LaTeX Formula
From Dark and Darker Wiki
Stats are currently up to date for: Patch:6.4#Hotfix 41Last updated on a previous Patch/Hotfix, but information is up to date.
Charts are created using the data points directly taken from the game. Therefore, if there is a mismatch between chart and the in game display, it is better to look at chart info.
For example, even though the formula might give 32.5, in game the display might get rounded to 33.
Stats that come from character's attributes.
Physical Power governs your Physical Power Bonus.
Strength governs your Physical Power.
0 Strength starts at 0 Physical Power.
LaTeX Formula
- More recently known as Physical Damage Bonus, Physical Power Bonus governs the potency of your physical damage dealing weapons, utility items, and abilities.
Physical Power governs your Physical Power Bonus.
0 Physical Power starts at -80% Physical Power Bonus.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
P_{hysicalPowerBonus}(P_{hysicalPower})=\left\{0 \le P_{hysicalPower}<5:-0.8+0.1\left|P_{hysicalPower}-0\right|,5 \le P_{hysicalPower}<7:-0.3+0.05\left|P_{hysicalPower}-5\right|,7 \le P_{hysicalPower}<11:-0.2+0.03\left|P_{hysicalPower}-7\right|,11 \le P_{hysicalPower}<15:-0.08+0.02\left|P_{hysicalPower}-11\right|,15 \le P_{hysicalPower}<50:0+0.01\left|P_{hysicalPower}-15\right|,50 \le P_{hysicalPower}<100:0.35+0.005\left|P_{hysicalPower}-50\right|\right\}
See Example for how to use.
Capped to -100%
Max Health determines your characters maximum Health.
Strength increases Max Health with 25% Scaling. See the Hybrid stat Max Health for more.
Max Health determines your characters maximum Health.
Vigor increases Max Health with 75% Scaling. See the Hybrid stat Max Health for more.
Affects the rate at which you restore health when Resting, but not when using Bandages.
Health Recovered per tick = Base Recovery * (1 + Health Recovery Bonus)
For example, a Barbarian resting with 95% Health Recovery Bonus will recover
Health Recovered every 2s = 1 * (1 + .95) = 1.95 Health
Vigor governs your Health Recovery.
0 Vigor starts at -55% Health Recovery.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
H_{ealthRecovery}(V_{igor})=\left\{0 \le V_{igor}<5:-0.55+0.05\left|V_{igor}-0\right|,5 \le V_{igor}<15:-0.3+0.03\left|V_{igor}-5\right|,15 \le V_{igor}<25:0+0.07\left|V_{igor}-15\right|,25 \le V_{igor}<35:0.7+0.05\left|V_{igor}-25\right|,35 \le V_{igor}<84:1.2+0.02\left|V_{igor}-35\right|,84 \le V_{igor}<85:2.18+0.01\left|V_{igor}-84\right|,85 \le V_{igor}<86:2.19+0.03\left|V_{igor}-85\right|,86 \le V_{igor}<100:2.22+0.02\left|V_{igor}-86\right|\right\}
See Example for how to use.
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.
Agility increases Action Speed with 25% Scaling. See the Hybrid stat Action Speed for more.
Move Speed governs the speed at which your character moves. This stat is also directly influenced by wearing gear. Every 1 point in Move Speed is equal to 0.3333...% Move Speed. The default Move Speed for each class is 300, which translates to 100% Move Speed, with penalties or bonuses provided based on Agility. Performing certain actions, such as attacking, or moving in certain directions will also affect Move Speed. Backwards = 60%, Crouch = 65%, Walk = 40%.
Agility governs your Move Speed.
0 Agility starts at -30 Move Speed.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
M_{oveSpeed}(A_{gility})=\left\{0 \le A_{gility}<15:-30+2\left|A_{gility}-0\right|,15 \le A_{gility}<45:0+1\left|A_{gility}-15\right|,45 \le A_{gility}<46:30+0\left|A_{gility}-45\right|,46 \le A_{gility}<47:30+1\left|A_{gility}-46\right|,47 \le A_{gility}<48:31+0\left|A_{gility}-47\right|,48 \le A_{gility}<49:31+1\left|A_{gility}-48\right|,49 \le A_{gility}<50:32+0\left|A_{gility}-49\right|,50 \le A_{gility}<51:32+1\left|A_{gility}-50\right|,51 \le A_{gility}<52:33+0\left|A_{gility}-51\right|,52 \le A_{gility}<53:33+1\left|A_{gility}-52\right|,53 \le A_{gility}<54:34+0\left|A_{gility}-53\right|,54 \le A_{gility}<55:34+1\left|A_{gility}-54\right|,55 \le A_{gility}<56:35+0\left|A_{gility}-55\right|,56 \le A_{gility}<57:35+1\left|A_{gility}-56\right|,57 \le A_{gility}<58:36+0\left|A_{gility}-57\right|,58 \le A_{gility}<59:36+1\left|A_{gility}-58\right|,59 \le A_{gility}<60:37+0\left|A_{gility}-59\right|,60 \le A_{gility}<61:37+1\left|A_{gility}-60\right|,61 \le A_{gility}<62:38+0\left|A_{gility}-61\right|,62 \le A_{gility}<63:38+1\left|A_{gility}-62\right|,63 \le A_{gility}<64:39+0\left|A_{gility}-63\right|,64 \le A_{gility}<65:39+1\left|A_{gility}-64\right|,65 \le A_{gility}<67:40+0\left|A_{gility}-65\right|,67 \le A_{gility}<68:40+1\left|A_{gility}-67\right|,68 \le A_{gility}<70:41+0\left|A_{gility}-68\right|,70 \le A_{gility}<71:41+1\left|A_{gility}-70\right|,71 \le A_{gility}<73:42+0\left|A_{gility}-71\right|,73 \le A_{gility}<74:42+1\left|A_{gility}-73\right|,74 \le A_{gility}<76:43+0\left|A_{gility}-74\right|,76 \le A_{gility}<77:43+1\left|A_{gility}-76\right|,77 \le A_{gility}<79:44+0\left|A_{gility}-77\right|,79 \le A_{gility}<80:44+1\left|A_{gility}-79\right|,80 \le A_{gility}<82:45+0\left|A_{gility}-80\right|,82 \le A_{gility}<83:45+1\left|A_{gility}-82\right|,83 \le A_{gility}<85:46+0\left|A_{gility}-83\right|,85 \le A_{gility}<86:46+1\left|A_{gility}-85\right|,86 \le A_{gility}<88:47+0\left|A_{gility}-86\right|,88 \le A_{gility}<89:47+1\left|A_{gility}-88\right|,89 \le A_{gility}<91:48+0\left|A_{gility}-89\right|,91 \le A_{gility}<92:48+1\left|A_{gility}-91\right|,92 \le A_{gility}<94:49+0\left|A_{gility}-92\right|,94 \le A_{gility}<95:49+1\left|A_{gility}-94\right|,95 \le A_{gility}<97:50+0\left|A_{gility}-95\right|,97 \le A_{gility}<98:50+1\left|A_{gility}-97\right|,98 \le A_{gility}<100:51+0\left|A_{gility}-98\right|\right\}
See Example for how to use.
Hard capped to 330 Movement speed
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
Agility increases Regular Interaction Speed with 40% Scaling. See the Hybrid stat Regular Interaction Speed for more.
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.
Dexterity increases Action Speed with 75% Scaling. See the Hybrid stat Action Speed for more.
Manual Dexterity determines how quickly Bard plays an instrument.
Dexterity governs your Manual Dexterity.
0 Dexterity starts at -15% Manual Dexterity.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
M_{anualDexterity}(D_{exterity})=\left\{0 \le D_{exterity}<15:-0.15+0.01\left|D_{exterity}-0\right|,15 \le D_{exterity}<23:0+0.03\left|D_{exterity}-15\right|,23 \le D_{exterity}<31:0.24+0.02\left|D_{exterity}-23\right|,31 \le D_{exterity}<37:0.4+0.01\left|D_{exterity}-31\right|,37 \le D_{exterity}<45:0.46+0.005\left|D_{exterity}-37\right|,45 \le D_{exterity}<95:0.5+0.001\left|D_{exterity}-45\right|,95 \le D_{exterity}<100:0.55+0\left|D_{exterity}-95\right|\right\}
See Example for how to use.
Item Equip Speed exclusively governs the speed at which you equip armors, as equipping weapons, jewelry and utility items is instant.
Dexterity governs your Item Equip Speed.
0 Dexterity starts at -95% Item Equip Speed.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
I_{temEquipSpeed}(D_{exterity})=\left\{0 \le D_{exterity}<1:-0.95+0\left|D_{exterity}-0\right|,1 \le D_{exterity}<2:-0.95+0.04\left|D_{exterity}-1\right|,2 \le D_{exterity}<15:-0.91+0.07\left|D_{exterity}-2\right|,15 \le D_{exterity}<35:0+0.05\left|D_{exterity}-15\right|,35 \le D_{exterity}<70:1+0.02\left|D_{exterity}-35\right|,70 \le D_{exterity}<100:1.7+0.01\left|D_{exterity}-70\right|\right\}
See Example for how to use.
Magic Power governs your Magic Power Bonus.
Will governs your Magical Power.
0 Will starts at 0 Magical Power.
LaTeX Formula
Magic Power bonus governs the potency of your magical spells, magical damage dealing abilities and magical healing abilities.
Magical Power governs your Magical Power Bonus.
0 Magical Power starts at -90% Magical Power Bonus.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
M_{agicalPowerBonus}(M_{agicalPower})=\left\{0 \le M_{agicalPower}<1:-0.9+0\left|M_{agicalPower}-0\right|,1 \le M_{agicalPower}<5:-0.9+0.1\left|M_{agicalPower}-1\right|,5 \le M_{agicalPower}<15:-0.5+0.05\left|M_{agicalPower}-5\right|,15 \le M_{agicalPower}<21:0+0.025\left|M_{agicalPower}-15\right|,21 \le M_{agicalPower}<40:0.15+0.02\left|M_{agicalPower}-21\right|,40 \le M_{agicalPower}<50:0.53+0.01\left|M_{agicalPower}-40\right|,50 \le M_{agicalPower}<100:0.63+0.005\left|M_{agicalPower}-50\right|\right\}
See Example for how to use.
Magic Resistance governs your Magical Damage Reduction.
Will governs your Magic Resistance.
0 Will starts at -20 Magic Resistance.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
M_{agicResistance}(W_{ill})=\left\{0 \le W_{ill}<5:-20+4\left|W_{ill}-0\right|,5 \le W_{ill}<35:0+3\left|W_{ill}-5\right|,35 \le W_{ill}<55:90+2\left|W_{ill}-35\right|,55 \le W_{ill}<66:130+1\left|W_{ill}-55\right|,66 \le W_{ill}<67:141+0\left|W_{ill}-66\right|,67 \le W_{ill}<68:141+1\left|W_{ill}-67\right|,68 \le W_{ill}<69:142+0\left|W_{ill}-68\right|,69 \le W_{ill}<70:142+1\left|W_{ill}-69\right|,70 \le W_{ill}<71:143+0\left|W_{ill}-70\right|,71 \le W_{ill}<72:143+1\left|W_{ill}-71\right|,72 \le W_{ill}<73:144+0\left|W_{ill}-72\right|,73 \le W_{ill}<74:144+1\left|W_{ill}-73\right|,74 \le W_{ill}<75:145+0\left|W_{ill}-74\right|,75 \le W_{ill}<76:145+1\left|W_{ill}-75\right|,76 \le W_{ill}<77:146+0\left|W_{ill}-76\right|,77 \le W_{ill}<78:146+1\left|W_{ill}-77\right|,78 \le W_{ill}<79:147+0\left|W_{ill}-78\right|,79 \le W_{ill}<80:147+1\left|W_{ill}-79\right|,80 \le W_{ill}<82:148+0\left|W_{ill}-80\right|,82 \le W_{ill}<83:148+1\left|W_{ill}-82\right|,83 \le W_{ill}<84:149+0\left|W_{ill}-83\right|,84 \le W_{ill}<85:149+1\left|W_{ill}-84\right|,85 \le W_{ill}<86:150+0\left|W_{ill}-85\right|,86 \le W_{ill}<87:150+1\left|W_{ill}-86\right|,87 \le W_{ill}<88:151+0\left|W_{ill}-87\right|,88 \le W_{ill}<89:151+1\left|W_{ill}-88\right|,89 \le W_{ill}<90:152+0\left|W_{ill}-89\right|,90 \le W_{ill}<91:152+1\left|W_{ill}-90\right|,91 \le W_{ill}<92:153+-1\left|W_{ill}-91\right|,92 \le W_{ill}<94:152+1\left|W_{ill}-92\right|,94 \le W_{ill}<95:154+0\left|W_{ill}-94\right|,95 \le W_{ill}<96:154+1\left|W_{ill}-95\right|,96 \le W_{ill}<97:155+0\left|W_{ill}-96\right|,97 \le W_{ill}<98:155+1\left|W_{ill}-97\right|,98 \le W_{ill}<99:156+0\left|W_{ill}-98\right|,99 \le W_{ill}<100:156+1\left|W_{ill}-99\right|\right\}
See Example for how to use.
Magical Damage Reduction governs your resistance to magical damage dealing weapons, spells and projectiles. Please note that there is currently a bug where Magical Damage Reduction is additively 10% lower than the following expected amounts.
Magic Resistance governs your Magical Damage Reduction.
-300 Magic Resistance starts at -595% Magical Damage Reduction.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
M_{agicalDamageReduction}(M_{agicResistance})=\left\{-300 \le M_{agicResistance}<-15:-5.95+0.02\left|M_{agicResistance}--300\right|,-15 \le M_{agicResistance}<10:-0.25+0.01\left|M_{agicResistance}--15\right|,10 \le M_{agicResistance}<19:0+0.005\left|M_{agicResistance}-10\right|,19 \le M_{agicResistance}<30:0.045+0.004\left|M_{agicResistance}-19\right|,30 \le M_{agicResistance}<40:0.089+0.003\left|M_{agicResistance}-30\right|,40 \le M_{agicResistance}<50:0.119+0.002\left|M_{agicResistance}-40\right|,50 \le M_{agicResistance}<100:0.139+0.001\left|M_{agicResistance}-50\right|,100 \le M_{agicResistance}<150:0.189+0.002\left|M_{agicResistance}-100\right|,150 \le M_{agicResistance}<250:0.289+0.003\left|M_{agicResistance}-150\right|,250 \le M_{agicResistance}<350:0.589+0.002\left|M_{agicResistance}-250\right|,350 \le M_{agicResistance}<500:0.789+0.001\left|M_{agicResistance}-350\right|\right\}
See Example for how to use.
Magical Damage Reduction is capped to 85%
Buff Duration governs the duration of temporary beneficial status effects.
Will governs your Buff Duration.
0 Will starts at -80% Buff Duration.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
B_{uffDuration}(W_{ill})=\left\{0 \le W_{ill}<5:-0.8+0.1\left|W_{ill}-0\right|,5 \le W_{ill}<7:-0.3+0.05\left|W_{ill}-5\right|,7 \le W_{ill}<11:-0.2+0.03\left|W_{ill}-7\right|,11 \le W_{ill}<15:-0.08+0.02\left|W_{ill}-11\right|,15 \le W_{ill}<50:0+0.01\left|W_{ill}-15\right|,50 \le W_{ill}<100:0.35+0.005\left|W_{ill}-50\right|\right\}
See Example for how to use.
Debuff Duration governs the duration of temporary negative status effects. A negative Debuff Duration is beneficial to have, as it will shorten the duration of debuffs. A positive Debuff Duration stat means debuffs last longer, which is detrimental to the player.
Will governs your Debuff Duration.
0 Will starts at 400% Debuff Duration.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
D_{ebuffDuration}(W_{ill})=\left\{0 \le W_{ill}<1:4+-1.667\left|W_{ill}-0\right|,1 \le W_{ill}<2:2.333+-0.833\left|W_{ill}-1\right|,2 \le W_{ill}<3:1.5+-0.5\left|W_{ill}-2\right|,3 \le W_{ill}<4:1+-0.333\left|W_{ill}-3\right|,4 \le W_{ill}<5:0.667+-0.238\left|W_{ill}-4\right|,5 \le W_{ill}<6:0.429+-0.096\left|W_{ill}-5\right|,6 \le W_{ill}<7:0.333+-0.083\left|W_{ill}-6\right|,7 \le W_{ill}<8:0.25+-0.045\left|W_{ill}-7\right|,8 \le W_{ill}<9:0.205+-0.042\left|W_{ill}-8\right|,9 \le W_{ill}<10:0.163+-0.039\left|W_{ill}-9\right|,10 \le W_{ill}<11:0.124+-0.037\left|W_{ill}-10\right|,11 \le W_{ill}<12:0.087+-0.023\left|W_{ill}-11\right|,12 \le W_{ill}<14:0.064+-0.022\left|W_{ill}-12\right|,14 \le W_{ill}<15:0.02+-0.02\left|W_{ill}-14\right|,15 \le W_{ill}<17:0+-0.01\left|W_{ill}-15\right|,17 \le W_{ill}<19:-0.02+-0.009\left|W_{ill}-17\right|,19 \le W_{ill}<20:-0.038+-0.01\left|W_{ill}-19\right|,20 \le W_{ill}<21:-0.048+-0.009\left|W_{ill}-20\right|,21 \le W_{ill}<22:-0.057+-0.008\left|W_{ill}-21\right|,22 \le W_{ill}<24:-0.065+-0.009\left|W_{ill}-22\right|,24 \le W_{ill}<29:-0.083+-0.008\left|W_{ill}-24\right|,29 \le W_{ill}<30:-0.123+-0.007\left|W_{ill}-29\right|,30 \le W_{ill}<31:-0.13+-0.008\left|W_{ill}-30\right|,31 \le W_{ill}<32:-0.138+-0.007\left|W_{ill}-31\right|,32 \le W_{ill}<33:-0.145+-0.008\left|W_{ill}-32\right|,33 \le W_{ill}<36:-0.153+-0.007\left|W_{ill}-33\right|,36 \le W_{ill}<37:-0.174+-0.006\left|W_{ill}-36\right|,37 \le W_{ill}<39:-0.18+-0.007\left|W_{ill}-37\right|,39 \le W_{ill}<41:-0.194+-0.006\left|W_{ill}-39\right|,41 \le W_{ill}<42:-0.206+-0.007\left|W_{ill}-41\right|,42 \le W_{ill}<46:-0.213+-0.006\left|W_{ill}-42\right|,46 \le W_{ill}<47:-0.237+-0.005\left|W_{ill}-46\right|,47 \le W_{ill}<49:-0.242+-0.006\left|W_{ill}-47\right|,49 \le W_{ill}<50:-0.254+-0.005\left|W_{ill}-49\right|,50 \le W_{ill}<52:-0.259+-0.003\left|W_{ill}-50\right|,52 \le W_{ill}<53:-0.265+-0.002\left|W_{ill}-52\right|,53 \le W_{ill}<55:-0.267+-0.003\left|W_{ill}-53\right|,55 \le W_{ill}<56:-0.273+-0.002\left|W_{ill}-55\right|,56 \le W_{ill}<58:-0.275+-0.003\left|W_{ill}-56\right|,58 \le W_{ill}<59:-0.281+-0.002\left|W_{ill}-58\right|,59 \le W_{ill}<60:-0.283+-0.003\left|W_{ill}-59\right|,60 \le W_{ill}<61:-0.286+-0.002\left|W_{ill}-60\right|,61 \le W_{ill}<62:-0.288+-0.003\left|W_{ill}-61\right|,62 \le W_{ill}<63:-0.291+-0.002\left|W_{ill}-62\right|,63 \le W_{ill}<64:-0.293+-0.003\left|W_{ill}-63\right|,64 \le W_{ill}<65:-0.296+-0.002\left|W_{ill}-64\right|,65 \le W_{ill}<66:-0.298+-0.003\left|W_{ill}-65\right|,66 \le W_{ill}<67:-0.301+-0.002\left|W_{ill}-66\right|,67 \le W_{ill}<68:-0.303+-0.003\left|W_{ill}-67\right|,68 \le W_{ill}<70:-0.306+-0.002\left|W_{ill}-68\right|,70 \le W_{ill}<71:-0.31+-0.003\left|W_{ill}-70\right|,71 \le W_{ill}<73:-0.313+-0.002\left|W_{ill}-71\right|,73 \le W_{ill}<74:-0.317+-0.003\left|W_{ill}-73\right|,74 \le W_{ill}<76:-0.32+-0.002\left|W_{ill}-74\right|,76 \le W_{ill}<77:-0.324+-0.003\left|W_{ill}-76\right|,77 \le W_{ill}<80:-0.327+-0.002\left|W_{ill}-77\right|,80 \le W_{ill}<81:-0.333+-0.003\left|W_{ill}-80\right|,81 \le W_{ill}<86:-0.336+-0.002\left|W_{ill}-81\right|,86 \le W_{ill}<87:-0.346+-0.003\left|W_{ill}-86\right|,87 \le W_{ill}<100:-0.349+-0.002\left|W_{ill}-87\right|\right\}
See Example for how to use.
Debuff Duration has a lower cap of -95%, meaning at minimum a debuff can last 1/20th of its base duration.
Magical Interaction Speed affects the speed with which the player interacts with magical objects, such as Shrines and Portals. See Action/Interaction/Cast_Speed for more.
Will governs your Magical Interaction Speed.
0 Will starts at -75% Magical Interaction Speed.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
M_{agicalInteractionSpeed}(W_{ill})=\left\{0 \le W_{ill}<15:-0.75+0.05\left|W_{ill}-0\right|,15 \le W_{ill}<25:0+0.07\left|W_{ill}-15\right|,25 \le W_{ill}<35:0.7+0.05\left|W_{ill}-25\right|,35 \le W_{ill}<84:1.2+0.02\left|W_{ill}-35\right|,84 \le W_{ill}<85:2.18+0.01\left|W_{ill}-84\right|,85 \le W_{ill}<86:2.19+0.03\left|W_{ill}-85\right|,86 \le W_{ill}<100:2.22+0.02\left|W_{ill}-86\right|\right\}
See Example for how to use.
Note that the Debuff Duration Bonus enchant converts into a negative Debuff Duration, decreasing the duration of debuffs on you.
Durations are not rounded and last their exact amount. However, actions that are performed in intervals, like Damage/Healing [time], are rounded down to the nearest integer, resulting in thresholds that players may want to take advantage of.
Spell Casting Speed governs the speed at which you cast magical spells. See Action/Interaction/Cast_Speed for more.
Knowledge governs your Spell Casting Speed.
0 Knowledge starts at -93% Spell Casting Speed.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
S_{pellCastingSpeed}(K_{nowledge})=\left\{0 \le K_{nowledge}<1:-0.93+0\left|K_{nowledge}-0\right|,1 \le K_{nowledge}<19:-0.93+0.05\left|K_{nowledge}-1\right|,19 \le K_{nowledge}<25:-0.03+0.03\left|K_{nowledge}-19\right|,25 \le K_{nowledge}<55:0.15+0.025\left|K_{nowledge}-25\right|,55 \le K_{nowledge}<85:0.9+0.02\left|K_{nowledge}-55\right|,85 \le K_{nowledge}<100:1.5+0.015\left|K_{nowledge}-85\right|\right\}
See Example for how to use.
Spell Casting Time = (Base Casting Time)/(1 + Spell Casting Speed)
Memory Capacity govern your spell/song cost cap, meaning equipping spells/songs that exceed this cap will not be usable.
Knowledge governs your Memory Capacity.
0 Knowledge starts at 0 Memory Capacity.
LaTeX Formula
Total Memory Capacity = ceil(Memory Cap from Knowledge * (1 + Memory Cap Bonus%)) + Add Memory Cap
Memory Cap Bonus% and Add Memory Cap are two different Enchantments.
For example, with 12 Memory Cap from 18 knowledge, +8 Add Memory Cap, and 7.7% Memory Cap Bonus, the final Memory Capacity will be
ceil(12 * 1.077) + 8 = 21 Memory Capacity
Increases the amount of Spell/(Skill?) Points (SP) you restore per tick.
Knowledge governs your Memory Recovery.
0 Knowledge starts at 43% Memory Recovery.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
M_{emoryRecovery}(K_{nowledge})=\left\{0 \le K_{nowledge}<28:0.43+0.015\left|K_{nowledge}-0\right|,28 \le K_{nowledge}<35:0.85+0.05\left|K_{nowledge}-28\right|,35 \le K_{nowledge}<84:1.2+0.02\left|K_{nowledge}-35\right|,84 \le K_{nowledge}<85:2.18+0.01\left|K_{nowledge}-84\right|,85 \le K_{nowledge}<86:2.19+0.03\left|K_{nowledge}-85\right|,86 \le K_{nowledge}<100:2.22+0.02\left|K_{nowledge}-86\right|\right\}
See Example for how to use.
SP Recharge per tick (SP/tick) = Base Recharge * (1 + Memory Recovery Bonus)
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
Resourcefulness increases Regular Interaction Speed with 60% Scaling. See the Hybrid stat Regular Interaction Speed for more.
Cooldown Reduction reduces the cooldowns of abilities/skills.
Resourcefulness governs your Cooldown Reduction.
0 Resourcefulness starts at -30% Cooldown Reduction.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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C_{ooldownReduction}(R_{esourcefulness})=\left\{0 \le R_{esourcefulness}<20:-0.3+0.02\left|R_{esourcefulness}-0\right|,20 \le R_{esourcefulness}<50:0.1+0.01\left|R_{esourcefulness}-20\right|,50 \le R_{esourcefulness}<100:0.4+0.005\left|R_{esourcefulness}-50\right|\right\}
See Example for how to use.
Persuasiveness determines the duration of Bard songs' buffs/debuffs.
Resourcefulness governs your Persuasiveness.
0 Resourcefulness starts at 0 Persuasiveness.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
P_{ersuasiveness}(R_{esourcefulness})=\left\{0 \le R_{esourcefulness}<35:0+1\left|R_{esourcefulness}-0\right|,35 \le R_{esourcefulness}<71:35+0.5\left|R_{esourcefulness}-35\right|,71 \le R_{esourcefulness}<99:53+0.25\left|R_{esourcefulness}-71\right|,99 \le R_{esourcefulness}<100:60+0\left|R_{esourcefulness}-99\right|\right\}
See Example for how to use.
Base buff duration formula:
Scaling x Persuasiveness
Each point in Persuasiveness over the base of 15 grants a 6.66% longer base duration.
The duration listed both in game and in a song's description at Bard represent the duration of the song at the base of 15 Persuasiveness. Some songs there are noted to not scale with Persuasiveness, meaning they always last the listed amount, before Buff/Debuff duration. Some songs technically apply no duration or their affect lasts only while Channeling, like Peacemaking and Chaotic Discord.
For example, Perfectly played Rousing Rhythms have 4.5x scaling and if Bard has 20 Persuasiveness, outgoing buff duration will be:
4.5 x 20 = 90
seconds
This will also get multiplied by the receiver's Buff Duration/Debuff Duration
Hybrid stats are stats which come from a combination of attributes. For example, Health is determined by both Strength and Vigor.
Max Health determines your characters maximum Health.
Strength and Vigor governs your Max Health.
Strength has 25% scaling, and Vigor has 75% scaling, which then get combined into a Sum and translated into MaxHealth.
Sum = Strength * 0.25 + Vigor * 0.75
0 Sum starts at 60 Max Health.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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M_{axHealth}(S_{um})=\left\{0 \le S_{um}<10:60+3\left|S_{um}-0\right|,10 \le S_{um}<50:90+2\left|S_{um}-10\right|,50 \le S_{um}<75:170+1\left|S_{um}-50\right|,75 \le S_{um}<100:195+0.5\left|S_{um}-75\right|\right\}
See Example for how to use.
Final Max Health formula with examples can be found on the Health page.
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables. See Action/Interaction/Cast_Speed for more.
Agility and Dexterity governs your Action Speed.
Agility has 25% scaling, and Dexterity has 75% scaling, which then get combined into a Sum and translated into ActionSpeed.
Sum = Agility * 0.25 + Dexterity * 0.75
0 Sum starts at -38% Action Speed.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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A_{ctionSpeed}(S_{um})=\left\{0 \le S_{um}<10:-0.38+0.03\left|S_{um}-0\right|,10 \le S_{um}<13:-0.08+0.02\left|S_{um}-10\right|,13 \le S_{um}<25:-0.02+0.01\left|S_{um}-13\right|,25 \le S_{um}<41:0.1+0.015\left|S_{um}-25\right|,41 \le S_{um}<50:0.34+0.01\left|S_{um}-41\right|,50 \le S_{um}<100:0.43+0.005\left|S_{um}-50\right|\right\}
See Example for how to use.
An Action Speed of 50% results in the animation lasting for only 67% of the base animation length.
New animation length = Base animation length / (1 + Action Speed)
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon. See Action/Interaction/Cast_Speed for more.
Agility and Resourcefulness governs your Regular Interaction Speed.
Agility has 40% scaling, and Resourcefulness has 60% scaling, which then get combined into a Sum and translated into RegularInteractionSpeed.
Sum = Agility * 0.4 + Resourcefulness * 0.6
0 Sum starts at -55% Regular Interaction Speed.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
R_{egularInteractionSpeed}(S_{um})=\left\{0 \le S_{um}<5:-0.55+0.05\left|S_{um}-0\right|,5 \le S_{um}<15:-0.3+0.03\left|S_{um}-5\right|,15 \le S_{um}<25:0+0.07\left|S_{um}-15\right|,25 \le S_{um}<35:0.7+0.05\left|S_{um}-25\right|,35 \le S_{um}<84:1.2+0.02\left|S_{um}-35\right|,84 \le S_{um}<85:2.18+0.01\left|S_{um}-84\right|,85 \le S_{um}<86:2.19+0.03\left|S_{um}-85\right|,86 \le S_{um}<100:2.22+0.02\left|S_{um}-86\right|\right\}
See Example for how to use.
New interaction length = Base interaction length / (1 + interaction speed)
For example, an Interaction Speed of 100% results in the interaction time lasting for only 50% of the base interaction length.
Surgical Kits have 50% scaling on regular interaction speed, therefore, their formula looks like
New interaction length = Base interaction length / (1 + interaction speed * .5)
Physical Damage Reduction governs your resistance to physical damage dealing weapons and projectiles. Unlike Magic Resistance that is increased by Will, Armor Rating does not have an attribute stat that it scales off.
Armor Rating governs your Physical Damage Reduction.
-300 Armor Rating starts at -619% Physical Damage Reduction.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
P_{hysicalDamageReduction}(A_{rmorRating})=\left\{-300 \le A_{rmorRating}<-3:-6.19+0.02\left|A_{rmorRating}--300\right|,-3 \le A_{rmorRating}<22:-0.25+0.01\left|A_{rmorRating}--3\right|,22 \le A_{rmorRating}<31:0+0.005\left|A_{rmorRating}-22\right|,31 \le A_{rmorRating}<42:0.045+0.004\left|A_{rmorRating}-31\right|,42 \le A_{rmorRating}<52:0.089+0.003\left|A_{rmorRating}-42\right|,52 \le A_{rmorRating}<62:0.119+0.002\left|A_{rmorRating}-52\right|,62 \le A_{rmorRating}<112:0.139+0.001\left|A_{rmorRating}-62\right|,112 \le A_{rmorRating}<175:0.189+0.002\left|A_{rmorRating}-112\right|,175 \le A_{rmorRating}<230:0.315+0.003\left|A_{rmorRating}-175\right|,230 \le A_{rmorRating}<317:0.48+0.002\left|A_{rmorRating}-230\right|,317 \le A_{rmorRating}<353:0.654+0.001\left|A_{rmorRating}-317\right|,353 \le A_{rmorRating}<368:0.69+0.001\left|A_{rmorRating}-353\right|,368 \le A_{rmorRating}<369:0.698+0\left|A_{rmorRating}-368\right|,369 \le A_{rmorRating}<370:0.698+0.001\left|A_{rmorRating}-369\right|,370 \le A_{rmorRating}<428:0.699+0.001\left|A_{rmorRating}-370\right|,428 \le A_{rmorRating}<429:0.728+-0.001\left|A_{rmorRating}-428\right|,429 \le A_{rmorRating}<450:0.727+0\left|A_{rmorRating}-429\right|,450 \le A_{rmorRating}<500:0.732+0\left|A_{rmorRating}-450\right|\right\}
See Example for how to use.
Physical Damage Reduction is capped to 75%
Impact Power governs the strength of your weapon strikes against a target, it determines if you can break objects and stagger blocking enemies.
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:
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 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
LaTeX Formula
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
L_{uckGrade02}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<1:1+0\left|L_{uckGrade}-0\right|,1 \le L_{uckGrade}<2:1+-0.001\left|L_{uckGrade}-1\right|,2 \le L_{uckGrade}<3:0.999+0\left|L_{uckGrade}-2\right|,3 \le L_{uckGrade}<4:0.999+-0.001\left|L_{uckGrade}-3\right|,4 \le L_{uckGrade}<5:0.998+0\left|L_{uckGrade}-4\right|,5 \le L_{uckGrade}<6:0.998+-0.001\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<7:0.997+0\left|L_{uckGrade}-6\right|,7 \le L_{uckGrade}<8:0.997+-0.001\left|L_{uckGrade}-7\right|,8 \le L_{uckGrade}<9:0.996+0\left|L_{uckGrade}-8\right|,9 \le L_{uckGrade}<10:0.996+-0.001\left|L_{uckGrade}-9\right|,10 \le L_{uckGrade}<11:0.995+0\left|L_{uckGrade}-10\right|,11 \le L_{uckGrade}<12:0.995+-0.001\left|L_{uckGrade}-11\right|,12 \le L_{uckGrade}<13:0.994+0\left|L_{uckGrade}-12\right|,13 \le L_{uckGrade}<14:0.994+-0.001\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<15:0.993+0\left|L_{uckGrade}-14\right|,15 \le L_{uckGrade}<16:0.993+-0.001\left|L_{uckGrade}-15\right|,16 \le L_{uckGrade}<17:0.992+0\left|L_{uckGrade}-16\right|,17 \le L_{uckGrade}<18:0.992+-0.001\left|L_{uckGrade}-17\right|,18 \le L_{uckGrade}<19:0.991+0\left|L_{uckGrade}-18\right|,19 \le L_{uckGrade}<20:0.991+-0.001\left|L_{uckGrade}-19\right|,20 \le L_{uckGrade}<21:0.99+0\left|L_{uckGrade}-20\right|,21 \le L_{uckGrade}<22:0.99+-0.001\left|L_{uckGrade}-21\right|,22 \le L_{uckGrade}<23:0.989+0\left|L_{uckGrade}-22\right|,23 \le L_{uckGrade}<24:0.989+-0.001\left|L_{uckGrade}-23\right|,24 \le L_{uckGrade}<25:0.988+0\left|L_{uckGrade}-24\right|,25 \le L_{uckGrade}<26:0.988+-0.001\left|L_{uckGrade}-25\right|,26 \le L_{uckGrade}<27:0.987+0\left|L_{uckGrade}-26\right|,27 \le L_{uckGrade}<28:0.987+-0.001\left|L_{uckGrade}-27\right|,28 \le L_{uckGrade}<29:0.986+0\left|L_{uckGrade}-28\right|,29 \le L_{uckGrade}<30:0.986+-0.001\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<31:0.985+0\left|L_{uckGrade}-30\right|,31 \le L_{uckGrade}<32:0.985+-0.001\left|L_{uckGrade}-31\right|,32 \le L_{uckGrade}<33:0.984+0\left|L_{uckGrade}-32\right|,33 \le L_{uckGrade}<34:0.984+-0.001\left|L_{uckGrade}-33\right|,34 \le L_{uckGrade}<35:0.983+0\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<36:0.983+-0.001\left|L_{uckGrade}-35\right|,36 \le L_{uckGrade}<37:0.982+0\left|L_{uckGrade}-36\right|,37 \le L_{uckGrade}<38:0.982+-0.001\left|L_{uckGrade}-37\right|,38 \le L_{uckGrade}<39:0.981+0\left|L_{uckGrade}-38\right|,39 \le L_{uckGrade}<40:0.981+-0.001\left|L_{uckGrade}-39\right|,40 \le L_{uckGrade}<41:0.98+0\left|L_{uckGrade}-40\right|,41 \le L_{uckGrade}<42:0.98+-0.001\left|L_{uckGrade}-41\right|,42 \le L_{uckGrade}<43:0.979+0\left|L_{uckGrade}-42\right|,43 \le L_{uckGrade}<44:0.979+-0.001\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<45:0.978+0\left|L_{uckGrade}-44\right|,45 \le L_{uckGrade}<46:0.978+-0.001\left|L_{uckGrade}-45\right|,46 \le L_{uckGrade}<47:0.977+0\left|L_{uckGrade}-46\right|,47 \le L_{uckGrade}<48:0.977+-0.001\left|L_{uckGrade}-47\right|,48 \le L_{uckGrade}<49:0.976+0\left|L_{uckGrade}-48\right|,49 \le L_{uckGrade}<50:0.976+-0.001\left|L_{uckGrade}-49\right|,50 \le L_{uckGrade}<51:0.975+0\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<52:0.975+-0.001\left|L_{uckGrade}-51\right|,52 \le L_{uckGrade}<53:0.974+0\left|L_{uckGrade}-52\right|,53 \le L_{uckGrade}<54:0.974+-0.001\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<55:0.973+0\left|L_{uckGrade}-54\right|,55 \le L_{uckGrade}<56:0.973+-0.001\left|L_{uckGrade}-55\right|,56 \le L_{uckGrade}<57:0.972+0\left|L_{uckGrade}-56\right|,57 \le L_{uckGrade}<58:0.972+-0.001\left|L_{uckGrade}-57\right|,58 \le L_{uckGrade}<59:0.971+0\left|L_{uckGrade}-58\right|,59 \le L_{uckGrade}<60:0.971+-0.001\left|L_{uckGrade}-59\right|,60 \le L_{uckGrade}<61:0.97+0\left|L_{uckGrade}-60\right|,61 \le L_{uckGrade}<62:0.97+-0.001\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<63:0.969+0\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<64:0.969+-0.001\left|L_{uckGrade}-63\right|,64 \le L_{uckGrade}<65:0.968+0\left|L_{uckGrade}-64\right|,65 \le L_{uckGrade}<66:0.968+-0.001\left|L_{uckGrade}-65\right|,66 \le L_{uckGrade}<67:0.967+0\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<68:0.967+-0.001\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<69:0.966+0\left|L_{uckGrade}-68\right|,69 \le L_{uckGrade}<70:0.966+-0.001\left|L_{uckGrade}-69\right|,70 \le L_{uckGrade}<71:0.965+0\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<72:0.965+-0.001\left|L_{uckGrade}-71\right|,72 \le L_{uckGrade}<73:0.964+0\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<74:0.964+-0.001\left|L_{uckGrade}-73\right|,74 \le L_{uckGrade}<75:0.963+0\left|L_{uckGrade}-74\right|,75 \le L_{uckGrade}<76:0.963+-0.001\left|L_{uckGrade}-75\right|,76 \le L_{uckGrade}<77:0.962+0\left|L_{uckGrade}-76\right|,77 \le L_{uckGrade}<78:0.962+-0.001\left|L_{uckGrade}-77\right|,78 \le L_{uckGrade}<79:0.961+0\left|L_{uckGrade}-78\right|,79 \le L_{uckGrade}<80:0.961+-0.001\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<81:0.96+0\left|L_{uckGrade}-80\right|,81 \le L_{uckGrade}<82:0.96+-0.001\left|L_{uckGrade}-81\right|,82 \le L_{uckGrade}<83:0.959+0\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<84:0.959+-0.001\left|L_{uckGrade}-83\right|,84 \le L_{uckGrade}<85:0.958+0\left|L_{uckGrade}-84\right|,85 \le L_{uckGrade}<86:0.958+-0.001\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<87:0.957+0\left|L_{uckGrade}-86\right|,87 \le L_{uckGrade}<88:0.957+-0.001\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<89:0.956+0\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<90:0.956+-0.001\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<91:0.955+0\left|L_{uckGrade}-90\right|,91 \le L_{uckGrade}<92:0.955+-0.001\left|L_{uckGrade}-91\right|,92 \le L_{uckGrade}<93:0.954+0\left|L_{uckGrade}-92\right|,93 \le L_{uckGrade}<94:0.954+-0.001\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<95:0.953+0\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<96:0.953+-0.001\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<97:0.952+0\left|L_{uckGrade}-96\right|,97 \le L_{uckGrade}<98:0.952+-0.001\left|L_{uckGrade}-97\right|,98 \le L_{uckGrade}<99:0.951+0\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<100:0.951+-0.001\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<101:0.95+0\left|L_{uckGrade}-100\right|,101 \le L_{uckGrade}<102:0.95+-0.001\left|L_{uckGrade}-101\right|,102 \le L_{uckGrade}<103:0.949+0\left|L_{uckGrade}-102\right|,103 \le L_{uckGrade}<104:0.949+-0.001\left|L_{uckGrade}-103\right|,104 \le L_{uckGrade}<105:0.948+0\left|L_{uckGrade}-104\right|,105 \le L_{uckGrade}<106:0.948+-0.001\left|L_{uckGrade}-105\right|,106 \le L_{uckGrade}<107:0.947+0\left|L_{uckGrade}-106\right|,107 \le L_{uckGrade}<108:0.947+-0.001\left|L_{uckGrade}-107\right|,108 \le L_{uckGrade}<109:0.946+0\left|L_{uckGrade}-108\right|,109 \le L_{uckGrade}<110:0.946+-0.001\left|L_{uckGrade}-109\right|,110 \le L_{uckGrade}<111:0.945+0\left|L_{uckGrade}-110\right|,111 \le L_{uckGrade}<112:0.945+-0.001\left|L_{uckGrade}-111\right|,112 \le L_{uckGrade}<113:0.944+0\left|L_{uckGrade}-112\right|,113 \le L_{uckGrade}<114:0.944+-0.001\left|L_{uckGrade}-113\right|,114 \le L_{uckGrade}<115:0.943+0\left|L_{uckGrade}-114\right|,115 \le L_{uckGrade}<116:0.943+-0.001\left|L_{uckGrade}-115\right|,116 \le L_{uckGrade}<117:0.942+0\left|L_{uckGrade}-116\right|,117 \le L_{uckGrade}<118:0.942+-0.001\left|L_{uckGrade}-117\right|,118 \le L_{uckGrade}<119:0.941+0\left|L_{uckGrade}-118\right|,119 \le L_{uckGrade}<120:0.941+-0.001\left|L_{uckGrade}-119\right|,120 \le L_{uckGrade}<121:0.94+0\left|L_{uckGrade}-120\right|,121 \le L_{uckGrade}<122:0.94+-0.001\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<123:0.939+0\left|L_{uckGrade}-122\right|,123 \le L_{uckGrade}<124:0.939+-0.001\left|L_{uckGrade}-123\right|,124 \le L_{uckGrade}<125:0.938+0\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<126:0.938+-0.001\left|L_{uckGrade}-125\right|,126 \le L_{uckGrade}<127:0.937+0\left|L_{uckGrade}-126\right|,127 \le L_{uckGrade}<128:0.937+-0.001\left|L_{uckGrade}-127\right|,128 \le L_{uckGrade}<129:0.936+0\left|L_{uckGrade}-128\right|,129 \le L_{uckGrade}<130:0.936+-0.001\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<131:0.935+0\left|L_{uckGrade}-130\right|,131 \le L_{uckGrade}<132:0.935+-0.001\left|L_{uckGrade}-131\right|,132 \le L_{uckGrade}<133:0.934+0\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<134:0.934+-0.001\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<135:0.933+0\left|L_{uckGrade}-134\right|,135 \le L_{uckGrade}<136:0.933+-0.001\left|L_{uckGrade}-135\right|,136 \le L_{uckGrade}<137:0.932+0\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<138:0.932+-0.001\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<139:0.931+0\left|L_{uckGrade}-138\right|,139 \le L_{uckGrade}<140:0.931+-0.001\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<141:0.93+0\left|L_{uckGrade}-140\right|,141 \le L_{uckGrade}<142:0.93+-0.001\left|L_{uckGrade}-141\right|,142 \le L_{uckGrade}<143:0.929+0\left|L_{uckGrade}-142\right|,143 \le L_{uckGrade}<144:0.929+-0.001\left|L_{uckGrade}-143\right|,144 \le L_{uckGrade}<145:0.928+0\left|L_{uckGrade}-144\right|,145 \le L_{uckGrade}<146:0.928+-0.001\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<147:0.927+0\left|L_{uckGrade}-146\right|,147 \le L_{uckGrade}<148:0.927+-0.001\left|L_{uckGrade}-147\right|,148 \le L_{uckGrade}<149:0.926+0\left|L_{uckGrade}-148\right|,149 \le L_{uckGrade}<150:0.926+-0.001\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<151:0.925+0\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:0.925+-0.001\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<153:0.924+0\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<154:0.924+-0.001\left|L_{uckGrade}-153\right|,154 \le L_{uckGrade}<155:0.923+0\left|L_{uckGrade}-154\right|,155 \le L_{uckGrade}<156:0.923+-0.001\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<157:0.922+0\left|L_{uckGrade}-156\right|,157 \le L_{uckGrade}<158:0.922+-0.001\left|L_{uckGrade}-157\right|,158 \le L_{uckGrade}<159:0.921+0\left|L_{uckGrade}-158\right|,159 \le L_{uckGrade}<160:0.921+-0.001\left|L_{uckGrade}-159\right|,160 \le L_{uckGrade}<161:0.92+0\left|L_{uckGrade}-160\right|,161 \le L_{uckGrade}<162:0.92+-0.001\left|L_{uckGrade}-161\right|,162 \le L_{uckGrade}<163:0.919+0\left|L_{uckGrade}-162\right|,163 \le L_{uckGrade}<164:0.919+-0.001\left|L_{uckGrade}-163\right|,164 \le L_{uckGrade}<165:0.918+0\left|L_{uckGrade}-164\right|,165 \le L_{uckGrade}<166:0.918+-0.001\left|L_{uckGrade}-165\right|,166 \le L_{uckGrade}<167:0.917+0\left|L_{uckGrade}-166\right|,167 \le L_{uckGrade}<168:0.917+-0.001\left|L_{uckGrade}-167\right|,168 \le L_{uckGrade}<169:0.916+0\left|L_{uckGrade}-168\right|,169 \le L_{uckGrade}<170:0.916+-0.001\left|L_{uckGrade}-169\right|,170 \le L_{uckGrade}<171:0.915+0\left|L_{uckGrade}-170\right|,171 \le L_{uckGrade}<172:0.915+-0.001\left|L_{uckGrade}-171\right|,172 \le L_{uckGrade}<173:0.914+0\left|L_{uckGrade}-172\right|,173 \le L_{uckGrade}<174:0.914+-0.001\left|L_{uckGrade}-173\right|,174 \le L_{uckGrade}<175:0.913+0\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<176:0.913+-0.001\left|L_{uckGrade}-175\right|,176 \le L_{uckGrade}<177:0.912+0\left|L_{uckGrade}-176\right|,177 \le L_{uckGrade}<178:0.912+-0.001\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<179:0.911+0\left|L_{uckGrade}-178\right|,179 \le L_{uckGrade}<180:0.911+-0.001\left|L_{uckGrade}-179\right|,180 \le L_{uckGrade}<181:0.91+0\left|L_{uckGrade}-180\right|,181 \le L_{uckGrade}<182:0.91+-0.001\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<183:0.909+0\left|L_{uckGrade}-182\right|,183 \le L_{uckGrade}<184:0.909+-0.001\left|L_{uckGrade}-183\right|,184 \le L_{uckGrade}<185:0.908+0\left|L_{uckGrade}-184\right|,185 \le L_{uckGrade}<186:0.908+-0.001\left|L_{uckGrade}-185\right|,186 \le L_{uckGrade}<187:0.907+0\left|L_{uckGrade}-186\right|,187 \le L_{uckGrade}<188:0.907+-0.001\left|L_{uckGrade}-187\right|,188 \le L_{uckGrade}<189:0.906+0\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<190:0.906+-0.001\left|L_{uckGrade}-189\right|,190 \le L_{uckGrade}<191:0.905+0\left|L_{uckGrade}-190\right|,191 \le L_{uckGrade}<192:0.905+-0.001\left|L_{uckGrade}-191\right|,192 \le L_{uckGrade}<193:0.904+0\left|L_{uckGrade}-192\right|,193 \le L_{uckGrade}<194:0.904+-0.001\left|L_{uckGrade}-193\right|,194 \le L_{uckGrade}<195:0.903+0\left|L_{uckGrade}-194\right|,195 \le L_{uckGrade}<196:0.903+-0.001\left|L_{uckGrade}-195\right|,196 \le L_{uckGrade}<197:0.902+0\left|L_{uckGrade}-196\right|,197 \le L_{uckGrade}<198:0.902+-0.001\left|L_{uckGrade}-197\right|,198 \le L_{uckGrade}<199:0.901+0\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<200:0.901+-0.001\left|L_{uckGrade}-199\right|,200 \le L_{uckGrade}<201:0.9+0\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<202:0.9+-0.001\left|L_{uckGrade}-201\right|,202 \le L_{uckGrade}<203:0.899+0\left|L_{uckGrade}-202\right|,203 \le L_{uckGrade}<204:0.899+-0.001\left|L_{uckGrade}-203\right|,204 \le L_{uckGrade}<205:0.898+0\left|L_{uckGrade}-204\right|,205 \le L_{uckGrade}<206:0.898+-0.001\left|L_{uckGrade}-205\right|,206 \le L_{uckGrade}<207:0.897+0\left|L_{uckGrade}-206\right|,207 \le L_{uckGrade}<208:0.897+-0.001\left|L_{uckGrade}-207\right|,208 \le L_{uckGrade}<209:0.896+0\left|L_{uckGrade}-208\right|,209 \le L_{uckGrade}<210:0.896+-0.001\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<211:0.895+0\left|L_{uckGrade}-210\right|,211 \le L_{uckGrade}<212:0.895+-0.001\left|L_{uckGrade}-211\right|,212 \le L_{uckGrade}<213:0.894+0\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<214:0.894+-0.001\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<215:0.893+0\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<216:0.893+-0.001\left|L_{uckGrade}-215\right|,216 \le L_{uckGrade}<217:0.892+0\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<218:0.892+-0.001\left|L_{uckGrade}-217\right|,218 \le L_{uckGrade}<219:0.891+0\left|L_{uckGrade}-218\right|,219 \le L_{uckGrade}<220:0.891+-0.001\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<221:0.89+0\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:0.89+-0.001\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:0.889+0\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:0.889+-0.001\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<225:0.888+0\left|L_{uckGrade}-224\right|,225 \le L_{uckGrade}<226:0.888+-0.001\left|L_{uckGrade}-225\right|,226 \le L_{uckGrade}<227:0.887+0\left|L_{uckGrade}-226\right|,227 \le L_{uckGrade}<228:0.887+-0.001\left|L_{uckGrade}-227\right|,228 \le L_{uckGrade}<229:0.886+0\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<230:0.886+-0.001\left|L_{uckGrade}-229\right|,230 \le L_{uckGrade}<231:0.885+0\left|L_{uckGrade}-230\right|,231 \le L_{uckGrade}<232:0.885+-0.001\left|L_{uckGrade}-231\right|,232 \le L_{uckGrade}<233:0.884+0\left|L_{uckGrade}-232\right|,233 \le L_{uckGrade}<234:0.884+-0.001\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<235:0.883+0\left|L_{uckGrade}-234\right|,235 \le L_{uckGrade}<236:0.883+-0.001\left|L_{uckGrade}-235\right|,236 \le L_{uckGrade}<237:0.882+0\left|L_{uckGrade}-236\right|,237 \le L_{uckGrade}<238:0.882+-0.001\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<239:0.881+0\left|L_{uckGrade}-238\right|,239 \le L_{uckGrade}<240:0.881+-0.001\left|L_{uckGrade}-239\right|,240 \le L_{uckGrade}<241:0.88+0\left|L_{uckGrade}-240\right|,241 \le L_{uckGrade}<242:0.88+-0.001\left|L_{uckGrade}-241\right|,242 \le L_{uckGrade}<243:0.879+0\left|L_{uckGrade}-242\right|,243 \le L_{uckGrade}<244:0.879+-0.001\left|L_{uckGrade}-243\right|,244 \le L_{uckGrade}<245:0.878+0\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<246:0.878+-0.001\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<247:0.877+0\left|L_{uckGrade}-246\right|,247 \le L_{uckGrade}<248:0.877+-0.001\left|L_{uckGrade}-247\right|,248 \le L_{uckGrade}<249:0.876+0\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<250:0.876+-0.001\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<251:0.875+0\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:0.875+-0.001\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<253:0.874+0\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<254:0.874+-0.001\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<255:0.873+0\left|L_{uckGrade}-254\right|,255 \le L_{uckGrade}<256:0.873+-0.001\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<257:0.872+0\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<258:0.872+-0.001\left|L_{uckGrade}-257\right|,258 \le L_{uckGrade}<259:0.871+0\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<260:0.871+-0.001\left|L_{uckGrade}-259\right|,260 \le L_{uckGrade}<261:0.87+0\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<262:0.87+-0.001\left|L_{uckGrade}-261\right|,262 \le L_{uckGrade}<263:0.869+0\left|L_{uckGrade}-262\right|,263 \le L_{uckGrade}<264:0.869+-0.001\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<265:0.868+0\left|L_{uckGrade}-264\right|,265 \le L_{uckGrade}<266:0.868+-0.001\left|L_{uckGrade}-265\right|,266 \le L_{uckGrade}<267:0.867+0\left|L_{uckGrade}-266\right|,267 \le L_{uckGrade}<268:0.867+-0.001\left|L_{uckGrade}-267\right|,268 \le L_{uckGrade}<269:0.866+0\left|L_{uckGrade}-268\right|,269 \le L_{uckGrade}<270:0.866+-0.001\left|L_{uckGrade}-269\right|,270 \le L_{uckGrade}<271:0.865+0\left|L_{uckGrade}-270\right|,271 \le L_{uckGrade}<272:0.865+-0.001\left|L_{uckGrade}-271\right|,272 \le L_{uckGrade}<273:0.864+0\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<274:0.864+-0.001\left|L_{uckGrade}-273\right|,274 \le L_{uckGrade}<275:0.863+0\left|L_{uckGrade}-274\right|,275 \le L_{uckGrade}<276:0.863+-0.001\left|L_{uckGrade}-275\right|,276 \le L_{uckGrade}<277:0.862+0\left|L_{uckGrade}-276\right|,277 \le L_{uckGrade}<278:0.862+-0.001\left|L_{uckGrade}-277\right|,278 \le L_{uckGrade}<279:0.861+0\left|L_{uckGrade}-278\right|,279 \le L_{uckGrade}<280:0.861+-0.001\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<281:0.86+0\left|L_{uckGrade}-280\right|,281 \le L_{uckGrade}<282:0.86+-0.001\left|L_{uckGrade}-281\right|,282 \le L_{uckGrade}<283:0.859+0\left|L_{uckGrade}-282\right|,283 \le L_{uckGrade}<284:0.859+-0.001\left|L_{uckGrade}-283\right|,284 \le L_{uckGrade}<285:0.858+0\left|L_{uckGrade}-284\right|,285 \le L_{uckGrade}<286:0.858+-0.001\left|L_{uckGrade}-285\right|,286 \le L_{uckGrade}<287:0.857+0\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<288:0.857+-0.001\left|L_{uckGrade}-287\right|,288 \le L_{uckGrade}<289:0.856+0\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<290:0.856+-0.001\left|L_{uckGrade}-289\right|,290 \le L_{uckGrade}<291:0.855+0\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<292:0.855+-0.001\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<293:0.854+0\left|L_{uckGrade}-292\right|,293 \le L_{uckGrade}<294:0.854+-0.001\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<295:0.853+0\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<296:0.853+-0.001\left|L_{uckGrade}-295\right|,296 \le L_{uckGrade}<297:0.852+0\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<298:0.852+-0.001\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<299:0.851+0\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<300:0.851+-0.001\left|L_{uckGrade}-299\right|,300 \le L_{uckGrade}<301:0.85+0\left|L_{uckGrade}-300\right|,301 \le L_{uckGrade}<302:0.85+-0.001\left|L_{uckGrade}-301\right|,302 \le L_{uckGrade}<303:0.849+0\left|L_{uckGrade}-302\right|,303 \le L_{uckGrade}<304:0.849+-0.001\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<305:0.848+0\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<306:0.848+-0.001\left|L_{uckGrade}-305\right|,306 \le L_{uckGrade}<307:0.847+0\left|L_{uckGrade}-306\right|,307 \le L_{uckGrade}<308:0.847+-0.001\left|L_{uckGrade}-307\right|,308 \le L_{uckGrade}<309:0.846+0\left|L_{uckGrade}-308\right|,309 \le L_{uckGrade}<310:0.846+-0.001\left|L_{uckGrade}-309\right|,310 \le L_{uckGrade}<311:0.845+0\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<312:0.845+-0.001\left|L_{uckGrade}-311\right|,312 \le L_{uckGrade}<313:0.844+0\left|L_{uckGrade}-312\right|,313 \le L_{uckGrade}<314:0.844+-0.001\left|L_{uckGrade}-313\right|,314 \le L_{uckGrade}<315:0.843+0\left|L_{uckGrade}-314\right|,315 \le L_{uckGrade}<316:0.843+-0.001\left|L_{uckGrade}-315\right|,316 \le L_{uckGrade}<317:0.842+0\left|L_{uckGrade}-316\right|,317 \le L_{uckGrade}<318:0.842+-0.001\left|L_{uckGrade}-317\right|,318 \le L_{uckGrade}<319:0.841+0\left|L_{uckGrade}-318\right|,319 \le L_{uckGrade}<320:0.841+-0.001\left|L_{uckGrade}-319\right|,320 \le L_{uckGrade}<321:0.84+0\left|L_{uckGrade}-320\right|,321 \le L_{uckGrade}<322:0.84+-0.001\left|L_{uckGrade}-321\right|,322 \le L_{uckGrade}<323:0.839+0\left|L_{uckGrade}-322\right|,323 \le L_{uckGrade}<324:0.839+-0.001\left|L_{uckGrade}-323\right|,324 \le L_{uckGrade}<325:0.838+0\left|L_{uckGrade}-324\right|,325 \le L_{uckGrade}<326:0.838+-0.001\left|L_{uckGrade}-325\right|,326 \le L_{uckGrade}<327:0.837+0\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<328:0.837+-0.001\left|L_{uckGrade}-327\right|,328 \le L_{uckGrade}<329:0.836+0\left|L_{uckGrade}-328\right|,329 \le L_{uckGrade}<330:0.836+-0.001\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<331:0.835+0\left|L_{uckGrade}-330\right|,331 \le L_{uckGrade}<332:0.835+-0.001\left|L_{uckGrade}-331\right|,332 \le L_{uckGrade}<333:0.834+0\left|L_{uckGrade}-332\right|,333 \le L_{uckGrade}<334:0.834+-0.001\left|L_{uckGrade}-333\right|,334 \le L_{uckGrade}<335:0.833+0\left|L_{uckGrade}-334\right|,335 \le L_{uckGrade}<336:0.833+-0.001\left|L_{uckGrade}-335\right|,336 \le L_{uckGrade}<337:0.832+0\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<338:0.832+-0.001\left|L_{uckGrade}-337\right|,338 \le L_{uckGrade}<339:0.831+0\left|L_{uckGrade}-338\right|,339 \le L_{uckGrade}<340:0.831+-0.001\left|L_{uckGrade}-339\right|,340 \le L_{uckGrade}<341:0.83+0\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<342:0.83+-0.001\left|L_{uckGrade}-341\right|,342 \le L_{uckGrade}<343:0.829+0\left|L_{uckGrade}-342\right|,343 \le L_{uckGrade}<344:0.829+-0.001\left|L_{uckGrade}-343\right|,344 \le L_{uckGrade}<345:0.828+0\left|L_{uckGrade}-344\right|,345 \le L_{uckGrade}<346:0.828+-0.001\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<347:0.827+0\left|L_{uckGrade}-346\right|,347 \le L_{uckGrade}<348:0.827+-0.001\left|L_{uckGrade}-347\right|,348 \le L_{uckGrade}<349:0.826+0\left|L_{uckGrade}-348\right|,349 \le L_{uckGrade}<350:0.826+-0.001\left|L_{uckGrade}-349\right|,350 \le L_{uckGrade}<351:0.825+0\left|L_{uckGrade}-350\right|,351 \le L_{uckGrade}<352:0.825+-0.001\left|L_{uckGrade}-351\right|,352 \le L_{uckGrade}<353:0.824+0\left|L_{uckGrade}-352\right|,353 \le L_{uckGrade}<354:0.824+-0.001\left|L_{uckGrade}-353\right|,354 \le L_{uckGrade}<355:0.823+0\left|L_{uckGrade}-354\right|,355 \le L_{uckGrade}<356:0.823+-0.001\left|L_{uckGrade}-355\right|,356 \le L_{uckGrade}<357:0.822+0\left|L_{uckGrade}-356\right|,357 \le L_{uckGrade}<358:0.822+-0.001\left|L_{uckGrade}-357\right|,358 \le L_{uckGrade}<359:0.821+0\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<360:0.821+-0.001\left|L_{uckGrade}-359\right|,360 \le L_{uckGrade}<361:0.82+0\left|L_{uckGrade}-360\right|,361 \le L_{uckGrade}<362:0.82+-0.001\left|L_{uckGrade}-361\right|,362 \le L_{uckGrade}<363:0.819+0\left|L_{uckGrade}-362\right|,363 \le L_{uckGrade}<364:0.819+-0.001\left|L_{uckGrade}-363\right|,364 \le L_{uckGrade}<365:0.818+0\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<366:0.818+-0.001\left|L_{uckGrade}-365\right|,366 \le L_{uckGrade}<367:0.817+0\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:0.817+-0.001\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<369:0.816+0\left|L_{uckGrade}-368\right|,369 \le L_{uckGrade}<370:0.816+-0.001\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<371:0.815+0\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<372:0.815+-0.001\left|L_{uckGrade}-371\right|,372 \le L_{uckGrade}<373:0.814+0\left|L_{uckGrade}-372\right|,373 \le L_{uckGrade}<374:0.814+-0.001\left|L_{uckGrade}-373\right|,374 \le L_{uckGrade}<375:0.813+0\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<376:0.813+-0.001\left|L_{uckGrade}-375\right|,376 \le L_{uckGrade}<377:0.812+0\left|L_{uckGrade}-376\right|,377 \le L_{uckGrade}<378:0.812+-0.001\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<379:0.811+0\left|L_{uckGrade}-378\right|,379 \le L_{uckGrade}<380:0.811+-0.001\left|L_{uckGrade}-379\right|,380 \le L_{uckGrade}<381:0.81+0\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<382:0.81+-0.001\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<383:0.809+0\left|L_{uckGrade}-382\right|,383 \le L_{uckGrade}<384:0.809+-0.001\left|L_{uckGrade}-383\right|,384 \le L_{uckGrade}<385:0.808+0\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<386:0.808+-0.001\left|L_{uckGrade}-385\right|,386 \le L_{uckGrade}<387:0.807+0\left|L_{uckGrade}-386\right|,387 \le L_{uckGrade}<388:0.807+-0.001\left|L_{uckGrade}-387\right|,388 \le L_{uckGrade}<389:0.806+0\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<390:0.806+-0.001\left|L_{uckGrade}-389\right|,390 \le L_{uckGrade}<391:0.805+0\left|L_{uckGrade}-390\right|,391 \le L_{uckGrade}<392:0.805+-0.001\left|L_{uckGrade}-391\right|,392 \le L_{uckGrade}<393:0.804+0\left|L_{uckGrade}-392\right|,393 \le L_{uckGrade}<394:0.804+-0.001\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<395:0.803+0\left|L_{uckGrade}-394\right|,395 \le L_{uckGrade}<396:0.803+-0.001\left|L_{uckGrade}-395\right|,396 \le L_{uckGrade}<397:0.802+0\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<398:0.802+-0.001\left|L_{uckGrade}-397\right|,398 \le L_{uckGrade}<399:0.801+0\left|L_{uckGrade}-398\right|,399 \le L_{uckGrade}<400:0.801+-0.001\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<401:0.8+0\left|L_{uckGrade}-400\right|,401 \le L_{uckGrade}<402:0.8+-0.001\left|L_{uckGrade}-401\right|,402 \le L_{uckGrade}<403:0.799+0\left|L_{uckGrade}-402\right|,403 \le L_{uckGrade}<404:0.799+-0.001\left|L_{uckGrade}-403\right|,404 \le L_{uckGrade}<405:0.798+0\left|L_{uckGrade}-404\right|,405 \le L_{uckGrade}<406:0.798+-0.001\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:0.797+0\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<408:0.797+-0.001\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<409:0.796+0\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<410:0.796+-0.001\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<411:0.795+0\left|L_{uckGrade}-410\right|,411 \le L_{uckGrade}<412:0.795+-0.001\left|L_{uckGrade}-411\right|,412 \le L_{uckGrade}<413:0.794+0\left|L_{uckGrade}-412\right|,413 \le L_{uckGrade}<414:0.794+-0.001\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<415:0.793+0\left|L_{uckGrade}-414\right|,415 \le L_{uckGrade}<416:0.793+-0.001\left|L_{uckGrade}-415\right|,416 \le L_{uckGrade}<417:0.792+0\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<418:0.792+-0.001\left|L_{uckGrade}-417\right|,418 \le L_{uckGrade}<419:0.791+0\left|L_{uckGrade}-418\right|,419 \le L_{uckGrade}<420:0.791+-0.001\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<421:0.79+0\left|L_{uckGrade}-420\right|,421 \le L_{uckGrade}<422:0.79+-0.001\left|L_{uckGrade}-421\right|,422 \le L_{uckGrade}<423:0.789+0\left|L_{uckGrade}-422\right|,423 \le L_{uckGrade}<424:0.789+-0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<425:0.788+0\left|L_{uckGrade}-424\right|,425 \le L_{uckGrade}<426:0.788+-0.001\left|L_{uckGrade}-425\right|,426 \le L_{uckGrade}<427:0.787+0\left|L_{uckGrade}-426\right|,427 \le L_{uckGrade}<428:0.787+-0.001\left|L_{uckGrade}-427\right|,428 \le L_{uckGrade}<429:0.786+0\left|L_{uckGrade}-428\right|,429 \le L_{uckGrade}<430:0.786+-0.001\left|L_{uckGrade}-429\right|,430 \le L_{uckGrade}<431:0.785+0\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<432:0.785+-0.001\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<433:0.784+0\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<434:0.784+-0.001\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<435:0.783+0\left|L_{uckGrade}-434\right|,435 \le L_{uckGrade}<436:0.783+-0.001\left|L_{uckGrade}-435\right|,436 \le L_{uckGrade}<437:0.782+0\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<438:0.782+-0.001\left|L_{uckGrade}-437\right|,438 \le L_{uckGrade}<439:0.781+0\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<440:0.781+-0.001\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<441:0.78+0\left|L_{uckGrade}-440\right|,441 \le L_{uckGrade}<442:0.78+-0.001\left|L_{uckGrade}-441\right|,442 \le L_{uckGrade}<443:0.779+0\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<444:0.779+-0.001\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<445:0.778+0\left|L_{uckGrade}-444\right|,445 \le L_{uckGrade}<446:0.778+-0.001\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<447:0.777+0\left|L_{uckGrade}-446\right|,447 \le L_{uckGrade}<448:0.777+-0.001\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<449:0.776+0\left|L_{uckGrade}-448\right|,449 \le L_{uckGrade}<450:0.776+-0.001\left|L_{uckGrade}-449\right|,450 \le L_{uckGrade}<451:0.775+0\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<452:0.775+-0.001\left|L_{uckGrade}-451\right|,452 \le L_{uckGrade}<453:0.774+0\left|L_{uckGrade}-452\right|,453 \le L_{uckGrade}<454:0.774+-0.001\left|L_{uckGrade}-453\right|,454 \le L_{uckGrade}<455:0.773+0\left|L_{uckGrade}-454\right|,455 \le L_{uckGrade}<456:0.773+-0.001\left|L_{uckGrade}-455\right|,456 \le L_{uckGrade}<457:0.772+0\left|L_{uckGrade}-456\right|,457 \le L_{uckGrade}<458:0.772+-0.001\left|L_{uckGrade}-457\right|,458 \le L_{uckGrade}<459:0.771+0\left|L_{uckGrade}-458\right|,459 \le L_{uckGrade}<460:0.771+-0.001\left|L_{uckGrade}-459\right|,460 \le L_{uckGrade}<461:0.77+0\left|L_{uckGrade}-460\right|,461 \le L_{uckGrade}<462:0.77+-0.001\left|L_{uckGrade}-461\right|,462 \le L_{uckGrade}<463:0.769+0\left|L_{uckGrade}-462\right|,463 \le L_{uckGrade}<464:0.769+-0.001\left|L_{uckGrade}-463\right|,464 \le L_{uckGrade}<465:0.768+0\left|L_{uckGrade}-464\right|,465 \le L_{uckGrade}<466:0.768+-0.001\left|L_{uckGrade}-465\right|,466 \le L_{uckGrade}<467:0.767+0\left|L_{uckGrade}-466\right|,467 \le L_{uckGrade}<468:0.767+-0.001\left|L_{uckGrade}-467\right|,468 \le L_{uckGrade}<469:0.766+0\left|L_{uckGrade}-468\right|,469 \le L_{uckGrade}<470:0.766+-0.001\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<471:0.765+0\left|L_{uckGrade}-470\right|,471 \le L_{uckGrade}<472:0.765+-0.001\left|L_{uckGrade}-471\right|,472 \le L_{uckGrade}<473:0.764+0\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<474:0.764+-0.001\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<475:0.763+0\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<476:0.763+-0.001\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<477:0.762+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<478:0.762+-0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:0.761+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<480:0.761+-0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:0.76+0\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:0.76+-0.001\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:0.759+0\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<484:0.759+-0.001\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<485:0.758+0\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<486:0.758+-0.001\left|L_{uckGrade}-485\right|,486 \le L_{uckGrade}<487:0.757+0\left|L_{uckGrade}-486\right|,487 \le L_{uckGrade}<488:0.757+-0.001\left|L_{uckGrade}-487\right|,488 \le L_{uckGrade}<489:0.756+0\left|L_{uckGrade}-488\right|,489 \le L_{uckGrade}<490:0.756+-0.001\left|L_{uckGrade}-489\right|,490 \le L_{uckGrade}<491:0.755+0\left|L_{uckGrade}-490\right|,491 \le L_{uckGrade}<492:0.755+-0.001\left|L_{uckGrade}-491\right|,492 \le L_{uckGrade}<493:0.754+0\left|L_{uckGrade}-492\right|,493 \le L_{uckGrade}<494:0.754+-0.001\left|L_{uckGrade}-493\right|,494 \le L_{uckGrade}<495:0.753+0\left|L_{uckGrade}-494\right|,495 \le L_{uckGrade}<496:0.753+-0.001\left|L_{uckGrade}-495\right|,496 \le L_{uckGrade}<497:0.752+0\left|L_{uckGrade}-496\right|,497 \le L_{uckGrade}<498:0.752+-0.001\left|L_{uckGrade}-497\right|,498 \le L_{uckGrade}<499:0.751+0\left|L_{uckGrade}-498\right|,499 \le L_{uckGrade}<500:0.751+-0.001\left|L_{uckGrade}-499\right|\right\}
See Example for how to use.
LaTeX Formula
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
L_{uckGrade04}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<7:1+0.01\left|L_{uckGrade}-0\right|,7 \le L_{uckGrade}<8:1.07+0.009\left|L_{uckGrade}-7\right|,8 \le L_{uckGrade}<12:1.079+0.01\left|L_{uckGrade}-8\right|,12 \le L_{uckGrade}<13:1.119+0.009\left|L_{uckGrade}-12\right|,13 \le L_{uckGrade}<16:1.128+0.01\left|L_{uckGrade}-13\right|,16 \le L_{uckGrade}<17:1.158+0.009\left|L_{uckGrade}-16\right|,17 \le L_{uckGrade}<19:1.167+0.01\left|L_{uckGrade}-17\right|,19 \le L_{uckGrade}<20:1.187+0.009\left|L_{uckGrade}-19\right|,20 \le L_{uckGrade}<21:1.196+0.01\left|L_{uckGrade}-20\right|,21 \le L_{uckGrade}<22:1.206+0.009\left|L_{uckGrade}-21\right|,22 \le L_{uckGrade}<23:1.215+0.01\left|L_{uckGrade}-22\right|,23 \le L_{uckGrade}<24:1.225+0.009\left|L_{uckGrade}-23\right|,24 \le L_{uckGrade}<26:1.234+0.01\left|L_{uckGrade}-24\right|,26 \le L_{uckGrade}<28:1.254+0.009\left|L_{uckGrade}-26\right|,28 \le L_{uckGrade}<29:1.272+0.01\left|L_{uckGrade}-28\right|,29 \le L_{uckGrade}<30:1.282+0.009\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<31:1.291+0.01\left|L_{uckGrade}-30\right|,31 \le L_{uckGrade}<33:1.301+0.009\left|L_{uckGrade}-31\right|,33 \le L_{uckGrade}<34:1.319+0.01\left|L_{uckGrade}-33\right|,34 \le L_{uckGrade}<36:1.329+0.009\left|L_{uckGrade}-34\right|,36 \le L_{uckGrade}<37:1.347+0.01\left|L_{uckGrade}-36\right|,37 \le L_{uckGrade}<40:1.357+0.009\left|L_{uckGrade}-37\right|,40 \le L_{uckGrade}<41:1.384+0.01\left|L_{uckGrade}-40\right|,41 \le L_{uckGrade}<49:1.394+0.009\left|L_{uckGrade}-41\right|,49 \le L_{uckGrade}<50:1.466+0.01\left|L_{uckGrade}-49\right|,50 \le L_{uckGrade}<51:1.476+0.009\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<52:1.485+0.008\left|L_{uckGrade}-51\right|,52 \le L_{uckGrade}<60:1.493+0.009\left|L_{uckGrade}-52\right|,60 \le L_{uckGrade}<61:1.565+0.008\left|L_{uckGrade}-60\right|,61 \le L_{uckGrade}<64:1.573+0.009\left|L_{uckGrade}-61\right|,64 \le L_{uckGrade}<65:1.6+0.008\left|L_{uckGrade}-64\right|,65 \le L_{uckGrade}<67:1.608+0.009\left|L_{uckGrade}-65\right|,67 \le L_{uckGrade}<68:1.626+0.008\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<70:1.634+0.009\left|L_{uckGrade}-68\right|,70 \le L_{uckGrade}<71:1.652+0.008\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<72:1.66+0.009\left|L_{uckGrade}-71\right|,72 \le L_{uckGrade}<73:1.669+0.008\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<75:1.677+0.009\left|L_{uckGrade}-73\right|,75 \le L_{uckGrade}<77:1.695+0.008\left|L_{uckGrade}-75\right|,77 \le L_{uckGrade}<78:1.711+0.009\left|L_{uckGrade}-77\right|,78 \le L_{uckGrade}<79:1.72+0.008\left|L_{uckGrade}-78\right|,79 \le L_{uckGrade}<80:1.728+0.009\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<81:1.737+0.008\left|L_{uckGrade}-80\right|,81 \le L_{uckGrade}<82:1.745+0.009\left|L_{uckGrade}-81\right|,82 \le L_{uckGrade}<84:1.754+0.008\left|L_{uckGrade}-82\right|,84 \le L_{uckGrade}<85:1.77+0.009\left|L_{uckGrade}-84\right|,85 \le L_{uckGrade}<88:1.779+0.008\left|L_{uckGrade}-85\right|,88 \le L_{uckGrade}<89:1.803+0.009\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<93:1.812+0.008\left|L_{uckGrade}-89\right|,93 \le L_{uckGrade}<94:1.844+0.009\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<107:1.853+0.008\left|L_{uckGrade}-94\right|,107 \le L_{uckGrade}<108:1.957+0.007\left|L_{uckGrade}-107\right|,108 \le L_{uckGrade}<112:1.964+0.008\left|L_{uckGrade}-108\right|,112 \le L_{uckGrade}<113:1.996+0.007\left|L_{uckGrade}-112\right|,113 \le L_{uckGrade}<116:2.003+0.008\left|L_{uckGrade}-113\right|,116 \le L_{uckGrade}<117:2.027+0.007\left|L_{uckGrade}-116\right|,117 \le L_{uckGrade}<119:2.034+0.008\left|L_{uckGrade}-117\right|,119 \le L_{uckGrade}<120:2.05+0.007\left|L_{uckGrade}-119\right|,120 \le L_{uckGrade}<121:2.057+0.008\left|L_{uckGrade}-120\right|,121 \le L_{uckGrade}<122:2.065+0.007\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<123:2.072+0.008\left|L_{uckGrade}-122\right|,123 \le L_{uckGrade}<124:2.08+0.007\left|L_{uckGrade}-123\right|,124 \le L_{uckGrade}<126:2.087+0.008\left|L_{uckGrade}-124\right|,126 \le L_{uckGrade}<128:2.103+0.007\left|L_{uckGrade}-126\right|,128 \le L_{uckGrade}<129:2.117+0.008\left|L_{uckGrade}-128\right|,129 \le L_{uckGrade}<130:2.125+0.007\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<131:2.132+0.008\left|L_{uckGrade}-130\right|,131 \le L_{uckGrade}<133:2.14+0.007\left|L_{uckGrade}-131\right|,133 \le L_{uckGrade}<134:2.154+0.008\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<136:2.162+0.007\left|L_{uckGrade}-134\right|,136 \le L_{uckGrade}<137:2.176+0.008\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<140:2.184+0.007\left|L_{uckGrade}-137\right|,140 \le L_{uckGrade}<141:2.205+0.008\left|L_{uckGrade}-140\right|,141 \le L_{uckGrade}<149:2.213+0.007\left|L_{uckGrade}-141\right|,149 \le L_{uckGrade}<150:2.269+0.008\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<151:2.277+0.007\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:2.284+0.006\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<160:2.29+0.007\left|L_{uckGrade}-152\right|,160 \le L_{uckGrade}<161:2.346+0.006\left|L_{uckGrade}-160\right|,161 \le L_{uckGrade}<164:2.352+0.007\left|L_{uckGrade}-161\right|,164 \le L_{uckGrade}<165:2.373+0.006\left|L_{uckGrade}-164\right|,165 \le L_{uckGrade}<167:2.379+0.007\left|L_{uckGrade}-165\right|,167 \le L_{uckGrade}<168:2.393+0.006\left|L_{uckGrade}-167\right|,168 \le L_{uckGrade}<170:2.399+0.007\left|L_{uckGrade}-168\right|,170 \le L_{uckGrade}<171:2.413+0.006\left|L_{uckGrade}-170\right|,171 \le L_{uckGrade}<172:2.419+0.007\left|L_{uckGrade}-171\right|,172 \le L_{uckGrade}<173:2.426+0.006\left|L_{uckGrade}-172\right|,173 \le L_{uckGrade}<175:2.432+0.007\left|L_{uckGrade}-173\right|,175 \le L_{uckGrade}<177:2.446+0.006\left|L_{uckGrade}-175\right|,177 \le L_{uckGrade}<178:2.458+0.007\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<179:2.465+0.006\left|L_{uckGrade}-178\right|,179 \le L_{uckGrade}<180:2.471+0.007\left|L_{uckGrade}-179\right|,180 \le L_{uckGrade}<181:2.478+0.006\left|L_{uckGrade}-180\right|,181 \le L_{uckGrade}<182:2.484+0.007\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<184:2.491+0.006\left|L_{uckGrade}-182\right|,184 \le L_{uckGrade}<185:2.503+0.007\left|L_{uckGrade}-184\right|,185 \le L_{uckGrade}<188:2.51+0.006\left|L_{uckGrade}-185\right|,188 \le L_{uckGrade}<189:2.528+0.007\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<193:2.535+0.006\left|L_{uckGrade}-189\right|,193 \le L_{uckGrade}<194:2.559+0.007\left|L_{uckGrade}-193\right|,194 \le L_{uckGrade}<207:2.566+0.006\left|L_{uckGrade}-194\right|,207 \le L_{uckGrade}<208:2.644+0.005\left|L_{uckGrade}-207\right|,208 \le L_{uckGrade}<212:2.649+0.006\left|L_{uckGrade}-208\right|,212 \le L_{uckGrade}<213:2.673+0.005\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<216:2.678+0.006\left|L_{uckGrade}-213\right|,216 \le L_{uckGrade}<217:2.696+0.005\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<219:2.701+0.006\left|L_{uckGrade}-217\right|,219 \le L_{uckGrade}<220:2.713+0.005\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<221:2.718+0.006\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:2.724+0.005\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:2.729+0.006\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:2.735+0.005\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<226:2.74+0.006\left|L_{uckGrade}-224\right|,226 \le L_{uckGrade}<228:2.752+0.005\left|L_{uckGrade}-226\right|,228 \le L_{uckGrade}<229:2.762+0.006\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<230:2.768+0.005\left|L_{uckGrade}-229\right|,230 \le L_{uckGrade}<231:2.773+0.006\left|L_{uckGrade}-230\right|,231 \le L_{uckGrade}<233:2.779+0.005\left|L_{uckGrade}-231\right|,233 \le L_{uckGrade}<234:2.789+0.006\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<236:2.795+0.005\left|L_{uckGrade}-234\right|,236 \le L_{uckGrade}<237:2.805+0.006\left|L_{uckGrade}-236\right|,237 \le L_{uckGrade}<240:2.811+0.005\left|L_{uckGrade}-237\right|,240 \le L_{uckGrade}<241:2.826+0.006\left|L_{uckGrade}-240\right|,241 \le L_{uckGrade}<249:2.832+0.005\left|L_{uckGrade}-241\right|,249 \le L_{uckGrade}<250:2.872+0.006\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<251:2.878+0.005\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:2.883+0.004\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<260:2.887+0.005\left|L_{uckGrade}-252\right|,260 \le L_{uckGrade}<261:2.927+0.004\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<264:2.931+0.005\left|L_{uckGrade}-261\right|,264 \le L_{uckGrade}<265:2.946+0.004\left|L_{uckGrade}-264\right|,265 \le L_{uckGrade}<267:2.95+0.005\left|L_{uckGrade}-265\right|,267 \le L_{uckGrade}<268:2.96+0.004\left|L_{uckGrade}-267\right|,268 \le L_{uckGrade}<270:2.964+0.005\left|L_{uckGrade}-268\right|,270 \le L_{uckGrade}<271:2.974+0.004\left|L_{uckGrade}-270\right|,271 \le L_{uckGrade}<272:2.978+0.005\left|L_{uckGrade}-271\right|,272 \le L_{uckGrade}<273:2.983+0.004\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<275:2.987+0.005\left|L_{uckGrade}-273\right|,275 \le L_{uckGrade}<277:2.997+0.004\left|L_{uckGrade}-275\right|,277 \le L_{uckGrade}<278:3.005+0.005\left|L_{uckGrade}-277\right|,278 \le L_{uckGrade}<279:3.01+0.004\left|L_{uckGrade}-278\right|,279 \le L_{uckGrade}<280:3.014+0.005\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<281:3.019+0.004\left|L_{uckGrade}-280\right|,281 \le L_{uckGrade}<282:3.023+0.005\left|L_{uckGrade}-281\right|,282 \le L_{uckGrade}<284:3.028+0.004\left|L_{uckGrade}-282\right|,284 \le L_{uckGrade}<285:3.036+0.005\left|L_{uckGrade}-284\right|,285 \le L_{uckGrade}<288:3.041+0.004\left|L_{uckGrade}-285\right|,288 \le L_{uckGrade}<289:3.053+0.005\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<293:3.058+0.004\left|L_{uckGrade}-289\right|,293 \le L_{uckGrade}<294:3.074+0.005\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<307:3.079+0.004\left|L_{uckGrade}-294\right|,307 \le L_{uckGrade}<308:3.131+0.003\left|L_{uckGrade}-307\right|,308 \le L_{uckGrade}<312:3.134+0.004\left|L_{uckGrade}-308\right|,312 \le L_{uckGrade}<313:3.15+0.003\left|L_{uckGrade}-312\right|,313 \le L_{uckGrade}<316:3.153+0.004\left|L_{uckGrade}-313\right|,316 \le L_{uckGrade}<317:3.165+0.003\left|L_{uckGrade}-316\right|,317 \le L_{uckGrade}<319:3.168+0.004\left|L_{uckGrade}-317\right|,319 \le L_{uckGrade}<320:3.176+0.003\left|L_{uckGrade}-319\right|,320 \le L_{uckGrade}<321:3.179+0.004\left|L_{uckGrade}-320\right|,321 \le L_{uckGrade}<322:3.183+0.003\left|L_{uckGrade}-321\right|,322 \le L_{uckGrade}<323:3.186+0.004\left|L_{uckGrade}-322\right|,323 \le L_{uckGrade}<324:3.19+0.003\left|L_{uckGrade}-323\right|,324 \le L_{uckGrade}<326:3.193+0.004\left|L_{uckGrade}-324\right|,326 \le L_{uckGrade}<328:3.201+0.003\left|L_{uckGrade}-326\right|,328 \le L_{uckGrade}<329:3.207+0.004\left|L_{uckGrade}-328\right|,329 \le L_{uckGrade}<330:3.211+0.003\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<331:3.214+0.004\left|L_{uckGrade}-330\right|,331 \le L_{uckGrade}<333:3.218+0.003\left|L_{uckGrade}-331\right|,333 \le L_{uckGrade}<334:3.224+0.004\left|L_{uckGrade}-333\right|,334 \le L_{uckGrade}<336:3.228+0.003\left|L_{uckGrade}-334\right|,336 \le L_{uckGrade}<337:3.234+0.004\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<340:3.238+0.003\left|L_{uckGrade}-337\right|,340 \le L_{uckGrade}<341:3.247+0.004\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<349:3.251+0.003\left|L_{uckGrade}-341\right|,349 \le L_{uckGrade}<350:3.275+0.004\left|L_{uckGrade}-349\right|,350 \le L_{uckGrade}<351:3.279+0.003\left|L_{uckGrade}-350\right|,351 \le L_{uckGrade}<352:3.282+0.002\left|L_{uckGrade}-351\right|,352 \le L_{uckGrade}<360:3.284+0.003\left|L_{uckGrade}-352\right|,360 \le L_{uckGrade}<361:3.308+0.002\left|L_{uckGrade}-360\right|,361 \le L_{uckGrade}<364:3.31+0.003\left|L_{uckGrade}-361\right|,364 \le L_{uckGrade}<365:3.319+0.002\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<367:3.321+0.003\left|L_{uckGrade}-365\right|,367 \le L_{uckGrade}<368:3.327+0.002\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<370:3.329+0.003\left|L_{uckGrade}-368\right|,370 \le L_{uckGrade}<371:3.335+0.002\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<372:3.337+0.003\left|L_{uckGrade}-371\right|,372 \le L_{uckGrade}<373:3.34+0.002\left|L_{uckGrade}-372\right|,373 \le L_{uckGrade}<375:3.342+0.003\left|L_{uckGrade}-373\right|,375 \le L_{uckGrade}<377:3.348+0.002\left|L_{uckGrade}-375\right|,377 \le L_{uckGrade}<378:3.352+0.003\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<379:3.355+0.002\left|L_{uckGrade}-378\right|,379 \le L_{uckGrade}<380:3.357+0.003\left|L_{uckGrade}-379\right|,380 \le L_{uckGrade}<381:3.36+0.002\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<382:3.362+0.003\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<384:3.365+0.002\left|L_{uckGrade}-382\right|,384 \le L_{uckGrade}<385:3.369+0.003\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<388:3.372+0.002\left|L_{uckGrade}-385\right|,388 \le L_{uckGrade}<389:3.378+0.003\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<393:3.381+0.002\left|L_{uckGrade}-389\right|,393 \le L_{uckGrade}<394:3.389+0.003\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<407:3.392+0.002\left|L_{uckGrade}-394\right|,407 \le L_{uckGrade}<408:3.418+0.001\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<412:3.419+0.002\left|L_{uckGrade}-408\right|,412 \le L_{uckGrade}<413:3.427+0.001\left|L_{uckGrade}-412\right|,413 \le L_{uckGrade}<416:3.428+0.002\left|L_{uckGrade}-413\right|,416 \le L_{uckGrade}<417:3.434+0.001\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<419:3.435+0.002\left|L_{uckGrade}-417\right|,419 \le L_{uckGrade}<420:3.439+0.001\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<421:3.44+0.002\left|L_{uckGrade}-420\right|,421 \le L_{uckGrade}<422:3.442+0.001\left|L_{uckGrade}-421\right|,422 \le L_{uckGrade}<423:3.443+0.002\left|L_{uckGrade}-422\right|,423 \le L_{uckGrade}<424:3.445+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<426:3.446+0.002\left|L_{uckGrade}-424\right|,426 \le L_{uckGrade}<428:3.45+0.001\left|L_{uckGrade}-426\right|,428 \le L_{uckGrade}<429:3.452+0.002\left|L_{uckGrade}-428\right|,429 \le L_{uckGrade}<430:3.454+0.001\left|L_{uckGrade}-429\right|,430 \le L_{uckGrade}<431:3.455+0.002\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<433:3.457+0.001\left|L_{uckGrade}-431\right|,433 \le L_{uckGrade}<434:3.459+0.002\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<436:3.461+0.001\left|L_{uckGrade}-434\right|,436 \le L_{uckGrade}<437:3.463+0.002\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<440:3.465+0.001\left|L_{uckGrade}-437\right|,440 \le L_{uckGrade}<441:3.468+0.002\left|L_{uckGrade}-440\right|,441 \le L_{uckGrade}<449:3.47+0.001\left|L_{uckGrade}-441\right|,449 \le L_{uckGrade}<450:3.478+0.002\left|L_{uckGrade}-449\right|,450 \le L_{uckGrade}<451:3.48+0.001\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<452:3.481+0\left|L_{uckGrade}-451\right|,452 \le L_{uckGrade}<460:3.481+0.001\left|L_{uckGrade}-452\right|,460 \le L_{uckGrade}<461:3.489+0\left|L_{uckGrade}-460\right|,461 \le L_{uckGrade}<464:3.489+0.001\left|L_{uckGrade}-461\right|,464 \le L_{uckGrade}<465:3.492+0\left|L_{uckGrade}-464\right|,465 \le L_{uckGrade}<467:3.492+0.001\left|L_{uckGrade}-465\right|,467 \le L_{uckGrade}<468:3.494+0\left|L_{uckGrade}-467\right|,468 \le L_{uckGrade}<470:3.494+0.001\left|L_{uckGrade}-468\right|,470 \le L_{uckGrade}<471:3.496+0\left|L_{uckGrade}-470\right|,471 \le L_{uckGrade}<472:3.496+0.001\left|L_{uckGrade}-471\right|,472 \le L_{uckGrade}<473:3.497+0\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<475:3.497+0.001\left|L_{uckGrade}-473\right|,475 \le L_{uckGrade}<477:3.499+0\left|L_{uckGrade}-475\right|,477 \le L_{uckGrade}<478:3.499+0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:3.5+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<480:3.5+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:3.501+0\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:3.501+0.001\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<484:3.502+0\left|L_{uckGrade}-482\right|,484 \le L_{uckGrade}<485:3.502+0.001\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<488:3.503+0\left|L_{uckGrade}-485\right|,488 \le L_{uckGrade}<489:3.503+0.001\left|L_{uckGrade}-488\right|,489 \le L_{uckGrade}<493:3.504+0\left|L_{uckGrade}-489\right|,493 \le L_{uckGrade}<494:3.504+0.001\left|L_{uckGrade}-493\right|,494 \le L_{uckGrade}<500:3.505+0\left|L_{uckGrade}-494\right|\right\}
See Example for how to use.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
L_{uckGrade05}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<1:1+0.012\left|L_{uckGrade}-0\right|,1 \le L_{uckGrade}<3:1.012+0.011\left|L_{uckGrade}-1\right|,3 \le L_{uckGrade}<4:1.034+0.012\left|L_{uckGrade}-3\right|,4 \le L_{uckGrade}<5:1.046+0.011\left|L_{uckGrade}-4\right|,5 \le L_{uckGrade}<6:1.057+0.012\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<8:1.069+0.011\left|L_{uckGrade}-6\right|,8 \le L_{uckGrade}<9:1.091+0.012\left|L_{uckGrade}-8\right|,9 \le L_{uckGrade}<12:1.103+0.011\left|L_{uckGrade}-9\right|,12 \le L_{uckGrade}<13:1.136+0.012\left|L_{uckGrade}-12\right|,13 \le L_{uckGrade}<18:1.148+0.011\left|L_{uckGrade}-13\right|,18 \le L_{uckGrade}<19:1.203+0.012\left|L_{uckGrade}-18\right|,19 \le L_{uckGrade}<26:1.215+0.011\left|L_{uckGrade}-19\right|,26 \le L_{uckGrade}<27:1.292+0.01\left|L_{uckGrade}-26\right|,27 \le L_{uckGrade}<32:1.302+0.011\left|L_{uckGrade}-27\right|,32 \le L_{uckGrade}<33:1.357+0.01\left|L_{uckGrade}-32\right|,33 \le L_{uckGrade}<36:1.367+0.011\left|L_{uckGrade}-33\right|,36 \le L_{uckGrade}<37:1.4+0.01\left|L_{uckGrade}-36\right|,37 \le L_{uckGrade}<38:1.41+0.011\left|L_{uckGrade}-37\right|,38 \le L_{uckGrade}<39:1.421+0.01\left|L_{uckGrade}-38\right|,39 \le L_{uckGrade}<41:1.431+0.011\left|L_{uckGrade}-39\right|,41 \le L_{uckGrade}<42:1.453+0.01\left|L_{uckGrade}-41\right|,42 \le L_{uckGrade}<43:1.463+0.011\left|L_{uckGrade}-42\right|,43 \le L_{uckGrade}<44:1.474+0.01\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<45:1.484+0.011\left|L_{uckGrade}-44\right|,45 \le L_{uckGrade}<46:1.495+0.01\left|L_{uckGrade}-45\right|,46 \le L_{uckGrade}<47:1.505+0.011\left|L_{uckGrade}-46\right|,47 \le L_{uckGrade}<49:1.516+0.01\left|L_{uckGrade}-47\right|,49 \le L_{uckGrade}<50:1.536+0.011\left|L_{uckGrade}-49\right|,50 \le L_{uckGrade}<51:1.547+0.01\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<52:1.557+0.011\left|L_{uckGrade}-51\right|,52 \le L_{uckGrade}<55:1.568+0.01\left|L_{uckGrade}-52\right|,55 \le L_{uckGrade}<56:1.598+0.011\left|L_{uckGrade}-55\right|,56 \le L_{uckGrade}<61:1.609+0.01\left|L_{uckGrade}-56\right|,61 \le L_{uckGrade}<62:1.659+0.011\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<69:1.67+0.01\left|L_{uckGrade}-62\right|,69 \le L_{uckGrade}<70:1.74+0.009\left|L_{uckGrade}-69\right|,70 \le L_{uckGrade}<75:1.749+0.01\left|L_{uckGrade}-70\right|,75 \le L_{uckGrade}<76:1.799+0.009\left|L_{uckGrade}-75\right|,76 \le L_{uckGrade}<79:1.808+0.01\left|L_{uckGrade}-76\right|,79 \le L_{uckGrade}<80:1.838+0.009\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<82:1.847+0.01\left|L_{uckGrade}-80\right|,82 \le L_{uckGrade}<83:1.867+0.009\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<84:1.876+0.01\left|L_{uckGrade}-83\right|,84 \le L_{uckGrade}<85:1.886+0.009\left|L_{uckGrade}-84\right|,85 \le L_{uckGrade}<86:1.895+0.01\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<87:1.905+0.009\left|L_{uckGrade}-86\right|,87 \le L_{uckGrade}<88:1.914+0.01\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<89:1.924+0.009\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<90:1.933+0.01\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<91:1.943+0.009\left|L_{uckGrade}-90\right|,91 \le L_{uckGrade}<92:1.952+0.01\left|L_{uckGrade}-91\right|,92 \le L_{uckGrade}<94:1.962+0.009\left|L_{uckGrade}-92\right|,94 \le L_{uckGrade}<95:1.98+0.01\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<97:1.99+0.009\left|L_{uckGrade}-95\right|,97 \le L_{uckGrade}<98:2.008+0.01\left|L_{uckGrade}-97\right|,98 \le L_{uckGrade}<101:2.018+0.009\left|L_{uckGrade}-98\right|,101 \le L_{uckGrade}<102:2.045+0.01\left|L_{uckGrade}-101\right|,102 \le L_{uckGrade}<116:2.055+0.009\left|L_{uckGrade}-102\right|,116 \le L_{uckGrade}<117:2.181+0.008\left|L_{uckGrade}-116\right|,117 \le L_{uckGrade}<121:2.189+0.009\left|L_{uckGrade}-117\right|,121 \le L_{uckGrade}<122:2.225+0.008\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<124:2.233+0.009\left|L_{uckGrade}-122\right|,124 \le L_{uckGrade}<125:2.251+0.008\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<126:2.259+0.009\left|L_{uckGrade}-125\right|,126 \le L_{uckGrade}<127:2.268+0.008\left|L_{uckGrade}-126\right|,127 \le L_{uckGrade}<129:2.276+0.009\left|L_{uckGrade}-127\right|,129 \le L_{uckGrade}<130:2.294+0.008\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<131:2.302+0.009\left|L_{uckGrade}-130\right|,131 \le L_{uckGrade}<132:2.311+0.008\left|L_{uckGrade}-131\right|,132 \le L_{uckGrade}<133:2.319+0.009\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<135:2.328+0.008\left|L_{uckGrade}-133\right|,135 \le L_{uckGrade}<136:2.344+0.009\left|L_{uckGrade}-135\right|,136 \le L_{uckGrade}<137:2.353+0.008\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<138:2.361+0.009\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<141:2.37+0.008\left|L_{uckGrade}-138\right|,141 \le L_{uckGrade}<142:2.394+0.009\left|L_{uckGrade}-141\right|,142 \le L_{uckGrade}<145:2.403+0.008\left|L_{uckGrade}-142\right|,145 \le L_{uckGrade}<146:2.427+0.009\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<159:2.436+0.008\left|L_{uckGrade}-146\right|,159 \le L_{uckGrade}<160:2.54+0.007\left|L_{uckGrade}-159\right|,160 \le L_{uckGrade}<164:2.547+0.008\left|L_{uckGrade}-160\right|,164 \le L_{uckGrade}<165:2.579+0.007\left|L_{uckGrade}-164\right|,165 \le L_{uckGrade}<167:2.586+0.008\left|L_{uckGrade}-165\right|,167 \le L_{uckGrade}<168:2.602+0.007\left|L_{uckGrade}-167\right|,168 \le L_{uckGrade}<170:2.609+0.008\left|L_{uckGrade}-168\right|,170 \le L_{uckGrade}<171:2.625+0.007\left|L_{uckGrade}-170\right|,171 \le L_{uckGrade}<172:2.632+0.008\left|L_{uckGrade}-171\right|,172 \le L_{uckGrade}<173:2.64+0.007\left|L_{uckGrade}-172\right|,173 \le L_{uckGrade}<174:2.647+0.008\left|L_{uckGrade}-173\right|,174 \le L_{uckGrade}<175:2.655+0.007\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<176:2.662+0.008\left|L_{uckGrade}-175\right|,176 \le L_{uckGrade}<177:2.67+0.007\left|L_{uckGrade}-176\right|,177 \le L_{uckGrade}<178:2.677+0.008\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<180:2.685+0.007\left|L_{uckGrade}-178\right|,180 \le L_{uckGrade}<181:2.699+0.008\left|L_{uckGrade}-180\right|,181 \le L_{uckGrade}<183:2.707+0.007\left|L_{uckGrade}-181\right|,183 \le L_{uckGrade}<184:2.721+0.008\left|L_{uckGrade}-183\right|,184 \le L_{uckGrade}<186:2.729+0.007\left|L_{uckGrade}-184\right|,186 \le L_{uckGrade}<187:2.743+0.008\left|L_{uckGrade}-186\right|,187 \le L_{uckGrade}<205:2.751+0.007\left|L_{uckGrade}-187\right|,205 \le L_{uckGrade}<206:2.877+0.006\left|L_{uckGrade}-205\right|,206 \le L_{uckGrade}<209:2.883+0.007\left|L_{uckGrade}-206\right|,209 \le L_{uckGrade}<210:2.904+0.006\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<212:2.91+0.007\left|L_{uckGrade}-210\right|,212 \le L_{uckGrade}<213:2.924+0.006\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<214:2.93+0.007\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<215:2.937+0.006\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<216:2.943+0.007\left|L_{uckGrade}-215\right|,216 \le L_{uckGrade}<217:2.95+0.006\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<218:2.956+0.007\left|L_{uckGrade}-217\right|,218 \le L_{uckGrade}<219:2.963+0.006\left|L_{uckGrade}-218\right|,219 \le L_{uckGrade}<220:2.969+0.007\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<221:2.976+0.006\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:2.982+0.007\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:2.989+0.006\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:2.995+0.007\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<226:3.002+0.006\left|L_{uckGrade}-224\right|,226 \le L_{uckGrade}<227:3.014+0.007\left|L_{uckGrade}-226\right|,227 \le L_{uckGrade}<230:3.021+0.006\left|L_{uckGrade}-227\right|,230 \le L_{uckGrade}<231:3.039+0.007\left|L_{uckGrade}-230\right|,231 \le L_{uckGrade}<248:3.046+0.006\left|L_{uckGrade}-231\right|,248 \le L_{uckGrade}<249:3.148+0.005\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<252:3.153+0.006\left|L_{uckGrade}-249\right|,252 \le L_{uckGrade}<253:3.171+0.005\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<255:3.176+0.006\left|L_{uckGrade}-253\right|,255 \le L_{uckGrade}<256:3.188+0.005\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<257:3.193+0.006\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<258:3.199+0.005\left|L_{uckGrade}-257\right|,258 \le L_{uckGrade}<260:3.204+0.006\left|L_{uckGrade}-258\right|,260 \le L_{uckGrade}<261:3.216+0.005\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<262:3.221+0.006\left|L_{uckGrade}-261\right|,262 \le L_{uckGrade}<263:3.227+0.005\left|L_{uckGrade}-262\right|,263 \le L_{uckGrade}<264:3.232+0.006\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<266:3.238+0.005\left|L_{uckGrade}-264\right|,266 \le L_{uckGrade}<267:3.248+0.006\left|L_{uckGrade}-266\right|,267 \le L_{uckGrade}<269:3.254+0.005\left|L_{uckGrade}-267\right|,269 \le L_{uckGrade}<270:3.264+0.006\left|L_{uckGrade}-269\right|,270 \le L_{uckGrade}<272:3.27+0.005\left|L_{uckGrade}-270\right|,272 \le L_{uckGrade}<273:3.28+0.006\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<278:3.286+0.005\left|L_{uckGrade}-273\right|,278 \le L_{uckGrade}<279:3.311+0.006\left|L_{uckGrade}-278\right|,279 \le L_{uckGrade}<287:3.317+0.005\left|L_{uckGrade}-279\right|,287 \le L_{uckGrade}<288:3.357+0.004\left|L_{uckGrade}-287\right|,288 \le L_{uckGrade}<293:3.361+0.005\left|L_{uckGrade}-288\right|,293 \le L_{uckGrade}<294:3.386+0.004\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<297:3.39+0.005\left|L_{uckGrade}-294\right|,297 \le L_{uckGrade}<298:3.405+0.004\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<299:3.409+0.005\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<300:3.414+0.004\left|L_{uckGrade}-299\right|,300 \le L_{uckGrade}<302:3.418+0.005\left|L_{uckGrade}-300\right|,302 \le L_{uckGrade}<303:3.428+0.004\left|L_{uckGrade}-302\right|,303 \le L_{uckGrade}<304:3.432+0.005\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<305:3.437+0.004\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<306:3.441+0.005\left|L_{uckGrade}-305\right|,306 \le L_{uckGrade}<307:3.446+0.004\left|L_{uckGrade}-306\right|,307 \le L_{uckGrade}<308:3.45+0.005\left|L_{uckGrade}-307\right|,308 \le L_{uckGrade}<310:3.455+0.004\left|L_{uckGrade}-308\right|,310 \le L_{uckGrade}<311:3.463+0.005\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<313:3.468+0.004\left|L_{uckGrade}-311\right|,313 \le L_{uckGrade}<314:3.476+0.005\left|L_{uckGrade}-313\right|,314 \le L_{uckGrade}<316:3.481+0.004\left|L_{uckGrade}-314\right|,316 \le L_{uckGrade}<317:3.489+0.005\left|L_{uckGrade}-316\right|,317 \le L_{uckGrade}<323:3.494+0.004\left|L_{uckGrade}-317\right|,323 \le L_{uckGrade}<324:3.518+0.005\left|L_{uckGrade}-323\right|,324 \le L_{uckGrade}<329:3.523+0.004\left|L_{uckGrade}-324\right|,329 \le L_{uckGrade}<330:3.543+0.003\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<336:3.546+0.004\left|L_{uckGrade}-330\right|,336 \le L_{uckGrade}<337:3.57+0.003\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<340:3.573+0.004\left|L_{uckGrade}-337\right|,340 \le L_{uckGrade}<341:3.585+0.003\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<342:3.588+0.004\left|L_{uckGrade}-341\right|,342 \le L_{uckGrade}<343:3.592+0.003\left|L_{uckGrade}-342\right|,343 \le L_{uckGrade}<345:3.595+0.004\left|L_{uckGrade}-343\right|,345 \le L_{uckGrade}<346:3.603+0.003\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<347:3.606+0.004\left|L_{uckGrade}-346\right|,347 \le L_{uckGrade}<348:3.61+0.003\left|L_{uckGrade}-347\right|,348 \le L_{uckGrade}<349:3.613+0.004\left|L_{uckGrade}-348\right|,349 \le L_{uckGrade}<350:3.617+0.003\left|L_{uckGrade}-349\right|,350 \le L_{uckGrade}<351:3.62+0.004\left|L_{uckGrade}-350\right|,351 \le L_{uckGrade}<352:3.624+0.003\left|L_{uckGrade}-351\right|,352 \le L_{uckGrade}<353:3.627+0.004\left|L_{uckGrade}-352\right|,353 \le L_{uckGrade}<355:3.631+0.003\left|L_{uckGrade}-353\right|,355 \le L_{uckGrade}<356:3.637+0.004\left|L_{uckGrade}-355\right|,356 \le L_{uckGrade}<359:3.641+0.003\left|L_{uckGrade}-356\right|,359 \le L_{uckGrade}<360:3.65+0.004\left|L_{uckGrade}-359\right|,360 \le L_{uckGrade}<364:3.654+0.003\left|L_{uckGrade}-360\right|,364 \le L_{uckGrade}<365:3.666+0.004\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<376:3.67+0.003\left|L_{uckGrade}-365\right|,376 \le L_{uckGrade}<377:3.703+0.002\left|L_{uckGrade}-376\right|,377 \le L_{uckGrade}<381:3.705+0.003\left|L_{uckGrade}-377\right|,381 \le L_{uckGrade}<382:3.717+0.002\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<384:3.719+0.003\left|L_{uckGrade}-382\right|,384 \le L_{uckGrade}<385:3.725+0.002\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<387:3.727+0.003\left|L_{uckGrade}-385\right|,387 \le L_{uckGrade}<388:3.733+0.002\left|L_{uckGrade}-387\right|,388 \le L_{uckGrade}<389:3.735+0.003\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<390:3.738+0.002\left|L_{uckGrade}-389\right|,390 \le L_{uckGrade}<391:3.74+0.003\left|L_{uckGrade}-390\right|,391 \le L_{uckGrade}<392:3.743+0.002\left|L_{uckGrade}-391\right|,392 \le L_{uckGrade}<393:3.745+0.003\left|L_{uckGrade}-392\right|,393 \le L_{uckGrade}<394:3.748+0.002\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<395:3.75+0.003\left|L_{uckGrade}-394\right|,395 \le L_{uckGrade}<396:3.753+0.002\left|L_{uckGrade}-395\right|,396 \le L_{uckGrade}<397:3.755+0.003\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<399:3.758+0.002\left|L_{uckGrade}-397\right|,399 \le L_{uckGrade}<400:3.762+0.003\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<403:3.765+0.002\left|L_{uckGrade}-400\right|,403 \le L_{uckGrade}<404:3.771+0.003\left|L_{uckGrade}-403\right|,404 \le L_{uckGrade}<409:3.774+0.002\left|L_{uckGrade}-404\right|,409 \le L_{uckGrade}<410:3.784+0.003\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<417:3.787+0.002\left|L_{uckGrade}-410\right|,417 \le L_{uckGrade}<418:3.801+0.001\left|L_{uckGrade}-417\right|,418 \le L_{uckGrade}<423:3.802+0.002\left|L_{uckGrade}-418\right|,423 \le L_{uckGrade}<424:3.812+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<427:3.813+0.002\left|L_{uckGrade}-424\right|,427 \le L_{uckGrade}<428:3.819+0.001\left|L_{uckGrade}-427\right|,428 \le L_{uckGrade}<430:3.82+0.002\left|L_{uckGrade}-428\right|,430 \le L_{uckGrade}<431:3.824+0.001\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<432:3.825+0.002\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<433:3.827+0.001\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<434:3.828+0.002\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<435:3.83+0.001\left|L_{uckGrade}-434\right|,435 \le L_{uckGrade}<436:3.831+0.002\left|L_{uckGrade}-435\right|,436 \le L_{uckGrade}<437:3.833+0.001\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<438:3.834+0.002\left|L_{uckGrade}-437\right|,438 \le L_{uckGrade}<439:3.836+0.001\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<440:3.837+0.002\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<442:3.839+0.001\left|L_{uckGrade}-440\right|,442 \le L_{uckGrade}<443:3.841+0.002\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<445:3.843+0.001\left|L_{uckGrade}-443\right|,445 \le L_{uckGrade}<446:3.845+0.002\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<450:3.847+0.001\left|L_{uckGrade}-446\right|,450 \le L_{uckGrade}<451:3.851+0.002\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<463:3.853+0.001\left|L_{uckGrade}-451\right|,463 \le L_{uckGrade}<464:3.865+0\left|L_{uckGrade}-463\right|,464 \le L_{uckGrade}<468:3.865+0.001\left|L_{uckGrade}-464\right|,468 \le L_{uckGrade}<469:3.869+0\left|L_{uckGrade}-468\right|,469 \le L_{uckGrade}<471:3.869+0.001\left|L_{uckGrade}-469\right|,471 \le L_{uckGrade}<472:3.871+0\left|L_{uckGrade}-471\right|,472 \le L_{uckGrade}<474:3.871+0.001\left|L_{uckGrade}-472\right|,474 \le L_{uckGrade}<475:3.873+0\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<476:3.873+0.001\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<477:3.874+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<478:3.874+0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:3.875+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<480:3.875+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:3.876+0\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:3.876+0.001\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:3.877+0\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<484:3.877+0.001\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<486:3.878+0\left|L_{uckGrade}-484\right|,486 \le L_{uckGrade}<487:3.878+0.001\left|L_{uckGrade}-486\right|,487 \le L_{uckGrade}<490:3.879+0\left|L_{uckGrade}-487\right|,490 \le L_{uckGrade}<491:3.879+0.001\left|L_{uckGrade}-490\right|,491 \le L_{uckGrade}<495:3.88+0\left|L_{uckGrade}-491\right|,495 \le L_{uckGrade}<496:3.88+0.001\left|L_{uckGrade}-495\right|,496 \le L_{uckGrade}<500:3.881+0\left|L_{uckGrade}-496\right|\right\}
See Example for how to use.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
L_{uckGrade06}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<6:1+0.013\left|L_{uckGrade}-0\right|,6 \le L_{uckGrade}<7:1.078+0.012\left|L_{uckGrade}-6\right|,7 \le L_{uckGrade}<11:1.09+0.013\left|L_{uckGrade}-7\right|,11 \le L_{uckGrade}<12:1.142+0.012\left|L_{uckGrade}-11\right|,12 \le L_{uckGrade}<14:1.154+0.013\left|L_{uckGrade}-12\right|,14 \le L_{uckGrade}<15:1.18+0.012\left|L_{uckGrade}-14\right|,15 \le L_{uckGrade}<16:1.192+0.013\left|L_{uckGrade}-15\right|,16 \le L_{uckGrade}<17:1.205+0.012\left|L_{uckGrade}-16\right|,17 \le L_{uckGrade}<19:1.217+0.013\left|L_{uckGrade}-17\right|,19 \le L_{uckGrade}<20:1.243+0.012\left|L_{uckGrade}-19\right|,20 \le L_{uckGrade}<21:1.255+0.013\left|L_{uckGrade}-20\right|,21 \le L_{uckGrade}<23:1.268+0.012\left|L_{uckGrade}-21\right|,23 \le L_{uckGrade}<24:1.292+0.013\left|L_{uckGrade}-23\right|,24 \le L_{uckGrade}<25:1.305+0.012\left|L_{uckGrade}-24\right|,25 \le L_{uckGrade}<26:1.317+0.013\left|L_{uckGrade}-25\right|,26 \le L_{uckGrade}<29:1.33+0.012\left|L_{uckGrade}-26\right|,29 \le L_{uckGrade}<30:1.366+0.013\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<34:1.379+0.012\left|L_{uckGrade}-30\right|,34 \le L_{uckGrade}<35:1.427+0.013\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<43:1.44+0.012\left|L_{uckGrade}-35\right|,43 \le L_{uckGrade}<44:1.536+0.011\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<48:1.547+0.012\left|L_{uckGrade}-44\right|,48 \le L_{uckGrade}<49:1.595+0.011\left|L_{uckGrade}-48\right|,49 \le L_{uckGrade}<52:1.606+0.012\left|L_{uckGrade}-49\right|,52 \le L_{uckGrade}<53:1.642+0.011\left|L_{uckGrade}-52\right|,53 \le L_{uckGrade}<54:1.653+0.012\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<55:1.665+0.011\left|L_{uckGrade}-54\right|,55 \le L_{uckGrade}<57:1.676+0.012\left|L_{uckGrade}-55\right|,57 \le L_{uckGrade}<58:1.7+0.011\left|L_{uckGrade}-57\right|,58 \le L_{uckGrade}<59:1.711+0.012\left|L_{uckGrade}-58\right|,59 \le L_{uckGrade}<61:1.723+0.011\left|L_{uckGrade}-59\right|,61 \le L_{uckGrade}<62:1.745+0.012\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<63:1.757+0.011\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<64:1.768+0.012\left|L_{uckGrade}-63\right|,64 \le L_{uckGrade}<66:1.78+0.011\left|L_{uckGrade}-64\right|,66 \le L_{uckGrade}<67:1.802+0.012\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<71:1.814+0.011\left|L_{uckGrade}-67\right|,71 \le L_{uckGrade}<72:1.858+0.012\left|L_{uckGrade}-71\right|,72 \le L_{uckGrade}<83:1.87+0.011\left|L_{uckGrade}-72\right|,83 \le L_{uckGrade}<84:1.991+0.01\left|L_{uckGrade}-83\right|,84 \le L_{uckGrade}<87:2.001+0.011\left|L_{uckGrade}-84\right|,87 \le L_{uckGrade}<88:2.034+0.01\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<91:2.044+0.011\left|L_{uckGrade}-88\right|,91 \le L_{uckGrade}<92:2.077+0.01\left|L_{uckGrade}-91\right|,92 \le L_{uckGrade}<93:2.087+0.011\left|L_{uckGrade}-92\right|,93 \le L_{uckGrade}<94:2.098+0.01\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<95:2.108+0.011\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<96:2.119+0.01\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<97:2.129+0.011\left|L_{uckGrade}-96\right|,97 \le L_{uckGrade}<98:2.14+0.01\left|L_{uckGrade}-97\right|,98 \le L_{uckGrade}<99:2.15+0.011\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<100:2.161+0.01\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<101:2.171+0.011\left|L_{uckGrade}-100\right|,101 \le L_{uckGrade}<103:2.182+0.01\left|L_{uckGrade}-101\right|,103 \le L_{uckGrade}<104:2.202+0.011\left|L_{uckGrade}-103\right|,104 \le L_{uckGrade}<106:2.213+0.01\left|L_{uckGrade}-104\right|,106 \le L_{uckGrade}<107:2.233+0.011\left|L_{uckGrade}-106\right|,107 \le L_{uckGrade}<113:2.244+0.01\left|L_{uckGrade}-107\right|,113 \le L_{uckGrade}<114:2.304+0.011\left|L_{uckGrade}-113\right|,114 \le L_{uckGrade}<118:2.315+0.01\left|L_{uckGrade}-114\right|,118 \le L_{uckGrade}<119:2.355+0.009\left|L_{uckGrade}-118\right|,119 \le L_{uckGrade}<125:2.364+0.01\left|L_{uckGrade}-119\right|,125 \le L_{uckGrade}<126:2.424+0.009\left|L_{uckGrade}-125\right|,126 \le L_{uckGrade}<128:2.433+0.01\left|L_{uckGrade}-126\right|,128 \le L_{uckGrade}<129:2.453+0.009\left|L_{uckGrade}-128\right|,129 \le L_{uckGrade}<131:2.462+0.01\left|L_{uckGrade}-129\right|,131 \le L_{uckGrade}<132:2.482+0.009\left|L_{uckGrade}-131\right|,132 \le L_{uckGrade}<133:2.491+0.01\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<134:2.501+0.009\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<135:2.51+0.01\left|L_{uckGrade}-134\right|,135 \le L_{uckGrade}<136:2.52+0.009\left|L_{uckGrade}-135\right|,136 \le L_{uckGrade}<137:2.529+0.01\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<138:2.539+0.009\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<139:2.548+0.01\left|L_{uckGrade}-138\right|,139 \le L_{uckGrade}<141:2.558+0.009\left|L_{uckGrade}-139\right|,141 \le L_{uckGrade}<142:2.576+0.01\left|L_{uckGrade}-141\right|,142 \le L_{uckGrade}<144:2.586+0.009\left|L_{uckGrade}-142\right|,144 \le L_{uckGrade}<145:2.604+0.01\left|L_{uckGrade}-144\right|,145 \le L_{uckGrade}<150:2.614+0.009\left|L_{uckGrade}-145\right|,150 \le L_{uckGrade}<151:2.659+0.01\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<158:2.669+0.009\left|L_{uckGrade}-151\right|,158 \le L_{uckGrade}<159:2.732+0.008\left|L_{uckGrade}-158\right|,159 \le L_{uckGrade}<163:2.74+0.009\left|L_{uckGrade}-159\right|,163 \le L_{uckGrade}<164:2.776+0.008\left|L_{uckGrade}-163\right|,164 \le L_{uckGrade}<167:2.784+0.009\left|L_{uckGrade}-164\right|,167 \le L_{uckGrade}<168:2.811+0.008\left|L_{uckGrade}-167\right|,168 \le L_{uckGrade}<170:2.819+0.009\left|L_{uckGrade}-168\right|,170 \le L_{uckGrade}<171:2.837+0.008\left|L_{uckGrade}-170\right|,171 \le L_{uckGrade}<172:2.845+0.009\left|L_{uckGrade}-171\right|,172 \le L_{uckGrade}<173:2.854+0.008\left|L_{uckGrade}-172\right|,173 \le L_{uckGrade}<174:2.862+0.009\left|L_{uckGrade}-173\right|,174 \le L_{uckGrade}<175:2.871+0.008\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<176:2.879+0.009\left|L_{uckGrade}-175\right|,176 \le L_{uckGrade}<178:2.888+0.008\left|L_{uckGrade}-176\right|,178 \le L_{uckGrade}<179:2.904+0.009\left|L_{uckGrade}-178\right|,179 \le L_{uckGrade}<181:2.913+0.008\left|L_{uckGrade}-179\right|,181 \le L_{uckGrade}<182:2.929+0.009\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<185:2.938+0.008\left|L_{uckGrade}-182\right|,185 \le L_{uckGrade}<186:2.962+0.009\left|L_{uckGrade}-185\right|,186 \le L_{uckGrade}<200:2.971+0.008\left|L_{uckGrade}-186\right|,200 \le L_{uckGrade}<201:3.083+0.007\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<204:3.09+0.008\left|L_{uckGrade}-201\right|,204 \le L_{uckGrade}<205:3.114+0.007\left|L_{uckGrade}-204\right|,205 \le L_{uckGrade}<207:3.121+0.008\left|L_{uckGrade}-205\right|,207 \le L_{uckGrade}<208:3.137+0.007\left|L_{uckGrade}-207\right|,208 \le L_{uckGrade}<209:3.144+0.008\left|L_{uckGrade}-208\right|,209 \le L_{uckGrade}<210:3.152+0.007\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<211:3.159+0.008\left|L_{uckGrade}-210\right|,211 \le L_{uckGrade}<212:3.167+0.007\left|L_{uckGrade}-211\right|,212 \le L_{uckGrade}<213:3.174+0.008\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<214:3.182+0.007\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<215:3.189+0.008\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<216:3.197+0.007\left|L_{uckGrade}-215\right|,216 \le L_{uckGrade}<217:3.204+0.008\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<219:3.212+0.007\left|L_{uckGrade}-217\right|,219 \le L_{uckGrade}<220:3.226+0.008\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<223:3.234+0.007\left|L_{uckGrade}-220\right|,223 \le L_{uckGrade}<224:3.255+0.008\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<239:3.263+0.007\left|L_{uckGrade}-224\right|,239 \le L_{uckGrade}<240:3.368+0.006\left|L_{uckGrade}-239\right|,240 \le L_{uckGrade}<243:3.374+0.007\left|L_{uckGrade}-240\right|,243 \le L_{uckGrade}<244:3.395+0.006\left|L_{uckGrade}-243\right|,244 \le L_{uckGrade}<245:3.401+0.007\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<246:3.408+0.006\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<248:3.414+0.007\left|L_{uckGrade}-246\right|,248 \le L_{uckGrade}<249:3.428+0.006\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<250:3.434+0.007\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<251:3.441+0.006\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:3.447+0.007\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<253:3.454+0.006\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<254:3.46+0.007\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<256:3.467+0.006\left|L_{uckGrade}-254\right|,256 \le L_{uckGrade}<257:3.479+0.007\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<259:3.486+0.006\left|L_{uckGrade}-257\right|,259 \le L_{uckGrade}<260:3.498+0.007\left|L_{uckGrade}-259\right|,260 \le L_{uckGrade}<264:3.505+0.006\left|L_{uckGrade}-260\right|,264 \le L_{uckGrade}<265:3.529+0.007\left|L_{uckGrade}-264\right|,265 \le L_{uckGrade}<274:3.536+0.006\left|L_{uckGrade}-265\right|,274 \le L_{uckGrade}<275:3.59+0.005\left|L_{uckGrade}-274\right|,275 \le L_{uckGrade}<279:3.595+0.006\left|L_{uckGrade}-275\right|,279 \le L_{uckGrade}<280:3.619+0.005\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<283:3.624+0.006\left|L_{uckGrade}-280\right|,283 \le L_{uckGrade}<284:3.642+0.005\left|L_{uckGrade}-283\right|,284 \le L_{uckGrade}<285:3.647+0.006\left|L_{uckGrade}-284\right|,285 \le L_{uckGrade}<286:3.653+0.005\left|L_{uckGrade}-285\right|,286 \le L_{uckGrade}<287:3.658+0.006\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<288:3.664+0.005\left|L_{uckGrade}-287\right|,288 \le L_{uckGrade}<289:3.669+0.006\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<290:3.675+0.005\left|L_{uckGrade}-289\right|,290 \le L_{uckGrade}<291:3.68+0.006\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<292:3.686+0.005\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<293:3.691+0.006\left|L_{uckGrade}-292\right|,293 \le L_{uckGrade}<294:3.697+0.005\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<295:3.702+0.006\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<298:3.708+0.005\left|L_{uckGrade}-295\right|,298 \le L_{uckGrade}<299:3.723+0.006\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<303:3.729+0.005\left|L_{uckGrade}-299\right|,303 \le L_{uckGrade}<304:3.749+0.006\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<312:3.755+0.005\left|L_{uckGrade}-304\right|,312 \le L_{uckGrade}<313:3.795+0.004\left|L_{uckGrade}-312\right|,313 \le L_{uckGrade}<318:3.799+0.005\left|L_{uckGrade}-313\right|,318 \le L_{uckGrade}<319:3.824+0.004\left|L_{uckGrade}-318\right|,319 \le L_{uckGrade}<321:3.828+0.005\left|L_{uckGrade}-319\right|,321 \le L_{uckGrade}<322:3.838+0.004\left|L_{uckGrade}-321\right|,322 \le L_{uckGrade}<324:3.842+0.005\left|L_{uckGrade}-322\right|,324 \le L_{uckGrade}<325:3.852+0.004\left|L_{uckGrade}-324\right|,325 \le L_{uckGrade}<326:3.856+0.005\left|L_{uckGrade}-325\right|,326 \le L_{uckGrade}<327:3.861+0.004\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<328:3.865+0.005\left|L_{uckGrade}-327\right|,328 \le L_{uckGrade}<329:3.87+0.004\left|L_{uckGrade}-328\right|,329 \le L_{uckGrade}<330:3.874+0.005\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<332:3.879+0.004\left|L_{uckGrade}-330\right|,332 \le L_{uckGrade}<333:3.887+0.005\left|L_{uckGrade}-332\right|,333 \le L_{uckGrade}<335:3.892+0.004\left|L_{uckGrade}-333\right|,335 \le L_{uckGrade}<336:3.9+0.005\left|L_{uckGrade}-335\right|,336 \le L_{uckGrade}<339:3.905+0.004\left|L_{uckGrade}-336\right|,339 \le L_{uckGrade}<340:3.917+0.005\left|L_{uckGrade}-339\right|,340 \le L_{uckGrade}<353:3.922+0.004\left|L_{uckGrade}-340\right|,353 \le L_{uckGrade}<354:3.974+0.003\left|L_{uckGrade}-353\right|,354 \le L_{uckGrade}<358:3.977+0.004\left|L_{uckGrade}-354\right|,358 \le L_{uckGrade}<359:3.993+0.003\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<361:3.996+0.004\left|L_{uckGrade}-359\right|,361 \le L_{uckGrade}<362:4.004+0.003\left|L_{uckGrade}-361\right|,362 \le L_{uckGrade}<363:4.007+0.004\left|L_{uckGrade}-362\right|,363 \le L_{uckGrade}<364:4.011+0.003\left|L_{uckGrade}-363\right|,364 \le L_{uckGrade}<365:4.014+0.004\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<366:4.018+0.003\left|L_{uckGrade}-365\right|,366 \le L_{uckGrade}<367:4.021+0.004\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:4.025+0.003\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<369:4.028+0.004\left|L_{uckGrade}-368\right|,369 \le L_{uckGrade}<371:4.032+0.003\left|L_{uckGrade}-369\right|,371 \le L_{uckGrade}<372:4.038+0.004\left|L_{uckGrade}-371\right|,372 \le L_{uckGrade}<374:4.042+0.003\left|L_{uckGrade}-372\right|,374 \le L_{uckGrade}<375:4.048+0.004\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<378:4.052+0.003\left|L_{uckGrade}-375\right|,378 \le L_{uckGrade}<379:4.061+0.004\left|L_{uckGrade}-378\right|,379 \le L_{uckGrade}<391:4.065+0.003\left|L_{uckGrade}-379\right|,391 \le L_{uckGrade}<392:4.101+0.002\left|L_{uckGrade}-391\right|,392 \le L_{uckGrade}<396:4.103+0.003\left|L_{uckGrade}-392\right|,396 \le L_{uckGrade}<397:4.115+0.002\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<399:4.117+0.003\left|L_{uckGrade}-397\right|,399 \le L_{uckGrade}<400:4.123+0.002\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<401:4.125+0.003\left|L_{uckGrade}-400\right|,401 \le L_{uckGrade}<402:4.128+0.002\left|L_{uckGrade}-401\right|,402 \le L_{uckGrade}<403:4.13+0.003\left|L_{uckGrade}-402\right|,403 \le L_{uckGrade}<404:4.133+0.002\left|L_{uckGrade}-403\right|,404 \le L_{uckGrade}<405:4.135+0.003\left|L_{uckGrade}-404\right|,405 \le L_{uckGrade}<406:4.138+0.002\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:4.14+0.003\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<408:4.143+0.002\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<409:4.145+0.003\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<411:4.148+0.002\left|L_{uckGrade}-409\right|,411 \le L_{uckGrade}<412:4.152+0.003\left|L_{uckGrade}-411\right|,412 \le L_{uckGrade}<415:4.155+0.002\left|L_{uckGrade}-412\right|,415 \le L_{uckGrade}<416:4.161+0.003\left|L_{uckGrade}-415\right|,416 \le L_{uckGrade}<432:4.164+0.002\left|L_{uckGrade}-416\right|,432 \le L_{uckGrade}<433:4.196+0.001\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<435:4.197+0.002\left|L_{uckGrade}-433\right|,435 \le L_{uckGrade}<436:4.201+0.001\left|L_{uckGrade}-435\right|,436 \le L_{uckGrade}<438:4.202+0.002\left|L_{uckGrade}-436\right|,438 \le L_{uckGrade}<439:4.206+0.001\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<440:4.207+0.002\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<441:4.209+0.001\left|L_{uckGrade}-440\right|,441 \le L_{uckGrade}<443:4.21+0.002\left|L_{uckGrade}-441\right|,443 \le L_{uckGrade}<445:4.214+0.001\left|L_{uckGrade}-443\right|,445 \le L_{uckGrade}<446:4.216+0.002\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<447:4.218+0.001\left|L_{uckGrade}-446\right|,447 \le L_{uckGrade}<448:4.219+0.002\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<450:4.221+0.001\left|L_{uckGrade}-448\right|,450 \le L_{uckGrade}<451:4.223+0.002\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<454:4.225+0.001\left|L_{uckGrade}-451\right|,454 \le L_{uckGrade}<455:4.228+0.002\left|L_{uckGrade}-454\right|,455 \le L_{uckGrade}<469:4.23+0.001\left|L_{uckGrade}-455\right|,469 \le L_{uckGrade}<470:4.244+0\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<473:4.244+0.001\left|L_{uckGrade}-470\right|,473 \le L_{uckGrade}<474:4.247+0\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<476:4.247+0.001\left|L_{uckGrade}-474\right|,476 \le L_{uckGrade}<477:4.249+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<478:4.249+0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:4.25+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<481:4.25+0.001\left|L_{uckGrade}-479\right|,481 \le L_{uckGrade}<482:4.252+0\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:4.252+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<485:4.253+0\left|L_{uckGrade}-483\right|,485 \le L_{uckGrade}<486:4.253+0.001\left|L_{uckGrade}-485\right|,486 \le L_{uckGrade}<488:4.254+0\left|L_{uckGrade}-486\right|,488 \le L_{uckGrade}<489:4.254+0.001\left|L_{uckGrade}-488\right|,489 \le L_{uckGrade}<491:4.255+0\left|L_{uckGrade}-489\right|,491 \le L_{uckGrade}<492:4.255+0.001\left|L_{uckGrade}-491\right|,492 \le L_{uckGrade}<499:4.256+0\left|L_{uckGrade}-492\right|,499 \le L_{uckGrade}<500:4.256+0.001\left|L_{uckGrade}-499\right|\right\}
See Example for how to use.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
L_{uckGrade07}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<1:1+0.014\left|L_{uckGrade}-0\right|,1 \le L_{uckGrade}<3:1.014+0.013\left|L_{uckGrade}-1\right|,3 \le L_{uckGrade}<4:1.04+0.014\left|L_{uckGrade}-3\right|,4 \le L_{uckGrade}<5:1.054+0.013\left|L_{uckGrade}-4\right|,5 \le L_{uckGrade}<6:1.067+0.014\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<8:1.081+0.013\left|L_{uckGrade}-6\right|,8 \le L_{uckGrade}<9:1.107+0.014\left|L_{uckGrade}-8\right|,9 \le L_{uckGrade}<13:1.121+0.013\left|L_{uckGrade}-9\right|,13 \le L_{uckGrade}<14:1.173+0.014\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<24:1.187+0.013\left|L_{uckGrade}-14\right|,24 \le L_{uckGrade}<25:1.317+0.012\left|L_{uckGrade}-24\right|,25 \le L_{uckGrade}<29:1.329+0.013\left|L_{uckGrade}-25\right|,29 \le L_{uckGrade}<30:1.381+0.012\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<32:1.393+0.013\left|L_{uckGrade}-30\right|,32 \le L_{uckGrade}<33:1.419+0.012\left|L_{uckGrade}-32\right|,33 \le L_{uckGrade}<34:1.431+0.013\left|L_{uckGrade}-33\right|,34 \le L_{uckGrade}<35:1.444+0.012\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<37:1.456+0.013\left|L_{uckGrade}-35\right|,37 \le L_{uckGrade}<39:1.482+0.012\left|L_{uckGrade}-37\right|,39 \le L_{uckGrade}<40:1.506+0.013\left|L_{uckGrade}-39\right|,40 \le L_{uckGrade}<41:1.519+0.012\left|L_{uckGrade}-40\right|,41 \le L_{uckGrade}<42:1.531+0.013\left|L_{uckGrade}-41\right|,42 \le L_{uckGrade}<44:1.544+0.012\left|L_{uckGrade}-42\right|,44 \le L_{uckGrade}<45:1.568+0.013\left|L_{uckGrade}-44\right|,45 \le L_{uckGrade}<47:1.581+0.012\left|L_{uckGrade}-45\right|,47 \le L_{uckGrade}<48:1.605+0.013\left|L_{uckGrade}-47\right|,48 \le L_{uckGrade}<64:1.618+0.012\left|L_{uckGrade}-48\right|,64 \le L_{uckGrade}<65:1.81+0.011\left|L_{uckGrade}-64\right|,65 \le L_{uckGrade}<67:1.821+0.012\left|L_{uckGrade}-65\right|,67 \le L_{uckGrade}<68:1.845+0.011\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<70:1.856+0.012\left|L_{uckGrade}-68\right|,70 \le L_{uckGrade}<71:1.88+0.011\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<73:1.891+0.012\left|L_{uckGrade}-71\right|,73 \le L_{uckGrade}<74:1.915+0.011\left|L_{uckGrade}-73\right|,74 \le L_{uckGrade}<75:1.926+0.012\left|L_{uckGrade}-74\right|,75 \le L_{uckGrade}<77:1.938+0.011\left|L_{uckGrade}-75\right|,77 \le L_{uckGrade}<78:1.96+0.012\left|L_{uckGrade}-77\right|,78 \le L_{uckGrade}<79:1.972+0.011\left|L_{uckGrade}-78\right|,79 \le L_{uckGrade}<80:1.983+0.012\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<82:1.995+0.011\left|L_{uckGrade}-80\right|,82 \le L_{uckGrade}<83:2.017+0.012\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<87:2.029+0.011\left|L_{uckGrade}-83\right|,87 \le L_{uckGrade}<88:2.073+0.012\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<99:2.085+0.011\left|L_{uckGrade}-88\right|,99 \le L_{uckGrade}<100:2.206+0.01\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<103:2.216+0.011\left|L_{uckGrade}-100\right|,103 \le L_{uckGrade}<104:2.249+0.01\left|L_{uckGrade}-103\right|,104 \le L_{uckGrade}<106:2.259+0.011\left|L_{uckGrade}-104\right|,106 \le L_{uckGrade}<107:2.281+0.01\left|L_{uckGrade}-106\right|,107 \le L_{uckGrade}<109:2.291+0.011\left|L_{uckGrade}-107\right|,109 \le L_{uckGrade}<110:2.313+0.01\left|L_{uckGrade}-109\right|,110 \le L_{uckGrade}<111:2.323+0.011\left|L_{uckGrade}-110\right|,111 \le L_{uckGrade}<112:2.334+0.01\left|L_{uckGrade}-111\right|,112 \le L_{uckGrade}<113:2.344+0.011\left|L_{uckGrade}-112\right|,113 \le L_{uckGrade}<114:2.355+0.01\left|L_{uckGrade}-113\right|,114 \le L_{uckGrade}<115:2.365+0.011\left|L_{uckGrade}-114\right|,115 \le L_{uckGrade}<117:2.376+0.01\left|L_{uckGrade}-115\right|,117 \le L_{uckGrade}<118:2.396+0.011\left|L_{uckGrade}-117\right|,118 \le L_{uckGrade}<121:2.407+0.01\left|L_{uckGrade}-118\right|,121 \le L_{uckGrade}<122:2.437+0.011\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<127:2.448+0.01\left|L_{uckGrade}-122\right|,127 \le L_{uckGrade}<128:2.498+0.011\left|L_{uckGrade}-127\right|,128 \le L_{uckGrade}<132:2.509+0.01\left|L_{uckGrade}-128\right|,132 \le L_{uckGrade}<133:2.549+0.009\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<139:2.558+0.01\left|L_{uckGrade}-133\right|,139 \le L_{uckGrade}<140:2.618+0.009\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<142:2.627+0.01\left|L_{uckGrade}-140\right|,142 \le L_{uckGrade}<143:2.647+0.009\left|L_{uckGrade}-142\right|,143 \le L_{uckGrade}<145:2.656+0.01\left|L_{uckGrade}-143\right|,145 \le L_{uckGrade}<146:2.676+0.009\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<147:2.685+0.01\left|L_{uckGrade}-146\right|,147 \le L_{uckGrade}<148:2.695+0.009\left|L_{uckGrade}-147\right|,148 \le L_{uckGrade}<149:2.704+0.01\left|L_{uckGrade}-148\right|,149 \le L_{uckGrade}<150:2.714+0.009\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<151:2.723+0.01\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:2.733+0.009\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<153:2.742+0.01\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<155:2.752+0.009\left|L_{uckGrade}-153\right|,155 \le L_{uckGrade}<156:2.77+0.01\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<159:2.78+0.009\left|L_{uckGrade}-156\right|,159 \le L_{uckGrade}<160:2.807+0.01\left|L_{uckGrade}-159\right|,160 \le L_{uckGrade}<174:2.817+0.009\left|L_{uckGrade}-160\right|,174 \le L_{uckGrade}<175:2.943+0.008\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<178:2.951+0.009\left|L_{uckGrade}-175\right|,178 \le L_{uckGrade}<179:2.978+0.008\left|L_{uckGrade}-178\right|,179 \le L_{uckGrade}<181:2.986+0.009\left|L_{uckGrade}-179\right|,181 \le L_{uckGrade}<182:3.004+0.008\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<183:3.012+0.009\left|L_{uckGrade}-182\right|,183 \le L_{uckGrade}<184:3.021+0.008\left|L_{uckGrade}-183\right|,184 \le L_{uckGrade}<185:3.029+0.009\left|L_{uckGrade}-184\right|,185 \le L_{uckGrade}<186:3.038+0.008\left|L_{uckGrade}-185\right|,186 \le L_{uckGrade}<187:3.046+0.009\left|L_{uckGrade}-186\right|,187 \le L_{uckGrade}<188:3.055+0.008\left|L_{uckGrade}-187\right|,188 \le L_{uckGrade}<189:3.063+0.009\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<190:3.072+0.008\left|L_{uckGrade}-189\right|,190 \le L_{uckGrade}<191:3.08+0.009\left|L_{uckGrade}-190\right|,191 \le L_{uckGrade}<193:3.089+0.008\left|L_{uckGrade}-191\right|,193 \le L_{uckGrade}<194:3.105+0.009\left|L_{uckGrade}-193\right|,194 \le L_{uckGrade}<198:3.114+0.008\left|L_{uckGrade}-194\right|,198 \le L_{uckGrade}<199:3.146+0.009\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<209:3.155+0.008\left|L_{uckGrade}-199\right|,209 \le L_{uckGrade}<210:3.235+0.007\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<214:3.242+0.008\left|L_{uckGrade}-210\right|,214 \le L_{uckGrade}<215:3.274+0.007\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<217:3.281+0.008\left|L_{uckGrade}-215\right|,217 \le L_{uckGrade}<218:3.297+0.007\left|L_{uckGrade}-217\right|,218 \le L_{uckGrade}<220:3.304+0.008\left|L_{uckGrade}-218\right|,220 \le L_{uckGrade}<221:3.32+0.007\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:3.327+0.008\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:3.335+0.007\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:3.342+0.008\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<225:3.35+0.007\left|L_{uckGrade}-224\right|,225 \le L_{uckGrade}<226:3.357+0.008\left|L_{uckGrade}-225\right|,226 \le L_{uckGrade}<228:3.365+0.007\left|L_{uckGrade}-226\right|,228 \le L_{uckGrade}<229:3.379+0.008\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<231:3.387+0.007\left|L_{uckGrade}-229\right|,231 \le L_{uckGrade}<232:3.401+0.008\left|L_{uckGrade}-231\right|,232 \le L_{uckGrade}<237:3.409+0.007\left|L_{uckGrade}-232\right|,237 \le L_{uckGrade}<238:3.444+0.008\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<244:3.452+0.007\left|L_{uckGrade}-238\right|,244 \le L_{uckGrade}<245:3.494+0.006\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<250:3.5+0.007\left|L_{uckGrade}-245\right|,250 \le L_{uckGrade}<251:3.535+0.006\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<253:3.541+0.007\left|L_{uckGrade}-251\right|,253 \le L_{uckGrade}<254:3.555+0.006\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<256:3.561+0.007\left|L_{uckGrade}-254\right|,256 \le L_{uckGrade}<257:3.575+0.006\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<258:3.581+0.007\left|L_{uckGrade}-257\right|,258 \le L_{uckGrade}<259:3.588+0.006\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<260:3.594+0.007\left|L_{uckGrade}-259\right|,260 \le L_{uckGrade}<261:3.601+0.006\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<262:3.607+0.007\left|L_{uckGrade}-261\right|,262 \le L_{uckGrade}<263:3.614+0.006\left|L_{uckGrade}-262\right|,263 \le L_{uckGrade}<264:3.62+0.007\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<266:3.627+0.006\left|L_{uckGrade}-264\right|,266 \le L_{uckGrade}<267:3.639+0.007\left|L_{uckGrade}-266\right|,267 \le L_{uckGrade}<270:3.646+0.006\left|L_{uckGrade}-267\right|,270 \le L_{uckGrade}<271:3.664+0.007\left|L_{uckGrade}-270\right|,271 \le L_{uckGrade}<286:3.671+0.006\left|L_{uckGrade}-271\right|,286 \le L_{uckGrade}<287:3.761+0.005\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<290:3.766+0.006\left|L_{uckGrade}-287\right|,290 \le L_{uckGrade}<291:3.784+0.005\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<292:3.789+0.006\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<293:3.795+0.005\left|L_{uckGrade}-292\right|,293 \le L_{uckGrade}<295:3.8+0.006\left|L_{uckGrade}-293\right|,295 \le L_{uckGrade}<296:3.812+0.005\left|L_{uckGrade}-295\right|,296 \le L_{uckGrade}<297:3.817+0.006\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<298:3.823+0.005\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<299:3.828+0.006\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<301:3.834+0.005\left|L_{uckGrade}-299\right|,301 \le L_{uckGrade}<302:3.844+0.006\left|L_{uckGrade}-301\right|,302 \le L_{uckGrade}<304:3.85+0.005\left|L_{uckGrade}-302\right|,304 \le L_{uckGrade}<305:3.86+0.006\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<308:3.866+0.005\left|L_{uckGrade}-305\right|,308 \le L_{uckGrade}<309:3.881+0.006\left|L_{uckGrade}-308\right|,309 \le L_{uckGrade}<322:3.887+0.005\left|L_{uckGrade}-309\right|,322 \le L_{uckGrade}<323:3.952+0.004\left|L_{uckGrade}-322\right|,323 \le L_{uckGrade}<326:3.956+0.005\left|L_{uckGrade}-323\right|,326 \le L_{uckGrade}<327:3.971+0.004\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<329:3.975+0.005\left|L_{uckGrade}-327\right|,329 \le L_{uckGrade}<330:3.985+0.004\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<331:3.989+0.005\left|L_{uckGrade}-330\right|,331 \le L_{uckGrade}<332:3.994+0.004\left|L_{uckGrade}-331\right|,332 \le L_{uckGrade}<334:3.998+0.005\left|L_{uckGrade}-332\right|,334 \le L_{uckGrade}<336:4.008+0.004\left|L_{uckGrade}-334\right|,336 \le L_{uckGrade}<337:4.016+0.005\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<338:4.021+0.004\left|L_{uckGrade}-337\right|,338 \le L_{uckGrade}<339:4.025+0.005\left|L_{uckGrade}-338\right|,339 \le L_{uckGrade}<341:4.03+0.004\left|L_{uckGrade}-339\right|,341 \le L_{uckGrade}<342:4.038+0.005\left|L_{uckGrade}-341\right|,342 \le L_{uckGrade}<345:4.043+0.004\left|L_{uckGrade}-342\right|,345 \le L_{uckGrade}<346:4.055+0.005\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<358:4.06+0.004\left|L_{uckGrade}-346\right|,358 \le L_{uckGrade}<359:4.108+0.003\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<363:4.111+0.004\left|L_{uckGrade}-359\right|,363 \le L_{uckGrade}<364:4.127+0.003\left|L_{uckGrade}-363\right|,364 \le L_{uckGrade}<366:4.13+0.004\left|L_{uckGrade}-364\right|,366 \le L_{uckGrade}<367:4.138+0.003\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:4.141+0.004\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<369:4.145+0.003\left|L_{uckGrade}-368\right|,369 \le L_{uckGrade}<370:4.148+0.004\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<371:4.152+0.003\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<372:4.155+0.004\left|L_{uckGrade}-371\right|,372 \le L_{uckGrade}<373:4.159+0.003\left|L_{uckGrade}-372\right|,373 \le L_{uckGrade}<374:4.162+0.004\left|L_{uckGrade}-373\right|,374 \le L_{uckGrade}<375:4.166+0.003\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<376:4.169+0.004\left|L_{uckGrade}-375\right|,376 \le L_{uckGrade}<379:4.173+0.003\left|L_{uckGrade}-376\right|,379 \le L_{uckGrade}<380:4.182+0.004\left|L_{uckGrade}-379\right|,380 \le L_{uckGrade}<383:4.186+0.003\left|L_{uckGrade}-380\right|,383 \le L_{uckGrade}<384:4.195+0.004\left|L_{uckGrade}-383\right|,384 \le L_{uckGrade}<394:4.199+0.003\left|L_{uckGrade}-384\right|,394 \le L_{uckGrade}<395:4.229+0.002\left|L_{uckGrade}-394\right|,395 \le L_{uckGrade}<399:4.231+0.003\left|L_{uckGrade}-395\right|,399 \le L_{uckGrade}<400:4.243+0.002\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<402:4.245+0.003\left|L_{uckGrade}-400\right|,402 \le L_{uckGrade}<403:4.251+0.002\left|L_{uckGrade}-402\right|,403 \le L_{uckGrade}<405:4.253+0.003\left|L_{uckGrade}-403\right|,405 \le L_{uckGrade}<406:4.259+0.002\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:4.261+0.003\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<408:4.264+0.002\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<409:4.266+0.003\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<410:4.269+0.002\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<411:4.271+0.003\left|L_{uckGrade}-410\right|,411 \le L_{uckGrade}<413:4.274+0.002\left|L_{uckGrade}-411\right|,413 \le L_{uckGrade}<414:4.278+0.003\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<416:4.281+0.002\left|L_{uckGrade}-414\right|,416 \le L_{uckGrade}<417:4.285+0.003\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<421:4.288+0.002\left|L_{uckGrade}-417\right|,421 \le L_{uckGrade}<422:4.296+0.003\left|L_{uckGrade}-421\right|,422 \le L_{uckGrade}<431:4.299+0.002\left|L_{uckGrade}-422\right|,431 \le L_{uckGrade}<432:4.317+0.001\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<436:4.318+0.002\left|L_{uckGrade}-432\right|,436 \le L_{uckGrade}<437:4.326+0.001\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<439:4.327+0.002\left|L_{uckGrade}-437\right|,439 \le L_{uckGrade}<440:4.331+0.001\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<442:4.332+0.002\left|L_{uckGrade}-440\right|,442 \le L_{uckGrade}<443:4.336+0.001\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<444:4.337+0.002\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<445:4.339+0.001\left|L_{uckGrade}-444\right|,445 \le L_{uckGrade}<446:4.34+0.002\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<447:4.342+0.001\left|L_{uckGrade}-446\right|,447 \le L_{uckGrade}<448:4.343+0.002\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<450:4.345+0.001\left|L_{uckGrade}-448\right|,450 \le L_{uckGrade}<451:4.347+0.002\left|L_{uckGrade}-450\right|,451 \le L_{uckGrade}<453:4.349+0.001\left|L_{uckGrade}-451\right|,453 \le L_{uckGrade}<454:4.351+0.002\left|L_{uckGrade}-453\right|,454 \le L_{uckGrade}<458:4.353+0.001\left|L_{uckGrade}-454\right|,458 \le L_{uckGrade}<459:4.357+0.002\left|L_{uckGrade}-458\right|,459 \le L_{uckGrade}<467:4.359+0.001\left|L_{uckGrade}-459\right|,467 \le L_{uckGrade}<468:4.367+0\left|L_{uckGrade}-467\right|,468 \le L_{uckGrade}<473:4.367+0.001\left|L_{uckGrade}-468\right|,473 \le L_{uckGrade}<474:4.372+0\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<476:4.372+0.001\left|L_{uckGrade}-474\right|,476 \le L_{uckGrade}<477:4.374+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<479:4.374+0.001\left|L_{uckGrade}-477\right|,479 \le L_{uckGrade}<480:4.376+0\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:4.376+0.001\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:4.377+0\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:4.377+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<484:4.378+0\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<485:4.378+0.001\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<487:4.379+0\left|L_{uckGrade}-485\right|,487 \le L_{uckGrade}<488:4.379+0.001\left|L_{uckGrade}-487\right|,488 \le L_{uckGrade}<490:4.38+0\left|L_{uckGrade}-488\right|,490 \le L_{uckGrade}<491:4.38+0.001\left|L_{uckGrade}-490\right|,491 \le L_{uckGrade}<496:4.381+0\left|L_{uckGrade}-491\right|,496 \le L_{uckGrade}<497:4.381+0.001\left|L_{uckGrade}-496\right|,497 \le L_{uckGrade}<500:4.382+0\left|L_{uckGrade}-497\right|\right\}
See Example for how to use.
To calculate the drop rate at X Luck there are three steps.
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.
Stats that come from weapons, armors or jewelry imbued with item Enchantments.
Enchantments that aren't traditional Stats and only exist in a Damage/Healing formula are listed below and can also be found in Damage_Calculation and Healing.
Enchantment | Description |
---|---|
Physical Healing | Increases True Physical Healing performed |
Magical Healing | Increases True Magical Healing performed |
Armor Penetration | Increases the amount of Physical Damage that bypasses enemy's Physical Damage Reduction |
Magic Penetration | Increases the amount of Magical Damage that bypasses enemy's Magical Damage Reduction |
Projectile Reduction | Decreases damage taken from projectiles (Arrows, Throwing Knives, etc.) |
Headshot Damage Reduction | Decreases Hit Location Multiplier additively if targeting the head |
True Physical Damage | Increases Physical Damage dealt that is not influenced by enemy defences |
True Magical Damage | Increases Magical Damage dealt that is not influenced by enemy defences |
Weapon Damage | Increases "Gear" Weapon Damage |
Additional Physical Damage | Increases Physical Damage dealt (not affected by Physical Power Bonus) |
Additional Magical Damage | Increases Magical Damage dealt (not affected by Magical Power Bonus) |
Luck | Increases Luck for obtaining items) |
For the possible values of Enchantments and their historical rolls, see Enchantment Values
These stats are not yet implemented.
Determines the bonus effectiveness of your utility items