{uckGrade}-1020\right|,1030 \le L_{uckGrade}<1070:1.842+0.001\left|L_{uckGrade}-1030\right|,1070 \le L_{uckGrade}<1080:1.87+0.001\left|L_{uckGrade}-1070\right|,1080 \le L_{uckGrade}<1240:1.878+0.001\left|L_{uckGrade}-1080\right|,1240 \le L_{uckGrade}<1250:1.99+0.001\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1290:1.996+0.001\left|L_{uckGrade}-1250\right|,1290 \le L_{uckGrade}<1300:2.024+0.001\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1330:2.03+0.001\left|L_{uckGrade}-1300\right|,1330 \le L_{uckGrade}<1340:2.051+0.001\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1360:2.057+0.001\left|L_{uckGrade}-1340\right|,1360 \le L_{uckGrade}<1370:2.071+0.001\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1380:2.077+0.001\left|L_{uckGrade}-1370\right|,1380 \le L_{uckGrade}<1390:2.084+0.001\left|L_{uckGrade}-1380\right|,1390 \le L_{uckGrade}<1400:2.09+0.001\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1410:2.097+0.001\left|L_{uckGrade}-1400\right|,1410 \le L_{uckGrade}<1430:2.103+0.001\left|L_{uckGrade}-1410\right|,1430 \le L_{uckGrade}<1450:2.117+0.001\left|L_{uckGrade}-1430\right|,1450 \le L_{uckGrade}<1460:2.129+0.001\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1470:2.136+0.001\left|L_{uckGrade}-1460\right|,1470 \le L_{uckGrade}<1480:2.142+0.001\left|L_{uckGrade}-1470\right|,1480 \le L_{uckGrade}<1490:2.149+0.001\left|L_{uckGrade}-1480\right|,1490 \le L_{uckGrade}<1500:2.155+0.001\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1520:2.162+0.001\left|L_{uckGrade}-1500\right|,1520 \le L_{uckGrade}<1530:2.174+0.001\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1550:2.181+0.001\left|L_{uckGrade}-1530\right|,1550 \le L_{uckGrade}<1560:2.193+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1600:2.2+0.001\left|L_{uckGrade}-1560\right|,1600 \le L_{uckGrade}<1610:2.224+0.001\left|L_{uckGrade}-1600\right|,1610 \le L_{uckGrade}<1680:2.231+0.001\left|L_{uckGrade}-1610\right|,1680 \le L_{uckGrade}<1690:2.273+0.001\left|L_{uckGrade}-1680\right|,1690 \le L_{uckGrade}<1730:2.28+0.001\left|L_{uckGrade}-1690\right|,1730 \le L_{uckGrade}<1740:2.304+0.001\left|L_{uckGrade}-1730\right|,1740 \le L_{uckGrade}<1810:2.309+0.001\left|L_{uckGrade}-1740\right|,1810 \le L_{uckGrade}<1820:2.351+0\left|L_{uckGrade}-1810\right|,1820 \le L_{uckGrade}<1850:2.356+0.001\left|L_{uckGrade}-1820\right|,1850 \le L_{uckGrade}<1860:2.374+0\left|L_{uckGrade}-1850\right|,1860 \le L_{uckGrade}<1890:2.379+0.001\left|L_{uckGrade}-1860\right|,1890 \le L_{uckGrade}<1900:2.397+0.001\left|L_{uckGrade}-1890\right|,1900 \le L_{uckGrade}<1910:2.402+0.001\left|L_{uckGrade}-1900\right|,1910 \le L_{uckGrade}<1920:2.408+0\left|L_{uckGrade}-1910\right|,1920 \le L_{uckGrade}<1940:2.413+0.001\left|L_{uckGrade}-1920\right|,1940 \le L_{uckGrade}<1950:2.425+0.001\left|L_{uckGrade}-1940\right|,1950 \le L_{uckGrade}<1960:2.43+0.001\left|L_{uckGrade}-1950\right|,1960 \le L_{uckGrade}<1970:2.436+0\left|L_{uckGrade}-1960\right|,1970 \le L_{uckGrade}<1980:2.441+0.001\left|L_{uckGrade}-1970\right|,1980 \le L_{uckGrade}<1990:2.447+0\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2000:2.452+0.001\left|L_{uckGrade}-1990\right|,2000 \le L_{uckGrade}<2010:2.458+0\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2020:2.463+0.001\left|L_{uckGrade}-2010\right|,2020 \le L_{uckGrade}<2030:2.469+0.001\left|L_{uckGrade}-2020\right|,2030 \le L_{uckGrade}<2040:2.474+0.001\left|L_{uckGrade}-2030\right|,2040 \le L_{uckGrade}<2060:2.48+0.001\left|L_{uckGrade}-2040\right|,2060 \le L_{uckGrade}<2070:2.49+0.001\left|L_{uckGrade}-2060\right|,2070 \le L_{uckGrade}<2090:2.496+0\left|L_{uckGrade}-2070\right|,2090 \le L_{uckGrade}<2100:2.506+0.001\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2130:2.512+0.001\left|L_{uckGrade}-2100\right|,2130 \le L_{uckGrade}<2140:2.527+0.001\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2190:2.533+0\left|L_{uckGrade}-2140\right|,2190 \le L_{uckGrade}<2200:2.558+0.001\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2320:2.564+0.001\left|L_{uckGrade}-2200\right|,2320 \le L_{uckGrade}<2330:2.624+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2380:2.628+0\left|L_{uckGrade}-2330\right|,2380 \le L_{uckGrade}<2390:2.653+0\left|L_{uckGrade}-2380\right|,2390 \le L_{uckGrade}<2410:2.657+0\left|L_{uckGrade}-2390\right|,2410 \le L_{uckGrade}<2420:2.667+0\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2450:2.671+0.001\left|L_{uckGrade}-2420\right|,2450 \le L_{uckGrade}<2460:2.686+0\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:2.69+0\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:2.695+0\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2500:2.699+0.001\left|L_{uckGrade}-2480\right|,2500 \le L_{uckGrade}<2510:2.709+0\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:2.713+0\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2530:2.718+0\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2540:2.722+0\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2550:2.727+0\left|L_{uckGrade}-2540\right|,2550 \le L_{uckGrade}<2560:2.731+0.001\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2580:2.736+0\left|L_{uckGrade}-2560\right|,2580 \le L_{uckGrade}<2590:2.744+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2600:2.749+0\left|L_{uckGrade}-2590\right|,2600 \le L_{uckGrade}<2610:2.753+0\left|L_{uckGrade}-2600\right|,2610 \le L_{uckGrade}<2630:2.758+0\left|L_{uckGrade}-2610\right|,2630 \le L_{uckGrade}<2640:2.766+0\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2670:2.771+0\left|L_{uckGrade}-2640\right|,2670 \le L_{uckGrade}<2680:2.783+0\left|L_{uckGrade}-2670\right|,2680 \le L_{uckGrade}<2720:2.788+0\left|L_{uckGrade}-2680\right|,2720 \le L_{uckGrade}<2730:2.804+0.001\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2880:2.809+0\left|L_{uckGrade}-2730\right|,2880 \le L_{uckGrade}<2890:2.869+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2940:2.872+0\left|L_{uckGrade}-2890\right|,2940 \le L_{uckGrade}<2950:2.892+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2970:2.895+0\left|L_{uckGrade}-2950\right|,2970 \le L_{uckGrade}<2980:2.903+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<3000:2.906+0\left|L_{uckGrade}-2980\right|,3000 \le L_{uckGrade}<3010:2.914+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3030:2.917+0\left|L_{uckGrade}-3010\right|,3030 \le L_{uckGrade}<3040:2.925+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3050:2.928+0\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3060:2.932+0\left|L_{uckGrade}-3050\right|,3060 \le L_{uckGrade}<3070:2.935+0\left|L_{uckGrade}-3060\right|,3070 \le L_{uckGrade}<3080:2.939+0\left|L_{uckGrade}-3070\right|,3080 \le L_{uckGrade}<3090:2.942+0\left|L_{uckGrade}-3080\right|,3090 \le L_{uckGrade}<3100:2.946+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3110:2.949+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3120:2.953+0\left|L_{uckGrade}-3110\right|,3120 \le L_{uckGrade}<3130:2.956+0\left|L_{uckGrade}-3120\right|,3130 \le L_{uckGrade}<3150:2.96+0\left|L_{uckGrade}-3130\right|,3150 \le L_{uckGrade}<3160:2.966+0\left|L_{uckGrade}-3150\right|,3160 \le L_{uckGrade}<3180:2.97+0\left|L_{uckGrade}-3160\right|,3180 \le L_{uckGrade}<3190:2.976+0\left|L_{uckGrade}-3180\right|,3190 \le L_{uckGrade}<3210:2.98+0\left|L_{uckGrade}-3190\right|,3210 \le L_{uckGrade}<3220:2.986+0\left|L_{uckGrade}-3210\right|,3220 \le L_{uckGrade}<3260:2.99+0\left|L_{uckGrade}-3220\right|,3260 \le L_{uckGrade}<3270:3.002+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3450:3.006+0\left|L_{uckGrade}-3270\right|,3450 \le L_{uckGrade}<3460:3.06+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3490:3.062+0\left|L_{uckGrade}-3460\right|,3490 \le L_{uckGrade}<3500:3.071+0\left|L_{uckGrade}-3490\right|,3500 \le L_{uckGrade}<3530:3.073+0\left|L_{uckGrade}-3500\right|,3530 \le L_{uckGrade}<3540:3.082+0\left|L_{uckGrade}-3530\right|,3540 \le L_{uckGrade}<3560:3.084+0\left|L_{uckGrade}-3540\right|,3560 \le L_{uckGrade}<3570:3.09+0\left|L_{uckGrade}-3560\right|,3570 \le L_{uckGrade}<3580:3.092+0\left|L_{uckGrade}-3570\right|,3580 \le L_{uckGrade}<3590:3.095+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3600:3.097+0\left|L_{uckGrade}-3590\right|,3600 \le L_{uckGrade}<3610:3.1+0\left|L_{uckGrade}-3600\right|,3610 \le L_{uckGrade}<3630:3.102+0\left|L_{uckGrade}-3610\right|,3630 \le L_{uckGrade}<3650:3.108+0\left|L_{uckGrade}-3630\right|,3650 \le L_{uckGrade}<3660:3.112+0\left|L_{uckGrade}-3650\right|,3660 \le L_{uckGrade}<3670:3.115+0\left|L_{uckGrade}-3660\right|,3670 \le L_{uckGrade}<3680:3.117+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3690:3.12+0\left|L_{uckGrade}-3680\right|,3690 \le L_{uckGrade}<3700:3.122+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3720:3.125+0\left|L_{uckGrade}-3700\right|,3720 \le L_{uckGrade}<3730:3.129+0\left|L_{uckGrade}-3720\right|,3730 \le L_{uckGrade}<3750:3.132+0\left|L_{uckGrade}-3730\right|,3750 \le L_{uckGrade}<3760:3.136+0\left|L_{uckGrade}-3750\right|,3760 \le L_{uckGrade}<3800:3.139+0\left|L_{uckGrade}-3760\right|,3800 \le L_{uckGrade}<3810:3.147+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<4000:3.15+0\left|L_{uckGrade}-3810\right|,4000 \le L_{uckGrade}<4010:3.188+0\left|L_{uckGrade}-4000\right|,4010 \le L_{uckGrade}<4050:3.189+0\left|L_{uckGrade}-4010\right|,4050 \le L_{uckGrade}<4060:3.197+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4080:3.198+0\left|L_{uckGrade}-4060\right|,4080 \le L_{uckGrade}<4090:3.202+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4110:3.203+0\left|L_{uckGrade}-4090\right|,4110 \le L_{uckGrade}<4120:3.207+0\left|L_{uckGrade}-4110\right|,4120 \le L_{uckGrade}<4130:3.208+0\left|L_{uckGrade}-4120\right|,4130 \le L_{uckGrade}<4140:3.21+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4160:3.211+0\left|L_{uckGrade}-4140\right|,4160 \le L_{uckGrade}<4170:3.215+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4180:3.216+0\left|L_{uckGrade}-4170\right|,4180 \le L_{uckGrade}<4190:3.218+0\left|L_{uckGrade}-4180\right|,4190 \le L_{uckGrade}<4200:3.219+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4220:3.221+0\left|L_{uckGrade}-4200\right|,4220 \le L_{uckGrade}<4230:3.223+0\left|L_{uckGrade}-4220\right|,4230 \le L_{uckGrade}<4240:3.225+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:3.226+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4270:3.228+0\left|L_{uckGrade}-4250\right|,4270 \le L_{uckGrade}<4280:3.23+0\left|L_{uckGrade}-4270\right|,4280 \le L_{uckGrade}<4300:3.232+0\left|L_{uckGrade}-4280\right|,4300 \le L_{uckGrade}<4310:3.234+0\left|L_{uckGrade}-4300\right|,4310 \le L_{uckGrade}<4340:3.236+0\left|L_{uckGrade}-4310\right|,4340 \le L_{uckGrade}<4350:3.239+0\left|L_{uckGrade}-4340\right|,4350 \le L_{uckGrade}<4430:3.241+0\left|L_{uckGrade}-4350\right|,4430 \le L_{uckGrade}<4440:3.249+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4470:3.251+0\left|L_{uckGrade}-4440\right|,4470 \le L_{uckGrade}<4480:3.254+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4560:3.254+0\left|L_{uckGrade}-4480\right|,4560 \le L_{uckGrade}<4570:3.262+0\left|L_{uckGrade}-4560\right|,4570 \le L_{uckGrade}<4600:3.262+0\left|L_{uckGrade}-4570\right|,4600 \le L_{uckGrade}<4610:3.265+0\left|L_{uckGrade}-4600\right|,4610 \le L_{uckGrade}<4630:3.265+0\left|L_{uckGrade}-4610\right|,4630 \le L_{uckGrade}<4640:3.267+0\left|L_{uckGrade}-4630\right|,4640 \le L_{uckGrade}<4660:3.267+0\left|L_{uckGrade}-4640\right|,4660 \le L_{uckGrade}<4670:3.269+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4690:3.269+0\left|L_{uckGrade}-4670\right|,4690 \le L_{uckGrade}<4700:3.271+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4710:3.271+0\left|L_{uckGrade}-4700\right|,4710 \le L_{uckGrade}<4720:3.272+0\left|L_{uckGrade}-4710\right|,4720 \le L_{uckGrade}<4730:3.272+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4740:3.273+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4750:3.273+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4760:3.274+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4770:3.274+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4790:3.275+0\left|L_{uckGrade}-4770\right|,4790 \le L_{uckGrade}<4800:3.275+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4820:3.276+0\left|L_{uckGrade}-4800\right|,4820 \le L_{uckGrade}<4830:3.276+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4850:3.277+0\left|L_{uckGrade}-4830\right|,4850 \le L_{uckGrade}<4860:3.277+0\left|L_{uckGrade}-4850\right|,4860 \le L_{uckGrade}<4890:3.278+0\left|L_{uckGrade}-4860\right|,4890 \le L_{uckGrade}<4900:3.278+0\left|L_{uckGrade}-4890\right|,4900 \le L_{uckGrade}<4980:3.279+0\left|L_{uckGrade}-4900\right|,4980 \le L_{uckGrade}<4990:3.279+0\left|L_{uckGrade}-4980\right|,4990 \le L_{uckGrade}<5000:3.28+0\left|L_{uckGrade}-4990\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}<20:1+0.001\left|L_{uckGrade}-0\right|,20 \le L_{uckGrade}<30:1.022+0.001\left|L_{uckGrade}-20\right|,30 \le L_{uckGrade}<50:1.032+0.001\left|L_{uckGrade}-30\right|,50 \le L_{uckGrade}<60:1.054+0.001\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<80:1.064+0.001\left|L_{uckGrade}-60\right|,80 \le L_{uckGrade}<90:1.086+0.001\left|L_{uckGrade}-80\right|,90 \le L_{uckGrade}<110:1.096+0.001\left|L_{uckGrade}-90\right|,110 \le L_{uckGrade}<120:1.118+0.001\left|L_{uckGrade}-110\right|,120 \le L_{uckGrade}<130:1.128+0.001\left|L_{uckGrade}-120\right|,130 \le L_{uckGrade}<140:1.139+0.001\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<150:1.149+0.001\left|L_{uckGrade}-140\right|,150 \le L_{uckGrade}<160:1.16+0.001\left|L_{uckGrade}-150\right|,160 \le L_{uckGrade}<170:1.17+0.001\left|L_{uckGrade}-160\right|,170 \le L_{uckGrade}<180:1.181+0.001\left|L_{uckGrade}-170\right|,180 \le L_{uckGrade}<190:1.191+0.001\left|L_{uckGrade}-180\right|,190 \le L_{uckGrade}<210:1.202+0.001\left|L_{uckGrade}-190\right|,210 \le L_{uckGrade}<220:1.222+0.001\left|L_{uckGrade}-210\right|,220 \le L_{uckGrade}<240:1.233+0.001\left|L_{uckGrade}-220\right|,240 \le L_{uckGrade}<250:1.253+0.001\left|L_{uckGrade}-240\right|,250 \le L_{uckGrade}<290:1.264+0.001\left|L_{uckGrade}-250\right|,290 \le L_{uckGrade}<300:1.304+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<450:1.315+0.001\left|L_{uckGrade}-300\right|,450 \le L_{uckGrade}<460:1.465+0.001\left|L_{uckGrade}-450\right|,460 \le L_{uckGrade}<500:1.474+0.001\left|L_{uckGrade}-460\right|,500 \le L_{uckGrade}<510:1.514+0.001\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<530:1.523+0.001\left|L_{uckGrade}-510\right|,530 \le L_{uckGrade}<540:1.543+0.001\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<560:1.552+0.001\left|L_{uckGrade}-540\right|,560 \le L_{uckGrade}<570:1.572+0.001\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<580:1.581+0.001\left|L_{uckGrade}-570\right|,580 \le L_{uckGrade}<590:1.591+0.001\left|L_{uckGrade}-580\right|,590 \le L_{uckGrade}<600:1.6+0.001\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<610:1.61+0.001\left|L_{uckGrade}-600\right|,610 \le L_{uckGrade}<620:1.619+0.001\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<630:1.629+0.001\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<640:1.638+0.001\left|L_{uckGrade}-630\right|,640 \le L_{uckGrade}<660:1.648+0.001\left|L_{uckGrade}-640\right|,660 \le L_{uckGrade}<670:1.666+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:1.676+0.001\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<690:1.685+0.001\left|L_{uckGrade}-680\right|,690 \le L_{uckGrade}<720:1.695+0.001\left|L_{uckGrade}-690\right|,720 \le L_{uckGrade}<730:1.722+0.001\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<770:1.732+0.001\left|L_{uckGrade}-730\right|,770 \le L_{uckGrade}<780:1.768+0.001\left|L_{uckGrade}-770\right|,780 \le L_{uckGrade}<890:1.778+0.001\left|L_{uckGrade}-780\right|,890 \le L_{uckGrade}<900:1.877+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<950:1.885+0.001\left|L_{uckGrade}-900\right|,950 \le L_{uckGrade}<960:1.93+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<980:1.938+0.001\left|L_{uckGrade}-960\right|,980 \le L_{uckGrade}<990:1.956+0.001\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1010:1.964+0.001\left|L_{uckGrade}-990\right|,1010 \le L_{uckGrade}<1020:1.982+0.001\left|L_{uckGrade}-1010\right|,1020 \le L_{uckGrade}<1040:1.99+0.001\left|L_{uckGrade}-1020\right|,1040 \le L_{uckGrade}<1050:2.008+0.001\left|L_{uckGrade}-1040\right|,1050 \le L_{uckGrade}<1060:2.016+0.001\left|L_{uckGrade}-1050\right|,1060 \le L_{uckGrade}<1070:2.025+0.001\left|L_{uckGrade}-1060\right|,1070 \le L_{uckGrade}<1080:2.033+0.001\left|L_{uckGrade}-1070\right|,1080 \le L_{uckGrade}<1090:2.042+0.001\left|L_{uckGrade}-1080\right|,1090 \le L_{uckGrade}<1100:2.05+0.001\left|L_{uckGrade}-1090\right|,1100 \le L_{uckGrade}<1120:2.059+0.001\left|L_{uckGrade}-1100\right|,1120 \le L_{uckGrade}<1130:2.075+0.001\left|L_{uckGrade}-1120\right|,1130 \le L_{uckGrade}<1150:2.084+0.001\left|L_{uckGrade}-1130\right|,1150 \le L_{uckGrade}<1160:2.1+0.001\left|L_{uckGrade}-1150\right|,1160 \le L_{uckGrade}<1180:2.109+0.001\left|L_{uckGrade}-1160\right|,1180 \le L_{uckGrade}<1190:2.125+0.001\left|L_{uckGrade}-1180\right|,1190 \le L_{uckGrade}<1240:2.134+0.001\left|L_{uckGrade}-1190\right|,1240 \le L_{uckGrade}<1250:2.174+0.001\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1360:2.183+0.001\left|L_{uckGrade}-1250\right|,1360 \le L_{uckGrade}<1370:2.271+0.001\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1410:2.278+0.001\left|L_{uckGrade}-1370\right|,1410 \le L_{uckGrade}<1420:2.31+0.001\left|L_{uckGrade}-1410\right|,1420 \le L_{uckGrade}<1440:2.317+0.001\left|L_{uckGrade}-1420\right|,1440 \le L_{uckGrade}<1450:2.333+0.001\left|L_{uckGrade}-1440\right|,1450 \le L_{uckGrade}<1470:2.34+0.001\left|L_{uckGrade}-1450\right|,1470 \le L_{uckGrade}<1480:2.356+0.001\left|L_{uckGrade}-1470\right|,1480 \le L_{uckGrade}<1500:2.363+0.001\left|L_{uckGrade}-1480\right|,1500 \le L_{uckGrade}<1510:2.379+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:2.386+0.001\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1530:2.394+0.001\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1540:2.401+0.001\left|L_{uckGrade}-1530\right|,1540 \le L_{uckGrade}<1550:2.409+0.001\left|L_{uckGrade}-1540\right|,1550 \le L_{uckGrade}<1560:2.416+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1580:2.424+0.001\left|L_{uckGrade}-1560\right|,1580 \le L_{uckGrade}<1590:2.438+0.001\left|L_{uckGrade}-1580\right|,1590 \le L_{uckGrade}<1600:2.446+0.001\left|L_{uckGrade}-1590\right|,1600 \le L_{uckGrade}<1610:2.453+0.001\left|L_{uckGrade}-1600\right|,1610 \le L_{uckGrade}<1640:2.461+0.001\left|L_{uckGrade}-1610\right|,1640 \le L_{uckGrade}<1650:2.482+0.001\left|L_{uckGrade}-1640\right|,1650 \le L_{uckGrade}<1680:2.49+0.001\left|L_{uckGrade}-1650\right|,1680 \le L_{uckGrade}<1690:2.511+0.001\left|L_{uckGrade}-1680\right|,1690 \le L_{uckGrade}<1840:2.519+0.001\left|L_{uckGrade}-1690\right|,1840 \le L_{uckGrade}<1850:2.624+0.001\left|L_{uckGrade}-1840\right|,1850 \le L_{uckGrade}<1880:2.63+0.001\left|L_{uckGrade}-1850\right|,1880 \le L_{uckGrade}<1890:2.651+0.001\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1920:2.657+0.001\left|L_{uckGrade}-1890\right|,1920 \le L_{uckGrade}<1930:2.678+0.001\left|L_{uckGrade}-1920\right|,1930 \le L_{uckGrade}<1940:2.684+0.001\left|L_{uckGrade}-1930\right|,1940 \le L_{uckGrade}<1950:2.691+0.001\left|L_{uckGrade}-1940\right|,1950 \le L_{uckGrade}<1970:2.697+0.001\left|L_{uckGrade}-1950\right|,1970 \le L_{uckGrade}<1980:2.711+0.001\left|L_{uckGrade}-1970\right|,1980 \le L_{uckGrade}<1990:2.717+0.001\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2000:2.724+0.001\left|L_{uckGrade}-1990\right|,2000 \le L_{uckGrade}<2010:2.73+0.001\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2020:2.737+0.001\left|L_{uckGrade}-2010\right|,2020 \le L_{uckGrade}<2030:2.743+0.001\left|L_{uckGrade}-2020\right|,2030 \le L_{uckGrade}<2050:2.75+0.001\left|L_{uckGrade}-2030\right|,2050 \le L_{uckGrade}<2060:2.762+0.001\left|L_{uckGrade}-2050\right|,2060 \le L_{uckGrade}<2080:2.769+0.001\left|L_{uckGrade}-2060\right|,2080 \le L_{uckGrade}<2090:2.781+0.001\left|L_{uckGrade}-2080\right|,2090 \le L_{uckGrade}<2120:2.788+0.001\left|L_{uckGrade}-2090\right|,2120 \le L_{uckGrade}<2130:2.806+0.001\left|L_{uckGrade}-2120\right|,2130 \le L_{uckGrade}<2180:2.813+0.001\left|L_{uckGrade}-2130\right|,2180 \le L_{uckGrade}<2190:2.843+0.001\left|L_{uckGrade}-2180\right|,2190 \le L_{uckGrade}<2270:2.85+0.001\left|L_{uckGrade}-2190\right|,2270 \le L_{uckGrade}<2280:2.898+0\left|L_{uckGrade}-2270\right|,2280 \le L_{uckGrade}<2330:2.903+0.001\left|L_{uckGrade}-2280\right|,2330 \le L_{uckGrade}<2340:2.933+0.001\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2370:2.938+0.001\left|L_{uckGrade}-2340\right|,2370 \le L_{uckGrade}<2380:2.956+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2400:2.961+0.001\left|L_{uckGrade}-2380\right|,2400 \le L_{uckGrade}<2410:2.973+0.001\left|L_{uckGrade}-2400\right|,2410 \le L_{uckGrade}<2420:2.978+0.001\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2430:2.984+0\left|L_{uckGrade}-2420\right|,2430 \le L_{uckGrade}<2440:2.989+0.001\left|L_{uckGrade}-2430\right|,2440 \le L_{uckGrade}<2450:2.995+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2460:3+0.001\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:3.006+0.001\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:3.011+0.001\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2490:3.017+0\left|L_{uckGrade}-2480\right|,2490 \le L_{uckGrade}<2500:3.022+0.001\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2520:3.028+0\left|L_{uckGrade}-2500\right|,2520 \le L_{uckGrade}<2530:3.038+0.001\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2550:3.044+0\left|L_{uckGrade}-2530\right|,2550 \le L_{uckGrade}<2560:3.054+0.001\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2580:3.06+0\left|L_{uckGrade}-2560\right|,2580 \le L_{uckGrade}<2590:3.07+0.001\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2650:3.076+0\left|L_{uckGrade}-2590\right|,2650 \le L_{uckGrade}<2660:3.106+0.001\left|L_{uckGrade}-2650\right|,2660 \le L_{uckGrade}<2720:3.112+0\left|L_{uckGrade}-2660\right|,2720 \le L_{uckGrade}<2730:3.142+0\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2790:3.146+0.001\left|L_{uckGrade}-2730\right|,2790 \le L_{uckGrade}<2800:3.176+0\left|L_{uckGrade}-2790\right|,2800 \le L_{uckGrade}<2820:3.18+0\left|L_{uckGrade}-2800\right|,2820 \le L_{uckGrade}<2830:3.19+0\left|L_{uckGrade}-2820\right|,2830 \le L_{uckGrade}<2850:3.194+0.001\left|L_{uckGrade}-2830\right|,2850 \le L_{uckGrade}<2860:3.204+0\left|L_{uckGrade}-2850\right|,2860 \le L_{uckGrade}<2880:3.208+0\left|L_{uckGrade}-2860\right|,2880 \le L_{uckGrade}<2890:3.218+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2900:3.222+0\left|L_{uckGrade}-2890\right|,2900 \le L_{uckGrade}<2910:3.227+0\left|L_{uckGrade}-2900\right|,2910 \le L_{uckGrade}<2920:3.231+0.001\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2930:3.236+0\left|L_{uckGrade}-2920\right|,2930 \le L_{uckGrade}<2940:3.24+0\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2950:3.245+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2960:3.249+0\left|L_{uckGrade}-2950\right|,2960 \le L_{uckGrade}<2970:3.254+0\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<2980:3.258+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<3000:3.263+0\left|L_{uckGrade}-2980\right|,3000 \le L_{uckGrade}<3010:3.271+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3040:3.276+0\left|L_{uckGrade}-3010\right|,3040 \le L_{uckGrade}<3050:3.288+0.001\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3100:3.293+0\left|L_{uckGrade}-3050\right|,3100 \le L_{uckGrade}<3110:3.313+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3200:3.318+0\left|L_{uckGrade}-3110\right|,3200 \le L_{uckGrade}<3210:3.354+0\left|L_{uckGrade}-3200\right|,3210 \le L_{uckGrade}<3260:3.357+0\left|L_{uckGrade}-3210\right|,3260 \le L_{uckGrade}<3270:3.377+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3290:3.38+0\left|L_{uckGrade}-3270\right|,3290 \le L_{uckGrade}<3300:3.388+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3320:3.391+0\left|L_{uckGrade}-3300\right|,3320 \le L_{uckGrade}<3330:3.399+0\left|L_{uckGrade}-3320\right|,3330 \le L_{uckGrade}<3350:3.402+0\left|L_{uckGrade}-3330\right|,3350 \le L_{uckGrade}<3360:3.41+0\left|L_{uckGrade}-3350\right|,3360 \le L_{uckGrade}<3370:3.413+0\left|L_{uckGrade}-3360\right|,3370 \le L_{uckGrade}<3380:3.417+0\left|L_{uckGrade}-3370\right|,3380 \le L_{uckGrade}<3390:3.42+0\left|L_{uckGrade}-3380\right|,3390 \le L_{uckGrade}<3400:3.424+0\left|L_{uckGrade}-3390\right|,3400 \le L_{uckGrade}<3410:3.427+0\left|L_{uckGrade}-3400\right|,3410 \le L_{uckGrade}<3430:3.431+0\left|L_{uckGrade}-3410\right|,3430 \le L_{uckGrade}<3440:3.437+0\left|L_{uckGrade}-3430\right|,3440 \le L_{uckGrade}<3450:3.441+0\left|L_{uckGrade}-3440\right|,3450 \le L_{uckGrade}<3460:3.444+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3480:3.448+0\left|L_{uckGrade}-3460\right|,3480 \le L_{uckGrade}<3490:3.454+0\left|L_{uckGrade}-3480\right|,3490 \le L_{uckGrade}<3530:3.458+0\left|L_{uckGrade}-3490\right|,3530 \le L_{uckGrade}<3540:3.47+0\left|L_{uckGrade}-3530\right|,3540 \le L_{uckGrade}<3690:3.474+0\left|L_{uckGrade}-3540\right|,3690 \le L_{uckGrade}<3700:3.519+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3740:3.521+0\left|L_{uckGrade}-3700\right|,3740 \le L_{uckGrade}<3750:3.533+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3770:3.535+0\left|L_{uckGrade}-3750\right|,3770 \le L_{uckGrade}<3780:3.541+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3800:3.543+0\left|L_{uckGrade}-3780\right|,3800 \le L_{uckGrade}<3810:3.549+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<3820:3.551+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3830:3.554+0\left|L_{uckGrade}-3820\right|,3830 \le L_{uckGrade}<3840:3.556+0\left|L_{uckGrade}-3830\right|,3840 \le L_{uckGrade}<3850:3.559+0\left|L_{uckGrade}-3840\right|,3850 \le L_{uckGrade}<3860:3.561+0\left|L_{uckGrade}-3850\right|,3860 \le L_{uckGrade}<3870:3.564+0\left|L_{uckGrade}-3860\right|,3870 \le L_{uckGrade}<3880:3.566+0\left|L_{uckGrade}-3870\right|,3880 \le L_{uckGrade}<3890:3.569+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3900:3.571+0\left|L_{uckGrade}-3890\right|,3900 \le L_{uckGrade}<3920:3.574+0\left|L_{uckGrade}-3900\right|,3920 \le L_{uckGrade}<3930:3.578+0\left|L_{uckGrade}-3920\right|,3930 \le L_{uckGrade}<3960:3.581+0\left|L_{uckGrade}-3930\right|,3960 \le L_{uckGrade}<3970:3.587+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<4010:3.59+0\left|L_{uckGrade}-3970\right|,4010 \le L_{uckGrade}<4020:3.598+0\left|L_{uckGrade}-4010\right|,4020 \le L_{uckGrade}<4140:3.601+0\left|L_{uckGrade}-4020\right|,4140 \le L_{uckGrade}<4150:3.625+0\left|L_{uckGrade}-4140\right|,4150 \le L_{uckGrade}<4190:3.626+0\left|L_{uckGrade}-4150\right|,4190 \le L_{uckGrade}<4200:3.634+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4230:3.635+0\left|L_{uckGrade}-4200\right|,4230 \le L_{uckGrade}<4240:3.641+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:3.642+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4260:3.644+0\left|L_{uckGrade}-4250\right|,4260 \le L_{uckGrade}<4280:3.645+0\left|L_{uckGrade}-4260\right|,4280 \le L_{uckGrade}<4290:3.649+0\left|L_{uckGrade}-4280\right|,4290 \le L_{uckGrade}<4300:3.65+0\left|L_{uckGrade}-4290\right|,4300 \le L_{uckGrade}<4310:3.652+0\left|L_{uckGrade}-4300\right|,4310 \le L_{uckGrade}<4320:3.653+0\left|L_{uckGrade}-4310\right|,4320 \le L_{uckGrade}<4330:3.655+0\left|L_{uckGrade}-4320\right|,4330 \le L_{uckGrade}<4340:3.656+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4360:3.658+0\left|L_{uckGrade}-4340\right|,4360 \le L_{uckGrade}<4370:3.66+0\left|L_{uckGrade}-4360\right|,4370 \le L_{uckGrade}<4380:3.662+0\left|L_{uckGrade}-4370\right|,4380 \le L_{uckGrade}<4390:3.663+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4420:3.665+0\left|L_{uckGrade}-4390\right|,4420 \le L_{uckGrade}<4430:3.668+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4470:3.67+0\left|L_{uckGrade}-4430\right|,4470 \le L_{uckGrade}<4480:3.674+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4610:3.676+0\left|L_{uckGrade}-4480\right|,4610 \le L_{uckGrade}<4620:3.689+0\left|L_{uckGrade}-4610\right|,4620 \le L_{uckGrade}<4660:3.689+0\left|L_{uckGrade}-4620\right|,4660 \le L_{uckGrade}<4670:3.693+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4690:3.693+0\left|L_{uckGrade}-4670\right|,4690 \le L_{uckGrade}<4700:3.695+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4720:3.695+0\left|L_{uckGrade}-4700\right|,4720 \le L_{uckGrade}<4730:3.697+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4740:3.697+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4750:3.698+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4760:3.698+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4770:3.699+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4780:3.699+0\left|L_{uckGrade}-4770\right|,4780 \le L_{uckGrade}<4790:3.7+0\left|L_{uckGrade}-4780\right|,4790 \le L_{uckGrade}<4800:3.7+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4810:3.701+0\left|L_{uckGrade}-4800\right|,4810 \le L_{uckGrade}<4820:3.701+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4840:3.702+0\left|L_{uckGrade}-4820\right|,4840 \le L_{uckGrade}<4850:3.702+0\left|L_{uckGrade}-4840\right|,4850 \le L_{uckGrade}<4870:3.703+0\left|L_{uckGrade}-4850\right|,4870 \le L_{uckGrade}<4880:3.703+0\left|L_{uckGrade}-4870\right|,4880 \le L_{uckGrade}<4910:3.704+0\left|L_{uckGrade}-4880\right|,4910 \le L_{uckGrade}<4920:3.704+0\left|L_{uckGrade}-4910\right|,4920 \le L_{uckGrade}<5000:3.705+0\left|L_{uckGrade}-4920\right|\right\}

See Example for how to use.


Probabilities from Luck

To calculate the drop rate at X Luck there are three steps.

  1. For each Luck Grade's Drop Rate apply the corresponding Luck Scalar.
  2. Find the dot product between the Luck Scalar vector at X Luck and the Base Rate.
    (This is the same as adding up each term from the first step.)
  3. 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.

The table below is the Drop Rate table of Quest Drops.

Every monster with a quest drop uses the Drop Rate table.
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, a Luck Grade's rate may be split between two Loot Drops.
This will not affect the calculations below, but they will determine an individual item's probability.

Luck Grade Drop Rate
Junk 220
Poor 250
Common 200
Uncommon 150
Rare 100
Epic 50
Legendary 20
Unique 10


Click expand to see the calculations for 0 and 250 Luck.

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.

Using the Luck Scalars at 0 Luck, the dot product is

Luck Grade Drop Probability at 0 Luck
Junk
Poor
Common
Uncommon
Rare
Epic
Legendary
Unique


Using the Luck Scalars at 250 Luck, the dot product is

Luck Grade Drop Probability at 250 Luck
Junk
Poor
Common
Uncommon
Rare
Epic
Legendary
Unique



Using the Luck Scalars at 500 Luck, the dot product is

Luck Grade Drop Probability at 500 Luck
Junk
Poor
Common
Uncommon
Rare
Epic
Legendary
Unique

The table below is the Drop Rate table of the Gold Coin Chest.

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.

Notice that despite the Gold Coin Chest's item rarity being unique, its Luck Grade is actually Common.
Item Rarity does not equal Luck Grade, despite the two being equal for most items.

Luck Grade Drop Rate
Junk 99900
Poor 0
Common 100
Uncommon 0
Rare 0
Epic 0
Legendary 0
Unique 0


Click expand to see the calculations for 0 and 250 Luck.

Using the Luck Scalars at 0 Luck, the dot product is

Luck Grade Drop Probability at 0 Luck
Junk
Poor
Common
Uncommon
Rare
Epic
Legendary
Unique

Using the Luck Scalars at 250 Luck, the dot product is

Luck Grade Drop Probability at 250 Luck
Junk
Poor
Common
Uncommon
Rare
Epic
Legendary
Unique



Using the Luck Scalars at 500 Luck, the dot product is

Luck Grade Drop Probability at 500 Luck
Junk
Poor
Common
Uncommon
Rare
Epic
Legendary
Unique

It's worth noting that you can calculate probability at X Luck from either the Drop Rate table or the Drop Probability at 0 Luck table.
Using the Drop Probability at 0 Luck table works because the Luck Scalars are all 1 and you have to normalize regardless of using the Drop Rate or the Probability at 0 Luck.

The wiki does not display the Drop Rate tables themselves, however it does show the alternative.

Retrieved from "http://darkanddarker.wiki.spellsandguns.com/index.php?title=Luck&oldid=25871"