Stats are currently up to date for: Patch:6.8#Patch 8$green
Charts
Charts are created using the data points directly taken from the game. Therefore, if there is a mismatch between chart and the in game display, it is better to look at chart info.
For example, even though the formula might give 32.5, in game the display might get rounded to 33.
Attributes
Stats that come from character's attributes.
Strength
Physical Power
Physical Power governs your Physical Power Bonus.
Strength governs your Physical Power.
0 Strength starts at 0 Physical Power.
- 0 -> 0
- 0 to 100 = 1 each, up to 100
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LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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P_{hysicalPower}(S_{trength})=\left\{0 \le S_{trength}<100:0+1\left|S_{trength}-0\right|\right\}
See Example for how to use.
Physical Power Bonus
- 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.
- 0 -> -80%
- 0 to 5 = 10% each, up to -30%
- 5 to 7 = 5% each, up to -20%
- 7 to 11 = 3% each, up to -8%
- 11 to 15 = 2% each, up to 0%
- 15 to 50 = 1% each, up to 35%
- 50 to 60 = 0.5% each, up to 40%
- 60 to 100 = 0.25% each, up to 50%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
P_{hysicalPowerBonus}(P_{hysicalPower})=\left\{0 \le P_{hysicalPower}<5:-0.8+0.1\left|P_{hysicalPower}-0\right|,5 \le P_{hysicalPower}<7:-0.3+0.05\left|P_{hysicalPower}-5\right|,7 \le P_{hysicalPower}<11:-0.2+0.03\left|P_{hysicalPower}-7\right|,11 \le P_{hysicalPower}<15:-0.08+0.02\left|P_{hysicalPower}-11\right|,15 \le P_{hysicalPower}<50:0+0.01\left|P_{hysicalPower}-15\right|,50 \le P_{hysicalPower}<60:0.35+0.005\left|P_{hysicalPower}-50\right|,60 \le P_{hysicalPower}<100:0.4+0.002\left|P_{hysicalPower}-60\right|\right\}
See Example for how to use.
Capped to -100%
Max Health from Strength
Max Health determines your characters maximum Health.
Strength increases Max Health with 25% Scaling. See the Hybrid stat Max Health for more.
Vigor
Max Health from Vigor
Max Health determines your characters maximum Health.
Vigor increases Max Health with 75% Scaling. See the Hybrid stat Max Health for more.
Health Recovery
Affects the rate at which you restore health when Resting, but not when using Bandages.
Health Recovered per tick = Base Recovery * (1 + Health Recovery Bonus)
For example, a Barbarian resting with 95% Health Recovery Bonus will recover
Health Recovered every 2s = 1 * (1 + .95) = 1.95 Health
Vigor governs your Health Recovery.
0 Vigor starts at -55% Health Recovery.
- 0 -> -55%
- 0 to 5 = 5% each, up to -30%
- 5 to 15 = 3% each, up to 0%
- 15 to 25 = 7% each, up to 70%
- 25 to 35 = 5% each, up to 120%
- 35 to 84 = 2% each, up to 218%
- 84 to 85 = 1% each, up to 219%
- 85 to 86 = 3% each, up to 222%
- 86 to 100 = 2% each, up to 250%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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H_{ealthRecovery}(V_{igor})=\left\{0 \le V_{igor}<5:-0.55+0.05\left|V_{igor}-0\right|,5 \le V_{igor}<15:-0.3+0.03\left|V_{igor}-5\right|,15 \le V_{igor}<25:0+0.07\left|V_{igor}-15\right|,25 \le V_{igor}<35:0.7+0.05\left|V_{igor}-25\right|,35 \le V_{igor}<84:1.2+0.02\left|V_{igor}-35\right|,84 \le V_{igor}<85:2.18+0.01\left|V_{igor}-84\right|,85 \le V_{igor}<86:2.19+0.03\left|V_{igor}-85\right|,86 \le V_{igor}<100:2.22+0.02\left|V_{igor}-86\right|\right\}
See Example for how to use.
Agility
Action Speed from Agility
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.
Agility increases Action Speed with 25% Scaling. See the Hybrid stat Action Speed for more.
Move Speed
Move Speed governs the speed at which your character moves. This stat is also directly influenced by wearing gear. Every 1 point in Move Speed is equal to 0.3333...% Move Speed. The default Move Speed for each class is 300, which translates to 100% Move Speed, with penalties or bonuses provided based on Agility. Performing certain actions, such as attacking, or moving in certain directions will also affect Move Speed. Backwards = 60%, Crouch = 45%, Walk = 45%.
Agility governs your Move Speed.
0 Agility starts at -10 Move Speed.
- 0 -> -10
- 0 to 10 = 0.5 each, up to -5
- 10 to 15 = 1 each, up to 0
- 15 to 75 = 0.75 each, up to 45
- 75 to 100 = 0.5 each, up to 57.5
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{oveSpeed}(A_{gility})=\left\{0 \le A_{gility}<10:-10+0.5\left|A_{gility}-0\right|,10 \le A_{gility}<15:-5+1\left|A_{gility}-10\right|,15 \le A_{gility}<75:0+0.75\left|A_{gility}-15\right|,75 \le A_{gility}<100:45+0.5\left|A_{gility}-75\right|\right\}
See Example for how to use.
Hard capped to 350 Movement speed
Regular Interaction Speed from Agility
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
Agility increases Regular Interaction Speed with 40% Scaling. See the Hybrid stat Regular Interaction Speed for more.
Dexterity
Action Speed from Dexterity
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables.
Dexterity increases Action Speed with 75% Scaling. See the Hybrid stat Action Speed for more.
Manual Dexterity
Manual Dexterity determines how quickly Bard plays an instrument.
Dexterity governs your Manual Dexterity.
0 Dexterity starts at -15% Manual Dexterity.
- 0 -> -15%
- 0 to 15 = 1% each, up to 0%
- 15 to 23 = 3% each, up to 24%
- 23 to 31 = 2% each, up to 40%
- 31 to 37 = 1% each, up to 46%
- 37 to 45 = 0.5% each, up to 50%
- 45 to 95 = 0.1% each, up to 55%
- 95 to 100 = 0% each, up to 55%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{anualDexterity}(D_{exterity})=\left\{0 \le D_{exterity}<15:-0.15+0.01\left|D_{exterity}-0\right|,15 \le D_{exterity}<23:0+0.03\left|D_{exterity}-15\right|,23 \le D_{exterity}<31:0.24+0.02\left|D_{exterity}-23\right|,31 \le D_{exterity}<37:0.4+0.01\left|D_{exterity}-31\right|,37 \le D_{exterity}<45:0.46+0.005\left|D_{exterity}-37\right|,45 \le D_{exterity}<95:0.5+0.001\left|D_{exterity}-45\right|,95 \le D_{exterity}<100:0.55+0\left|D_{exterity}-95\right|\right\}
See Example for how to use.
Item Equip Speed
Item Equip Speed exclusively governs the speed at which you equip armors, as equipping weapons, jewelry and utility items is instant.
Dexterity governs your Item Equip Speed.
0 Dexterity starts at -95% Item Equip Speed.
- 0 -> -95%
- 0 to 1 = 0% each, up to -95%
- 1 to 2 = 4% each, up to -91%
- 2 to 15 = 7% each, up to 0%
- 15 to 35 = 5% each, up to 100%
- 35 to 70 = 2% each, up to 170%
- 70 to 100 = 1% each, up to 200%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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I_{temEquipSpeed}(D_{exterity})=\left\{0 \le D_{exterity}<1:-0.95+0\left|D_{exterity}-0\right|,1 \le D_{exterity}<2:-0.95+0.04\left|D_{exterity}-1\right|,2 \le D_{exterity}<15:-0.91+0.07\left|D_{exterity}-2\right|,15 \le D_{exterity}<35:0+0.05\left|D_{exterity}-15\right|,35 \le D_{exterity}<70:1+0.02\left|D_{exterity}-35\right|,70 \le D_{exterity}<100:1.7+0.01\left|D_{exterity}-70\right|\right\}
See Example for how to use.
Will
Magic Power
Magic Power governs your Magic Power Bonus.
Will governs your Magical Power.
0 Will starts at 0 Magical Power.
- 0 -> 0
- 0 to 100 = 1 each, up to 100
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LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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M_{agicalPower}(W_{ill})=\left\{0 \le W_{ill}<100:0+1\left|W_{ill}-0\right|\right\}
See Example for how to use.
Magic Power Bonus
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 -80% Magical Power Bonus.
- 0 -> -80%
- 0 to 5 = 10% each, up to -30%
- 5 to 7 = 5% each, up to -20%
- 7 to 11 = 3% each, up to -8%
- 11 to 15 = 2% each, up to 0%
- 15 to 50 = 1% each, up to 35%
- 50 to 60 = 0.5% each, up to 40%
- 60 to 100 = 0.25% each, up to 50%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{agicalPowerBonus}(M_{agicalPower})=\left\{0 \le M_{agicalPower}<5:-0.8+0.1\left|M_{agicalPower}-0\right|,5 \le M_{agicalPower}<7:-0.3+0.05\left|M_{agicalPower}-5\right|,7 \le M_{agicalPower}<11:-0.2+0.03\left|M_{agicalPower}-7\right|,11 \le M_{agicalPower}<15:-0.08+0.02\left|M_{agicalPower}-11\right|,15 \le M_{agicalPower}<50:0+0.01\left|M_{agicalPower}-15\right|,50 \le M_{agicalPower}<60:0.35+0.005\left|M_{agicalPower}-50\right|,60 \le M_{agicalPower}<100:0.4+0.002\left|M_{agicalPower}-60\right|\right\}
See Example for how to use.
Magic Resistance
Magic Resistance governs your Magical Damage Reduction.
Will governs your Magic Resistance.
0 Will starts at -20 Magic Resistance.
- 0 -> -20
- 0 to 5 = 4 each, up to 0
- 5 to 15 = 3 each, up to 30
- 15 to 33 = 4 each, up to 102
- 33 to 48 = 3 each, up to 147
- 48 to 58 = 2 each, up to 167
- 58 to 100 = 1 each, up to 209
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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M_{agicResistance}(W_{ill})=\left\{0 \le W_{ill}<5:-20+4\left|W_{ill}-0\right|,5 \le W_{ill}<15:0+3\left|W_{ill}-5\right|,15 \le W_{ill}<33:30+4\left|W_{ill}-15\right|,33 \le W_{ill}<48:102+3\left|W_{ill}-33\right|,48 \le W_{ill}<58:147+2\left|W_{ill}-48\right|,58 \le W_{ill}<100:167+1\left|W_{ill}-58\right|\right\}
See Example for how to use.
Magical Damage Reduction
Magical Damage Reduction governs your resistance to magical damage dealing weapons, spells and projectiles. 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.
- -300 -> -595%
- -300 to -15 = 2% each, up to -25%
- -15 to 8 = 1% each, up to -2%
- 8 to 18 = 0.5% each, up to 3%
- 18 to 33 = 0.4% each, up to 9%
- 33 to 53 = 0.3% each, up to 15%
- 53 to 85 = 0.25% each, up to 23%
- 85 to 280 = 0.2% each, up to 62%
- 280 to 340 = 0.15% each, up to 71%
- 340 to 430 = 0.1% each, up to 80%
- 430 to 500 = 0.05% each, up to 83.5%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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M_{agicalDamageReduction}(M_{agicResistance})=\left\{-300 \le M_{agicResistance}<-15:-5.95+0.02\left|M_{agicResistance}--300\right|,-15 \le M_{agicResistance}<8:-0.25+0.01\left|M_{agicResistance}--15\right|,8 \le M_{agicResistance}<18:-0.02+0.005\left|M_{agicResistance}-8\right|,18 \le M_{agicResistance}<33:0.03+0.004\left|M_{agicResistance}-18\right|,33 \le M_{agicResistance}<53:0.09+0.003\left|M_{agicResistance}-33\right|,53 \le M_{agicResistance}<85:0.15+0.003\left|M_{agicResistance}-53\right|,85 \le M_{agicResistance}<280:0.23+0.002\left|M_{agicResistance}-85\right|,280 \le M_{agicResistance}<340:0.62+0.001\left|M_{agicResistance}-280\right|,340 \le M_{agicResistance}<430:0.71+0.001\left|M_{agicResistance}-340\right|,430 \le M_{agicResistance}<500:0.8+0\left|M_{agicResistance}-430\right|\right\}
See Example for how to use.
Magical Damage Reduction is capped to 85%
Buff Duration
Buff Duration governs the duration of temporary beneficial status effects.
Will governs your Buff Duration.
0 Will starts at -80% Buff Duration.
- 0 -> -80%
- 0 to 5 = 10% each, up to -30%
- 5 to 7 = 5% each, up to -20%
- 7 to 11 = 3% each, up to -8%
- 11 to 15 = 2% each, up to 0%
- 15 to 50 = 1% each, up to 35%
- 50 to 100 = 0.5% each, up to 60%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
B_{uffDuration}(W_{ill})=\left\{0 \le W_{ill}<5:-0.8+0.1\left|W_{ill}-0\right|,5 \le W_{ill}<7:-0.3+0.05\left|W_{ill}-5\right|,7 \le W_{ill}<11:-0.2+0.03\left|W_{ill}-7\right|,11 \le W_{ill}<15:-0.08+0.02\left|W_{ill}-11\right|,15 \le W_{ill}<50:0+0.01\left|W_{ill}-15\right|,50 \le W_{ill}<100:0.35+0.005\left|W_{ill}-50\right|\right\}
See Example for how to use.
Debuff Duration
Debuff Duration governs the duration of temporary negative status effects. A negative Debuff Duration is beneficial to have, as it will shorten the duration of debuffs. A positive Debuff Duration stat means debuffs last longer, which is detrimental to the player.
Will governs your Debuff Duration.
0 Will starts at 400% Debuff Duration.
- 0 -> 400%
- 0 to 1 = -166.7% each, up to 233.3%
- 1 to 2 = -83.3% each, up to 150%
- 2 to 3 = -50% each, up to 100%
- 3 to 4 = -33.3% each, up to 66.7%
- 4 to 5 = -23.8% each, up to 42.9%
- 5 to 6 = -9.6% each, up to 33.3%
- 6 to 7 = -8.3% each, up to 25%
- 7 to 8 = -4.5% each, up to 20.5%
- 8 to 9 = -4.2% each, up to 16.3%
- 9 to 10 = -3.9% each, up to 12.4%
- 10 to 11 = -3.7% each, up to 8.7%
- 11 to 12 = -2.3% each, up to 6.4%
- 12 to 14 = -2.2% each, up to 2%
- 14 to 15 = -2% each, up to 0%
- 15 to 17 = -1% each, up to -2%
- 17 to 19 = -0.9% each, up to -3.8%
- 19 to 20 = -1% each, up to -4.8%
- 20 to 21 = -0.9% each, up to -5.7%
- 21 to 22 = -0.8% each, up to -6.5%
- 22 to 24 = -0.9% each, up to -8.3%
- 24 to 29 = -0.8% each, up to -12.3%
- 29 to 30 = -0.7% each, up to -13%
- 30 to 31 = -0.8% each, up to -13.8%
- 31 to 32 = -0.7% each, up to -14.5%
- 32 to 33 = -0.8% each, up to -15.3%
- 33 to 36 = -0.7% each, up to -17.4%
- 36 to 37 = -0.6% each, up to -18%
- 37 to 39 = -0.7% each, up to -19.4%
- 39 to 41 = -0.6% each, up to -20.6%
- 41 to 42 = -0.7% each, up to -21.3%
- 42 to 46 = -0.6% each, up to -23.7%
- 46 to 47 = -0.5% each, up to -24.2%
- 47 to 49 = -0.6% each, up to -25.4%
- 49 to 50 = -0.5% each, up to -25.9%
- 50 to 52 = -0.3% each, up to -26.5%
- 52 to 53 = -0.2% each, up to -26.7%
- 53 to 55 = -0.3% each, up to -27.3%
- 55 to 56 = -0.2% each, up to -27.5%
- 56 to 58 = -0.3% each, up to -28.1%
- 58 to 59 = -0.2% each, up to -28.3%
- 59 to 60 = -0.3% each, up to -28.6%
- 60 to 61 = -0.2% each, up to -28.8%
- 61 to 62 = -0.3% each, up to -29.1%
- 62 to 63 = -0.2% each, up to -29.3%
- 63 to 64 = -0.3% each, up to -29.6%
- 64 to 65 = -0.2% each, up to -29.8%
- 65 to 66 = -0.3% each, up to -30.1%
- 66 to 67 = -0.2% each, up to -30.3%
- 67 to 68 = -0.3% each, up to -30.6%
- 68 to 70 = -0.2% each, up to -31%
- 70 to 71 = -0.3% each, up to -31.3%
- 71 to 73 = -0.2% each, up to -31.7%
- 73 to 74 = -0.3% each, up to -32%
- 74 to 76 = -0.2% each, up to -32.4%
- 76 to 77 = -0.3% each, up to -32.7%
- 77 to 80 = -0.2% each, up to -33.3%
- 80 to 81 = -0.3% each, up to -33.6%
- 81 to 86 = -0.2% each, up to -34.6%
- 86 to 87 = -0.3% each, up to -34.9%
- 87 to 100 = -0.2% each, up to -37.5%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
D_{ebuffDuration}(W_{ill})=\left\{0 \le W_{ill}<1:4+-1.667\left|W_{ill}-0\right|,1 \le W_{ill}<2:2.333+-0.833\left|W_{ill}-1\right|,2 \le W_{ill}<3:1.5+-0.5\left|W_{ill}-2\right|,3 \le W_{ill}<4:1+-0.333\left|W_{ill}-3\right|,4 \le W_{ill}<5:0.667+-0.238\left|W_{ill}-4\right|,5 \le W_{ill}<6:0.429+-0.096\left|W_{ill}-5\right|,6 \le W_{ill}<7:0.333+-0.083\left|W_{ill}-6\right|,7 \le W_{ill}<8:0.25+-0.045\left|W_{ill}-7\right|,8 \le W_{ill}<9:0.205+-0.042\left|W_{ill}-8\right|,9 \le W_{ill}<10:0.163+-0.039\left|W_{ill}-9\right|,10 \le W_{ill}<11:0.124+-0.037\left|W_{ill}-10\right|,11 \le W_{ill}<12:0.087+-0.023\left|W_{ill}-11\right|,12 \le W_{ill}<14:0.064+-0.022\left|W_{ill}-12\right|,14 \le W_{ill}<15:0.02+-0.02\left|W_{ill}-14\right|,15 \le W_{ill}<17:0+-0.01\left|W_{ill}-15\right|,17 \le W_{ill}<19:-0.02+-0.009\left|W_{ill}-17\right|,19 \le W_{ill}<20:-0.038+-0.01\left|W_{ill}-19\right|,20 \le W_{ill}<21:-0.048+-0.009\left|W_{ill}-20\right|,21 \le W_{ill}<22:-0.057+-0.008\left|W_{ill}-21\right|,22 \le W_{ill}<24:-0.065+-0.009\left|W_{ill}-22\right|,24 \le W_{ill}<29:-0.083+-0.008\left|W_{ill}-24\right|,29 \le W_{ill}<30:-0.123+-0.007\left|W_{ill}-29\right|,30 \le W_{ill}<31:-0.13+-0.008\left|W_{ill}-30\right|,31 \le W_{ill}<32:-0.138+-0.007\left|W_{ill}-31\right|,32 \le W_{ill}<33:-0.145+-0.008\left|W_{ill}-32\right|,33 \le W_{ill}<36:-0.153+-0.007\left|W_{ill}-33\right|,36 \le W_{ill}<37:-0.174+-0.006\left|W_{ill}-36\right|,37 \le W_{ill}<39:-0.18+-0.007\left|W_{ill}-37\right|,39 \le W_{ill}<41:-0.194+-0.006\left|W_{ill}-39\right|,41 \le W_{ill}<42:-0.206+-0.007\left|W_{ill}-41\right|,42 \le W_{ill}<46:-0.213+-0.006\left|W_{ill}-42\right|,46 \le W_{ill}<47:-0.237+-0.005\left|W_{ill}-46\right|,47 \le W_{ill}<49:-0.242+-0.006\left|W_{ill}-47\right|,49 \le W_{ill}<50:-0.254+-0.005\left|W_{ill}-49\right|,50 \le W_{ill}<52:-0.259+-0.003\left|W_{ill}-50\right|,52 \le W_{ill}<53:-0.265+-0.002\left|W_{ill}-52\right|,53 \le W_{ill}<55:-0.267+-0.003\left|W_{ill}-53\right|,55 \le W_{ill}<56:-0.273+-0.002\left|W_{ill}-55\right|,56 \le W_{ill}<58:-0.275+-0.003\left|W_{ill}-56\right|,58 \le W_{ill}<59:-0.281+-0.002\left|W_{ill}-58\right|,59 \le W_{ill}<60:-0.283+-0.003\left|W_{ill}-59\right|,60 \le W_{ill}<61:-0.286+-0.002\left|W_{ill}-60\right|,61 \le W_{ill}<62:-0.288+-0.003\left|W_{ill}-61\right|,62 \le W_{ill}<63:-0.291+-0.002\left|W_{ill}-62\right|,63 \le W_{ill}<64:-0.293+-0.003\left|W_{ill}-63\right|,64 \le W_{ill}<65:-0.296+-0.002\left|W_{ill}-64\right|,65 \le W_{ill}<66:-0.298+-0.003\left|W_{ill}-65\right|,66 \le W_{ill}<67:-0.301+-0.002\left|W_{ill}-66\right|,67 \le W_{ill}<68:-0.303+-0.003\left|W_{ill}-67\right|,68 \le W_{ill}<70:-0.306+-0.002\left|W_{ill}-68\right|,70 \le W_{ill}<71:-0.31+-0.003\left|W_{ill}-70\right|,71 \le W_{ill}<73:-0.313+-0.002\left|W_{ill}-71\right|,73 \le W_{ill}<74:-0.317+-0.003\left|W_{ill}-73\right|,74 \le W_{ill}<76:-0.32+-0.002\left|W_{ill}-74\right|,76 \le W_{ill}<77:-0.324+-0.003\left|W_{ill}-76\right|,77 \le W_{ill}<80:-0.327+-0.002\left|W_{ill}-77\right|,80 \le W_{ill}<81:-0.333+-0.003\left|W_{ill}-80\right|,81 \le W_{ill}<86:-0.336+-0.002\left|W_{ill}-81\right|,86 \le W_{ill}<87:-0.346+-0.003\left|W_{ill}-86\right|,87 \le W_{ill}<100:-0.349+-0.002\left|W_{ill}-87\right|\right\}
See Example for how to use.
Debuff Duration has a lower cap of -95%, meaning at minimum a debuff can last 1/20th of its base duration.
Magical Interaction Speed
Magical Interaction Speed affects the speed with which the player interacts with magical objects, such as Shrines and Portals. See Action/Interaction/Cast_Speed for more.
Will governs your Magical Interaction Speed.
0 Will starts at -75% Magical Interaction Speed.
- 0 -> -75%
- 0 to 15 = 5% each, up to 0%
- 15 to 25 = 7% each, up to 70%
- 25 to 35 = 5% each, up to 120%
- 35 to 84 = 2% each, up to 218%
- 84 to 85 = 1% each, up to 219%
- 85 to 86 = 3% each, up to 222%
- 86 to 100 = 2% each, up to 250%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{agicalInteractionSpeed}(W_{ill})=\left\{0 \le W_{ill}<15:-0.75+0.05\left|W_{ill}-0\right|,15 \le W_{ill}<25:0+0.07\left|W_{ill}-15\right|,25 \le W_{ill}<35:0.7+0.05\left|W_{ill}-25\right|,35 \le W_{ill}<84:1.2+0.02\left|W_{ill}-35\right|,84 \le W_{ill}<85:2.18+0.01\left|W_{ill}-84\right|,85 \le W_{ill}<86:2.19+0.03\left|W_{ill}-85\right|,86 \le W_{ill}<100:2.22+0.02\left|W_{ill}-86\right|\right\}
See Example for how to use.
Note that the Debuff Duration Bonus enchant converts into a negative Debuff Duration, decreasing the duration of debuffs on you.
Durations are not rounded and last their exact amount. However, actions that are performed in intervals, like Damage/Healing [time], are rounded down to the nearest integer, resulting in thresholds that players may want to take advantage of.
Knowledge
Spell Casting Speed
Spell Casting Speed governs the speed at which you cast magical spells. See Action/Interaction/Cast_Speed for more.
Knowledge governs your Spell Casting Speed.
0 Knowledge starts at -60% Spell Casting Speed.
- 0 -> -60%
- 0 to 5 = 5% each, up to -35%
- 5 to 10 = 4% each, up to -15%
- 10 to 20 = 3% each, up to 15%
- 20 to 50 = 2.5% each, up to 90%
- 50 to 80 = 2% each, up to 150%
- 80 to 100 = 1.5% each, up to 180%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
S_{pellCastingSpeed}(K_{nowledge})=\left\{0 \le K_{nowledge}<5:-0.6+0.05\left|K_{nowledge}-0\right|,5 \le K_{nowledge}<10:-0.35+0.04\left|K_{nowledge}-5\right|,10 \le K_{nowledge}<20:-0.15+0.03\left|K_{nowledge}-10\right|,20 \le K_{nowledge}<50:0.15+0.025\left|K_{nowledge}-20\right|,50 \le K_{nowledge}<80:0.9+0.02\left|K_{nowledge}-50\right|,80 \le K_{nowledge}<100:1.5+0.015\left|K_{nowledge}-80\right|\right\}
See Example for how to use.
Spell Casting Time = (Base Casting Time)/(1 + Spell Casting Speed)
- A Spell Casting Speed of 50% results in the casting time lasting for only 67% of the base casting time.
- A Spell Casting Speed of 100% results in the casting time lasting for only 50% of the base casting time.
Memory Capacity
Memory Capacity govern your spell/song cost cap, meaning equipping spells/songs that exceed this cap will not be usable.
Knowledge governs your Memory Capacity.
0 Knowledge starts at 0 Memory Capacity.
- 0 -> 0
- 0 to 6 = 0 each, up to 0
- 6 to 100 = 1 each, up to 94
Expand
LaTeX Formula
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M_{emoryCapacity}(K_{nowledge})=\left\{0 \le K_{nowledge}<6:0+0\left|K_{nowledge}-0\right|,6 \le K_{nowledge}<100:0+1\left|K_{nowledge}-6\right|\right\}
See Example for how to use.
Total Memory Capacity = ceil(Memory Cap from Knowledge * (1 + Memory Cap Bonus%)) + Add Memory Cap
Memory Cap Bonus% and Add Memory Cap are two different Enchantments.
For example, with 12 Memory Cap from 18 knowledge, +8 Add Memory Cap, and 7.7% Memory Cap Bonus, the final Memory Capacity will be
ceil(12 * 1.077) + 8 = 21 Memory Capacity
Memory Recovery
Increases the amount of Spell/(Skill?) Points (SP) you restore per tick.
Knowledge governs your Memory Recovery.
0 Knowledge starts at 43% Memory Recovery.
- 0 -> 43%
- 0 to 28 = 1.5% each, up to 85%
- 28 to 35 = 5% each, up to 120%
- 35 to 84 = 2% each, up to 218%
- 84 to 85 = 1% each, up to 219%
- 85 to 86 = 3% each, up to 222%
- 86 to 100 = 2% each, up to 250%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
M_{emoryRecovery}(K_{nowledge})=\left\{0 \le K_{nowledge}<28:0.43+0.015\left|K_{nowledge}-0\right|,28 \le K_{nowledge}<35:0.85+0.05\left|K_{nowledge}-28\right|,35 \le K_{nowledge}<84:1.2+0.02\left|K_{nowledge}-35\right|,84 \le K_{nowledge}<85:2.18+0.01\left|K_{nowledge}-84\right|,85 \le K_{nowledge}<86:2.19+0.03\left|K_{nowledge}-85\right|,86 \le K_{nowledge}<100:2.22+0.02\left|K_{nowledge}-86\right|\right\}
See Example for how to use.
SP Recharge per tick (SP/tick) = Base Recharge * (1 + Memory Recovery Bonus)
Resourcefulness
Regular Interaction Speed from Resourcefulness
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon.
Resourcefulness increases Regular Interaction Speed with 60% Scaling. See the Hybrid stat Regular Interaction Speed for more.
Persuasiveness
Persuasiveness determines the duration of Bard songs' buffs/debuffs.
Resourcefulness governs your Persuasiveness.
0 Resourcefulness starts at 0 Persuasiveness.
- 0 -> 0
- 0 to 35 = 1 each, up to 35
- 35 to 71 = 0.5 each, up to 53
- 71 to 99 = 0.25 each, up to 60
- 99 to 100 = 0 each, up to 60
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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P_{ersuasiveness}(R_{esourcefulness})=\left\{0 \le R_{esourcefulness}<35:0+1\left|R_{esourcefulness}-0\right|,35 \le R_{esourcefulness}<71:35+0.5\left|R_{esourcefulness}-35\right|,71 \le R_{esourcefulness}<99:53+0.25\left|R_{esourcefulness}-71\right|,99 \le R_{esourcefulness}<100:60+0\left|R_{esourcefulness}-99\right|\right\}
See Example for how to use.
Base buff duration formula:
Scaling x Persuasiveness
Each point in Persuasiveness over the base of 15 grants a 6.66% longer base duration.
The duration listed both in game and in a song's description at Bard represent the duration of the song at the base of 15 Persuasiveness. Some songs there are noted to not scale with Persuasiveness, meaning they always last the listed amount, before Buff/Debuff duration. Some songs technically apply no duration or their affect lasts only while Channeling, like Peacemaking and Chaotic Discord.
For example, Perfectly played Rousing Rhythms have 4.5x scaling and if Bard has 20 Persuasiveness, outgoing buff duration will be:
4.5 x 20 = 90
seconds
This will also get multiplied by the receiver's Buff Duration/Debuff Duration
Buff Duration Calculator
Hybrid Stats
Hybrid stats are stats which come from a combination of attributes. For example, Health is determined by both Strength and Vigor.
Max Health
Max Health determines your characters maximum Health.
Could not find stat in Template:Stats_Data
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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Could not find stat in Template:Stats_Data
See Example for how to use.
Final Max Health formula with examples can be found on the Health page.
Action Speed
Action Speed governs the speed at which you interact with your weapons, meaning stowing, swapping, reloading or attacking with weapons, as well as the speed of usage of consumables. See Action/Interaction/Cast_Speed for more.
Agility and Dexterity governs your Action Speed.
Agility gives 0.25 Action Speed Rating, and Dexterity gives 0.75 Action Speed Rating, which then get summed into a total Action Speed Rating and finally converted into Action Speed using the graph.
Action Speed Rating = Agility * 0.25 + Dexterity * 0.75
0 Action Speed Rating starts at -38% Action Speed.
- 0 -> -38%
- 0 to 10 = 3% each, up to -8%
- 10 to 13 = 2% each, up to -2%
- 13 to 25 = 1% each, up to 10%
- 25 to 41 = 1.5% each, up to 34%
- 41 to 50 = 1% each, up to 43%
- 50 to 100 = 0.5% each, up to 68%
Expand
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
Regular Interaction Speed governs the speed at which you interact with objects/mechanisms in the dungeon. See Action/Interaction/Cast_Speed for more.
Agility and Resourcefulness governs your Regular Interaction Speed.
Agility gives 0.4 Regular Interaction Speed Rating, and Resourcefulness gives 0.6 Regular Interaction Speed Rating, which then get summed into a total Regular Interaction Speed Rating and finally converted into Regular Interaction Speed using the graph.
Regular Interaction Speed Rating = Agility * 0.4 + Resourcefulness * 0.6
0 Regular Interaction Speed Rating starts at -26% Regular Interaction Speed.
- 0 -> -26%
- 0 to 7 = 2% each, up to -12%
- 7 to 15 = 1.5% each, up to 0%
- 15 to 20 = 7% each, up to 35%
- 20 to 25 = 6% each, up to 65%
- 25 to 30 = 5% each, up to 90%
- 30 to 35 = 4% each, up to 110%
- 35 to 40 = 3% each, up to 125%
- 40 to 45 = 2% each, up to 135%
- 45 to 100 = 1% each, up to 190%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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R_{egularInteractionSpeed}(S_{um})=\left\{0 \le S_{um}<7:-0.26+0.02\left|S_{um}-0\right|,7 \le S_{um}<15:-0.12+0.015\left|S_{um}-7\right|,15 \le S_{um}<20:0+0.07\left|S_{um}-15\right|,20 \le S_{um}<25:0.35+0.06\left|S_{um}-20\right|,25 \le S_{um}<30:0.65+0.05\left|S_{um}-25\right|,30 \le S_{um}<35:0.9+0.04\left|S_{um}-30\right|,35 \le S_{um}<40:1.1+0.03\left|S_{um}-35\right|,40 \le S_{um}<45:1.25+0.02\left|S_{um}-40\right|,45 \le S_{um}<100:1.35+0.01\left|S_{um}-45\right|\right\}
See Example for how to use.
New interaction length = Base interaction length / (1 + interaction speed)
For example, an Interaction Speed of 100% results in the interaction time lasting for only 50% of the base interaction length.
Surgical Kits have 50% scaling on regular interaction speed, therefore, their formula looks like
New interaction length = Base interaction length / (1 + interaction speed * .5)
Other Stats
Physical Damage Reduction
Physical Damage Reduction governs your resistance to physical damage dealing weapons and projectiles. Unlike Magic Resistance that is increased by Will, Armor Rating does not have an attribute stat that it scales off.
Armor Rating governs your Physical Damage Reduction.
-300 Armor Rating starts at -619% Physical Damage Reduction.
- -300 -> -619%
- -300 to -12 = 2% each, up to -43%
- -12 to -4 = 1.5% each, up to -31%
- -4 to 0 = 1.2% each, up to -26.2%
- 0 to 20 = 1% each, up to -6.2%
- 20 to 30 = 0.5% each, up to -1.2%
- 30 to 45 = 0.4% each, up to 4.8%
- 45 to 65 = 0.3% each, up to 10.8%
- 65 to 125 = 0.25% each, up to 25.8%
- 125 to 275 = 0.2% each, up to 55.8%
- 275 to 312 = 0.15% each, up to 61.35%
- 312 to 313 = 0.12% each, up to 61.47%
- 313 to 314 = 0.18% each, up to 61.65%
- 314 to 315 = 0.15% each, up to 61.8%
- 315 to 374 = 0.1% each, up to 67.7%
- 374 to 455 = 0.05% each, up to 71.75%
- 455 to 456 = 0.03% each, up to 71.78%
- 456 to 457 = 0.07% each, up to 71.85%
- 457 to 475 = 0.05% each, up to 72.75%
- 475 to 476 = 0.03% each, up to 72.78%
- 476 to 477 = 0.065% each, up to 72.845%
- 477 to 478 = 0.055% each, up to 72.9%
- 478 to 500 = 0.05% each, up to 74%
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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P_{hysicalDamageReduction}(A_{rmorRating})=\left\{-300 \le A_{rmorRating}<-12:-6.19+0.02\left|A_{rmorRating}--300\right|,-12 \le A_{rmorRating}<-4:-0.43+0.015\left|A_{rmorRating}--12\right|,-4 \le A_{rmorRating}<0:-0.31+0.012\left|A_{rmorRating}--4\right|,0 \le A_{rmorRating}<20:-0.262+0.01\left|A_{rmorRating}-0\right|,20 \le A_{rmorRating}<30:-0.062+0.005\left|A_{rmorRating}-20\right|,30 \le A_{rmorRating}<45:-0.012+0.004\left|A_{rmorRating}-30\right|,45 \le A_{rmorRating}<65:0.048+0.003\left|A_{rmorRating}-45\right|,65 \le A_{rmorRating}<125:0.108+0.003\left|A_{rmorRating}-65\right|,125 \le A_{rmorRating}<275:0.258+0.002\left|A_{rmorRating}-125\right|,275 \le A_{rmorRating}<312:0.558+0.001\left|A_{rmorRating}-275\right|,312 \le A_{rmorRating}<313:0.614+0.001\left|A_{rmorRating}-312\right|,313 \le A_{rmorRating}<314:0.615+0.002\left|A_{rmorRating}-313\right|,314 \le A_{rmorRating}<315:0.617+0.001\left|A_{rmorRating}-314\right|,315 \le A_{rmorRating}<374:0.618+0.001\left|A_{rmorRating}-315\right|,374 \le A_{rmorRating}<455:0.677+0\left|A_{rmorRating}-374\right|,455 \le A_{rmorRating}<456:0.718+0\left|A_{rmorRating}-455\right|,456 \le A_{rmorRating}<457:0.718+0.001\left|A_{rmorRating}-456\right|,457 \le A_{rmorRating}<475:0.719+0.001\left|A_{rmorRating}-457\right|,475 \le A_{rmorRating}<476:0.728+0\left|A_{rmorRating}-475\right|,476 \le A_{rmorRating}<477:0.728+0.001\left|A_{rmorRating}-476\right|,477 \le A_{rmorRating}<478:0.728+0.001\left|A_{rmorRating}-477\right|,478 \le A_{rmorRating}<500:0.729+0.001\left|A_{rmorRating}-478\right|\right\}
See Example for how to use.
Physical Damage Reduction is capped to 75%
Impact Power
Impact Power governs the strength of your weapon strikes against a target, it determines if you can break objects and stagger blocking enemies.
Luck
Loot is rolled when you open the container or kill the mob.
Whoever opens the loot first or kills the mob first is the person whose luck is used to calculate the drops.
(It is not confirmed if Bard's Unchained Harmony rolls the loot table when it opens the containers.)
Luck is capped at 500.
It is possible to get maximum of 450 Luck in the game currently:
Loot Drop Tables and Drop Rate Tables
Each drop instance makes use of three pieces of information: the Loot Drop table, the Drop Rate table, and the player's Luck.
Loot Drop tables list all possible items for a specific drop instance, and for each item therein it associates a Luck Grade.
Drop Rate tables assign a "rate" to each Luck Grade; when normalized, these rates represent the probability of getting a drop of that Luck Grade.
Each Luck Grade's drop rate is split evenly between items that share that Luck Grade. This means that items sharing a Loot Drop table and Luck Grade, will always have the same probability of dropping.
However, be aware that Monsters and Containers can have multiple Loot Drop Tables, each with their own Drop Rate table. See Lich for example.
A Drop can be rolled more than once, but each roll is independent of the others.
Lich rolls their gear Loot and Drop tables twice, theoretically making it possible (though extremely unlikely) to get two Artifacts from a single HR Lich kill.
Luck Scalar
Luck Scalars are one piece of information needed to calculate drop probability at X Luck.
The calculation is not a simple multiplication, so do not expect Uniques to be 4.382 times more common at 500 Luck.
The true effect of Luck varies depending on Drop Rate tables and Loot Drop tables.
Luck Scalar Table
Luck
|
0
|
50
|
100
|
150
|
200
|
250
|
300
|
350
|
400
|
450
|
500
|
Junk |
1.000 |
0.950 |
0.900 |
0.850 |
0.800 |
0.750 |
0.700 |
0.650 |
0.600 |
0.550 |
0.500
|
Poor |
1.000 |
0.950 |
0.900 |
0.850 |
0.800 |
0.750 |
0.700 |
0.650 |
0.600 |
0.550 |
0.500
|
Common |
1.000 |
0.975 |
0.950 |
0.925 |
0.900 |
0.875 |
0.850 |
0.825 |
0.800 |
0.775 |
0.750
|
Uncommon |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000 |
1.000
|
Rare |
1.000 |
1.476 |
1.901 |
2.277 |
2.602 |
2.878 |
3.103 |
3.279 |
3.404 |
3.480 |
3.505
|
Epic |
1.000 |
1.547 |
2.036 |
2.468 |
2.842 |
3.159 |
3.418 |
3.620 |
3.765 |
3.751 |
3.881
|
Legendary |
1.000 |
1.618 |
2.171 |
2.659 |
3.083 |
3.441 |
3.734 |
3.962 |
4.125 |
4.223 |
4.257
|
Unique |
1.000 |
1.642 |
2.216 |
2.723 |
3.163 |
3.535 |
3.839 |
4.076 |
4.245 |
4.347 |
4.382
|
If the Luck Scalar Table and Graph don't cover a Scalar value you wish to see, use the desmos graph.
The desmos graph displays the LaTeX equations which are continuous curves, but keep in mind that fractional values of Luck do not exist.
Luck Scalar Graph
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
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L_{uckGrade00}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade01}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade02}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade03}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade04}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<130:1+0\left|L_{uckGrade}-0\right|,130 \le L_{uckGrade}<140:1.039+0\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<220:1.041+0\left|L_{uckGrade}-140\right|,220 \le L_{uckGrade}<230:1.065+0\left|L_{uckGrade}-220\right|,230 \le L_{uckGrade}<290:1.067+0\left|L_{uckGrade}-230\right|,290 \le L_{uckGrade}<300:1.085+0\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<340:1.087+0\left|L_{uckGrade}-300\right|,340 \le L_{uckGrade}<350:1.099+0\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<390:1.101+0\left|L_{uckGrade}-350\right|,390 \le L_{uckGrade}<400:1.113+0\left|L_{uckGrade}-390\right|,400 \le L_{uckGrade}<430:1.115+0\left|L_{uckGrade}-400\right|,430 \le L_{uckGrade}<440:1.124+0\left|L_{uckGrade}-430\right|,440 \le L_{uckGrade}<470:1.126+0\left|L_{uckGrade}-440\right|,470 \le L_{uckGrade}<480:1.135+0\left|L_{uckGrade}-470\right|,480 \le L_{uckGrade}<500:1.137+0\left|L_{uckGrade}-480\right|,500 \le L_{uckGrade}<510:1.143+0\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<530:1.145+0\left|L_{uckGrade}-510\right|,530 \le L_{uckGrade}<540:1.151+0\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<560:1.153+0\left|L_{uckGrade}-540\right|,560 \le L_{uckGrade}<570:1.159+0\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<590:1.161+0\left|L_{uckGrade}-570\right|,590 \le L_{uckGrade}<600:1.167+0\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<620:1.169+0\left|L_{uckGrade}-600\right|,620 \le L_{uckGrade}<630:1.175+0\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<650:1.177+0\left|L_{uckGrade}-630\right|,650 \le L_{uckGrade}<660:1.183+0\left|L_{uckGrade}-650\right|,660 \le L_{uckGrade}<670:1.185+0\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:1.188+0\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<700:1.19+0\left|L_{uckGrade}-680\right|,700 \le L_{uckGrade}<710:1.196+0\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<720:1.198+0\left|L_{uckGrade}-710\right|,720 \le L_{uckGrade}<730:1.201+0\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<740:1.203+0\left|L_{uckGrade}-730\right|,740 \le L_{uckGrade}<750:1.206+0\left|L_{uckGrade}-740\right|,750 \le L_{uckGrade}<760:1.208+0\left|L_{uckGrade}-750\right|,760 \le L_{uckGrade}<770:1.211+0\left|L_{uckGrade}-760\right|,770 \le L_{uckGrade}<790:1.213+0\left|L_{uckGrade}-770\right|,790 \le L_{uckGrade}<800:1.219+0\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<810:1.221+0\left|L_{uckGrade}-800\right|,810 \le L_{uckGrade}<820:1.224+0\left|L_{uckGrade}-810\right|,820 \le L_{uckGrade}<830:1.226+0\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<840:1.229+0\left|L_{uckGrade}-830\right|,840 \le L_{uckGrade}<850:1.231+0\left|L_{uckGrade}-840\right|,850 \le L_{uckGrade}<860:1.234+0\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<870:1.236+0\left|L_{uckGrade}-860\right|,870 \le L_{uckGrade}<880:1.239+0\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<890:1.241+0\left|L_{uckGrade}-880\right|,890 \le L_{uckGrade}<910:1.244+0\left|L_{uckGrade}-890\right|,910 \le L_{uckGrade}<920:1.248+0\left|L_{uckGrade}-910\right|,920 \le L_{uckGrade}<930:1.251+0\left|L_{uckGrade}-920\right|,930 \le L_{uckGrade}<940:1.253+0\left|L_{uckGrade}-930\right|,940 \le L_{uckGrade}<950:1.256+0\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<960:1.258+0\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<980:1.261+0\left|L_{uckGrade}-960\right|,980 \le L_{uckGrade}<990:1.265+0\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1000:1.268+0\left|L_{uckGrade}-990\right|,1000 \le L_{uckGrade}<1010:1.27+0\left|L_{uckGrade}-1000\right|,1010 \le L_{uckGrade}<1030:1.273+0\left|L_{uckGrade}-1010\right|,1030 \le L_{uckGrade}<1040:1.277+0\left|L_{uckGrade}-1030\right|,1040 \le L_{uckGrade}<1050:1.28+0\left|L_{uckGrade}-1040\right|,1050 \le L_{uckGrade}<1060:1.282+0\left|L_{uckGrade}-1050\right|,1060 \le L_{uckGrade}<1080:1.285+0\left|L_{uckGrade}-1060\right|,1080 \le L_{uckGrade}<1090:1.289+0\left|L_{uckGrade}-1080\right|,1090 \le L_{uckGrade}<1110:1.292+0\left|L_{uckGrade}-1090\right|,1110 \le L_{uckGrade}<1120:1.296+0\left|L_{uckGrade}-1110\right|,1120 \le L_{uckGrade}<1140:1.299+0\left|L_{uckGrade}-1120\right|,1140 \le L_{uckGrade}<1150:1.303+0\left|L_{uckGrade}-1140\right|,1150 \le L_{uckGrade}<1170:1.306+0\left|L_{uckGrade}-1150\right|,1170 \le L_{uckGrade}<1180:1.31+0\left|L_{uckGrade}-1170\right|,1180 \le L_{uckGrade}<1210:1.313+0\left|L_{uckGrade}-1180\right|,1210 \le L_{uckGrade}<1220:1.319+0\left|L_{uckGrade}-1210\right|,1220 \le L_{uckGrade}<1240:1.322+0\left|L_{uckGrade}-1220\right|,1240 \le L_{uckGrade}<1250:1.326+0\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1290:1.329+0\left|L_{uckGrade}-1250\right|,1290 \le L_{uckGrade}<1300:1.337+0\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1330:1.34+0\left|L_{uckGrade}-1300\right|,1330 \le L_{uckGrade}<1340:1.346+0\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1390:1.349+0\left|L_{uckGrade}-1340\right|,1390 \le L_{uckGrade}<1400:1.359+0\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1460:1.362+0\left|L_{uckGrade}-1400\right|,1460 \le L_{uckGrade}<1470:1.374+0\left|L_{uckGrade}-1460\right|,1470 \le L_{uckGrade}<1560:1.377+0\left|L_{uckGrade}-1470\right|,1560 \le L_{uckGrade}<1570:1.395+0\left|L_{uckGrade}-1560\right|,1570 \le L_{uckGrade}<1770:1.398+0\left|L_{uckGrade}-1570\right|,1770 \le L_{uckGrade}<1780:1.438+0\left|L_{uckGrade}-1770\right|,1780 \le L_{uckGrade}<1880:1.439+0\left|L_{uckGrade}-1780\right|,1880 \le L_{uckGrade}<1890:1.459+0\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1950:1.46+0\left|L_{uckGrade}-1890\right|,1950 \le L_{uckGrade}<1960:1.472+0\left|L_{uckGrade}-1950\right|,1960 \le L_{uckGrade}<2000:1.473+0\left|L_{uckGrade}-1960\right|,2000 \le L_{uckGrade}<2010:1.481+0\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2050:1.482+0\left|L_{uckGrade}-2010\right|,2050 \le L_{uckGrade}<2060:1.49+0\left|L_{uckGrade}-2050\right|,2060 \le L_{uckGrade}<2090:1.491+0\left|L_{uckGrade}-2060\right|,2090 \le L_{uckGrade}<2100:1.497+0\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2130:1.498+0\left|L_{uckGrade}-2100\right|,2130 \le L_{uckGrade}<2140:1.504+0\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2160:1.505+0\left|L_{uckGrade}-2140\right|,2160 \le L_{uckGrade}<2170:1.509+0\left|L_{uckGrade}-2160\right|,2170 \le L_{uckGrade}<2190:1.51+0\left|L_{uckGrade}-2170\right|,2190 \le L_{uckGrade}<2200:1.514+0\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2220:1.515+0\left|L_{uckGrade}-2200\right|,2220 \le L_{uckGrade}<2230:1.519+0\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2250:1.52+0\left|L_{uckGrade}-2230\right|,2250 \le L_{uckGrade}<2260:1.524+0\left|L_{uckGrade}-2250\right|,2260 \le L_{uckGrade}<2280:1.525+0\left|L_{uckGrade}-2260\right|,2280 \le L_{uckGrade}<2290:1.529+0\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2310:1.53+0\left|L_{uckGrade}-2290\right|,2310 \le L_{uckGrade}<2320:1.534+0\left|L_{uckGrade}-2310\right|,2320 \le L_{uckGrade}<2330:1.535+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2340:1.537+0\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2360:1.538+0\left|L_{uckGrade}-2340\right|,2360 \le L_{uckGrade}<2370:1.542+0\left|L_{uckGrade}-2360\right|,2370 \le L_{uckGrade}<2380:1.543+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2390:1.545+0\left|L_{uckGrade}-2380\right|,2390 \le L_{uckGrade}<2400:1.546+0\left|L_{uckGrade}-2390\right|,2400 \le L_{uckGrade}<2410:1.548+0\left|L_{uckGrade}-2400\right|,2410 \le L_{uckGrade}<2430:1.549+0\left|L_{uckGrade}-2410\right|,2430 \le L_{uckGrade}<2440:1.553+0\left|L_{uckGrade}-2430\right|,2440 \le L_{uckGrade}<2450:1.554+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2460:1.556+0\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:1.557+0\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:1.559+0\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2490:1.56+0\left|L_{uckGrade}-2480\right|,2490 \le L_{uckGrade}<2500:1.562+0\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2510:1.563+0\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:1.565+0\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2530:1.566+0\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2540:1.568+0\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2550:1.569+0\left|L_{uckGrade}-2540\right|,2550 \le L_{uckGrade}<2560:1.571+0\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2570:1.572+0\left|L_{uckGrade}-2560\right|,2570 \le L_{uckGrade}<2580:1.574+0\left|L_{uckGrade}-2570\right|,2580 \le L_{uckGrade}<2590:1.575+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2610:1.577+0\left|L_{uckGrade}-2590\right|,2610 \le L_{uckGrade}<2620:1.579+0\left|L_{uckGrade}-2610\right|,2620 \le L_{uckGrade}<2630:1.581+0\left|L_{uckGrade}-2620\right|,2630 \le L_{uckGrade}<2640:1.582+0\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2650:1.584+0\left|L_{uckGrade}-2640\right|,2650 \le L_{uckGrade}<2660:1.585+0\left|L_{uckGrade}-2650\right|,2660 \le L_{uckGrade}<2680:1.587+0\left|L_{uckGrade}-2660\right|,2680 \le L_{uckGrade}<2690:1.589+0\left|L_{uckGrade}-2680\right|,2690 \le L_{uckGrade}<2710:1.591+0\left|L_{uckGrade}-2690\right|,2710 \le L_{uckGrade}<2720:1.593+0\left|L_{uckGrade}-2710\right|,2720 \le L_{uckGrade}<2730:1.595+0\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2740:1.596+0\left|L_{uckGrade}-2730\right|,2740 \le L_{uckGrade}<2760:1.598+0\left|L_{uckGrade}-2740\right|,2760 \le L_{uckGrade}<2770:1.6+0\left|L_{uckGrade}-2760\right|,2770 \le L_{uckGrade}<2790:1.602+0\left|L_{uckGrade}-2770\right|,2790 \le L_{uckGrade}<2800:1.604+0\left|L_{uckGrade}-2790\right|,2800 \le L_{uckGrade}<2820:1.606+0\left|L_{uckGrade}-2800\right|,2820 \le L_{uckGrade}<2830:1.608+0\left|L_{uckGrade}-2820\right|,2830 \le L_{uckGrade}<2860:1.61+0\left|L_{uckGrade}-2830\right|,2860 \le L_{uckGrade}<2870:1.613+0\left|L_{uckGrade}-2860\right|,2870 \le L_{uckGrade}<2890:1.615+0\left|L_{uckGrade}-2870\right|,2890 \le L_{uckGrade}<2900:1.617+0\left|L_{uckGrade}-2890\right|,2900 \le L_{uckGrade}<2930:1.619+0\left|L_{uckGrade}-2900\right|,2930 \le L_{uckGrade}<2940:1.622+0\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2980:1.624+0\left|L_{uckGrade}-2940\right|,2980 \le L_{uckGrade}<2990:1.628+0\left|L_{uckGrade}-2980\right|,2990 \le L_{uckGrade}<3030:1.63+0\left|L_{uckGrade}-2990\right|,3030 \le L_{uckGrade}<3040:1.634+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3090:1.636+0\left|L_{uckGrade}-3040\right|,3090 \le L_{uckGrade}<3100:1.641+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3170:1.643+0\left|L_{uckGrade}-3100\right|,3170 \le L_{uckGrade}<3180:1.65+0\left|L_{uckGrade}-3170\right|,3180 \le L_{uckGrade}<3500:1.652+0\left|L_{uckGrade}-3180\right|,3500 \le L_{uckGrade}<3510:1.684+0\left|L_{uckGrade}-3500\right|,3510 \le L_{uckGrade}<3580:1.684+0\left|L_{uckGrade}-3510\right|,3580 \le L_{uckGrade}<3590:1.691+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3640:1.691+0\left|L_{uckGrade}-3590\right|,3640 \le L_{uckGrade}<3650:1.696+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3690:1.696+0\left|L_{uckGrade}-3650\right|,3690 \le L_{uckGrade}<3700:1.7+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3730:1.7+0\left|L_{uckGrade}-3700\right|,3730 \le L_{uckGrade}<3740:1.703+0\left|L_{uckGrade}-3730\right|,3740 \le L_{uckGrade}<3770:1.703+0\left|L_{uckGrade}-3740\right|,3770 \le L_{uckGrade}<3780:1.706+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3810:1.706+0\left|L_{uckGrade}-3780\right|,3810 \le L_{uckGrade}<3820:1.709+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3840:1.709+0\left|L_{uckGrade}-3820\right|,3840 \le L_{uckGrade}<3850:1.711+0\left|L_{uckGrade}-3840\right|,3850 \le L_{uckGrade}<3880:1.711+0\left|L_{uckGrade}-3850\right|,3880 \le L_{uckGrade}<3890:1.714+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3910:1.714+0\left|L_{uckGrade}-3890\right|,3910 \le L_{uckGrade}<3920:1.716+0\left|L_{uckGrade}-3910\right|,3920 \le L_{uckGrade}<3930:1.716+0\left|L_{uckGrade}-3920\right|,3930 \le L_{uckGrade}<3940:1.717+0\left|L_{uckGrade}-3930\right|,3940 \le L_{uckGrade}<3960:1.717+0\left|L_{uckGrade}-3940\right|,3960 \le L_{uckGrade}<3970:1.719+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3990:1.719+0\left|L_{uckGrade}-3970\right|,3990 \le L_{uckGrade}<4000:1.721+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4010:1.721+0\left|L_{uckGrade}-4000\right|,4010 \le L_{uckGrade}<4020:1.722+0\left|L_{uckGrade}-4010\right|,4020 \le L_{uckGrade}<4040:1.722+0\left|L_{uckGrade}-4020\right|,4040 \le L_{uckGrade}<4050:1.724+0\left|L_{uckGrade}-4040\right|,4050 \le L_{uckGrade}<4060:1.724+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4070:1.725+0\left|L_{uckGrade}-4060\right|,4070 \le L_{uckGrade}<4080:1.725+0\left|L_{uckGrade}-4070\right|,4080 \le L_{uckGrade}<4090:1.726+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4100:1.726+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4110:1.727+0\left|L_{uckGrade}-4100\right|,4110 \le L_{uckGrade}<4130:1.727+0\left|L_{uckGrade}-4110\right|,4130 \le L_{uckGrade}<4140:1.729+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4150:1.729+0\left|L_{uckGrade}-4140\right|,4150 \le L_{uckGrade}<4160:1.73+0\left|L_{uckGrade}-4150\right|,4160 \le L_{uckGrade}<4170:1.73+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4180:1.731+0\left|L_{uckGrade}-4170\right|,4180 \le L_{uckGrade}<4190:1.731+0\left|L_{uckGrade}-4180\right|,4190 \le L_{uckGrade}<4200:1.732+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4210:1.732+0\left|L_{uckGrade}-4200\right|,4210 \le L_{uckGrade}<4230:1.733+0\left|L_{uckGrade}-4210\right|,4230 \le L_{uckGrade}<4240:1.733+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:1.734+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4260:1.734+0\left|L_{uckGrade}-4250\right|,4260 \le L_{uckGrade}<4270:1.735+0\left|L_{uckGrade}-4260\right|,4270 \le L_{uckGrade}<4280:1.735+0\left|L_{uckGrade}-4270\right|,4280 \le L_{uckGrade}<4290:1.736+0\left|L_{uckGrade}-4280\right|,4290 \le L_{uckGrade}<4300:1.736+0\left|L_{uckGrade}-4290\right|,4300 \le L_{uckGrade}<4320:1.737+0\left|L_{uckGrade}-4300\right|,4320 \le L_{uckGrade}<4330:1.737+0\left|L_{uckGrade}-4320\right|,4330 \le L_{uckGrade}<4340:1.738+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4350:1.738+0\left|L_{uckGrade}-4340\right|,4350 \le L_{uckGrade}<4370:1.739+0\left|L_{uckGrade}-4350\right|,4370 \le L_{uckGrade}<4380:1.739+0\left|L_{uckGrade}-4370\right|,4380 \le L_{uckGrade}<4390:1.74+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4400:1.74+0\left|L_{uckGrade}-4390\right|,4400 \le L_{uckGrade}<4420:1.741+0\left|L_{uckGrade}-4400\right|,4420 \le L_{uckGrade}<4430:1.741+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4450:1.742+0\left|L_{uckGrade}-4430\right|,4450 \le L_{uckGrade}<4460:1.742+0\left|L_{uckGrade}-4450\right|,4460 \le L_{uckGrade}<4480:1.743+0\left|L_{uckGrade}-4460\right|,4480 \le L_{uckGrade}<4490:1.743+0\left|L_{uckGrade}-4480\right|,4490 \le L_{uckGrade}<4520:1.744+0\left|L_{uckGrade}-4490\right|,4520 \le L_{uckGrade}<4530:1.744+0\left|L_{uckGrade}-4520\right|,4530 \le L_{uckGrade}<4550:1.745+0\left|L_{uckGrade}-4530\right|,4550 \le L_{uckGrade}<4560:1.745+0\left|L_{uckGrade}-4550\right|,4560 \le L_{uckGrade}<4590:1.746+0\left|L_{uckGrade}-4560\right|,4590 \le L_{uckGrade}<4600:1.746+0\left|L_{uckGrade}-4590\right|,4600 \le L_{uckGrade}<4630:1.747+0\left|L_{uckGrade}-4600\right|,4630 \le L_{uckGrade}<4640:1.747+0\left|L_{uckGrade}-4630\right|,4640 \le L_{uckGrade}<4680:1.748+0\left|L_{uckGrade}-4640\right|,4680 \le L_{uckGrade}<4690:1.748+0\left|L_{uckGrade}-4680\right|,4690 \le L_{uckGrade}<4740:1.749+0\left|L_{uckGrade}-4690\right|,4740 \le L_{uckGrade}<4750:1.749+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4820:1.75+0\left|L_{uckGrade}-4750\right|,4820 \le L_{uckGrade}<4830:1.75+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4990:1.751+0\left|L_{uckGrade}-4830\right|,4990 \le L_{uckGrade}<5000:1.751+0\left|L_{uckGrade}-4990\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade05}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<10:1+0.001\left|L_{uckGrade}-0\right|,10 \le L_{uckGrade}<20:1.006+0.001\left|L_{uckGrade}-10\right|,20 \le L_{uckGrade}<50:1.013+0.001\left|L_{uckGrade}-20\right|,50 \le L_{uckGrade}<60:1.031+0.001\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<90:1.038+0.001\left|L_{uckGrade}-60\right|,90 \le L_{uckGrade}<100:1.056+0.001\left|L_{uckGrade}-90\right|,100 \le L_{uckGrade}<140:1.063+0.001\left|L_{uckGrade}-100\right|,140 \le L_{uckGrade}<150:1.087+0.001\left|L_{uckGrade}-140\right|,150 \le L_{uckGrade}<370:1.094+0.001\left|L_{uckGrade}-150\right|,370 \le L_{uckGrade}<380:1.226+0.001\left|L_{uckGrade}-370\right|,380 \le L_{uckGrade}<430:1.231+0.001\left|L_{uckGrade}-380\right|,430 \le L_{uckGrade}<440:1.261+0.001\left|L_{uckGrade}-430\right|,440 \le L_{uckGrade}<470:1.266+0.001\left|L_{uckGrade}-440\right|,470 \le L_{uckGrade}<480:1.284+0\left|L_{uckGrade}-470\right|,480 \le L_{uckGrade}<500:1.289+0.001\left|L_{uckGrade}-480\right|,500 \le L_{uckGrade}<510:1.301+0.001\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<530:1.306+0.001\left|L_{uckGrade}-510\right|,530 \le L_{uckGrade}<540:1.318+0\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<560:1.323+0.001\left|L_{uckGrade}-540\right|,560 \le L_{uckGrade}<570:1.335+0.001\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<590:1.34+0.001\left|L_{uckGrade}-570\right|,590 \le L_{uckGrade}<600:1.352+0\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<610:1.357+0.001\left|L_{uckGrade}-600\right|,610 \le L_{uckGrade}<620:1.363+0.001\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<630:1.368+0.001\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<640:1.374+0\left|L_{uckGrade}-630\right|,640 \le L_{uckGrade}<650:1.379+0.001\left|L_{uckGrade}-640\right|,650 \le L_{uckGrade}<660:1.385+0\left|L_{uckGrade}-650\right|,660 \le L_{uckGrade}<670:1.39+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:1.396+0.001\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<690:1.401+0.001\left|L_{uckGrade}-680\right|,690 \le L_{uckGrade}<700:1.407+0\left|L_{uckGrade}-690\right|,700 \le L_{uckGrade}<710:1.412+0.001\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<730:1.418+0.001\left|L_{uckGrade}-710\right|,730 \le L_{uckGrade}<740:1.428+0.001\left|L_{uckGrade}-730\right|,740 \le L_{uckGrade}<750:1.434+0.001\left|L_{uckGrade}-740\right|,750 \le L_{uckGrade}<760:1.439+0.001\left|L_{uckGrade}-750\right|,760 \le L_{uckGrade}<780:1.445+0.001\left|L_{uckGrade}-760\right|,780 \le L_{uckGrade}<790:1.455+0.001\left|L_{uckGrade}-780\right|,790 \le L_{uckGrade}<810:1.461+0.001\left|L_{uckGrade}-790\right|,810 \le L_{uckGrade}<820:1.471+0.001\left|L_{uckGrade}-810\right|,820 \le L_{uckGrade}<850:1.477+0\left|L_{uckGrade}-820\right|,850 \le L_{uckGrade}<860:1.492+0.001\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<890:1.498+0\left|L_{uckGrade}-860\right|,890 \le L_{uckGrade}<900:1.513+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<950:1.519+0.001\left|L_{uckGrade}-900\right|,950 \le L_{uckGrade}<960:1.544+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<1140:1.55+0\left|L_{uckGrade}-960\right|,1140 \le L_{uckGrade}<1150:1.64+0\left|L_{uckGrade}-1140\right|,1150 \le L_{uckGrade}<1200:1.644+0.001\left|L_{uckGrade}-1150\right|,1200 \le L_{uckGrade}<1210:1.669+0\left|L_{uckGrade}-1200\right|,1210 \le L_{uckGrade}<1250:1.673+0.001\left|L_{uckGrade}-1210\right|,1250 \le L_{uckGrade}<1260:1.693+0\left|L_{uckGrade}-1250\right|,1260 \le L_{uckGrade}<1280:1.697+0.001\left|L_{uckGrade}-1260\right|,1280 \le L_{uckGrade}<1290:1.707+0\left|L_{uckGrade}-1280\right|,1290 \le L_{uckGrade}<1320:1.711+0\left|L_{uckGrade}-1290\right|,1320 \le L_{uckGrade}<1330:1.726+0\left|L_{uckGrade}-1320\right|,1330 \le L_{uckGrade}<1340:1.73+0.001\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1350:1.735+0\left|L_{uckGrade}-1340\right|,1350 \le L_{uckGrade}<1370:1.739+0.001\left|L_{uckGrade}-1350\right|,1370 \le L_{uckGrade}<1380:1.749+0\left|L_{uckGrade}-1370\right|,1380 \le L_{uckGrade}<1390:1.753+0.001\left|L_{uckGrade}-1380\right|,1390 \le L_{uckGrade}<1400:1.758+0\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1420:1.762+0.001\left|L_{uckGrade}-1400\right|,1420 \le L_{uckGrade}<1430:1.772+0\left|L_{uckGrade}-1420\right|,1430 \le L_{uckGrade}<1440:1.776+0\left|L_{uckGrade}-1430\right|,1440 \le L_{uckGrade}<1450:1.781+0\left|L_{uckGrade}-1440\right|,1450 \le L_{uckGrade}<1460:1.785+0.001\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1480:1.79+0\left|L_{uckGrade}-1460\right|,1480 \le L_{uckGrade}<1490:1.798+0\left|L_{uckGrade}-1480\right|,1490 \le L_{uckGrade}<1500:1.803+0\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1510:1.807+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:1.812+0\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1530:1.816+0\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1550:1.821+0\left|L_{uckGrade}-1530\right|,1550 \le L_{uckGrade}<1560:1.829+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1580:1.834+0\left|L_{uckGrade}-1560\right|,1580 \le L_{uckGrade}<1590:1.842+0\left|L_{uckGrade}-1580\right|,1590 \le L_{uckGrade}<1610:1.847+0\left|L_{uckGrade}-1590\right|,1610 \le L_{uckGrade}<1620:1.855+0.001\left|L_{uckGrade}-1610\right|,1620 \le L_{uckGrade}<1650:1.86+0\left|L_{uckGrade}-1620\right|,1650 \le L_{uckGrade}<1660:1.872+0\left|L_{uckGrade}-1650\right|,1660 \le L_{uckGrade}<1690:1.877+0\left|L_{uckGrade}-1660\right|,1690 \le L_{uckGrade}<1700:1.889+0\left|L_{uckGrade}-1690\right|,1700 \le L_{uckGrade}<1770:1.894+0\left|L_{uckGrade}-1700\right|,1770 \le L_{uckGrade}<1780:1.922+0.001\left|L_{uckGrade}-1770\right|,1780 \le L_{uckGrade}<1910:1.927+0\left|L_{uckGrade}-1780\right|,1910 \le L_{uckGrade}<1920:1.979+0\left|L_{uckGrade}-1910\right|,1920 \le L_{uckGrade}<1980:1.982+0\left|L_{uckGrade}-1920\right|,1980 \le L_{uckGrade}<1990:2.006+0\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2030:2.009+0\left|L_{uckGrade}-1990\right|,2030 \le L_{uckGrade}<2040:2.025+0\left|L_{uckGrade}-2030\right|,2040 \le L_{uckGrade}<2070:2.028+0\left|L_{uckGrade}-2040\right|,2070 \le L_{uckGrade}<2080:2.04+0\left|L_{uckGrade}-2070\right|,2080 \le L_{uckGrade}<2100:2.043+0\left|L_{uckGrade}-2080\right|,2100 \le L_{uckGrade}<2110:2.051+0\left|L_{uckGrade}-2100\right|,2110 \le L_{uckGrade}<2130:2.054+0\left|L_{uckGrade}-2110\right|,2130 \le L_{uckGrade}<2140:2.062+0\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2150:2.065+0\left|L_{uckGrade}-2140\right|,2150 \le L_{uckGrade}<2160:2.069+0\left|L_{uckGrade}-2150\right|,2160 \le L_{uckGrade}<2180:2.072+0\left|L_{uckGrade}-2160\right|,2180 \le L_{uckGrade}<2190:2.08+0\left|L_{uckGrade}-2180\right|,2190 \le L_{uckGrade}<2200:2.083+0\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2210:2.087+0\left|L_{uckGrade}-2200\right|,2210 \le L_{uckGrade}<2220:2.09+0\left|L_{uckGrade}-2210\right|,2220 \le L_{uckGrade}<2230:2.094+0\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2240:2.097+0\left|L_{uckGrade}-2230\right|,2240 \le L_{uckGrade}<2250:2.101+0\left|L_{uckGrade}-2240\right|,2250 \le L_{uckGrade}<2260:2.104+0\left|L_{uckGrade}-2250\right|,2260 \le L_{uckGrade}<2270:2.108+0\left|L_{uckGrade}-2260\right|,2270 \le L_{uckGrade}<2280:2.111+0\left|L_{uckGrade}-2270\right|,2280 \le L_{uckGrade}<2290:2.115+0\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2300:2.118+0\left|L_{uckGrade}-2290\right|,2300 \le L_{uckGrade}<2320:2.122+0\left|L_{uckGrade}-2300\right|,2320 \le L_{uckGrade}<2330:2.128+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2340:2.132+0\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2350:2.135+0\left|L_{uckGrade}-2340\right|,2350 \le L_{uckGrade}<2370:2.139+0\left|L_{uckGrade}-2350\right|,2370 \le L_{uckGrade}<2380:2.145+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2410:2.149+0\left|L_{uckGrade}-2380\right|,2410 \le L_{uckGrade}<2420:2.158+0\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2440:2.162+0\left|L_{uckGrade}-2420\right|,2440 \le L_{uckGrade}<2450:2.168+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2490:2.172+0\left|L_{uckGrade}-2450\right|,2490 \le L_{uckGrade}<2500:2.184+0\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2580:2.188+0\left|L_{uckGrade}-2500\right|,2580 \le L_{uckGrade}<2590:2.212+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2680:2.216+0\left|L_{uckGrade}-2590\right|,2680 \le L_{uckGrade}<2690:2.243+0\left|L_{uckGrade}-2680\right|,2690 \le L_{uckGrade}<2760:2.245+0\left|L_{uckGrade}-2690\right|,2760 \le L_{uckGrade}<2770:2.266+0\left|L_{uckGrade}-2760\right|,2770 \le L_{uckGrade}<2810:2.268+0\left|L_{uckGrade}-2770\right|,2810 \le L_{uckGrade}<2820:2.28+0\left|L_{uckGrade}-2810\right|,2820 \le L_{uckGrade}<2850:2.282+0\left|L_{uckGrade}-2820\right|,2850 \le L_{uckGrade}<2860:2.291+0\left|L_{uckGrade}-2850\right|,2860 \le L_{uckGrade}<2880:2.293+0\left|L_{uckGrade}-2860\right|,2880 \le L_{uckGrade}<2890:2.299+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2910:2.301+0\left|L_{uckGrade}-2890\right|,2910 \le L_{uckGrade}<2920:2.307+0\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2940:2.309+0\left|L_{uckGrade}-2920\right|,2940 \le L_{uckGrade}<2950:2.315+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2960:2.317+0\left|L_{uckGrade}-2950\right|,2960 \le L_{uckGrade}<2970:2.32+0\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<2990:2.322+0\left|L_{uckGrade}-2970\right|,2990 \le L_{uckGrade}<3000:2.328+0\left|L_{uckGrade}-2990\right|,3000 \le L_{uckGrade}<3010:2.33+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3020:2.333+0\left|L_{uckGrade}-3010\right|,3020 \le L_{uckGrade}<3030:2.335+0\left|L_{uckGrade}-3020\right|,3030 \le L_{uckGrade}<3040:2.338+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3050:2.34+0\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3060:2.343+0\left|L_{uckGrade}-3050\right|,3060 \le L_{uckGrade}<3070:2.345+0\left|L_{uckGrade}-3060\right|,3070 \le L_{uckGrade}<3090:2.348+0\left|L_{uckGrade}-3070\right|,3090 \le L_{uckGrade}<3100:2.352+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3110:2.355+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3120:2.357+0\left|L_{uckGrade}-3110\right|,3120 \le L_{uckGrade}<3140:2.36+0\left|L_{uckGrade}-3120\right|,3140 \le L_{uckGrade}<3150:2.364+0\left|L_{uckGrade}-3140\right|,3150 \le L_{uckGrade}<3170:2.367+0\left|L_{uckGrade}-3150\right|,3170 \le L_{uckGrade}<3180:2.371+0\left|L_{uckGrade}-3170\right|,3180 \le L_{uckGrade}<3200:2.374+0\left|L_{uckGrade}-3180\right|,3200 \le L_{uckGrade}<3210:2.378+0\left|L_{uckGrade}-3200\right|,3210 \le L_{uckGrade}<3240:2.381+0\left|L_{uckGrade}-3210\right|,3240 \le L_{uckGrade}<3250:2.387+0\left|L_{uckGrade}-3240\right|,3250 \le L_{uckGrade}<3290:2.39+0\left|L_{uckGrade}-3250\right|,3290 \le L_{uckGrade}<3300:2.398+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3400:2.401+0\left|L_{uckGrade}-3300\right|,3400 \le L_{uckGrade}<3410:2.421+0\left|L_{uckGrade}-3400\right|,3410 \le L_{uckGrade}<3440:2.424+0\left|L_{uckGrade}-3410\right|,3440 \le L_{uckGrade}<3450:2.43+0\left|L_{uckGrade}-3440\right|,3450 \le L_{uckGrade}<3550:2.431+0\left|L_{uckGrade}-3450\right|,3550 \le L_{uckGrade}<3560:2.451+0\left|L_{uckGrade}-3550\right|,3560 \le L_{uckGrade}<3600:2.452+0\left|L_{uckGrade}-3560\right|,3600 \le L_{uckGrade}<3610:2.46+0\left|L_{uckGrade}-3600\right|,3610 \le L_{uckGrade}<3640:2.461+0\left|L_{uckGrade}-3610\right|,3640 \le L_{uckGrade}<3650:2.467+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3670:2.468+0\left|L_{uckGrade}-3650\right|,3670 \le L_{uckGrade}<3680:2.472+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3700:2.473+0\left|L_{uckGrade}-3680\right|,3700 \le L_{uckGrade}<3710:2.477+0\left|L_{uckGrade}-3700\right|,3710 \le L_{uckGrade}<3730:2.478+0\left|L_{uckGrade}-3710\right|,3730 \le L_{uckGrade}<3740:2.482+0\left|L_{uckGrade}-3730\right|,3740 \le L_{uckGrade}<3750:2.483+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3760:2.485+0\left|L_{uckGrade}-3750\right|,3760 \le L_{uckGrade}<3770:2.486+0\left|L_{uckGrade}-3760\right|,3770 \le L_{uckGrade}<3780:2.488+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3800:2.489+0\left|L_{uckGrade}-3780\right|,3800 \le L_{uckGrade}<3810:2.493+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<3820:2.494+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3830:2.496+0\left|L_{uckGrade}-3820\right|,3830 \le L_{uckGrade}<3840:2.497+0\left|L_{uckGrade}-3830\right|,3840 \le L_{uckGrade}<3860:2.499+0\left|L_{uckGrade}-3840\right|,3860 \le L_{uckGrade}<3870:2.501+0\left|L_{uckGrade}-3860\right|,3870 \le L_{uckGrade}<3880:2.503+0\left|L_{uckGrade}-3870\right|,3880 \le L_{uckGrade}<3890:2.504+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3900:2.506+0\left|L_{uckGrade}-3890\right|,3900 \le L_{uckGrade}<3910:2.507+0\left|L_{uckGrade}-3900\right|,3910 \le L_{uckGrade}<3930:2.509+0\left|L_{uckGrade}-3910\right|,3930 \le L_{uckGrade}<3940:2.511+0\left|L_{uckGrade}-3930\right|,3940 \le L_{uckGrade}<3960:2.513+0\left|L_{uckGrade}-3940\right|,3960 \le L_{uckGrade}<3970:2.515+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3990:2.517+0\left|L_{uckGrade}-3970\right|,3990 \le L_{uckGrade}<4000:2.519+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4030:2.521+0\left|L_{uckGrade}-4000\right|,4030 \le L_{uckGrade}<4040:2.524+0\left|L_{uckGrade}-4030\right|,4040 \le L_{uckGrade}<4090:2.526+0\left|L_{uckGrade}-4040\right|,4090 \le L_{uckGrade}<4100:2.531+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4330:2.533+0\left|L_{uckGrade}-4100\right|,4330 \le L_{uckGrade}<4340:2.556+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4380:2.556+0\left|L_{uckGrade}-4340\right|,4380 \le L_{uckGrade}<4390:2.56+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4430:2.56+0\left|L_{uckGrade}-4390\right|,4430 \le L_{uckGrade}<4440:2.564+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4460:2.564+0\left|L_{uckGrade}-4440\right|,4460 \le L_{uckGrade}<4470:2.566+0\left|L_{uckGrade}-4460\right|,4470 \le L_{uckGrade}<4490:2.566+0\left|L_{uckGrade}-4470\right|,4490 \le L_{uckGrade}<4500:2.568+0\left|L_{uckGrade}-4490\right|,4500 \le L_{uckGrade}<4520:2.568+0\left|L_{uckGrade}-4500\right|,4520 \le L_{uckGrade}<4530:2.57+0\left|L_{uckGrade}-4520\right|,4530 \le L_{uckGrade}<4540:2.57+0\left|L_{uckGrade}-4530\right|,4540 \le L_{uckGrade}<4550:2.571+0\left|L_{uckGrade}-4540\right|,4550 \le L_{uckGrade}<4560:2.571+0\left|L_{uckGrade}-4550\right|,4560 \le L_{uckGrade}<4570:2.572+0\left|L_{uckGrade}-4560\right|,4570 \le L_{uckGrade}<4590:2.572+0\left|L_{uckGrade}-4570\right|,4590 \le L_{uckGrade}<4600:2.574+0\left|L_{uckGrade}-4590\right|,4600 \le L_{uckGrade}<4610:2.574+0\left|L_{uckGrade}-4600\right|,4610 \le L_{uckGrade}<4620:2.575+0\left|L_{uckGrade}-4610\right|,4620 \le L_{uckGrade}<4630:2.575+0\left|L_{uckGrade}-4620\right|,4630 \le L_{uckGrade}<4650:2.576+0\left|L_{uckGrade}-4630\right|,4650 \le L_{uckGrade}<4660:2.576+0\left|L_{uckGrade}-4650\right|,4660 \le L_{uckGrade}<4670:2.577+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4680:2.577+0\left|L_{uckGrade}-4670\right|,4680 \le L_{uckGrade}<4690:2.578+0\left|L_{uckGrade}-4680\right|,4690 \le L_{uckGrade}<4700:2.578+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4720:2.579+0\left|L_{uckGrade}-4700\right|,4720 \le L_{uckGrade}<4730:2.579+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4750:2.58+0\left|L_{uckGrade}-4730\right|,4750 \le L_{uckGrade}<4760:2.58+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4790:2.581+0\left|L_{uckGrade}-4760\right|,4790 \le L_{uckGrade}<4800:2.581+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4830:2.582+0\left|L_{uckGrade}-4800\right|,4830 \le L_{uckGrade}<4840:2.582+0\left|L_{uckGrade}-4830\right|,4840 \le L_{uckGrade}<4880:2.583+0\left|L_{uckGrade}-4840\right|,4880 \le L_{uckGrade}<4890:2.583+0\left|L_{uckGrade}-4880\right|,4890 \le L_{uckGrade}<5000:2.584+0\left|L_{uckGrade}-4890\right|\right\}
See Example for how to use.
Expand
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all.
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L_{uckGrade06}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<150:1+0.001\left|L_{uckGrade}-0\right|,150 \le L_{uckGrade}<160:1.135+0.001\left|L_{uckGrade}-150\right|,160 \le L_{uckGrade}<200:1.143+0.001\left|L_{uckGrade}-160\right|,200 \le L_{uckGrade}<210:1.179+0.001\left|L_{uckGrade}-200\right|,210 \le L_{uckGrade}<230:1.187+0.001\left|L_{uckGrade}-210\right|,230 \le L_{uckGrade}<240:1.205+0.001\left|L_{uckGrade}-230\right|,240 \le L_{uckGrade}<260:1.213+0.001\left|L_{uckGrade}-240\right|,260 \le L_{uckGrade}<270:1.231+0.001\left|L_{uckGrade}-260\right|,270 \le L_{uckGrade}<290:1.239+0.001\left|L_{uckGrade}-270\right|,290 \le L_{uckGrade}<300:1.257+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<310:1.265+0.001\left|L_{uckGrade}-300\right|,310 \le L_{uckGrade}<320:1.274+0.001\left|L_{uckGrade}-310\right|,320 \le L_{uckGrade}<330:1.282+0.001\left|L_{uckGrade}-320\right|,330 \le L_{uckGrade}<340:1.291+0.001\left|L_{uckGrade}-330\right|,340 \le L_{uckGrade}<350:1.299+0.001\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<360:1.308+0.001\left|L_{uckGrade}-350\right|,360 \le L_{uckGrade}<370:1.316+0.001\left|L_{uckGrade}-360\right|,370 \le L_{uckGrade}<390:1.325+0.001\left|L_{uckGrade}-370\right|,390 \le L_{uckGrade}<400:1.341+0.001\left|L_{uckGrade}-390\right|,400 \le L_{uckGrade}<410:1.35+0.001\left|L_{uckGrade}-400\right|,410 \le L_{uckGrade}<420:1.358+0.001\left|L_{uckGrade}-410\right|,420 \le L_{uckGrade}<450:1.367+0.001\left|L_{uckGrade}-420\right|,450 \le L_{uckGrade}<460:1.391+0.001\left|L_{uckGrade}-450\right|,460 \le L_{uckGrade}<490:1.4+0.001\left|L_{uckGrade}-460\right|,490 \le L_{uckGrade}<500:1.424+0.001\left|L_{uckGrade}-490\right|,500 \le L_{uckGrade}<550:1.433+0.001\left|L_{uckGrade}-500\right|,550 \le L_{uckGrade}<560:1.473+0.001\left|L_{uckGrade}-550\right|,560 \le L_{uckGrade}<660:1.482+0.001\left|L_{uckGrade}-560\right|,660 \le L_{uckGrade}<670:1.562+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<720:1.569+0.001\left|L_{uckGrade}-670\right|,720 \le L_{uckGrade}<730:1.609+0.001\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<760:1.616+0.001\left|L_{uckGrade}-730\right|,760 \le L_{uckGrade}<770:1.64+0.001\left|L_{uckGrade}-760\right|,770 \le L_{uckGrade}<790:1.647+0.001\left|L_{uckGrade}-770\right|,790 \le L_{uckGrade}<800:1.663+0.001\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<820:1.67+0.001\left|L_{uckGrade}-800\right|,820 \le L_{uckGrade}<830:1.686+0.001\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<850:1.693+0.001\left|L_{uckGrade}-830\right|,850 \le L_{uckGrade}<860:1.709+0.001\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<870:1.716+0.001\left|L_{uckGrade}-860\right|,870 \le L_{uckGrade}<880:1.724+0.001\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<890:1.731+0.001\left|L_{uckGrade}-880\right|,890 \le L_{uckGrade}<900:1.739+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<910:1.746+0.001\left|L_{uckGrade}-900\right|,910 \le L_{uckGrade}<930:1.754+0.001\left|L_{uckGrade}-910\right|,930 \le L_{uckGrade}<940:1.768+0.001\left|L_{uckGrade}-930\right|,940 \le L_{uckGrade}<950:1.776+0.001\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<960:1.783+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<980:1.791+0.001\left|L_{uckGrade}-960\right|,980 \le L_{uckGrade}<990:1.805+0.001\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1020:1.813+0.001\left|L_{uckGrade}-990\right|,1020 \le L_{uckGrade}<1030:1.834+0.001\left|L_{uckGrade}-1020\right|,1030 \le L_{uckGrade}<1070:1.842+0.001\left|L_{uckGrade}-1030\right|,1070 \le L_{uckGrade}<1080:1.87+0.001\left|L_{uckGrade}-1070\right|,1080 \le L_{uckGrade}<1240:1.878+0.001\left|L_{uckGrade}-1080\right|,1240 \le L_{uckGrade}<1250:1.99+0.001\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1290:1.996+0.001\left|L_{uckGrade}-1250\right|,1290 \le L_{uckGrade}<1300:2.024+0.001\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1330:2.03+0.001\left|L_{uckGrade}-1300\right|,1330 \le L_{uckGrade}<1340:2.051+0.001\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1360:2.057+0.001\left|L_{uckGrade}-1340\right|,1360 \le L_{uckGrade}<1370:2.071+0.001\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1380:2.077+0.001\left|L_{uckGrade}-1370\right|,1380 \le L_{uckGrade}<1390:2.084+0.001\left|L_{uckGrade}-1380\right|,1390 \le L_{uckGrade}<1400:2.09+0.001\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1410:2.097+0.001\left|L_{uckGrade}-1400\right|,1410 \le L_{uckGrade}<1430:2.103+0.001\left|L_{uckGrade}-1410\right|,1430 \le L_{uckGrade}<1450:2.117+0.001\left|L_{uckGrade}-1430\right|,1450 \le L_{uckGrade}<1460:2.129+0.001\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1470:2.136+0.001\left|L_{uckGrade}-1460\right|,1470 \le L_{uckGrade}<1480:2.142+0.001\left|L_{uckGrade}-1470\right|,1480 \le L_{uckGrade}<1490:2.149+0.001\left|L_{uckGrade}-1480\right|,1490 \le L_{uckGrade}<1500:2.155+0.001\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1520:2.162+0.001\left|L_{uckGrade}-1500\right|,1520 \le L_{uckGrade}<1530:2.174+0.001\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1550:2.181+0.001\left|L_{uckGrade}-1530\right|,1550 \le L_{uckGrade}<1560:2.193+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1600:2.2+0.001\left|L_{uckGrade}-1560\right|,1600 \le L_{uckGrade}<1610:2.224+0.001\left|L_{uckGrade}-1600\right|,1610 \le L_{uckGrade}<1680:2.231+0.001\left|L_{uckGrade}-1610\right|,1680 \le L_{uckGrade}<1690:2.273+0.001\left|L_{uckGrade}-1680\right|,1690 \le L_{uckGrade}<1730:2.28+0.001\left|L_{uckGrade}-1690\right|,1730 \le L_{uckGrade}<1740:2.304+0.001\left|L_{uckGrade}-1730\right|,1740 \le L_{uckGrade}<1810:2.309+0.001\left|L_{uckGrade}-1740\right|,1810 \le L_{uckGrade}<1820:2.351+0\left|L_{uckGrade}-1810\right|,1820 \le L_{uckGrade}<1850:2.356+0.001\left|L_{uckGrade}-1820\right|,1850 \le L_{uckGrade}<1860:2.374+0\left|L_{uckGrade}-1850\right|,1860 \le L_{uckGrade}<1890:2.379+0.001\left|L_{uckGrade}-1860\right|,1890 \le L_{uckGrade}<1900:2.397+0.001\left|L_{uckGrade}-1890\right|,1900 \le L_{uckGrade}<1910:2.402+0.001\left|L_{uckGrade}-1900\right|,1910 \le L_{uckGrade}<1920:2.408+0\left|L_{uckGrade}-1910\right|,1920 \le L_{uckGrade}<1940:2.413+0.001\left|L_{uckGrade}-1920\right|,1940 \le L_{uckGrade}<1950:2.425+0.001\left|L_{uckGrade}-1940\right|,1950 \le L_{uckGrade}<1960:2.43+0.001\left|L_{uckGrade}-1950\right|,1960 \le L_{uckGrade}<1970:2.436+0\left|L_{uckGrade}-1960\right|,1970 \le L_{uckGrade}<1980:2.441+0.001\left|L_{uckGrade}-1970\right|,1980 \le L_{uckGrade}<1990:2.447+0\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2000:2.452+0.001\left|L_{uckGrade}-1990\right|,2000 \le L_{uckGrade}<2010:2.458+0\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2020:2.463+0.001\left|L_{uckGrade}-2010\right|,2020 \le L_{uckGrade}<2030:2.469+0.001\left|L_{uckGrade}-2020\right|,2030 \le L_{uckGrade}<2040:2.474+0.001\left|L_{uckGrade}-2030\right|,2040 \le L_{uckGrade}<2060:2.48+0.001\left|L_{uckGrade}-2040\right|,2060 \le L_{uckGrade}<2070:2.49+0.001\left|L_{uckGrade}-2060\right|,2070 \le L_{uckGrade}<2090:2.496+0\left|L_{uckGrade}-2070\right|,2090 \le L_{uckGrade}<2100:2.506+0.001\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2130:2.512+0.001\left|L_{uckGrade}-2100\right|,2130 \le L_{uckGrade}<2140:2.527+0.001\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2190:2.533+0\left|L_{uckGrade}-2140\right|,2190 \le L_{uckGrade}<2200:2.558+0.001\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2320:2.564+0.001\left|L_{uckGrade}-2200\right|,2320 \le L_{uckGrade}<2330:2.624+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2380:2.628+0\left|L_{uckGrade}-2330\right|,2380 \le L_{uckGrade}<2390:2.653+0\left|L_{uckGrade}-2380\right|,2390 \le L_{uckGrade}<2410:2.657+0\left|L_{uckGrade}-2390\right|,2410 \le L_{uckGrade}<2420:2.667+0\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2450:2.671+0.001\left|L_{uckGrade}-2420\right|,2450 \le L_{uckGrade}<2460:2.686+0\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:2.69+0\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:2.695+0\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2500:2.699+0.001\left|L_{uckGrade}-2480\right|,2500 \le L_{uckGrade}<2510:2.709+0\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:2.713+0\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2530:2.718+0\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2540:2.722+0\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2550:2.727+0\left|L_{uckGrade}-2540\right|,2550 \le L_{uckGrade}<2560:2.731+0.001\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2580:2.736+0\left|L_{uckGrade}-2560\right|,2580 \le L_{uckGrade}<2590:2.744+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2600:2.749+0\left|L_{uckGrade}-2590\right|,2600 \le L_{uckGrade}<2610:2.753+0\left|L_{uckGrade}-2600\right|,2610 \le L_{uckGrade}<2630:2.758+0\left|L_{uckGrade}-2610\right|,2630 \le L_{uckGrade}<2640:2.766+0\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2670:2.771+0\left|L_{uckGrade}-2640\right|,2670 \le L_{uckGrade}<2680:2.783+0\left|L_{uckGrade}-2670\right|,2680 \le L_{uckGrade}<2720:2.788+0\left|L_{uckGrade}-2680\right|,2720 \le L_{uckGrade}<2730:2.804+0.001\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2880:2.809+0\left|L_{uckGrade}-2730\right|,2880 \le L_{uckGrade}<2890:2.869+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2940:2.872+0\left|L_{uckGrade}-2890\right|,2940 \le L_{uckGrade}<2950:2.892+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2970:2.895+0\left|L_{uckGrade}-2950\right|,2970 \le L_{uckGrade}<2980:2.903+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<3000:2.906+0\left|L_{uckGrade}-2980\right|,3000 \le L_{uckGrade}<3010:2.914+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3030:2.917+0\left|L_{uckGrade}-3010\right|,3030 \le L_{uckGrade}<3040:2.925+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3050:2.928+0\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3060:2.932+0\left|L_{uckGrade}-3050\right|,3060 \le L_{uckGrade}<3070:2.935+0\left|L_{uckGrade}-3060\right|,3070 \le L_{uckGrade}<3080:2.939+0\left|L_{uckGrade}-3070\right|,3080 \le L_{uckGrade}<3090:2.942+0\left|L_{uckGrade}-3080\right|,3090 \le L_{uckGrade}<3100:2.946+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3110:2.949+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3120:2.953+0\left|L_{uckGrade}-3110\right|,3120 \le L_{uckGrade}<3130:2.956+0\left|L_{uckGrade}-3120\right|,3130 \le L_{uckGrade}<3150:2.96+0\left|L_{uckGrade}-3130\right|,3150 \le L_{uckGrade}<3160:2.966+0\left|L_{uckGrade}-3150\right|,3160 \le L_{uckGrade}<3180:2.97+0\left|L_{uckGrade}-3160\right|,3180 \le L_{uckGrade}<3190:2.976+0\left|L_{uckGrade}-3180\right|,3190 \le L_{uckGrade}<3210:2.98+0\left|L_{uckGrade}-3190\right|,3210 \le L_{uckGrade}<3220:2.986+0\left|L_{uckGrade}-3210\right|,3220 \le L_{uckGrade}<3260:2.99+0\left|L_{uckGrade}-3220\right|,3260 \le L_{uckGrade}<3270:3.002+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3450:3.006+0\left|L_{uckGrade}-3270\right|,3450 \le L_{uckGrade}<3460:3.06+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3490:3.062+0\left|L_{uckGrade}-3460\right|,3490 \le L_{uckGrade}<3500:3.071+0\left|L_{uckGrade}-3490\right|,3500 \le L_{uckGrade}<3530:3.073+0\left|L_{uckGrade}-3500\right|,3530 \le L_{uckGrade}<3540:3.082+0\left|L_{uckGrade}-3530\right|,3540 \le L_{uckGrade}<3560:3.084+0\left|L_{uckGrade}-3540\right|,3560 \le L_{uckGrade}<3570:3.09+0\left|L_{uckGrade}-3560\right|,3570 \le L_{uckGrade}<3580:3.092+0\left|L_{uckGrade}-3570\right|,3580 \le L_{uckGrade}<3590:3.095+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3600:3.097+0\left|L_{uckGrade}-3590\right|,3600 \le L_{uckGrade}<3610:3.1+0\left|L_{uckGrade}-3600\right|,3610 \le L_{uckGrade}<3630:3.102+0\left|L_{uckGrade}-3610\right|,3630 \le L_{uckGrade}<3650:3.108+0\left|L_{uckGrade}-3630\right|,3650 \le L_{uckGrade}<3660:3.112+0\left|L_{uckGrade}-3650\right|,3660 \le L_{uckGrade}<3670:3.115+0\left|L_{uckGrade}-3660\right|,3670 \le L_{uckGrade}<3680:3.117+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3690:3.12+0\left|L_{uckGrade}-3680\right|,3690 \le L_{uckGrade}<3700:3.122+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3720:3.125+0\left|L_{uckGrade}-3700\right|,3720 \le L_{uckGrade}<3730:3.129+0\left|L_{uckGrade}-3720\right|,3730 \le L_{uckGrade}<3750:3.132+0\left|L_{uckGrade}-3730\right|,3750 \le L_{uckGrade}<3760:3.136+0\left|L_{uckGrade}-3750\right|,3760 \le L_{uckGrade}<3800:3.139+0\left|L_{uckGrade}-3760\right|,3800 \le L_{uckGrade}<3810:3.147+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<4000:3.15+0\left|L_{uckGrade}-3810\right|,4000 \le L_{uckGrade}<4010:3.188+0\left|L_{uckGrade}-4000\right|,4010 \le L_{uckGrade}<4050:3.189+0\left|L_{uckGrade}-4010\right|,4050 \le L_{uckGrade}<4060:3.197+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4080:3.198+0\left|L_{uckGrade}-4060\right|,4080 \le L_{uckGrade}<4090:3.202+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4110:3.203+0\left|L_{uckGrade}-4090\right|,4110 \le L_{uckGrade}<4120:3.207+0\left|L_{uckGrade}-4110\right|,4120 \le L_{uckGrade}<4130:3.208+0\left|L_{uckGrade}-4120\right|,4130 \le L_{uckGrade}<4140:3.21+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4160:3.211+0\left|L_{uckGrade}-4140\right|,4160 \le L_{uckGrade}<4170:3.215+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4180:3.216+0\left|L_{uckGrade}-4170\right|,4180 \le L_{uckGrade}<4190:3.218+0\left|L_{uckGrade}-4180\right|,4190 \le L_{uckGrade}<4200:3.219+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4220:3.221+0\left|L_{uckGrade}-4200\right|,4220 \le L_{uckGrade}<4230:3.223+0\left|L_{uckGrade}-4220\right|,4230 \le L_{uckGrade}<4240:3.225+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:3.226+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4270:3.228+0\left|L_{uckGrade}-4250\right|,4270 \le L_{uckGrade}<4280:3.23+0\left|L_{uckGrade}-4270\right|,4280 \le L_{uckGrade}<4300:3.232+0\left|L_{uckGrade}-4280\right|,4300 \le L_{uckGrade}<4310:3.234+0\left|L_{uckGrade}-4300\right|,4310 \le L_{uckGrade}<4340:3.236+0\left|L_{uckGrade}-4310\right|,4340 \le L_{uckGrade}<4350:3.239+0\left|L_{uckGrade}-4340\right|,4350 \le L_{uckGrade}<4430:3.241+0\left|L_{uckGrade}-4350\right|,4430 \le L_{uckGrade}<4440:3.249+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4470:3.251+0\left|L_{uckGrade}-4440\right|,4470 \le L_{uckGrade}<4480:3.254+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4560:3.254+0\left|L_{uckGrade}-4480\right|,4560 \le L_{uckGrade}<4570:3.262+0\left|L_{uckGrade}-4560\right|,4570 \le L_{uckGrade}<4600:3.262+0\left|L_{uckGrade}-4570\right|,4600 \le L_{uckGrade}<4610:3.265+0\left|L_{uckGrade}-4600\right|,4610 \le L_{uckGrade}<4630:3.265+0\left|L_{uckGrade}-4610\right|,4630 \le L_{uckGrade}<4640:3.267+0\left|L_{uckGrade}-4630\right|,4640 \le L_{uckGrade}<4660:3.267+0\left|L_{uckGrade}-4640\right|,4660 \le L_{uckGrade}<4670:3.269+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4690:3.269+0\left|L_{uckGrade}-4670\right|,4690 \le L_{uckGrade}<4700:3.271+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4710:3.271+0\left|L_{uckGrade}-4700\right|,4710 \le L_{uckGrade}<4720:3.272+0\left|L_{uckGrade}-4710\right|,4720 \le L_{uckGrade}<4730:3.272+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4740:3.273+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4750:3.273+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4760:3.274+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4770:3.274+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4790:3.275+0\left|L_{uckGrade}-4770\right|,4790 \le L_{uckGrade}<4800:3.275+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4820:3.276+0\left|L_{uckGrade}-4800\right|,4820 \le L_{uckGrade}<4830:3.276+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4850:3.277+0\left|L_{uckGrade}-4830\right|,4850 \le L_{uckGrade}<4860:3.277+0\left|L_{uckGrade}-4850\right|,4860 \le L_{uckGrade}<4890:3.278+0\left|L_{uckGrade}-4860\right|,4890 \le L_{uckGrade}<4900:3.278+0\left|L_{uckGrade}-4890\right|,4900 \le L_{uckGrade}<4980:3.279+0\left|L_{uckGrade}-4900\right|,4980 \le L_{uckGrade}<4990:3.279+0\left|L_{uckGrade}-4980\right|,4990 \le L_{uckGrade}<5000:3.28+0\left|L_{uckGrade}-4990\right|\right\}
See Example for how to use.
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L_{uckGrade07}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<20:1+0.001\left|L_{uckGrade}-0\right|,20 \le L_{uckGrade}<30:1.022+0.001\left|L_{uckGrade}-20\right|,30 \le L_{uckGrade}<50:1.032+0.001\left|L_{uckGrade}-30\right|,50 \le L_{uckGrade}<60:1.054+0.001\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<80:1.064+0.001\left|L_{uckGrade}-60\right|,80 \le L_{uckGrade}<90:1.086+0.001\left|L_{uckGrade}-80\right|,90 \le L_{uckGrade}<110:1.096+0.001\left|L_{uckGrade}-90\right|,110 \le L_{uckGrade}<120:1.118+0.001\left|L_{uckGrade}-110\right|,120 \le L_{uckGrade}<130:1.128+0.001\left|L_{uckGrade}-120\right|,130 \le L_{uckGrade}<140:1.139+0.001\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<150:1.149+0.001\left|L_{uckGrade}-140\right|,150 \le L_{uckGrade}<160:1.16+0.001\left|L_{uckGrade}-150\right|,160 \le L_{uckGrade}<170:1.17+0.001\left|L_{uckGrade}-160\right|,170 \le L_{uckGrade}<180:1.181+0.001\left|L_{uckGrade}-170\right|,180 \le L_{uckGrade}<190:1.191+0.001\left|L_{uckGrade}-180\right|,190 \le L_{uckGrade}<210:1.202+0.001\left|L_{uckGrade}-190\right|,210 \le L_{uckGrade}<220:1.222+0.001\left|L_{uckGrade}-210\right|,220 \le L_{uckGrade}<240:1.233+0.001\left|L_{uckGrade}-220\right|,240 \le L_{uckGrade}<250:1.253+0.001\left|L_{uckGrade}-240\right|,250 \le L_{uckGrade}<290:1.264+0.001\left|L_{uckGrade}-250\right|,290 \le L_{uckGrade}<300:1.304+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<450:1.315+0.001\left|L_{uckGrade}-300\right|,450 \le L_{uckGrade}<460:1.465+0.001\left|L_{uckGrade}-450\right|,460 \le L_{uckGrade}<500:1.474+0.001\left|L_{uckGrade}-460\right|,500 \le L_{uckGrade}<510:1.514+0.001\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<530:1.523+0.001\left|L_{uckGrade}-510\right|,530 \le L_{uckGrade}<540:1.543+0.001\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<560:1.552+0.001\left|L_{uckGrade}-540\right|,560 \le L_{uckGrade}<570:1.572+0.001\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<580:1.581+0.001\left|L_{uckGrade}-570\right|,580 \le L_{uckGrade}<590:1.591+0.001\left|L_{uckGrade}-580\right|,590 \le L_{uckGrade}<600:1.6+0.001\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<610:1.61+0.001\left|L_{uckGrade}-600\right|,610 \le L_{uckGrade}<620:1.619+0.001\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<630:1.629+0.001\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<640:1.638+0.001\left|L_{uckGrade}-630\right|,640 \le L_{uckGrade}<660:1.648+0.001\left|L_{uckGrade}-640\right|,660 \le L_{uckGrade}<670:1.666+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:1.676+0.001\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<690:1.685+0.001\left|L_{uckGrade}-680\right|,690 \le L_{uckGrade}<720:1.695+0.001\left|L_{uckGrade}-690\right|,720 \le L_{uckGrade}<730:1.722+0.001\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<770:1.732+0.001\left|L_{uckGrade}-730\right|,770 \le L_{uckGrade}<780:1.768+0.001\left|L_{uckGrade}-770\right|,780 \le L_{uckGrade}<890:1.778+0.001\left|L_{uckGrade}-780\right|,890 \le L_{uckGrade}<900:1.877+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<950:1.885+0.001\left|L_{uckGrade}-900\right|,950 \le L_{uckGrade}<960:1.93+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<980:1.938+0.001\left|L_{uckGrade}-960\right|,980 \le L_{uckGrade}<990:1.956+0.001\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1010:1.964+0.001\left|L_{uckGrade}-990\right|,1010 \le L_{uckGrade}<1020:1.982+0.001\left|L_{uckGrade}-1010\right|,1020 \le L_{uckGrade}<1040:1.99+0.001\left|L_{uckGrade}-1020\right|,1040 \le L_{uckGrade}<1050:2.008+0.001\left|L_{uckGrade}-1040\right|,1050 \le L_{uckGrade}<1060:2.016+0.001\left|L_{uckGrade}-1050\right|,1060 \le L_{uckGrade}<1070:2.025+0.001\left|L_{uckGrade}-1060\right|,1070 \le L_{uckGrade}<1080:2.033+0.001\left|L_{uckGrade}-1070\right|,1080 \le L_{uckGrade}<1090:2.042+0.001\left|L_{uckGrade}-1080\right|,1090 \le L_{uckGrade}<1100:2.05+0.001\left|L_{uckGrade}-1090\right|,1100 \le L_{uckGrade}<1120:2.059+0.001\left|L_{uckGrade}-1100\right|,1120 \le L_{uckGrade}<1130:2.075+0.001\left|L_{uckGrade}-1120\right|,1130 \le L_{uckGrade}<1150:2.084+0.001\left|L_{uckGrade}-1130\right|,1150 \le L_{uckGrade}<1160:2.1+0.001\left|L_{uckGrade}-1150\right|,1160 \le L_{uckGrade}<1180:2.109+0.001\left|L_{uckGrade}-1160\right|,1180 \le L_{uckGrade}<1190:2.125+0.001\left|L_{uckGrade}-1180\right|,1190 \le L_{uckGrade}<1240:2.134+0.001\left|L_{uckGrade}-1190\right|,1240 \le L_{uckGrade}<1250:2.174+0.001\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1360:2.183+0.001\left|L_{uckGrade}-1250\right|,1360 \le L_{uckGrade}<1370:2.271+0.001\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1410:2.278+0.001\left|L_{uckGrade}-1370\right|,1410 \le L_{uckGrade}<1420:2.31+0.001\left|L_{uckGrade}-1410\right|,1420 \le L_{uckGrade}<1440:2.317+0.001\left|L_{uckGrade}-1420\right|,1440 \le L_{uckGrade}<1450:2.333+0.001\left|L_{uckGrade}-1440\right|,1450 \le L_{uckGrade}<1470:2.34+0.001\left|L_{uckGrade}-1450\right|,1470 \le L_{uckGrade}<1480:2.356+0.001\left|L_{uckGrade}-1470\right|,1480 \le L_{uckGrade}<1500:2.363+0.001\left|L_{uckGrade}-1480\right|,1500 \le L_{uckGrade}<1510:2.379+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:2.386+0.001\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1530:2.394+0.001\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1540:2.401+0.001\left|L_{uckGrade}-1530\right|,1540 \le L_{uckGrade}<1550:2.409+0.001\left|L_{uckGrade}-1540\right|,1550 \le L_{uckGrade}<1560:2.416+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1580:2.424+0.001\left|L_{uckGrade}-1560\right|,1580 \le L_{uckGrade}<1590:2.438+0.001\left|L_{uckGrade}-1580\right|,1590 \le L_{uckGrade}<1600:2.446+0.001\left|L_{uckGrade}-1590\right|,1600 \le L_{uckGrade}<1610:2.453+0.001\left|L_{uckGrade}-1600\right|,1610 \le L_{uckGrade}<1640:2.461+0.001\left|L_{uckGrade}-1610\right|,1640 \le L_{uckGrade}<1650:2.482+0.001\left|L_{uckGrade}-1640\right|,1650 \le L_{uckGrade}<1680:2.49+0.001\left|L_{uckGrade}-1650\right|,1680 \le L_{uckGrade}<1690:2.511+0.001\left|L_{uckGrade}-1680\right|,1690 \le L_{uckGrade}<1840:2.519+0.001\left|L_{uckGrade}-1690\right|,1840 \le L_{uckGrade}<1850:2.624+0.001\left|L_{uckGrade}-1840\right|,1850 \le L_{uckGrade}<1880:2.63+0.001\left|L_{uckGrade}-1850\right|,1880 \le L_{uckGrade}<1890:2.651+0.001\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1920:2.657+0.001\left|L_{uckGrade}-1890\right|,1920 \le L_{uckGrade}<1930:2.678+0.001\left|L_{uckGrade}-1920\right|,1930 \le L_{uckGrade}<1940:2.684+0.001\left|L_{uckGrade}-1930\right|,1940 \le L_{uckGrade}<1950:2.691+0.001\left|L_{uckGrade}-1940\right|,1950 \le L_{uckGrade}<1970:2.697+0.001\left|L_{uckGrade}-1950\right|,1970 \le L_{uckGrade}<1980:2.711+0.001\left|L_{uckGrade}-1970\right|,1980 \le L_{uckGrade}<1990:2.717+0.001\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2000:2.724+0.001\left|L_{uckGrade}-1990\right|,2000 \le L_{uckGrade}<2010:2.73+0.001\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2020:2.737+0.001\left|L_{uckGrade}-2010\right|,2020 \le L_{uckGrade}<2030:2.743+0.001\left|L_{uckGrade}-2020\right|,2030 \le L_{uckGrade}<2050:2.75+0.001\left|L_{uckGrade}-2030\right|,2050 \le L_{uckGrade}<2060:2.762+0.001\left|L_{uckGrade}-2050\right|,2060 \le L_{uckGrade}<2080:2.769+0.001\left|L_{uckGrade}-2060\right|,2080 \le L_{uckGrade}<2090:2.781+0.001\left|L_{uckGrade}-2080\right|,2090 \le L_{uckGrade}<2120:2.788+0.001\left|L_{uckGrade}-2090\right|,2120 \le L_{uckGrade}<2130:2.806+0.001\left|L_{uckGrade}-2120\right|,2130 \le L_{uckGrade}<2180:2.813+0.001\left|L_{uckGrade}-2130\right|,2180 \le L_{uckGrade}<2190:2.843+0.001\left|L_{uckGrade}-2180\right|,2190 \le L_{uckGrade}<2270:2.85+0.001\left|L_{uckGrade}-2190\right|,2270 \le L_{uckGrade}<2280:2.898+0\left|L_{uckGrade}-2270\right|,2280 \le L_{uckGrade}<2330:2.903+0.001\left|L_{uckGrade}-2280\right|,2330 \le L_{uckGrade}<2340:2.933+0.001\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2370:2.938+0.001\left|L_{uckGrade}-2340\right|,2370 \le L_{uckGrade}<2380:2.956+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2400:2.961+0.001\left|L_{uckGrade}-2380\right|,2400 \le L_{uckGrade}<2410:2.973+0.001\left|L_{uckGrade}-2400\right|,2410 \le L_{uckGrade}<2420:2.978+0.001\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2430:2.984+0\left|L_{uckGrade}-2420\right|,2430 \le L_{uckGrade}<2440:2.989+0.001\left|L_{uckGrade}-2430\right|,2440 \le L_{uckGrade}<2450:2.995+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2460:3+0.001\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:3.006+0.001\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:3.011+0.001\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2490:3.017+0\left|L_{uckGrade}-2480\right|,2490 \le L_{uckGrade}<2500:3.022+0.001\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2520:3.028+0\left|L_{uckGrade}-2500\right|,2520 \le L_{uckGrade}<2530:3.038+0.001\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2550:3.044+0\left|L_{uckGrade}-2530\right|,2550 \le L_{uckGrade}<2560:3.054+0.001\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2580:3.06+0\left|L_{uckGrade}-2560\right|,2580 \le L_{uckGrade}<2590:3.07+0.001\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2650:3.076+0\left|L_{uckGrade}-2590\right|,2650 \le L_{uckGrade}<2660:3.106+0.001\left|L_{uckGrade}-2650\right|,2660 \le L_{uckGrade}<2720:3.112+0\left|L_{uckGrade}-2660\right|,2720 \le L_{uckGrade}<2730:3.142+0\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2790:3.146+0.001\left|L_{uckGrade}-2730\right|,2790 \le L_{uckGrade}<2800:3.176+0\left|L_{uckGrade}-2790\right|,2800 \le L_{uckGrade}<2820:3.18+0\left|L_{uckGrade}-2800\right|,2820 \le L_{uckGrade}<2830:3.19+0\left|L_{uckGrade}-2820\right|,2830 \le L_{uckGrade}<2850:3.194+0.001\left|L_{uckGrade}-2830\right|,2850 \le L_{uckGrade}<2860:3.204+0\left|L_{uckGrade}-2850\right|,2860 \le L_{uckGrade}<2880:3.208+0\left|L_{uckGrade}-2860\right|,2880 \le L_{uckGrade}<2890:3.218+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2900:3.222+0\left|L_{uckGrade}-2890\right|,2900 \le L_{uckGrade}<2910:3.227+0\left|L_{uckGrade}-2900\right|,2910 \le L_{uckGrade}<2920:3.231+0.001\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2930:3.236+0\left|L_{uckGrade}-2920\right|,2930 \le L_{uckGrade}<2940:3.24+0\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2950:3.245+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2960:3.249+0\left|L_{uckGrade}-2950\right|,2960 \le L_{uckGrade}<2970:3.254+0\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<2980:3.258+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<3000:3.263+0\left|L_{uckGrade}-2980\right|,3000 \le L_{uckGrade}<3010:3.271+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3040:3.276+0\left|L_{uckGrade}-3010\right|,3040 \le L_{uckGrade}<3050:3.288+0.001\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3100:3.293+0\left|L_{uckGrade}-3050\right|,3100 \le L_{uckGrade}<3110:3.313+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3200:3.318+0\left|L_{uckGrade}-3110\right|,3200 \le L_{uckGrade}<3210:3.354+0\left|L_{uckGrade}-3200\right|,3210 \le L_{uckGrade}<3260:3.357+0\left|L_{uckGrade}-3210\right|,3260 \le L_{uckGrade}<3270:3.377+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3290:3.38+0\left|L_{uckGrade}-3270\right|,3290 \le L_{uckGrade}<3300:3.388+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3320:3.391+0\left|L_{uckGrade}-3300\right|,3320 \le L_{uckGrade}<3330:3.399+0\left|L_{uckGrade}-3320\right|,3330 \le L_{uckGrade}<3350:3.402+0\left|L_{uckGrade}-3330\right|,3350 \le L_{uckGrade}<3360:3.41+0\left|L_{uckGrade}-3350\right|,3360 \le L_{uckGrade}<3370:3.413+0\left|L_{uckGrade}-3360\right|,3370 \le L_{uckGrade}<3380:3.417+0\left|L_{uckGrade}-3370\right|,3380 \le L_{uckGrade}<3390:3.42+0\left|L_{uckGrade}-3380\right|,3390 \le L_{uckGrade}<3400:3.424+0\left|L_{uckGrade}-3390\right|,3400 \le L_{uckGrade}<3410:3.427+0\left|L_{uckGrade}-3400\right|,3410 \le L_{uckGrade}<3430:3.431+0\left|L_{uckGrade}-3410\right|,3430 \le L_{uckGrade}<3440:3.437+0\left|L_{uckGrade}-3430\right|,3440 \le L_{uckGrade}<3450:3.441+0\left|L_{uckGrade}-3440\right|,3450 \le L_{uckGrade}<3460:3.444+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3480:3.448+0\left|L_{uckGrade}-3460\right|,3480 \le L_{uckGrade}<3490:3.454+0\left|L_{uckGrade}-3480\right|,3490 \le L_{uckGrade}<3530:3.458+0\left|L_{uckGrade}-3490\right|,3530 \le L_{uckGrade}<3540:3.47+0\left|L_{uckGrade}-3530\right|,3540 \le L_{uckGrade}<3690:3.474+0\left|L_{uckGrade}-3540\right|,3690 \le L_{uckGrade}<3700:3.519+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3740:3.521+0\left|L_{uckGrade}-3700\right|,3740 \le L_{uckGrade}<3750:3.533+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3770:3.535+0\left|L_{uckGrade}-3750\right|,3770 \le L_{uckGrade}<3780:3.541+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3800:3.543+0\left|L_{uckGrade}-3780\right|,3800 \le L_{uckGrade}<3810:3.549+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<3820:3.551+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3830:3.554+0\left|L_{uckGrade}-3820\right|,3830 \le L_{uckGrade}<3840:3.556+0\left|L_{uckGrade}-3830\right|,3840 \le L_{uckGrade}<3850:3.559+0\left|L_{uckGrade}-3840\right|,3850 \le L_{uckGrade}<3860:3.561+0\left|L_{uckGrade}-3850\right|,3860 \le L_{uckGrade}<3870:3.564+0\left|L_{uckGrade}-3860\right|,3870 \le L_{uckGrade}<3880:3.566+0\left|L_{uckGrade}-3870\right|,3880 \le L_{uckGrade}<3890:3.569+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3900:3.571+0\left|L_{uckGrade}-3890\right|,3900 \le L_{uckGrade}<3920:3.574+0\left|L_{uckGrade}-3900\right|,3920 \le L_{uckGrade}<3930:3.578+0\left|L_{uckGrade}-3920\right|,3930 \le L_{uckGrade}<3960:3.581+0\left|L_{uckGrade}-3930\right|,3960 \le L_{uckGrade}<3970:3.587+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<4010:3.59+0\left|L_{uckGrade}-3970\right|,4010 \le L_{uckGrade}<4020:3.598+0\left|L_{uckGrade}-4010\right|,4020 \le L_{uckGrade}<4140:3.601+0\left|L_{uckGrade}-4020\right|,4140 \le L_{uckGrade}<4150:3.625+0\left|L_{uckGrade}-4140\right|,4150 \le L_{uckGrade}<4190:3.626+0\left|L_{uckGrade}-4150\right|,4190 \le L_{uckGrade}<4200:3.634+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4230:3.635+0\left|L_{uckGrade}-4200\right|,4230 \le L_{uckGrade}<4240:3.641+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:3.642+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4260:3.644+0\left|L_{uckGrade}-4250\right|,4260 \le L_{uckGrade}<4280:3.645+0\left|L_{uckGrade}-4260\right|,4280 \le L_{uckGrade}<4290:3.649+0\left|L_{uckGrade}-4280\right|,4290 \le L_{uckGrade}<4300:3.65+0\left|L_{uckGrade}-4290\right|,4300 \le L_{uckGrade}<4310:3.652+0\left|L_{uckGrade}-4300\right|,4310 \le L_{uckGrade}<4320:3.653+0\left|L_{uckGrade}-4310\right|,4320 \le L_{uckGrade}<4330:3.655+0\left|L_{uckGrade}-4320\right|,4330 \le L_{uckGrade}<4340:3.656+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4360:3.658+0\left|L_{uckGrade}-4340\right|,4360 \le L_{uckGrade}<4370:3.66+0\left|L_{uckGrade}-4360\right|,4370 \le L_{uckGrade}<4380:3.662+0\left|L_{uckGrade}-4370\right|,4380 \le L_{uckGrade}<4390:3.663+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4420:3.665+0\left|L_{uckGrade}-4390\right|,4420 \le L_{uckGrade}<4430:3.668+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4470:3.67+0\left|L_{uckGrade}-4430\right|,4470 \le L_{uckGrade}<4480:3.674+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4610:3.676+0\left|L_{uckGrade}-4480\right|,4610 \le L_{uckGrade}<4620:3.689+0\left|L_{uckGrade}-4610\right|,4620 \le L_{uckGrade}<4660:3.689+0\left|L_{uckGrade}-4620\right|,4660 \le L_{uckGrade}<4670:3.693+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4690:3.693+0\left|L_{uckGrade}-4670\right|,4690 \le L_{uckGrade}<4700:3.695+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4720:3.695+0\left|L_{uckGrade}-4700\right|,4720 \le L_{uckGrade}<4730:3.697+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4740:3.697+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4750:3.698+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4760:3.698+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4770:3.699+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4780:3.699+0\left|L_{uckGrade}-4770\right|,4780 \le L_{uckGrade}<4790:3.7+0\left|L_{uckGrade}-4780\right|,4790 \le L_{uckGrade}<4800:3.7+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4810:3.701+0\left|L_{uckGrade}-4800\right|,4810 \le L_{uckGrade}<4820:3.701+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4840:3.702+0\left|L_{uckGrade}-4820\right|,4840 \le L_{uckGrade}<4850:3.702+0\left|L_{uckGrade}-4840\right|,4850 \le L_{uckGrade}<4870:3.703+0\left|L_{uckGrade}-4850\right|,4870 \le L_{uckGrade}<4880:3.703+0\left|L_{uckGrade}-4870\right|,4880 \le L_{uckGrade}<4910:3.704+0\left|L_{uckGrade}-4880\right|,4910 \le L_{uckGrade}<4920:3.704+0\left|L_{uckGrade}-4910\right|,4920 \le L_{uckGrade}<5000:3.705+0\left|L_{uckGrade}-4920\right|\right\}
See Example for how to use.
Probabilities from Luck
To calculate the drop rate at X Luck there are three steps.
- For each Luck Grade's Drop Rate apply the corresponding Luck Scalar.
- Find the dot product between the Luck Scalar vector at X Luck and the Base Rate.
(This is the same as adding up each term from the first step.)
- For each term in the first step divide by the dot product from the second step to get the new drop rate at X Luck.
The table below is the Drop Rate table of Quest Drops.
Every monster with a quest drop uses the Drop Rate table.
However, depending on the monster's Loot Drop Table, many of the Luck Grade rates will be associated with dropping nothing.
And in other instances, like Demon Centaur, a Luck Grade's rate may be split between two Loot Drops.
This will not affect the calculations below, but they will determine an individual item's probability.
Luck Grade |
Drop Rate
|
Junk |
220
|
Poor |
250
|
Common |
200
|
Uncommon |
150
|
Rare |
100
|
Epic |
50
|
Legendary |
20
|
Unique |
10
|
Click expand to see the calculations for 0 and 250 Luck.
Expand
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.
Expand
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.
Enchantment Stats
Stats that come from weapons, armors or jewelry imbued with item Enchantments.
Enchantments that aren't traditional Stats and only exist in a Damage/Healing formula are listed below and can also be found in Damage_Calculation and Healing.
For the possible values of Enchantments and their historical rolls, see Enchantment Values
Unimplemented Stats
These stats are not yet implemented.
Utility Effectiveness
Determines the bonus effectiveness of your utility items
I can't believe that the physical and magical curves in a game could be modified to be the same. This is too strange. Are the basic damage of melee weapons and magic weapons the same concept? What is the difference between physical damage and magical damage? This is a ridiculous change. I think there is a better solution to weaken the magic profession.I think game planners are being lazy when making this decision.
With this latest patch the notes have:
- Flattened the Physical Damage Bonus (PDB) curve at the upper end.
- Updated the Magical Damage Bonus (MDB) curve so it now matches the new PDB curve.
But in testing last night I noticed that the PDB chart still matches what is in game, while the MDB chart doesn't. Was the PDB chart updated while the other wasn't or is something else going on?
is luck working?
Something seems off with the physical power and the Magic Power chart, as a naked fighter I have 16 Physical Power, shouldn't I have 15? When I equip riveted gloves it jumps to 17 which is correct according to the graph. The same goes for Magic Power
Numbers between Magical Resistance chart and in game (Magic Resist Rating) doesn't match
A nude Fighter has 15 will which equals to 30 Magic Rating, which equals to 7,8 Magic Resis OK
But
A nude Druid has 18 will, looking at the chart this should be equal to 30 + (from 15 to 33: 4 each) 3 X 4 = 12 --> 42 Magic Resist Rating which would be equal to (33 magic resis bottom segment) 9% + (from 33 to 53: 0,3 each) 9 X 0,3 = 11,7% Magic Resis
However in game a nude Druid is displayed with 52 Magic Rating and 14,7% Magic Resis (A player with 52 magic resis does actually adds up to 14,7 magic resis, so it is the will conversion which is different in the chart)
200——300护甲值的物理伤害减免实际上比统计表上的少了0.1%
Which one is better to stack if fighting against Wizard/Warlock?
title
Did they revert the armor scaling nerf? Why does it say 175 to 230 = 0.3% each, up to 48%, it used to be 0.25% per after they nerfed it?
Why can't the loss duration bonus and gain duration bonus be applied to others?
"Cooldown Reduction reduces the cooldowns of skills/perks. Reduced cooldown length = Base Cooldown * (1 - Cooldown Reduction)
Note that perk cooldowns are in the form of a buff/debuff and are additionally affected by Buff/Debuff Duration. Reduced cooldown length = Post buff/debuff duration cooldown * (1 - Cooldown Reduction)"
Since some skills/perk also is affected by Buff/Debuff, how do you implement that to the total skill's cooldown time?
The Item Equip Speed speed section says that weapons equip instantly and therefore don't benefit from the stat, but equipping a Hand Crossbow as a Rogue does seem to have a progress bar (progress circle?). I haven't tested anything with other classes.
Physical damage reduction curve currently isn't correct; they updated it about 3 days ago for Early Access Hotfix #55: "Slightly lowered the amount of Physical Damage Resistance earned per Armor Rating within the upper sweet spot of the curve (~200 Armor Rating.)".
I tested it to double check, and the armor does indeed have some new sort of scaling in the 175-230 region that isn't described above. When I increased armor from 175 to 181, I gained 1.5% reduction instead of the expected 1.8% damage reduction (33% total), and when I increased it by another 15 armor to 196, instead of gaining 4.5% reduction, I only gained 3.7% (36.7% total)
After reading over this wiki to better understand the game and how it works, and finally reaching this page, I feel like this is something I need to point out and see if anyone else agrees: Knowledge is a really frustrating stat because of it's inequality between martial and caster classes.
I understand that Ironmace can't just give every non-caster class a base 5 in Knowledge like Barb has and allocate those extra points somewhere more useful, but it's also somewhat annoying to see that it's not even uniform amongst the other martial classes. Rogue has 10, Ranger has 12, and Fighter has 15. Granted, Fighter has 15 in *everything*, but still, I find it strange and a little irritating that the only true "dump stat" for martials is still at least a two-digit number for everything but Barb. I know Multiclassing used to be a thing sometime before the current update, which I guess is the only reason that Knowledge might be useful on a martial class, but without Multiclassing in the game currently it just feels bad to see these points allocated into a stat that does precisely nothing for martials.
And even WITH Multiclassing, only Fighter has a base Knowledge stat comparable to any of the casting classes (Warlock in particular with their base 15) to make it actually useful in any degree - which feels wrong to me, coming from a Dungeons & Dragons background. In Dungeons & Dragons, Rangers are half-casters while Eldritch Knight Fighters are only third-casters - same as Arcane Trickster Rogues. Yet based on Knowledge in this game, Fighters are on par with Warlocks, Rangers are like half-casters, and Rogues like third-casters. I know that Dark and Darker isn't meant to be one-to-one with Dungeons & Dragons (despite both sharing the D&D/DnD abbreviation, humorously enough), but it still just feels wrong to me. Even from a purely Dark and Darker perspective, if the intent is to give some martials a little bit better Knowledge to incentivize/permit multiclassing into casting, would 10 or 12 base Knowledge even be worth it? Even base 15 Knowledge feels a little limited with it's Memory Cap of 9; a base Cap of 6, and especially 4, just sounds like an awful waste of a Skill slot and Weapon slot to me. And that's even before considering the extra Knowledge, Memory Cap, Casting Speed, etc. rolls you'd want on gear just to catch up and make multiclass casting worth it - rolls which are actively competing against the standard desirable rolls for Rogues and Rangers.
Does anyone else share this sentiment about Knowledge on non-casters being a point of contention? I almost feel like Knowledge should have some other effect that isn't specifically casting-related. After all, every other stat in the game has something it influences that makes it necessary to some degree, like Action and Regular Action Speeds. Why should Knowledge be the only one that gives absolutely no upside to classes that don't have spells, yet still have upwards of 10 Knowledge? I don't even have a proposition as to what Knowledge could influence, because everything else stat-wise makes sense and is well-thought out. Knowledge just feels really weird as a stat that's only important for casters. It almost makes me think that it should be removed, and things like Memory Capacity, Recovery, and Spellcasting Speed should be delegated to other stats. But that would be unfair to casters in the same way that it's currently unfair to martial classes (well, not the SAME way; more like the opposite side of the same coin). I don't know, maybe I'm weird for thinking about it in this way, but seeing how the other stats work compared to Knowledge, it just makes Knowledge feel somewhat flawed, without an obvious fix or solution.
The curve and the spell casting speed calculation are wrong. We now have more spell casting speed than mentioned on the wiki. I did the tests by comparing and calculating with the knowledge on the game. The same may be true of regular interaction speed, which was changed at the same time as spell casting speed.
If a class can manage pull off more than 100% Armor Penetration, Example: 125% Armor Penetration 58 Windlass Crossbow
Will it do a bit more damage?
Thank you in advance!
Does Poisoned Weapon from Rogue is affected by Magic Resist?
What stats should we prioritize to increase damage with bows?
I know that the current move speed limit is 350, if my stats are calculated to 380 and I use a -30 weapon, will I move at 350 or 320?
Does this work, assuming I've got the weapon out in hand when I interact?
Does weapon damage on a spellbook make the spells more powerful? hit more?
Is any stat affect reload speed for crossbow and bow ?