Luck

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

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

Whoever opens a container first or deals the killing blow to a monster is the person whose luck is used to calculate the drops.

Any individual point of Luck contributes to a change in drop chances. However, luck is hard capped to 500; any points beyond 500 won't make a difference.

Ideal Sources of Luck:

• 30 from max level religion blessing
• 100 from Bard's Wanderer's Luck.
• 150 luck roll from a Great Potion of Luck
• 1200 from max enchantment rolls on unique gear
  • 200 each on Chest, Legs, Necklace
  • 100 each on Head, Foot, Hand, Cloak, Ring (x2)

Loot Tables and Drop Rate Tables

Each drop instance makes use of three pieces of information: the Loot table, the Drop Rate table, and the player's Luck.

Loot 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 Table and Luck Grade, will always have the same probability of dropping.
However, be aware that Monsters and Containers can have multiple Loot 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.
The Elite variant of Lich rolls their main gear Loot and Drop tables a total of 3 times, theoretically making it possible (though extremely unlikely) to get 3 identical Artifacts from a single Elite Lich kill.

Luck Scalar

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

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

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

Additionally, luck works with a hidden property called Luck Grade. Many loot tables will match item rarity one to one with item luck grade, but there are exceptions, see the Cave Troll's quest drops for a counterexample.

Luck Scalar Graphs

Updated for Patch:6.11#Hotfix 114!

LaTeX Formula

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

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

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

See Example for how to use.

LaTeX Formula

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

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

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

See Example for how to use.

LaTeX Formula

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

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

L_{uckGrade02}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<500:1+-0.001\left|L_{uckGrade}-0\right|\right\}

See Example for how to use.

LaTeX Formula

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

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

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

See Example for how to use.

LaTeX Formula

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

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

L_{uckGrade04}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<13:1+0.003\left|L_{uckGrade}-0\right|,13 \le L_{uckGrade}<14:1.039+0.002\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<22:1.041+0.003\left|L_{uckGrade}-14\right|,22 \le L_{uckGrade}<23:1.065+0.002\left|L_{uckGrade}-22\right|,23 \le L_{uckGrade}<29:1.067+0.003\left|L_{uckGrade}-23\right|,29 \le L_{uckGrade}<30:1.085+0.002\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<34:1.087+0.003\left|L_{uckGrade}-30\right|,34 \le L_{uckGrade}<35:1.099+0.002\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<39:1.101+0.003\left|L_{uckGrade}-35\right|,39 \le L_{uckGrade}<40:1.113+0.002\left|L_{uckGrade}-39\right|,40 \le L_{uckGrade}<43:1.115+0.003\left|L_{uckGrade}-40\right|,43 \le L_{uckGrade}<44:1.124+0.002\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<47:1.126+0.003\left|L_{uckGrade}-44\right|,47 \le L_{uckGrade}<48:1.135+0.002\left|L_{uckGrade}-47\right|,48 \le L_{uckGrade}<50:1.137+0.003\left|L_{uckGrade}-48\right|,50 \le L_{uckGrade}<51:1.143+0.002\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<53:1.145+0.003\left|L_{uckGrade}-51\right|,53 \le L_{uckGrade}<54:1.151+0.002\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<56:1.153+0.003\left|L_{uckGrade}-54\right|,56 \le L_{uckGrade}<57:1.159+0.002\left|L_{uckGrade}-56\right|,57 \le L_{uckGrade}<59:1.161+0.003\left|L_{uckGrade}-57\right|,59 \le L_{uckGrade}<60:1.167+0.002\left|L_{uckGrade}-59\right|,60 \le L_{uckGrade}<62:1.169+0.003\left|L_{uckGrade}-60\right|,62 \le L_{uckGrade}<63:1.175+0.002\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<65:1.177+0.003\left|L_{uckGrade}-63\right|,65 \le L_{uckGrade}<66:1.183+0.002\left|L_{uckGrade}-65\right|,66 \le L_{uckGrade}<67:1.185+0.003\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<68:1.188+0.002\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<70:1.19+0.003\left|L_{uckGrade}-68\right|,70 \le L_{uckGrade}<71:1.196+0.002\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<72:1.198+0.003\left|L_{uckGrade}-71\right|,72 \le L_{uckGrade}<73:1.201+0.002\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<74:1.203+0.003\left|L_{uckGrade}-73\right|,74 \le L_{uckGrade}<75:1.206+0.002\left|L_{uckGrade}-74\right|,75 \le L_{uckGrade}<76:1.208+0.003\left|L_{uckGrade}-75\right|,76 \le L_{uckGrade}<77:1.211+0.002\left|L_{uckGrade}-76\right|,77 \le L_{uckGrade}<79:1.213+0.003\left|L_{uckGrade}-77\right|,79 \le L_{uckGrade}<80:1.219+0.002\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<81:1.221+0.003\left|L_{uckGrade}-80\right|,81 \le L_{uckGrade}<82:1.224+0.002\left|L_{uckGrade}-81\right|,82 \le L_{uckGrade}<83:1.226+0.003\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<84:1.229+0.002\left|L_{uckGrade}-83\right|,84 \le L_{uckGrade}<85:1.231+0.003\left|L_{uckGrade}-84\right|,85 \le L_{uckGrade}<86:1.234+0.002\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<87:1.236+0.003\left|L_{uckGrade}-86\right|,87 \le L_{uckGrade}<88:1.239+0.002\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<89:1.241+0.003\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<91:1.244+0.002\left|L_{uckGrade}-89\right|,91 \le L_{uckGrade}<92:1.248+0.003\left|L_{uckGrade}-91\right|,92 \le L_{uckGrade}<93:1.251+0.002\left|L_{uckGrade}-92\right|,93 \le L_{uckGrade}<94:1.253+0.003\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<95:1.256+0.002\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<96:1.258+0.003\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<98:1.261+0.002\left|L_{uckGrade}-96\right|,98 \le L_{uckGrade}<99:1.265+0.003\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<100:1.268+0.002\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<101:1.27+0.003\left|L_{uckGrade}-100\right|,101 \le L_{uckGrade}<103:1.273+0.002\left|L_{uckGrade}-101\right|,103 \le L_{uckGrade}<104:1.277+0.003\left|L_{uckGrade}-103\right|,104 \le L_{uckGrade}<105:1.28+0.002\left|L_{uckGrade}-104\right|,105 \le L_{uckGrade}<106:1.282+0.003\left|L_{uckGrade}-105\right|,106 \le L_{uckGrade}<108:1.285+0.002\left|L_{uckGrade}-106\right|,108 \le L_{uckGrade}<109:1.289+0.003\left|L_{uckGrade}-108\right|,109 \le L_{uckGrade}<111:1.292+0.002\left|L_{uckGrade}-109\right|,111 \le L_{uckGrade}<112:1.296+0.003\left|L_{uckGrade}-111\right|,112 \le L_{uckGrade}<114:1.299+0.002\left|L_{uckGrade}-112\right|,114 \le L_{uckGrade}<115:1.303+0.003\left|L_{uckGrade}-114\right|,115 \le L_{uckGrade}<117:1.306+0.002\left|L_{uckGrade}-115\right|,117 \le L_{uckGrade}<118:1.31+0.003\left|L_{uckGrade}-117\right|,118 \le L_{uckGrade}<121:1.313+0.002\left|L_{uckGrade}-118\right|,121 \le L_{uckGrade}<122:1.319+0.003\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<124:1.322+0.002\left|L_{uckGrade}-122\right|,124 \le L_{uckGrade}<125:1.326+0.003\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<129:1.329+0.002\left|L_{uckGrade}-125\right|,129 \le L_{uckGrade}<130:1.337+0.003\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<133:1.34+0.002\left|L_{uckGrade}-130\right|,133 \le L_{uckGrade}<134:1.346+0.003\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<139:1.349+0.002\left|L_{uckGrade}-134\right|,139 \le L_{uckGrade}<140:1.359+0.003\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<146:1.362+0.002\left|L_{uckGrade}-140\right|,146 \le L_{uckGrade}<147:1.374+0.003\left|L_{uckGrade}-146\right|,147 \le L_{uckGrade}<156:1.377+0.002\left|L_{uckGrade}-147\right|,156 \le L_{uckGrade}<157:1.395+0.003\left|L_{uckGrade}-156\right|,157 \le L_{uckGrade}<177:1.398+0.002\left|L_{uckGrade}-157\right|,177 \le L_{uckGrade}<178:1.438+0.001\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<188:1.439+0.002\left|L_{uckGrade}-178\right|,188 \le L_{uckGrade}<189:1.459+0.001\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<195:1.46+0.002\left|L_{uckGrade}-189\right|,195 \le L_{uckGrade}<196:1.472+0.001\left|L_{uckGrade}-195\right|,196 \le L_{uckGrade}<200:1.473+0.002\left|L_{uckGrade}-196\right|,200 \le L_{uckGrade}<201:1.481+0.001\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<205:1.482+0.002\left|L_{uckGrade}-201\right|,205 \le L_{uckGrade}<206:1.49+0.001\left|L_{uckGrade}-205\right|,206 \le L_{uckGrade}<209:1.491+0.002\left|L_{uckGrade}-206\right|,209 \le L_{uckGrade}<210:1.497+0.001\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<213:1.498+0.002\left|L_{uckGrade}-210\right|,213 \le L_{uckGrade}<214:1.504+0.001\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<216:1.505+0.002\left|L_{uckGrade}-214\right|,216 \le L_{uckGrade}<217:1.509+0.001\left|L_{uckGrade}-216\right|,217 \le L_{uckGrade}<219:1.51+0.002\left|L_{uckGrade}-217\right|,219 \le L_{uckGrade}<220:1.514+0.001\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<222:1.515+0.002\left|L_{uckGrade}-220\right|,222 \le L_{uckGrade}<223:1.519+0.001\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<225:1.52+0.002\left|L_{uckGrade}-223\right|,225 \le L_{uckGrade}<226:1.524+0.001\left|L_{uckGrade}-225\right|,226 \le L_{uckGrade}<228:1.525+0.002\left|L_{uckGrade}-226\right|,228 \le L_{uckGrade}<229:1.529+0.001\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<231:1.53+0.002\left|L_{uckGrade}-229\right|,231 \le L_{uckGrade}<232:1.534+0.001\left|L_{uckGrade}-231\right|,232 \le L_{uckGrade}<233:1.535+0.002\left|L_{uckGrade}-232\right|,233 \le L_{uckGrade}<234:1.537+0.001\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<236:1.538+0.002\left|L_{uckGrade}-234\right|,236 \le L_{uckGrade}<237:1.542+0.001\left|L_{uckGrade}-236\right|,237 \le L_{uckGrade}<238:1.543+0.002\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<239:1.545+0.001\left|L_{uckGrade}-238\right|,239 \le L_{uckGrade}<240:1.546+0.002\left|L_{uckGrade}-239\right|,240 \le L_{uckGrade}<241:1.548+0.001\left|L_{uckGrade}-240\right|,241 \le L_{uckGrade}<243:1.549+0.002\left|L_{uckGrade}-241\right|,243 \le L_{uckGrade}<244:1.553+0.001\left|L_{uckGrade}-243\right|,244 \le L_{uckGrade}<245:1.554+0.002\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<246:1.556+0.001\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<247:1.557+0.002\left|L_{uckGrade}-246\right|,247 \le L_{uckGrade}<248:1.559+0.001\left|L_{uckGrade}-247\right|,248 \le L_{uckGrade}<249:1.56+0.002\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<250:1.562+0.001\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<251:1.563+0.002\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:1.565+0.001\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<253:1.566+0.002\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<254:1.568+0.001\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<255:1.569+0.002\left|L_{uckGrade}-254\right|,255 \le L_{uckGrade}<256:1.571+0.001\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<257:1.572+0.002\left|L_{uckGrade}-256\right|,257 \le L_{uckGrade}<258:1.574+0.001\left|L_{uckGrade}-257\right|,258 \le L_{uckGrade}<259:1.575+0.002\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<261:1.577+0.001\left|L_{uckGrade}-259\right|,261 \le L_{uckGrade}<262:1.579+0.002\left|L_{uckGrade}-261\right|,262 \le L_{uckGrade}<263:1.581+0.001\left|L_{uckGrade}-262\right|,263 \le L_{uckGrade}<264:1.582+0.002\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<265:1.584+0.001\left|L_{uckGrade}-264\right|,265 \le L_{uckGrade}<266:1.585+0.002\left|L_{uckGrade}-265\right|,266 \le L_{uckGrade}<268:1.587+0.001\left|L_{uckGrade}-266\right|,268 \le L_{uckGrade}<269:1.589+0.002\left|L_{uckGrade}-268\right|,269 \le L_{uckGrade}<271:1.591+0.001\left|L_{uckGrade}-269\right|,271 \le L_{uckGrade}<272:1.593+0.002\left|L_{uckGrade}-271\right|,272 \le L_{uckGrade}<273:1.595+0.001\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<274:1.596+0.002\left|L_{uckGrade}-273\right|,274 \le L_{uckGrade}<276:1.598+0.001\left|L_{uckGrade}-274\right|,276 \le L_{uckGrade}<277:1.6+0.002\left|L_{uckGrade}-276\right|,277 \le L_{uckGrade}<279:1.602+0.001\left|L_{uckGrade}-277\right|,279 \le L_{uckGrade}<280:1.604+0.002\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<282:1.606+0.001\left|L_{uckGrade}-280\right|,282 \le L_{uckGrade}<283:1.608+0.002\left|L_{uckGrade}-282\right|,283 \le L_{uckGrade}<286:1.61+0.001\left|L_{uckGrade}-283\right|,286 \le L_{uckGrade}<287:1.613+0.002\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<289:1.615+0.001\left|L_{uckGrade}-287\right|,289 \le L_{uckGrade}<290:1.617+0.002\left|L_{uckGrade}-289\right|,290 \le L_{uckGrade}<293:1.619+0.001\left|L_{uckGrade}-290\right|,293 \le L_{uckGrade}<294:1.622+0.002\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<298:1.624+0.001\left|L_{uckGrade}-294\right|,298 \le L_{uckGrade}<299:1.628+0.002\left|L_{uckGrade}-298\right|,299 \le L_{uckGrade}<303:1.63+0.001\left|L_{uckGrade}-299\right|,303 \le L_{uckGrade}<304:1.634+0.002\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<309:1.636+0.001\left|L_{uckGrade}-304\right|,309 \le L_{uckGrade}<310:1.641+0.002\left|L_{uckGrade}-309\right|,310 \le L_{uckGrade}<317:1.643+0.001\left|L_{uckGrade}-310\right|,317 \le L_{uckGrade}<318:1.65+0.002\left|L_{uckGrade}-317\right|,318 \le L_{uckGrade}<350:1.652+0.001\left|L_{uckGrade}-318\right|,350 \le L_{uckGrade}<351:1.684+0\left|L_{uckGrade}-350\right|,351 \le L_{uckGrade}<358:1.684+0.001\left|L_{uckGrade}-351\right|,358 \le L_{uckGrade}<359:1.691+0\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<364:1.691+0.001\left|L_{uckGrade}-359\right|,364 \le L_{uckGrade}<365:1.696+0\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<369:1.696+0.001\left|L_{uckGrade}-365\right|,369 \le L_{uckGrade}<370:1.7+0\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<373:1.7+0.001\left|L_{uckGrade}-370\right|,373 \le L_{uckGrade}<374:1.703+0\left|L_{uckGrade}-373\right|,374 \le L_{uckGrade}<377:1.703+0.001\left|L_{uckGrade}-374\right|,377 \le L_{uckGrade}<378:1.706+0\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<381:1.706+0.001\left|L_{uckGrade}-378\right|,381 \le L_{uckGrade}<382:1.709+0\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<384:1.709+0.001\left|L_{uckGrade}-382\right|,384 \le L_{uckGrade}<385:1.711+0\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<388:1.711+0.001\left|L_{uckGrade}-385\right|,388 \le L_{uckGrade}<389:1.714+0\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<391:1.714+0.001\left|L_{uckGrade}-389\right|,391 \le L_{uckGrade}<392:1.716+0\left|L_{uckGrade}-391\right|,392 \le L_{uckGrade}<393:1.716+0.001\left|L_{uckGrade}-392\right|,393 \le L_{uckGrade}<394:1.717+0\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<396:1.717+0.001\left|L_{uckGrade}-394\right|,396 \le L_{uckGrade}<397:1.719+0\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<399:1.719+0.001\left|L_{uckGrade}-397\right|,399 \le L_{uckGrade}<400:1.721+0\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<401:1.721+0.001\left|L_{uckGrade}-400\right|,401 \le L_{uckGrade}<402:1.722+0\left|L_{uckGrade}-401\right|,402 \le L_{uckGrade}<404:1.722+0.001\left|L_{uckGrade}-402\right|,404 \le L_{uckGrade}<405:1.724+0\left|L_{uckGrade}-404\right|,405 \le L_{uckGrade}<406:1.724+0.001\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:1.725+0\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<408:1.725+0.001\left|L_{uckGrade}-407\right|,408 \le L_{uckGrade}<409:1.726+0\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<410:1.726+0.001\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<411:1.727+0\left|L_{uckGrade}-410\right|,411 \le L_{uckGrade}<413:1.727+0.001\left|L_{uckGrade}-411\right|,413 \le L_{uckGrade}<414:1.729+0\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<415:1.729+0.001\left|L_{uckGrade}-414\right|,415 \le L_{uckGrade}<416:1.73+0\left|L_{uckGrade}-415\right|,416 \le L_{uckGrade}<417:1.73+0.001\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<418:1.731+0\left|L_{uckGrade}-417\right|,418 \le L_{uckGrade}<419:1.731+0.001\left|L_{uckGrade}-418\right|,419 \le L_{uckGrade}<420:1.732+0\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<421:1.732+0.001\left|L_{uckGrade}-420\right|,421 \le L_{uckGrade}<423:1.733+0\left|L_{uckGrade}-421\right|,423 \le L_{uckGrade}<424:1.733+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<425:1.734+0\left|L_{uckGrade}-424\right|,425 \le L_{uckGrade}<426:1.734+0.001\left|L_{uckGrade}-425\right|,426 \le L_{uckGrade}<427:1.735+0\left|L_{uckGrade}-426\right|,427 \le L_{uckGrade}<428:1.735+0.001\left|L_{uckGrade}-427\right|,428 \le L_{uckGrade}<429:1.736+0\left|L_{uckGrade}-428\right|,429 \le L_{uckGrade}<430:1.736+0.001\left|L_{uckGrade}-429\right|,430 \le L_{uckGrade}<432:1.737+0\left|L_{uckGrade}-430\right|,432 \le L_{uckGrade}<433:1.737+0.001\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<434:1.738+0\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<435:1.738+0.001\left|L_{uckGrade}-434\right|,435 \le L_{uckGrade}<437:1.739+0\left|L_{uckGrade}-435\right|,437 \le L_{uckGrade}<438:1.739+0.001\left|L_{uckGrade}-437\right|,438 \le L_{uckGrade}<439:1.74+0\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<440:1.74+0.001\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<442:1.741+0\left|L_{uckGrade}-440\right|,442 \le L_{uckGrade}<443:1.741+0.001\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<445:1.742+0\left|L_{uckGrade}-443\right|,445 \le L_{uckGrade}<446:1.742+0.001\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<448:1.743+0\left|L_{uckGrade}-446\right|,448 \le L_{uckGrade}<449:1.743+0.001\left|L_{uckGrade}-448\right|,449 \le L_{uckGrade}<452:1.744+0\left|L_{uckGrade}-449\right|,452 \le L_{uckGrade}<453:1.744+0.001\left|L_{uckGrade}-452\right|,453 \le L_{uckGrade}<455:1.745+0\left|L_{uckGrade}-453\right|,455 \le L_{uckGrade}<456:1.745+0.001\left|L_{uckGrade}-455\right|,456 \le L_{uckGrade}<459:1.746+0\left|L_{uckGrade}-456\right|,459 \le L_{uckGrade}<460:1.746+0.001\left|L_{uckGrade}-459\right|,460 \le L_{uckGrade}<463:1.747+0\left|L_{uckGrade}-460\right|,463 \le L_{uckGrade}<464:1.747+0.001\left|L_{uckGrade}-463\right|,464 \le L_{uckGrade}<468:1.748+0\left|L_{uckGrade}-464\right|,468 \le L_{uckGrade}<469:1.748+0.001\left|L_{uckGrade}-468\right|,469 \le L_{uckGrade}<474:1.749+0\left|L_{uckGrade}-469\right|,474 \le L_{uckGrade}<475:1.749+0.001\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<482:1.75+0\left|L_{uckGrade}-475\right|,482 \le L_{uckGrade}<483:1.75+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<499:1.751+0\left|L_{uckGrade}-483\right|,499 \le L_{uckGrade}<500:1.751+0.001\left|L_{uckGrade}-499\right|\right\}

See Example for how to use.

LaTeX Formula

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

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

L_{uckGrade05}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<1:1+0.006\left|L_{uckGrade}-0\right|,1 \le L_{uckGrade}<2:1.006+0.007\left|L_{uckGrade}-1\right|,2 \le L_{uckGrade}<5:1.013+0.006\left|L_{uckGrade}-2\right|,5 \le L_{uckGrade}<6:1.031+0.007\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<9:1.038+0.006\left|L_{uckGrade}-6\right|,9 \le L_{uckGrade}<10:1.056+0.007\left|L_{uckGrade}-9\right|,10 \le L_{uckGrade}<14:1.063+0.006\left|L_{uckGrade}-10\right|,14 \le L_{uckGrade}<15:1.087+0.007\left|L_{uckGrade}-14\right|,15 \le L_{uckGrade}<37:1.094+0.006\left|L_{uckGrade}-15\right|,37 \le L_{uckGrade}<38:1.226+0.005\left|L_{uckGrade}-37\right|,38 \le L_{uckGrade}<43:1.231+0.006\left|L_{uckGrade}-38\right|,43 \le L_{uckGrade}<44:1.261+0.005\left|L_{uckGrade}-43\right|,44 \le L_{uckGrade}<47:1.266+0.006\left|L_{uckGrade}-44\right|,47 \le L_{uckGrade}<48:1.284+0.005\left|L_{uckGrade}-47\right|,48 \le L_{uckGrade}<50:1.289+0.006\left|L_{uckGrade}-48\right|,50 \le L_{uckGrade}<51:1.301+0.005\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<53:1.306+0.006\left|L_{uckGrade}-51\right|,53 \le L_{uckGrade}<54:1.318+0.005\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<56:1.323+0.006\left|L_{uckGrade}-54\right|,56 \le L_{uckGrade}<57:1.335+0.005\left|L_{uckGrade}-56\right|,57 \le L_{uckGrade}<59:1.34+0.006\left|L_{uckGrade}-57\right|,59 \le L_{uckGrade}<60:1.352+0.005\left|L_{uckGrade}-59\right|,60 \le L_{uckGrade}<61:1.357+0.006\left|L_{uckGrade}-60\right|,61 \le L_{uckGrade}<62:1.363+0.005\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<63:1.368+0.006\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<64:1.374+0.005\left|L_{uckGrade}-63\right|,64 \le L_{uckGrade}<65:1.379+0.006\left|L_{uckGrade}-64\right|,65 \le L_{uckGrade}<66:1.385+0.005\left|L_{uckGrade}-65\right|,66 \le L_{uckGrade}<67:1.39+0.006\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<68:1.396+0.005\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<69:1.401+0.006\left|L_{uckGrade}-68\right|,69 \le L_{uckGrade}<70:1.407+0.005\left|L_{uckGrade}-69\right|,70 \le L_{uckGrade}<71:1.412+0.006\left|L_{uckGrade}-70\right|,71 \le L_{uckGrade}<73:1.418+0.005\left|L_{uckGrade}-71\right|,73 \le L_{uckGrade}<74:1.428+0.006\left|L_{uckGrade}-73\right|,74 \le L_{uckGrade}<75:1.434+0.005\left|L_{uckGrade}-74\right|,75 \le L_{uckGrade}<76:1.439+0.006\left|L_{uckGrade}-75\right|,76 \le L_{uckGrade}<78:1.445+0.005\left|L_{uckGrade}-76\right|,78 \le L_{uckGrade}<79:1.455+0.006\left|L_{uckGrade}-78\right|,79 \le L_{uckGrade}<81:1.461+0.005\left|L_{uckGrade}-79\right|,81 \le L_{uckGrade}<82:1.471+0.006\left|L_{uckGrade}-81\right|,82 \le L_{uckGrade}<85:1.477+0.005\left|L_{uckGrade}-82\right|,85 \le L_{uckGrade}<86:1.492+0.006\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<89:1.498+0.005\left|L_{uckGrade}-86\right|,89 \le L_{uckGrade}<90:1.513+0.006\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<95:1.519+0.005\left|L_{uckGrade}-90\right|,95 \le L_{uckGrade}<96:1.544+0.006\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<114:1.55+0.005\left|L_{uckGrade}-96\right|,114 \le L_{uckGrade}<115:1.64+0.004\left|L_{uckGrade}-114\right|,115 \le L_{uckGrade}<120:1.644+0.005\left|L_{uckGrade}-115\right|,120 \le L_{uckGrade}<121:1.669+0.004\left|L_{uckGrade}-120\right|,121 \le L_{uckGrade}<125:1.673+0.005\left|L_{uckGrade}-121\right|,125 \le L_{uckGrade}<126:1.693+0.004\left|L_{uckGrade}-125\right|,126 \le L_{uckGrade}<128:1.697+0.005\left|L_{uckGrade}-126\right|,128 \le L_{uckGrade}<129:1.707+0.004\left|L_{uckGrade}-128\right|,129 \le L_{uckGrade}<132:1.711+0.005\left|L_{uckGrade}-129\right|,132 \le L_{uckGrade}<133:1.726+0.004\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<134:1.73+0.005\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<135:1.735+0.004\left|L_{uckGrade}-134\right|,135 \le L_{uckGrade}<137:1.739+0.005\left|L_{uckGrade}-135\right|,137 \le L_{uckGrade}<138:1.749+0.004\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<139:1.753+0.005\left|L_{uckGrade}-138\right|,139 \le L_{uckGrade}<140:1.758+0.004\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<142:1.762+0.005\left|L_{uckGrade}-140\right|,142 \le L_{uckGrade}<143:1.772+0.004\left|L_{uckGrade}-142\right|,143 \le L_{uckGrade}<144:1.776+0.005\left|L_{uckGrade}-143\right|,144 \le L_{uckGrade}<145:1.781+0.004\left|L_{uckGrade}-144\right|,145 \le L_{uckGrade}<146:1.785+0.005\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<148:1.79+0.004\left|L_{uckGrade}-146\right|,148 \le L_{uckGrade}<149:1.798+0.005\left|L_{uckGrade}-148\right|,149 \le L_{uckGrade}<150:1.803+0.004\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<151:1.807+0.005\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:1.812+0.004\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<153:1.816+0.005\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<155:1.821+0.004\left|L_{uckGrade}-153\right|,155 \le L_{uckGrade}<156:1.829+0.005\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<158:1.834+0.004\left|L_{uckGrade}-156\right|,158 \le L_{uckGrade}<159:1.842+0.005\left|L_{uckGrade}-158\right|,159 \le L_{uckGrade}<161:1.847+0.004\left|L_{uckGrade}-159\right|,161 \le L_{uckGrade}<162:1.855+0.005\left|L_{uckGrade}-161\right|,162 \le L_{uckGrade}<165:1.86+0.004\left|L_{uckGrade}-162\right|,165 \le L_{uckGrade}<166:1.872+0.005\left|L_{uckGrade}-165\right|,166 \le L_{uckGrade}<169:1.877+0.004\left|L_{uckGrade}-166\right|,169 \le L_{uckGrade}<170:1.889+0.005\left|L_{uckGrade}-169\right|,170 \le L_{uckGrade}<177:1.894+0.004\left|L_{uckGrade}-170\right|,177 \le L_{uckGrade}<178:1.922+0.005\left|L_{uckGrade}-177\right|,178 \le L_{uckGrade}<191:1.927+0.004\left|L_{uckGrade}-178\right|,191 \le L_{uckGrade}<192:1.979+0.003\left|L_{uckGrade}-191\right|,192 \le L_{uckGrade}<198:1.982+0.004\left|L_{uckGrade}-192\right|,198 \le L_{uckGrade}<199:2.006+0.003\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<203:2.009+0.004\left|L_{uckGrade}-199\right|,203 \le L_{uckGrade}<204:2.025+0.003\left|L_{uckGrade}-203\right|,204 \le L_{uckGrade}<207:2.028+0.004\left|L_{uckGrade}-204\right|,207 \le L_{uckGrade}<208:2.04+0.003\left|L_{uckGrade}-207\right|,208 \le L_{uckGrade}<210:2.043+0.004\left|L_{uckGrade}-208\right|,210 \le L_{uckGrade}<211:2.051+0.003\left|L_{uckGrade}-210\right|,211 \le L_{uckGrade}<213:2.054+0.004\left|L_{uckGrade}-211\right|,213 \le L_{uckGrade}<214:2.062+0.003\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<215:2.065+0.004\left|L_{uckGrade}-214\right|,215 \le L_{uckGrade}<216:2.069+0.003\left|L_{uckGrade}-215\right|,216 \le L_{uckGrade}<218:2.072+0.004\left|L_{uckGrade}-216\right|,218 \le L_{uckGrade}<219:2.08+0.003\left|L_{uckGrade}-218\right|,219 \le L_{uckGrade}<220:2.083+0.004\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<221:2.087+0.003\left|L_{uckGrade}-220\right|,221 \le L_{uckGrade}<222:2.09+0.004\left|L_{uckGrade}-221\right|,222 \le L_{uckGrade}<223:2.094+0.003\left|L_{uckGrade}-222\right|,223 \le L_{uckGrade}<224:2.097+0.004\left|L_{uckGrade}-223\right|,224 \le L_{uckGrade}<225:2.101+0.003\left|L_{uckGrade}-224\right|,225 \le L_{uckGrade}<226:2.104+0.004\left|L_{uckGrade}-225\right|,226 \le L_{uckGrade}<227:2.108+0.003\left|L_{uckGrade}-226\right|,227 \le L_{uckGrade}<228:2.111+0.004\left|L_{uckGrade}-227\right|,228 \le L_{uckGrade}<229:2.115+0.003\left|L_{uckGrade}-228\right|,229 \le L_{uckGrade}<230:2.118+0.004\left|L_{uckGrade}-229\right|,230 \le L_{uckGrade}<232:2.122+0.003\left|L_{uckGrade}-230\right|,232 \le L_{uckGrade}<233:2.128+0.004\left|L_{uckGrade}-232\right|,233 \le L_{uckGrade}<234:2.132+0.003\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<235:2.135+0.004\left|L_{uckGrade}-234\right|,235 \le L_{uckGrade}<237:2.139+0.003\left|L_{uckGrade}-235\right|,237 \le L_{uckGrade}<238:2.145+0.004\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<241:2.149+0.003\left|L_{uckGrade}-238\right|,241 \le L_{uckGrade}<242:2.158+0.004\left|L_{uckGrade}-241\right|,242 \le L_{uckGrade}<244:2.162+0.003\left|L_{uckGrade}-242\right|,244 \le L_{uckGrade}<245:2.168+0.004\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<249:2.172+0.003\left|L_{uckGrade}-245\right|,249 \le L_{uckGrade}<250:2.184+0.004\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<258:2.188+0.003\left|L_{uckGrade}-250\right|,258 \le L_{uckGrade}<259:2.212+0.004\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<268:2.216+0.003\left|L_{uckGrade}-259\right|,268 \le L_{uckGrade}<269:2.243+0.002\left|L_{uckGrade}-268\right|,269 \le L_{uckGrade}<276:2.245+0.003\left|L_{uckGrade}-269\right|,276 \le L_{uckGrade}<277:2.266+0.002\left|L_{uckGrade}-276\right|,277 \le L_{uckGrade}<281:2.268+0.003\left|L_{uckGrade}-277\right|,281 \le L_{uckGrade}<282:2.28+0.002\left|L_{uckGrade}-281\right|,282 \le L_{uckGrade}<285:2.282+0.003\left|L_{uckGrade}-282\right|,285 \le L_{uckGrade}<286:2.291+0.002\left|L_{uckGrade}-285\right|,286 \le L_{uckGrade}<288:2.293+0.003\left|L_{uckGrade}-286\right|,288 \le L_{uckGrade}<289:2.299+0.002\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<291:2.301+0.003\left|L_{uckGrade}-289\right|,291 \le L_{uckGrade}<292:2.307+0.002\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<294:2.309+0.003\left|L_{uckGrade}-292\right|,294 \le L_{uckGrade}<295:2.315+0.002\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<296:2.317+0.003\left|L_{uckGrade}-295\right|,296 \le L_{uckGrade}<297:2.32+0.002\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<299:2.322+0.003\left|L_{uckGrade}-297\right|,299 \le L_{uckGrade}<300:2.328+0.002\left|L_{uckGrade}-299\right|,300 \le L_{uckGrade}<301:2.33+0.003\left|L_{uckGrade}-300\right|,301 \le L_{uckGrade}<302:2.333+0.002\left|L_{uckGrade}-301\right|,302 \le L_{uckGrade}<303:2.335+0.003\left|L_{uckGrade}-302\right|,303 \le L_{uckGrade}<304:2.338+0.002\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<305:2.34+0.003\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<306:2.343+0.002\left|L_{uckGrade}-305\right|,306 \le L_{uckGrade}<307:2.345+0.003\left|L_{uckGrade}-306\right|,307 \le L_{uckGrade}<309:2.348+0.002\left|L_{uckGrade}-307\right|,309 \le L_{uckGrade}<310:2.352+0.003\left|L_{uckGrade}-309\right|,310 \le L_{uckGrade}<311:2.355+0.002\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<312:2.357+0.003\left|L_{uckGrade}-311\right|,312 \le L_{uckGrade}<314:2.36+0.002\left|L_{uckGrade}-312\right|,314 \le L_{uckGrade}<315:2.364+0.003\left|L_{uckGrade}-314\right|,315 \le L_{uckGrade}<317:2.367+0.002\left|L_{uckGrade}-315\right|,317 \le L_{uckGrade}<318:2.371+0.003\left|L_{uckGrade}-317\right|,318 \le L_{uckGrade}<320:2.374+0.002\left|L_{uckGrade}-318\right|,320 \le L_{uckGrade}<321:2.378+0.003\left|L_{uckGrade}-320\right|,321 \le L_{uckGrade}<324:2.381+0.002\left|L_{uckGrade}-321\right|,324 \le L_{uckGrade}<325:2.387+0.003\left|L_{uckGrade}-324\right|,325 \le L_{uckGrade}<329:2.39+0.002\left|L_{uckGrade}-325\right|,329 \le L_{uckGrade}<330:2.398+0.003\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<340:2.401+0.002\left|L_{uckGrade}-330\right|,340 \le L_{uckGrade}<341:2.421+0.003\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<344:2.424+0.002\left|L_{uckGrade}-341\right|,344 \le L_{uckGrade}<345:2.43+0.001\left|L_{uckGrade}-344\right|,345 \le L_{uckGrade}<355:2.431+0.002\left|L_{uckGrade}-345\right|,355 \le L_{uckGrade}<356:2.451+0.001\left|L_{uckGrade}-355\right|,356 \le L_{uckGrade}<360:2.452+0.002\left|L_{uckGrade}-356\right|,360 \le L_{uckGrade}<361:2.46+0.001\left|L_{uckGrade}-360\right|,361 \le L_{uckGrade}<364:2.461+0.002\left|L_{uckGrade}-361\right|,364 \le L_{uckGrade}<365:2.467+0.001\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<367:2.468+0.002\left|L_{uckGrade}-365\right|,367 \le L_{uckGrade}<368:2.472+0.001\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<370:2.473+0.002\left|L_{uckGrade}-368\right|,370 \le L_{uckGrade}<371:2.477+0.001\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<373:2.478+0.002\left|L_{uckGrade}-371\right|,373 \le L_{uckGrade}<374:2.482+0.001\left|L_{uckGrade}-373\right|,374 \le L_{uckGrade}<375:2.483+0.002\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<376:2.485+0.001\left|L_{uckGrade}-375\right|,376 \le L_{uckGrade}<377:2.486+0.002\left|L_{uckGrade}-376\right|,377 \le L_{uckGrade}<378:2.488+0.001\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<380:2.489+0.002\left|L_{uckGrade}-378\right|,380 \le L_{uckGrade}<381:2.493+0.001\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<382:2.494+0.002\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<383:2.496+0.001\left|L_{uckGrade}-382\right|,383 \le L_{uckGrade}<384:2.497+0.002\left|L_{uckGrade}-383\right|,384 \le L_{uckGrade}<386:2.499+0.001\left|L_{uckGrade}-384\right|,386 \le L_{uckGrade}<387:2.501+0.002\left|L_{uckGrade}-386\right|,387 \le L_{uckGrade}<388:2.503+0.001\left|L_{uckGrade}-387\right|,388 \le L_{uckGrade}<389:2.504+0.002\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<390:2.506+0.001\left|L_{uckGrade}-389\right|,390 \le L_{uckGrade}<391:2.507+0.002\left|L_{uckGrade}-390\right|,391 \le L_{uckGrade}<393:2.509+0.001\left|L_{uckGrade}-391\right|,393 \le L_{uckGrade}<394:2.511+0.002\left|L_{uckGrade}-393\right|,394 \le L_{uckGrade}<396:2.513+0.001\left|L_{uckGrade}-394\right|,396 \le L_{uckGrade}<397:2.515+0.002\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<399:2.517+0.001\left|L_{uckGrade}-397\right|,399 \le L_{uckGrade}<400:2.519+0.002\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<403:2.521+0.001\left|L_{uckGrade}-400\right|,403 \le L_{uckGrade}<404:2.524+0.002\left|L_{uckGrade}-403\right|,404 \le L_{uckGrade}<409:2.526+0.001\left|L_{uckGrade}-404\right|,409 \le L_{uckGrade}<410:2.531+0.002\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<433:2.533+0.001\left|L_{uckGrade}-410\right|,433 \le L_{uckGrade}<434:2.556+0\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<438:2.556+0.001\left|L_{uckGrade}-434\right|,438 \le L_{uckGrade}<439:2.56+0\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<443:2.56+0.001\left|L_{uckGrade}-439\right|,443 \le L_{uckGrade}<444:2.564+0\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<446:2.564+0.001\left|L_{uckGrade}-444\right|,446 \le L_{uckGrade}<447:2.566+0\left|L_{uckGrade}-446\right|,447 \le L_{uckGrade}<449:2.566+0.001\left|L_{uckGrade}-447\right|,449 \le L_{uckGrade}<450:2.568+0\left|L_{uckGrade}-449\right|,450 \le L_{uckGrade}<452:2.568+0.001\left|L_{uckGrade}-450\right|,452 \le L_{uckGrade}<453:2.57+0\left|L_{uckGrade}-452\right|,453 \le L_{uckGrade}<454:2.57+0.001\left|L_{uckGrade}-453\right|,454 \le L_{uckGrade}<455:2.571+0\left|L_{uckGrade}-454\right|,455 \le L_{uckGrade}<456:2.571+0.001\left|L_{uckGrade}-455\right|,456 \le L_{uckGrade}<457:2.572+0\left|L_{uckGrade}-456\right|,457 \le L_{uckGrade}<459:2.572+0.001\left|L_{uckGrade}-457\right|,459 \le L_{uckGrade}<460:2.574+0\left|L_{uckGrade}-459\right|,460 \le L_{uckGrade}<461:2.574+0.001\left|L_{uckGrade}-460\right|,461 \le L_{uckGrade}<462:2.575+0\left|L_{uckGrade}-461\right|,462 \le L_{uckGrade}<463:2.575+0.001\left|L_{uckGrade}-462\right|,463 \le L_{uckGrade}<465:2.576+0\left|L_{uckGrade}-463\right|,465 \le L_{uckGrade}<466:2.576+0.001\left|L_{uckGrade}-465\right|,466 \le L_{uckGrade}<467:2.577+0\left|L_{uckGrade}-466\right|,467 \le L_{uckGrade}<468:2.577+0.001\left|L_{uckGrade}-467\right|,468 \le L_{uckGrade}<469:2.578+0\left|L_{uckGrade}-468\right|,469 \le L_{uckGrade}<470:2.578+0.001\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<472:2.579+0\left|L_{uckGrade}-470\right|,472 \le L_{uckGrade}<473:2.579+0.001\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<475:2.58+0\left|L_{uckGrade}-473\right|,475 \le L_{uckGrade}<476:2.58+0.001\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<479:2.581+0\left|L_{uckGrade}-476\right|,479 \le L_{uckGrade}<480:2.581+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<483:2.582+0\left|L_{uckGrade}-480\right|,483 \le L_{uckGrade}<484:2.582+0.001\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<488:2.583+0\left|L_{uckGrade}-484\right|,488 \le L_{uckGrade}<489:2.583+0.001\left|L_{uckGrade}-488\right|,489 \le L_{uckGrade}<500:2.584+0\left|L_{uckGrade}-489\right|\right\}

See Example for how to use.

LaTeX Formula

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

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

L_{uckGrade06}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<15:1+0.009\left|L_{uckGrade}-0\right|,15 \le L_{uckGrade}<16:1.135+0.008\left|L_{uckGrade}-15\right|,16 \le L_{uckGrade}<20:1.143+0.009\left|L_{uckGrade}-16\right|,20 \le L_{uckGrade}<21:1.179+0.008\left|L_{uckGrade}-20\right|,21 \le L_{uckGrade}<23:1.187+0.009\left|L_{uckGrade}-21\right|,23 \le L_{uckGrade}<24:1.205+0.008\left|L_{uckGrade}-23\right|,24 \le L_{uckGrade}<26:1.213+0.009\left|L_{uckGrade}-24\right|,26 \le L_{uckGrade}<27:1.231+0.008\left|L_{uckGrade}-26\right|,27 \le L_{uckGrade}<29:1.239+0.009\left|L_{uckGrade}-27\right|,29 \le L_{uckGrade}<30:1.257+0.008\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<31:1.265+0.009\left|L_{uckGrade}-30\right|,31 \le L_{uckGrade}<32:1.274+0.008\left|L_{uckGrade}-31\right|,32 \le L_{uckGrade}<33:1.282+0.009\left|L_{uckGrade}-32\right|,33 \le L_{uckGrade}<34:1.291+0.008\left|L_{uckGrade}-33\right|,34 \le L_{uckGrade}<35:1.299+0.009\left|L_{uckGrade}-34\right|,35 \le L_{uckGrade}<36:1.308+0.008\left|L_{uckGrade}-35\right|,36 \le L_{uckGrade}<37:1.316+0.009\left|L_{uckGrade}-36\right|,37 \le L_{uckGrade}<39:1.325+0.008\left|L_{uckGrade}-37\right|,39 \le L_{uckGrade}<40:1.341+0.009\left|L_{uckGrade}-39\right|,40 \le L_{uckGrade}<41:1.35+0.008\left|L_{uckGrade}-40\right|,41 \le L_{uckGrade}<42:1.358+0.009\left|L_{uckGrade}-41\right|,42 \le L_{uckGrade}<45:1.367+0.008\left|L_{uckGrade}-42\right|,45 \le L_{uckGrade}<46:1.391+0.009\left|L_{uckGrade}-45\right|,46 \le L_{uckGrade}<49:1.4+0.008\left|L_{uckGrade}-46\right|,49 \le L_{uckGrade}<50:1.424+0.009\left|L_{uckGrade}-49\right|,50 \le L_{uckGrade}<55:1.433+0.008\left|L_{uckGrade}-50\right|,55 \le L_{uckGrade}<56:1.473+0.009\left|L_{uckGrade}-55\right|,56 \le L_{uckGrade}<66:1.482+0.008\left|L_{uckGrade}-56\right|,66 \le L_{uckGrade}<67:1.562+0.007\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<72:1.569+0.008\left|L_{uckGrade}-67\right|,72 \le L_{uckGrade}<73:1.609+0.007\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<76:1.616+0.008\left|L_{uckGrade}-73\right|,76 \le L_{uckGrade}<77:1.64+0.007\left|L_{uckGrade}-76\right|,77 \le L_{uckGrade}<79:1.647+0.008\left|L_{uckGrade}-77\right|,79 \le L_{uckGrade}<80:1.663+0.007\left|L_{uckGrade}-79\right|,80 \le L_{uckGrade}<82:1.67+0.008\left|L_{uckGrade}-80\right|,82 \le L_{uckGrade}<83:1.686+0.007\left|L_{uckGrade}-82\right|,83 \le L_{uckGrade}<85:1.693+0.008\left|L_{uckGrade}-83\right|,85 \le L_{uckGrade}<86:1.709+0.007\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<87:1.716+0.008\left|L_{uckGrade}-86\right|,87 \le L_{uckGrade}<88:1.724+0.007\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<89:1.731+0.008\left|L_{uckGrade}-88\right|,89 \le L_{uckGrade}<90:1.739+0.007\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<91:1.746+0.008\left|L_{uckGrade}-90\right|,91 \le L_{uckGrade}<93:1.754+0.007\left|L_{uckGrade}-91\right|,93 \le L_{uckGrade}<94:1.768+0.008\left|L_{uckGrade}-93\right|,94 \le L_{uckGrade}<95:1.776+0.007\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<96:1.783+0.008\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<98:1.791+0.007\left|L_{uckGrade}-96\right|,98 \le L_{uckGrade}<99:1.805+0.008\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<102:1.813+0.007\left|L_{uckGrade}-99\right|,102 \le L_{uckGrade}<103:1.834+0.008\left|L_{uckGrade}-102\right|,103 \le L_{uckGrade}<107:1.842+0.007\left|L_{uckGrade}-103\right|,107 \le L_{uckGrade}<108:1.87+0.008\left|L_{uckGrade}-107\right|,108 \le L_{uckGrade}<124:1.878+0.007\left|L_{uckGrade}-108\right|,124 \le L_{uckGrade}<125:1.99+0.006\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<129:1.996+0.007\left|L_{uckGrade}-125\right|,129 \le L_{uckGrade}<130:2.024+0.006\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<133:2.03+0.007\left|L_{uckGrade}-130\right|,133 \le L_{uckGrade}<134:2.051+0.006\left|L_{uckGrade}-133\right|,134 \le L_{uckGrade}<136:2.057+0.007\left|L_{uckGrade}-134\right|,136 \le L_{uckGrade}<137:2.071+0.006\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<138:2.077+0.007\left|L_{uckGrade}-137\right|,138 \le L_{uckGrade}<139:2.084+0.006\left|L_{uckGrade}-138\right|,139 \le L_{uckGrade}<140:2.09+0.007\left|L_{uckGrade}-139\right|,140 \le L_{uckGrade}<141:2.097+0.006\left|L_{uckGrade}-140\right|,141 \le L_{uckGrade}<143:2.103+0.007\left|L_{uckGrade}-141\right|,143 \le L_{uckGrade}<145:2.117+0.006\left|L_{uckGrade}-143\right|,145 \le L_{uckGrade}<146:2.129+0.007\left|L_{uckGrade}-145\right|,146 \le L_{uckGrade}<147:2.136+0.006\left|L_{uckGrade}-146\right|,147 \le L_{uckGrade}<148:2.142+0.007\left|L_{uckGrade}-147\right|,148 \le L_{uckGrade}<149:2.149+0.006\left|L_{uckGrade}-148\right|,149 \le L_{uckGrade}<150:2.155+0.007\left|L_{uckGrade}-149\right|,150 \le L_{uckGrade}<152:2.162+0.006\left|L_{uckGrade}-150\right|,152 \le L_{uckGrade}<153:2.174+0.007\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<155:2.181+0.006\left|L_{uckGrade}-153\right|,155 \le L_{uckGrade}<156:2.193+0.007\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<160:2.2+0.006\left|L_{uckGrade}-156\right|,160 \le L_{uckGrade}<161:2.224+0.007\left|L_{uckGrade}-160\right|,161 \le L_{uckGrade}<168:2.231+0.006\left|L_{uckGrade}-161\right|,168 \le L_{uckGrade}<169:2.273+0.007\left|L_{uckGrade}-168\right|,169 \le L_{uckGrade}<173:2.28+0.006\left|L_{uckGrade}-169\right|,173 \le L_{uckGrade}<174:2.304+0.005\left|L_{uckGrade}-173\right|,174 \le L_{uckGrade}<181:2.309+0.006\left|L_{uckGrade}-174\right|,181 \le L_{uckGrade}<182:2.351+0.005\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<185:2.356+0.006\left|L_{uckGrade}-182\right|,185 \le L_{uckGrade}<186:2.374+0.005\left|L_{uckGrade}-185\right|,186 \le L_{uckGrade}<189:2.379+0.006\left|L_{uckGrade}-186\right|,189 \le L_{uckGrade}<190:2.397+0.005\left|L_{uckGrade}-189\right|,190 \le L_{uckGrade}<191:2.402+0.006\left|L_{uckGrade}-190\right|,191 \le L_{uckGrade}<192:2.408+0.005\left|L_{uckGrade}-191\right|,192 \le L_{uckGrade}<194:2.413+0.006\left|L_{uckGrade}-192\right|,194 \le L_{uckGrade}<195:2.425+0.005\left|L_{uckGrade}-194\right|,195 \le L_{uckGrade}<196:2.43+0.006\left|L_{uckGrade}-195\right|,196 \le L_{uckGrade}<197:2.436+0.005\left|L_{uckGrade}-196\right|,197 \le L_{uckGrade}<198:2.441+0.006\left|L_{uckGrade}-197\right|,198 \le L_{uckGrade}<199:2.447+0.005\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<200:2.452+0.006\left|L_{uckGrade}-199\right|,200 \le L_{uckGrade}<201:2.458+0.005\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<202:2.463+0.006\left|L_{uckGrade}-201\right|,202 \le L_{uckGrade}<203:2.469+0.005\left|L_{uckGrade}-202\right|,203 \le L_{uckGrade}<204:2.474+0.006\left|L_{uckGrade}-203\right|,204 \le L_{uckGrade}<206:2.48+0.005\left|L_{uckGrade}-204\right|,206 \le L_{uckGrade}<207:2.49+0.006\left|L_{uckGrade}-206\right|,207 \le L_{uckGrade}<209:2.496+0.005\left|L_{uckGrade}-207\right|,209 \le L_{uckGrade}<210:2.506+0.006\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<213:2.512+0.005\left|L_{uckGrade}-210\right|,213 \le L_{uckGrade}<214:2.527+0.006\left|L_{uckGrade}-213\right|,214 \le L_{uckGrade}<219:2.533+0.005\left|L_{uckGrade}-214\right|,219 \le L_{uckGrade}<220:2.558+0.006\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<232:2.564+0.005\left|L_{uckGrade}-220\right|,232 \le L_{uckGrade}<233:2.624+0.004\left|L_{uckGrade}-232\right|,233 \le L_{uckGrade}<238:2.628+0.005\left|L_{uckGrade}-233\right|,238 \le L_{uckGrade}<239:2.653+0.004\left|L_{uckGrade}-238\right|,239 \le L_{uckGrade}<241:2.657+0.005\left|L_{uckGrade}-239\right|,241 \le L_{uckGrade}<242:2.667+0.004\left|L_{uckGrade}-241\right|,242 \le L_{uckGrade}<245:2.671+0.005\left|L_{uckGrade}-242\right|,245 \le L_{uckGrade}<246:2.686+0.004\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<247:2.69+0.005\left|L_{uckGrade}-246\right|,247 \le L_{uckGrade}<248:2.695+0.004\left|L_{uckGrade}-247\right|,248 \le L_{uckGrade}<250:2.699+0.005\left|L_{uckGrade}-248\right|,250 \le L_{uckGrade}<251:2.709+0.004\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:2.713+0.005\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<253:2.718+0.004\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<254:2.722+0.005\left|L_{uckGrade}-253\right|,254 \le L_{uckGrade}<255:2.727+0.004\left|L_{uckGrade}-254\right|,255 \le L_{uckGrade}<256:2.731+0.005\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<258:2.736+0.004\left|L_{uckGrade}-256\right|,258 \le L_{uckGrade}<259:2.744+0.005\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<260:2.749+0.004\left|L_{uckGrade}-259\right|,260 \le L_{uckGrade}<261:2.753+0.005\left|L_{uckGrade}-260\right|,261 \le L_{uckGrade}<263:2.758+0.004\left|L_{uckGrade}-261\right|,263 \le L_{uckGrade}<264:2.766+0.005\left|L_{uckGrade}-263\right|,264 \le L_{uckGrade}<267:2.771+0.004\left|L_{uckGrade}-264\right|,267 \le L_{uckGrade}<268:2.783+0.005\left|L_{uckGrade}-267\right|,268 \le L_{uckGrade}<272:2.788+0.004\left|L_{uckGrade}-268\right|,272 \le L_{uckGrade}<273:2.804+0.005\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<288:2.809+0.004\left|L_{uckGrade}-273\right|,288 \le L_{uckGrade}<289:2.869+0.003\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<294:2.872+0.004\left|L_{uckGrade}-289\right|,294 \le L_{uckGrade}<295:2.892+0.003\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<297:2.895+0.004\left|L_{uckGrade}-295\right|,297 \le L_{uckGrade}<298:2.903+0.003\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<300:2.906+0.004\left|L_{uckGrade}-298\right|,300 \le L_{uckGrade}<301:2.914+0.003\left|L_{uckGrade}-300\right|,301 \le L_{uckGrade}<303:2.917+0.004\left|L_{uckGrade}-301\right|,303 \le L_{uckGrade}<304:2.925+0.003\left|L_{uckGrade}-303\right|,304 \le L_{uckGrade}<305:2.928+0.004\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<306:2.932+0.003\left|L_{uckGrade}-305\right|,306 \le L_{uckGrade}<307:2.935+0.004\left|L_{uckGrade}-306\right|,307 \le L_{uckGrade}<308:2.939+0.003\left|L_{uckGrade}-307\right|,308 \le L_{uckGrade}<309:2.942+0.004\left|L_{uckGrade}-308\right|,309 \le L_{uckGrade}<310:2.946+0.003\left|L_{uckGrade}-309\right|,310 \le L_{uckGrade}<311:2.949+0.004\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<312:2.953+0.003\left|L_{uckGrade}-311\right|,312 \le L_{uckGrade}<313:2.956+0.004\left|L_{uckGrade}-312\right|,313 \le L_{uckGrade}<315:2.96+0.003\left|L_{uckGrade}-313\right|,315 \le L_{uckGrade}<316:2.966+0.004\left|L_{uckGrade}-315\right|,316 \le L_{uckGrade}<318:2.97+0.003\left|L_{uckGrade}-316\right|,318 \le L_{uckGrade}<319:2.976+0.004\left|L_{uckGrade}-318\right|,319 \le L_{uckGrade}<321:2.98+0.003\left|L_{uckGrade}-319\right|,321 \le L_{uckGrade}<322:2.986+0.004\left|L_{uckGrade}-321\right|,322 \le L_{uckGrade}<326:2.99+0.003\left|L_{uckGrade}-322\right|,326 \le L_{uckGrade}<327:3.002+0.004\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<345:3.006+0.003\left|L_{uckGrade}-327\right|,345 \le L_{uckGrade}<346:3.06+0.002\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<349:3.062+0.003\left|L_{uckGrade}-346\right|,349 \le L_{uckGrade}<350:3.071+0.002\left|L_{uckGrade}-349\right|,350 \le L_{uckGrade}<353:3.073+0.003\left|L_{uckGrade}-350\right|,353 \le L_{uckGrade}<354:3.082+0.002\left|L_{uckGrade}-353\right|,354 \le L_{uckGrade}<356:3.084+0.003\left|L_{uckGrade}-354\right|,356 \le L_{uckGrade}<357:3.09+0.002\left|L_{uckGrade}-356\right|,357 \le L_{uckGrade}<358:3.092+0.003\left|L_{uckGrade}-357\right|,358 \le L_{uckGrade}<359:3.095+0.002\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<360:3.097+0.003\left|L_{uckGrade}-359\right|,360 \le L_{uckGrade}<361:3.1+0.002\left|L_{uckGrade}-360\right|,361 \le L_{uckGrade}<363:3.102+0.003\left|L_{uckGrade}-361\right|,363 \le L_{uckGrade}<365:3.108+0.002\left|L_{uckGrade}-363\right|,365 \le L_{uckGrade}<366:3.112+0.003\left|L_{uckGrade}-365\right|,366 \le L_{uckGrade}<367:3.115+0.002\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:3.117+0.003\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<369:3.12+0.002\left|L_{uckGrade}-368\right|,369 \le L_{uckGrade}<370:3.122+0.003\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<372:3.125+0.002\left|L_{uckGrade}-370\right|,372 \le L_{uckGrade}<373:3.129+0.003\left|L_{uckGrade}-372\right|,373 \le L_{uckGrade}<375:3.132+0.002\left|L_{uckGrade}-373\right|,375 \le L_{uckGrade}<376:3.136+0.003\left|L_{uckGrade}-375\right|,376 \le L_{uckGrade}<380:3.139+0.002\left|L_{uckGrade}-376\right|,380 \le L_{uckGrade}<381:3.147+0.003\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<400:3.15+0.002\left|L_{uckGrade}-381\right|,400 \le L_{uckGrade}<401:3.188+0.001\left|L_{uckGrade}-400\right|,401 \le L_{uckGrade}<405:3.189+0.002\left|L_{uckGrade}-401\right|,405 \le L_{uckGrade}<406:3.197+0.001\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<408:3.198+0.002\left|L_{uckGrade}-406\right|,408 \le L_{uckGrade}<409:3.202+0.001\left|L_{uckGrade}-408\right|,409 \le L_{uckGrade}<411:3.203+0.002\left|L_{uckGrade}-409\right|,411 \le L_{uckGrade}<412:3.207+0.001\left|L_{uckGrade}-411\right|,412 \le L_{uckGrade}<413:3.208+0.002\left|L_{uckGrade}-412\right|,413 \le L_{uckGrade}<414:3.21+0.001\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<416:3.211+0.002\left|L_{uckGrade}-414\right|,416 \le L_{uckGrade}<417:3.215+0.001\left|L_{uckGrade}-416\right|,417 \le L_{uckGrade}<418:3.216+0.002\left|L_{uckGrade}-417\right|,418 \le L_{uckGrade}<419:3.218+0.001\left|L_{uckGrade}-418\right|,419 \le L_{uckGrade}<420:3.219+0.002\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<422:3.221+0.001\left|L_{uckGrade}-420\right|,422 \le L_{uckGrade}<423:3.223+0.002\left|L_{uckGrade}-422\right|,423 \le L_{uckGrade}<424:3.225+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<425:3.226+0.002\left|L_{uckGrade}-424\right|,425 \le L_{uckGrade}<427:3.228+0.001\left|L_{uckGrade}-425\right|,427 \le L_{uckGrade}<428:3.23+0.002\left|L_{uckGrade}-427\right|,428 \le L_{uckGrade}<430:3.232+0.001\left|L_{uckGrade}-428\right|,430 \le L_{uckGrade}<431:3.234+0.002\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<434:3.236+0.001\left|L_{uckGrade}-431\right|,434 \le L_{uckGrade}<435:3.239+0.002\left|L_{uckGrade}-434\right|,435 \le L_{uckGrade}<443:3.241+0.001\left|L_{uckGrade}-435\right|,443 \le L_{uckGrade}<444:3.249+0.002\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<447:3.251+0.001\left|L_{uckGrade}-444\right|,447 \le L_{uckGrade}<448:3.254+0\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<456:3.254+0.001\left|L_{uckGrade}-448\right|,456 \le L_{uckGrade}<457:3.262+0\left|L_{uckGrade}-456\right|,457 \le L_{uckGrade}<460:3.262+0.001\left|L_{uckGrade}-457\right|,460 \le L_{uckGrade}<461:3.265+0\left|L_{uckGrade}-460\right|,461 \le L_{uckGrade}<463:3.265+0.001\left|L_{uckGrade}-461\right|,463 \le L_{uckGrade}<464:3.267+0\left|L_{uckGrade}-463\right|,464 \le L_{uckGrade}<466:3.267+0.001\left|L_{uckGrade}-464\right|,466 \le L_{uckGrade}<467:3.269+0\left|L_{uckGrade}-466\right|,467 \le L_{uckGrade}<469:3.269+0.001\left|L_{uckGrade}-467\right|,469 \le L_{uckGrade}<470:3.271+0\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<471:3.271+0.001\left|L_{uckGrade}-470\right|,471 \le L_{uckGrade}<472:3.272+0\left|L_{uckGrade}-471\right|,472 \le L_{uckGrade}<473:3.272+0.001\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<474:3.273+0\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<475:3.273+0.001\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<476:3.274+0\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<477:3.274+0.001\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<479:3.275+0\left|L_{uckGrade}-477\right|,479 \le L_{uckGrade}<480:3.275+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<482:3.276+0\left|L_{uckGrade}-480\right|,482 \le L_{uckGrade}<483:3.276+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<485:3.277+0\left|L_{uckGrade}-483\right|,485 \le L_{uckGrade}<486:3.277+0.001\left|L_{uckGrade}-485\right|,486 \le L_{uckGrade}<489:3.278+0\left|L_{uckGrade}-486\right|,489 \le L_{uckGrade}<490:3.278+0.001\left|L_{uckGrade}-489\right|,490 \le L_{uckGrade}<498:3.279+0\left|L_{uckGrade}-490\right|,498 \le L_{uckGrade}<499:3.279+0.001\left|L_{uckGrade}-498\right|,499 \le L_{uckGrade}<500:3.28+0\left|L_{uckGrade}-499\right|\right\}

See Example for how to use.

LaTeX Formula

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

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

L_{uckGrade07}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<2:1+0.011\left|L_{uckGrade}-0\right|,2 \le L_{uckGrade}<3:1.022+0.01\left|L_{uckGrade}-2\right|,3 \le L_{uckGrade}<5:1.032+0.011\left|L_{uckGrade}-3\right|,5 \le L_{uckGrade}<6:1.054+0.01\left|L_{uckGrade}-5\right|,6 \le L_{uckGrade}<8:1.064+0.011\left|L_{uckGrade}-6\right|,8 \le L_{uckGrade}<9:1.086+0.01\left|L_{uckGrade}-8\right|,9 \le L_{uckGrade}<11:1.096+0.011\left|L_{uckGrade}-9\right|,11 \le L_{uckGrade}<12:1.118+0.01\left|L_{uckGrade}-11\right|,12 \le L_{uckGrade}<13:1.128+0.011\left|L_{uckGrade}-12\right|,13 \le L_{uckGrade}<14:1.139+0.01\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<15:1.149+0.011\left|L_{uckGrade}-14\right|,15 \le L_{uckGrade}<16:1.16+0.01\left|L_{uckGrade}-15\right|,16 \le L_{uckGrade}<17:1.17+0.011\left|L_{uckGrade}-16\right|,17 \le L_{uckGrade}<18:1.181+0.01\left|L_{uckGrade}-17\right|,18 \le L_{uckGrade}<19:1.191+0.011\left|L_{uckGrade}-18\right|,19 \le L_{uckGrade}<21:1.202+0.01\left|L_{uckGrade}-19\right|,21 \le L_{uckGrade}<22:1.222+0.011\left|L_{uckGrade}-21\right|,22 \le L_{uckGrade}<24:1.233+0.01\left|L_{uckGrade}-22\right|,24 \le L_{uckGrade}<25:1.253+0.011\left|L_{uckGrade}-24\right|,25 \le L_{uckGrade}<29:1.264+0.01\left|L_{uckGrade}-25\right|,29 \le L_{uckGrade}<30:1.304+0.011\left|L_{uckGrade}-29\right|,30 \le L_{uckGrade}<45:1.315+0.01\left|L_{uckGrade}-30\right|,45 \le L_{uckGrade}<46:1.465+0.009\left|L_{uckGrade}-45\right|,46 \le L_{uckGrade}<50:1.474+0.01\left|L_{uckGrade}-46\right|,50 \le L_{uckGrade}<51:1.514+0.009\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<53:1.523+0.01\left|L_{uckGrade}-51\right|,53 \le L_{uckGrade}<54:1.543+0.009\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<56:1.552+0.01\left|L_{uckGrade}-54\right|,56 \le L_{uckGrade}<57:1.572+0.009\left|L_{uckGrade}-56\right|,57 \le L_{uckGrade}<58:1.581+0.01\left|L_{uckGrade}-57\right|,58 \le L_{uckGrade}<59:1.591+0.009\left|L_{uckGrade}-58\right|,59 \le L_{uckGrade}<60:1.6+0.01\left|L_{uckGrade}-59\right|,60 \le L_{uckGrade}<61:1.61+0.009\left|L_{uckGrade}-60\right|,61 \le L_{uckGrade}<62:1.619+0.01\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<63:1.629+0.009\left|L_{uckGrade}-62\right|,63 \le L_{uckGrade}<64:1.638+0.01\left|L_{uckGrade}-63\right|,64 \le L_{uckGrade}<66:1.648+0.009\left|L_{uckGrade}-64\right|,66 \le L_{uckGrade}<67:1.666+0.01\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<68:1.676+0.009\left|L_{uckGrade}-67\right|,68 \le L_{uckGrade}<69:1.685+0.01\left|L_{uckGrade}-68\right|,69 \le L_{uckGrade}<72:1.695+0.009\left|L_{uckGrade}-69\right|,72 \le L_{uckGrade}<73:1.722+0.01\left|L_{uckGrade}-72\right|,73 \le L_{uckGrade}<77:1.732+0.009\left|L_{uckGrade}-73\right|,77 \le L_{uckGrade}<78:1.768+0.01\left|L_{uckGrade}-77\right|,78 \le L_{uckGrade}<89:1.778+0.009\left|L_{uckGrade}-78\right|,89 \le L_{uckGrade}<90:1.877+0.008\left|L_{uckGrade}-89\right|,90 \le L_{uckGrade}<95:1.885+0.009\left|L_{uckGrade}-90\right|,95 \le L_{uckGrade}<96:1.93+0.008\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<98:1.938+0.009\left|L_{uckGrade}-96\right|,98 \le L_{uckGrade}<99:1.956+0.008\left|L_{uckGrade}-98\right|,99 \le L_{uckGrade}<101:1.964+0.009\left|L_{uckGrade}-99\right|,101 \le L_{uckGrade}<102:1.982+0.008\left|L_{uckGrade}-101\right|,102 \le L_{uckGrade}<104:1.99+0.009\left|L_{uckGrade}-102\right|,104 \le L_{uckGrade}<105:2.008+0.008\left|L_{uckGrade}-104\right|,105 \le L_{uckGrade}<106:2.016+0.009\left|L_{uckGrade}-105\right|,106 \le L_{uckGrade}<107:2.025+0.008\left|L_{uckGrade}-106\right|,107 \le L_{uckGrade}<108:2.033+0.009\left|L_{uckGrade}-107\right|,108 \le L_{uckGrade}<109:2.042+0.008\left|L_{uckGrade}-108\right|,109 \le L_{uckGrade}<110:2.05+0.009\left|L_{uckGrade}-109\right|,110 \le L_{uckGrade}<112:2.059+0.008\left|L_{uckGrade}-110\right|,112 \le L_{uckGrade}<113:2.075+0.009\left|L_{uckGrade}-112\right|,113 \le L_{uckGrade}<115:2.084+0.008\left|L_{uckGrade}-113\right|,115 \le L_{uckGrade}<116:2.1+0.009\left|L_{uckGrade}-115\right|,116 \le L_{uckGrade}<118:2.109+0.008\left|L_{uckGrade}-116\right|,118 \le L_{uckGrade}<119:2.125+0.009\left|L_{uckGrade}-118\right|,119 \le L_{uckGrade}<124:2.134+0.008\left|L_{uckGrade}-119\right|,124 \le L_{uckGrade}<125:2.174+0.009\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<136:2.183+0.008\left|L_{uckGrade}-125\right|,136 \le L_{uckGrade}<137:2.271+0.007\left|L_{uckGrade}-136\right|,137 \le L_{uckGrade}<141:2.278+0.008\left|L_{uckGrade}-137\right|,141 \le L_{uckGrade}<142:2.31+0.007\left|L_{uckGrade}-141\right|,142 \le L_{uckGrade}<144:2.317+0.008\left|L_{uckGrade}-142\right|,144 \le L_{uckGrade}<145:2.333+0.007\left|L_{uckGrade}-144\right|,145 \le L_{uckGrade}<147:2.34+0.008\left|L_{uckGrade}-145\right|,147 \le L_{uckGrade}<148:2.356+0.007\left|L_{uckGrade}-147\right|,148 \le L_{uckGrade}<150:2.363+0.008\left|L_{uckGrade}-148\right|,150 \le L_{uckGrade}<151:2.379+0.007\left|L_{uckGrade}-150\right|,151 \le L_{uckGrade}<152:2.386+0.008\left|L_{uckGrade}-151\right|,152 \le L_{uckGrade}<153:2.394+0.007\left|L_{uckGrade}-152\right|,153 \le L_{uckGrade}<154:2.401+0.008\left|L_{uckGrade}-153\right|,154 \le L_{uckGrade}<155:2.409+0.007\left|L_{uckGrade}-154\right|,155 \le L_{uckGrade}<156:2.416+0.008\left|L_{uckGrade}-155\right|,156 \le L_{uckGrade}<158:2.424+0.007\left|L_{uckGrade}-156\right|,158 \le L_{uckGrade}<159:2.438+0.008\left|L_{uckGrade}-158\right|,159 \le L_{uckGrade}<160:2.446+0.007\left|L_{uckGrade}-159\right|,160 \le L_{uckGrade}<161:2.453+0.008\left|L_{uckGrade}-160\right|,161 \le L_{uckGrade}<164:2.461+0.007\left|L_{uckGrade}-161\right|,164 \le L_{uckGrade}<165:2.482+0.008\left|L_{uckGrade}-164\right|,165 \le L_{uckGrade}<168:2.49+0.007\left|L_{uckGrade}-165\right|,168 \le L_{uckGrade}<169:2.511+0.008\left|L_{uckGrade}-168\right|,169 \le L_{uckGrade}<184:2.519+0.007\left|L_{uckGrade}-169\right|,184 \le L_{uckGrade}<185:2.624+0.006\left|L_{uckGrade}-184\right|,185 \le L_{uckGrade}<188:2.63+0.007\left|L_{uckGrade}-185\right|,188 \le L_{uckGrade}<189:2.651+0.006\left|L_{uckGrade}-188\right|,189 \le L_{uckGrade}<192:2.657+0.007\left|L_{uckGrade}-189\right|,192 \le L_{uckGrade}<193:2.678+0.006\left|L_{uckGrade}-192\right|,193 \le L_{uckGrade}<194:2.684+0.007\left|L_{uckGrade}-193\right|,194 \le L_{uckGrade}<195:2.691+0.006\left|L_{uckGrade}-194\right|,195 \le L_{uckGrade}<197:2.697+0.007\left|L_{uckGrade}-195\right|,197 \le L_{uckGrade}<198:2.711+0.006\left|L_{uckGrade}-197\right|,198 \le L_{uckGrade}<199:2.717+0.007\left|L_{uckGrade}-198\right|,199 \le L_{uckGrade}<200:2.724+0.006\left|L_{uckGrade}-199\right|,200 \le L_{uckGrade}<201:2.73+0.007\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<202:2.737+0.006\left|L_{uckGrade}-201\right|,202 \le L_{uckGrade}<203:2.743+0.007\left|L_{uckGrade}-202\right|,203 \le L_{uckGrade}<205:2.75+0.006\left|L_{uckGrade}-203\right|,205 \le L_{uckGrade}<206:2.762+0.007\left|L_{uckGrade}-205\right|,206 \le L_{uckGrade}<208:2.769+0.006\left|L_{uckGrade}-206\right|,208 \le L_{uckGrade}<209:2.781+0.007\left|L_{uckGrade}-208\right|,209 \le L_{uckGrade}<212:2.788+0.006\left|L_{uckGrade}-209\right|,212 \le L_{uckGrade}<213:2.806+0.007\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<218:2.813+0.006\left|L_{uckGrade}-213\right|,218 \le L_{uckGrade}<219:2.843+0.007\left|L_{uckGrade}-218\right|,219 \le L_{uckGrade}<227:2.85+0.006\left|L_{uckGrade}-219\right|,227 \le L_{uckGrade}<228:2.898+0.005\left|L_{uckGrade}-227\right|,228 \le L_{uckGrade}<233:2.903+0.006\left|L_{uckGrade}-228\right|,233 \le L_{uckGrade}<234:2.933+0.005\left|L_{uckGrade}-233\right|,234 \le L_{uckGrade}<237:2.938+0.006\left|L_{uckGrade}-234\right|,237 \le L_{uckGrade}<238:2.956+0.005\left|L_{uckGrade}-237\right|,238 \le L_{uckGrade}<240:2.961+0.006\left|L_{uckGrade}-238\right|,240 \le L_{uckGrade}<241:2.973+0.005\left|L_{uckGrade}-240\right|,241 \le L_{uckGrade}<242:2.978+0.006\left|L_{uckGrade}-241\right|,242 \le L_{uckGrade}<243:2.984+0.005\left|L_{uckGrade}-242\right|,243 \le L_{uckGrade}<244:2.989+0.006\left|L_{uckGrade}-243\right|,244 \le L_{uckGrade}<245:2.995+0.005\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<246:3+0.006\left|L_{uckGrade}-245\right|,246 \le L_{uckGrade}<247:3.006+0.005\left|L_{uckGrade}-246\right|,247 \le L_{uckGrade}<248:3.011+0.006\left|L_{uckGrade}-247\right|,248 \le L_{uckGrade}<249:3.017+0.005\left|L_{uckGrade}-248\right|,249 \le L_{uckGrade}<250:3.022+0.006\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<252:3.028+0.005\left|L_{uckGrade}-250\right|,252 \le L_{uckGrade}<253:3.038+0.006\left|L_{uckGrade}-252\right|,253 \le L_{uckGrade}<255:3.044+0.005\left|L_{uckGrade}-253\right|,255 \le L_{uckGrade}<256:3.054+0.006\left|L_{uckGrade}-255\right|,256 \le L_{uckGrade}<258:3.06+0.005\left|L_{uckGrade}-256\right|,258 \le L_{uckGrade}<259:3.07+0.006\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<265:3.076+0.005\left|L_{uckGrade}-259\right|,265 \le L_{uckGrade}<266:3.106+0.006\left|L_{uckGrade}-265\right|,266 \le L_{uckGrade}<272:3.112+0.005\left|L_{uckGrade}-266\right|,272 \le L_{uckGrade}<273:3.142+0.004\left|L_{uckGrade}-272\right|,273 \le L_{uckGrade}<279:3.146+0.005\left|L_{uckGrade}-273\right|,279 \le L_{uckGrade}<280:3.176+0.004\left|L_{uckGrade}-279\right|,280 \le L_{uckGrade}<282:3.18+0.005\left|L_{uckGrade}-280\right|,282 \le L_{uckGrade}<283:3.19+0.004\left|L_{uckGrade}-282\right|,283 \le L_{uckGrade}<285:3.194+0.005\left|L_{uckGrade}-283\right|,285 \le L_{uckGrade}<286:3.204+0.004\left|L_{uckGrade}-285\right|,286 \le L_{uckGrade}<288:3.208+0.005\left|L_{uckGrade}-286\right|,288 \le L_{uckGrade}<289:3.218+0.004\left|L_{uckGrade}-288\right|,289 \le L_{uckGrade}<290:3.222+0.005\left|L_{uckGrade}-289\right|,290 \le L_{uckGrade}<291:3.227+0.004\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<292:3.231+0.005\left|L_{uckGrade}-291\right|,292 \le L_{uckGrade}<293:3.236+0.004\left|L_{uckGrade}-292\right|,293 \le L_{uckGrade}<294:3.24+0.005\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<295:3.245+0.004\left|L_{uckGrade}-294\right|,295 \le L_{uckGrade}<296:3.249+0.005\left|L_{uckGrade}-295\right|,296 \le L_{uckGrade}<297:3.254+0.004\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<298:3.258+0.005\left|L_{uckGrade}-297\right|,298 \le L_{uckGrade}<300:3.263+0.004\left|L_{uckGrade}-298\right|,300 \le L_{uckGrade}<301:3.271+0.005\left|L_{uckGrade}-300\right|,301 \le L_{uckGrade}<304:3.276+0.004\left|L_{uckGrade}-301\right|,304 \le L_{uckGrade}<305:3.288+0.005\left|L_{uckGrade}-304\right|,305 \le L_{uckGrade}<310:3.293+0.004\left|L_{uckGrade}-305\right|,310 \le L_{uckGrade}<311:3.313+0.005\left|L_{uckGrade}-310\right|,311 \le L_{uckGrade}<320:3.318+0.004\left|L_{uckGrade}-311\right|,320 \le L_{uckGrade}<321:3.354+0.003\left|L_{uckGrade}-320\right|,321 \le L_{uckGrade}<326:3.357+0.004\left|L_{uckGrade}-321\right|,326 \le L_{uckGrade}<327:3.377+0.003\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<329:3.38+0.004\left|L_{uckGrade}-327\right|,329 \le L_{uckGrade}<330:3.388+0.003\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<332:3.391+0.004\left|L_{uckGrade}-330\right|,332 \le L_{uckGrade}<333:3.399+0.003\left|L_{uckGrade}-332\right|,333 \le L_{uckGrade}<335:3.402+0.004\left|L_{uckGrade}-333\right|,335 \le L_{uckGrade}<336:3.41+0.003\left|L_{uckGrade}-335\right|,336 \le L_{uckGrade}<337:3.413+0.004\left|L_{uckGrade}-336\right|,337 \le L_{uckGrade}<338:3.417+0.003\left|L_{uckGrade}-337\right|,338 \le L_{uckGrade}<339:3.42+0.004\left|L_{uckGrade}-338\right|,339 \le L_{uckGrade}<340:3.424+0.003\left|L_{uckGrade}-339\right|,340 \le L_{uckGrade}<341:3.427+0.004\left|L_{uckGrade}-340\right|,341 \le L_{uckGrade}<343:3.431+0.003\left|L_{uckGrade}-341\right|,343 \le L_{uckGrade}<344:3.437+0.004\left|L_{uckGrade}-343\right|,344 \le L_{uckGrade}<345:3.441+0.003\left|L_{uckGrade}-344\right|,345 \le L_{uckGrade}<346:3.444+0.004\left|L_{uckGrade}-345\right|,346 \le L_{uckGrade}<348:3.448+0.003\left|L_{uckGrade}-346\right|,348 \le L_{uckGrade}<349:3.454+0.004\left|L_{uckGrade}-348\right|,349 \le L_{uckGrade}<353:3.458+0.003\left|L_{uckGrade}-349\right|,353 \le L_{uckGrade}<354:3.47+0.004\left|L_{uckGrade}-353\right|,354 \le L_{uckGrade}<369:3.474+0.003\left|L_{uckGrade}-354\right|,369 \le L_{uckGrade}<370:3.519+0.002\left|L_{uckGrade}-369\right|,370 \le L_{uckGrade}<374:3.521+0.003\left|L_{uckGrade}-370\right|,374 \le L_{uckGrade}<375:3.533+0.002\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<377:3.535+0.003\left|L_{uckGrade}-375\right|,377 \le L_{uckGrade}<378:3.541+0.002\left|L_{uckGrade}-377\right|,378 \le L_{uckGrade}<380:3.543+0.003\left|L_{uckGrade}-378\right|,380 \le L_{uckGrade}<381:3.549+0.002\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<382:3.551+0.003\left|L_{uckGrade}-381\right|,382 \le L_{uckGrade}<383:3.554+0.002\left|L_{uckGrade}-382\right|,383 \le L_{uckGrade}<384:3.556+0.003\left|L_{uckGrade}-383\right|,384 \le L_{uckGrade}<385:3.559+0.002\left|L_{uckGrade}-384\right|,385 \le L_{uckGrade}<386:3.561+0.003\left|L_{uckGrade}-385\right|,386 \le L_{uckGrade}<387:3.564+0.002\left|L_{uckGrade}-386\right|,387 \le L_{uckGrade}<388:3.566+0.003\left|L_{uckGrade}-387\right|,388 \le L_{uckGrade}<389:3.569+0.002\left|L_{uckGrade}-388\right|,389 \le L_{uckGrade}<390:3.571+0.003\left|L_{uckGrade}-389\right|,390 \le L_{uckGrade}<392:3.574+0.002\left|L_{uckGrade}-390\right|,392 \le L_{uckGrade}<393:3.578+0.003\left|L_{uckGrade}-392\right|,393 \le L_{uckGrade}<396:3.581+0.002\left|L_{uckGrade}-393\right|,396 \le L_{uckGrade}<397:3.587+0.003\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<401:3.59+0.002\left|L_{uckGrade}-397\right|,401 \le L_{uckGrade}<402:3.598+0.003\left|L_{uckGrade}-401\right|,402 \le L_{uckGrade}<414:3.601+0.002\left|L_{uckGrade}-402\right|,414 \le L_{uckGrade}<415:3.625+0.001\left|L_{uckGrade}-414\right|,415 \le L_{uckGrade}<419:3.626+0.002\left|L_{uckGrade}-415\right|,419 \le L_{uckGrade}<420:3.634+0.001\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<423:3.635+0.002\left|L_{uckGrade}-420\right|,423 \le L_{uckGrade}<424:3.641+0.001\left|L_{uckGrade}-423\right|,424 \le L_{uckGrade}<425:3.642+0.002\left|L_{uckGrade}-424\right|,425 \le L_{uckGrade}<426:3.644+0.001\left|L_{uckGrade}-425\right|,426 \le L_{uckGrade}<428:3.645+0.002\left|L_{uckGrade}-426\right|,428 \le L_{uckGrade}<429:3.649+0.001\left|L_{uckGrade}-428\right|,429 \le L_{uckGrade}<430:3.65+0.002\left|L_{uckGrade}-429\right|,430 \le L_{uckGrade}<431:3.652+0.001\left|L_{uckGrade}-430\right|,431 \le L_{uckGrade}<432:3.653+0.002\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<433:3.655+0.001\left|L_{uckGrade}-432\right|,433 \le L_{uckGrade}<434:3.656+0.002\left|L_{uckGrade}-433\right|,434 \le L_{uckGrade}<436:3.658+0.001\left|L_{uckGrade}-434\right|,436 \le L_{uckGrade}<437:3.66+0.002\left|L_{uckGrade}-436\right|,437 \le L_{uckGrade}<438:3.662+0.001\left|L_{uckGrade}-437\right|,438 \le L_{uckGrade}<439:3.663+0.002\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<442:3.665+0.001\left|L_{uckGrade}-439\right|,442 \le L_{uckGrade}<443:3.668+0.002\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<447:3.67+0.001\left|L_{uckGrade}-443\right|,447 \le L_{uckGrade}<448:3.674+0.002\left|L_{uckGrade}-447\right|,448 \le L_{uckGrade}<461:3.676+0.001\left|L_{uckGrade}-448\right|,461 \le L_{uckGrade}<462:3.689+0\left|L_{uckGrade}-461\right|,462 \le L_{uckGrade}<466:3.689+0.001\left|L_{uckGrade}-462\right|,466 \le L_{uckGrade}<467:3.693+0\left|L_{uckGrade}-466\right|,467 \le L_{uckGrade}<469:3.693+0.001\left|L_{uckGrade}-467\right|,469 \le L_{uckGrade}<470:3.695+0\left|L_{uckGrade}-469\right|,470 \le L_{uckGrade}<472:3.695+0.001\left|L_{uckGrade}-470\right|,472 \le L_{uckGrade}<473:3.697+0\left|L_{uckGrade}-472\right|,473 \le L_{uckGrade}<474:3.697+0.001\left|L_{uckGrade}-473\right|,474 \le L_{uckGrade}<475:3.698+0\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<476:3.698+0.001\left|L_{uckGrade}-475\right|,476 \le L_{uckGrade}<477:3.699+0\left|L_{uckGrade}-476\right|,477 \le L_{uckGrade}<478:3.699+0.001\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:3.7+0\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<480:3.7+0.001\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:3.701+0\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:3.701+0.001\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<484:3.702+0\left|L_{uckGrade}-482\right|,484 \le L_{uckGrade}<485:3.702+0.001\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<487:3.703+0\left|L_{uckGrade}-485\right|,487 \le L_{uckGrade}<488:3.703+0.001\left|L_{uckGrade}-487\right|,488 \le L_{uckGrade}<491:3.704+0\left|L_{uckGrade}-488\right|,491 \le L_{uckGrade}<492:3.704+0.001\left|L_{uckGrade}-491\right|,492 \le L_{uckGrade}<500:3.705+0\left|L_{uckGrade}-492\right|\right\}

See Example for how to use.

LaTeX Formula

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

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

L_{uckGrade08}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<2:1+0.013\left|L_{uckGrade}-0\right|,2 \le L_{uckGrade}<3:1.026+0.012\left|L_{uckGrade}-2\right|,3 \le L_{uckGrade}<6:1.038+0.013\left|L_{uckGrade}-3\right|,6 \le L_{uckGrade}<7:1.077+0.012\left|L_{uckGrade}-6\right|,7 \le L_{uckGrade}<9:1.089+0.013\left|L_{uckGrade}-7\right|,9 \le L_{uckGrade}<10:1.115+0.012\left|L_{uckGrade}-9\right|,10 \le L_{uckGrade}<11:1.127+0.013\left|L_{uckGrade}-10\right|,11 \le L_{uckGrade}<12:1.14+0.012\left|L_{uckGrade}-11\right|,12 \le L_{uckGrade}<13:1.152+0.013\left|L_{uckGrade}-12\right|,13 \le L_{uckGrade}<14:1.165+0.012\left|L_{uckGrade}-13\right|,14 \le L_{uckGrade}<15:1.177+0.013\left|L_{uckGrade}-14\right|,15 \le L_{uckGrade}<16:1.19+0.012\left|L_{uckGrade}-15\right|,16 \le L_{uckGrade}<17:1.202+0.013\left|L_{uckGrade}-16\right|,17 \le L_{uckGrade}<19:1.215+0.012\left|L_{uckGrade}-17\right|,19 \le L_{uckGrade}<20:1.239+0.013\left|L_{uckGrade}-19\right|,20 \le L_{uckGrade}<23:1.252+0.012\left|L_{uckGrade}-20\right|,23 \le L_{uckGrade}<24:1.288+0.013\left|L_{uckGrade}-23\right|,24 \le L_{uckGrade}<28:1.301+0.012\left|L_{uckGrade}-24\right|,28 \le L_{uckGrade}<29:1.349+0.013\left|L_{uckGrade}-28\right|,29 \le L_{uckGrade}<36:1.362+0.012\left|L_{uckGrade}-29\right|,36 \le L_{uckGrade}<37:1.446+0.011\left|L_{uckGrade}-36\right|,37 \le L_{uckGrade}<42:1.457+0.012\left|L_{uckGrade}-37\right|,42 \le L_{uckGrade}<43:1.517+0.011\left|L_{uckGrade}-42\right|,43 \le L_{uckGrade}<45:1.528+0.012\left|L_{uckGrade}-43\right|,45 \le L_{uckGrade}<46:1.552+0.011\left|L_{uckGrade}-45\right|,46 \le L_{uckGrade}<48:1.563+0.012\left|L_{uckGrade}-46\right|,48 \le L_{uckGrade}<49:1.587+0.011\left|L_{uckGrade}-48\right|,49 \le L_{uckGrade}<50:1.598+0.012\left|L_{uckGrade}-49\right|,50 \le L_{uckGrade}<51:1.61+0.011\left|L_{uckGrade}-50\right|,51 \le L_{uckGrade}<52:1.621+0.012\left|L_{uckGrade}-51\right|,52 \le L_{uckGrade}<53:1.633+0.011\left|L_{uckGrade}-52\right|,53 \le L_{uckGrade}<54:1.644+0.012\left|L_{uckGrade}-53\right|,54 \le L_{uckGrade}<55:1.656+0.011\left|L_{uckGrade}-54\right|,55 \le L_{uckGrade}<56:1.667+0.012\left|L_{uckGrade}-55\right|,56 \le L_{uckGrade}<58:1.679+0.011\left|L_{uckGrade}-56\right|,58 \le L_{uckGrade}<59:1.701+0.012\left|L_{uckGrade}-58\right|,59 \le L_{uckGrade}<61:1.713+0.011\left|L_{uckGrade}-59\right|,61 \le L_{uckGrade}<62:1.735+0.012\left|L_{uckGrade}-61\right|,62 \le L_{uckGrade}<66:1.747+0.011\left|L_{uckGrade}-62\right|,66 \le L_{uckGrade}<67:1.791+0.012\left|L_{uckGrade}-66\right|,67 \le L_{uckGrade}<76:1.803+0.011\left|L_{uckGrade}-67\right|,76 \le L_{uckGrade}<77:1.902+0.01\left|L_{uckGrade}-76\right|,77 \le L_{uckGrade}<81:1.912+0.011\left|L_{uckGrade}-77\right|,81 \le L_{uckGrade}<82:1.956+0.01\left|L_{uckGrade}-81\right|,82 \le L_{uckGrade}<85:1.966+0.011\left|L_{uckGrade}-82\right|,85 \le L_{uckGrade}<86:1.999+0.01\left|L_{uckGrade}-85\right|,86 \le L_{uckGrade}<87:2.009+0.011\left|L_{uckGrade}-86\right|,87 \le L_{uckGrade}<88:2.02+0.01\left|L_{uckGrade}-87\right|,88 \le L_{uckGrade}<90:2.03+0.011\left|L_{uckGrade}-88\right|,90 \le L_{uckGrade}<91:2.052+0.01\left|L_{uckGrade}-90\right|,91 \le L_{uckGrade}<92:2.062+0.011\left|L_{uckGrade}-91\right|,92 \le L_{uckGrade}<94:2.073+0.01\left|L_{uckGrade}-92\right|,94 \le L_{uckGrade}<95:2.093+0.011\left|L_{uckGrade}-94\right|,95 \le L_{uckGrade}<96:2.104+0.01\left|L_{uckGrade}-95\right|,96 \le L_{uckGrade}<97:2.114+0.011\left|L_{uckGrade}-96\right|,97 \le L_{uckGrade}<99:2.125+0.01\left|L_{uckGrade}-97\right|,99 \le L_{uckGrade}<100:2.145+0.011\left|L_{uckGrade}-99\right|,100 \le L_{uckGrade}<104:2.156+0.01\left|L_{uckGrade}-100\right|,104 \le L_{uckGrade}<105:2.196+0.011\left|L_{uckGrade}-104\right|,105 \le L_{uckGrade}<116:2.207+0.01\left|L_{uckGrade}-105\right|,116 \le L_{uckGrade}<117:2.317+0.009\left|L_{uckGrade}-116\right|,117 \le L_{uckGrade}<121:2.326+0.01\left|L_{uckGrade}-117\right|,121 \le L_{uckGrade}<122:2.366+0.009\left|L_{uckGrade}-121\right|,122 \le L_{uckGrade}<124:2.375+0.01\left|L_{uckGrade}-122\right|,124 \le L_{uckGrade}<125:2.395+0.009\left|L_{uckGrade}-124\right|,125 \le L_{uckGrade}<127:2.404+0.01\left|L_{uckGrade}-125\right|,127 \le L_{uckGrade}<128:2.424+0.009\left|L_{uckGrade}-127\right|,128 \le L_{uckGrade}<129:2.433+0.01\left|L_{uckGrade}-128\right|,129 \le L_{uckGrade}<130:2.443+0.009\left|L_{uckGrade}-129\right|,130 \le L_{uckGrade}<131:2.452+0.01\left|L_{uckGrade}-130\right|,131 \le L_{uckGrade}<132:2.462+0.009\left|L_{uckGrade}-131\right|,132 \le L_{uckGrade}<133:2.471+0.01\left|L_{uckGrade}-132\right|,133 \le L_{uckGrade}<135:2.481+0.009\left|L_{uckGrade}-133\right|,135 \le L_{uckGrade}<136:2.499+0.01\left|L_{uckGrade}-135\right|,136 \le L_{uckGrade}<138:2.509+0.009\left|L_{uckGrade}-136\right|,138 \le L_{uckGrade}<139:2.527+0.01\left|L_{uckGrade}-138\right|,139 \le L_{uckGrade}<142:2.537+0.009\left|L_{uckGrade}-139\right|,142 \le L_{uckGrade}<143:2.564+0.01\left|L_{uckGrade}-142\right|,143 \le L_{uckGrade}<156:2.574+0.009\left|L_{uckGrade}-143\right|,156 \le L_{uckGrade}<157:2.691+0.008\left|L_{uckGrade}-156\right|,157 \le L_{uckGrade}<160:2.699+0.009\left|L_{uckGrade}-157\right|,160 \le L_{uckGrade}<161:2.726+0.008\left|L_{uckGrade}-160\right|,161 \le L_{uckGrade}<163:2.734+0.009\left|L_{uckGrade}-161\right|,163 \le L_{uckGrade}<164:2.752+0.008\left|L_{uckGrade}-163\right|,164 \le L_{uckGrade}<166:2.76+0.009\left|L_{uckGrade}-164\right|,166 \le L_{uckGrade}<167:2.778+0.008\left|L_{uckGrade}-166\right|,167 \le L_{uckGrade}<168:2.786+0.009\left|L_{uckGrade}-167\right|,168 \le L_{uckGrade}<169:2.795+0.008\left|L_{uckGrade}-168\right|,169 \le L_{uckGrade}<170:2.803+0.009\left|L_{uckGrade}-169\right|,170 \le L_{uckGrade}<171:2.812+0.008\left|L_{uckGrade}-170\right|,171 \le L_{uckGrade}<172:2.82+0.009\left|L_{uckGrade}-171\right|,172 \le L_{uckGrade}<174:2.829+0.008\left|L_{uckGrade}-172\right|,174 \le L_{uckGrade}<175:2.845+0.009\left|L_{uckGrade}-174\right|,175 \le L_{uckGrade}<176:2.854+0.008\left|L_{uckGrade}-175\right|,176 \le L_{uckGrade}<177:2.862+0.009\left|L_{uckGrade}-176\right|,177 \le L_{uckGrade}<181:2.871+0.008\left|L_{uckGrade}-177\right|,181 \le L_{uckGrade}<182:2.903+0.009\left|L_{uckGrade}-181\right|,182 \le L_{uckGrade}<196:2.912+0.008\left|L_{uckGrade}-182\right|,196 \le L_{uckGrade}<197:3.024+0.007\left|L_{uckGrade}-196\right|,197 \le L_{uckGrade}<200:3.031+0.008\left|L_{uckGrade}-197\right|,200 \le L_{uckGrade}<201:3.055+0.007\left|L_{uckGrade}-200\right|,201 \le L_{uckGrade}<203:3.062+0.008\left|L_{uckGrade}-201\right|,203 \le L_{uckGrade}<204:3.078+0.007\left|L_{uckGrade}-203\right|,204 \le L_{uckGrade}<205:3.085+0.008\left|L_{uckGrade}-204\right|,205 \le L_{uckGrade}<206:3.093+0.007\left|L_{uckGrade}-205\right|,206 \le L_{uckGrade}<207:3.1+0.008\left|L_{uckGrade}-206\right|,207 \le L_{uckGrade}<208:3.108+0.007\left|L_{uckGrade}-207\right|,208 \le L_{uckGrade}<209:3.115+0.008\left|L_{uckGrade}-208\right|,209 \le L_{uckGrade}<210:3.123+0.007\left|L_{uckGrade}-209\right|,210 \le L_{uckGrade}<211:3.13+0.008\left|L_{uckGrade}-210\right|,211 \le L_{uckGrade}<212:3.138+0.007\left|L_{uckGrade}-211\right|,212 \le L_{uckGrade}<213:3.145+0.008\left|L_{uckGrade}-212\right|,213 \le L_{uckGrade}<215:3.153+0.007\left|L_{uckGrade}-213\right|,215 \le L_{uckGrade}<216:3.167+0.008\left|L_{uckGrade}-215\right|,216 \le L_{uckGrade}<219:3.175+0.007\left|L_{uckGrade}-216\right|,219 \le L_{uckGrade}<220:3.196+0.008\left|L_{uckGrade}-219\right|,220 \le L_{uckGrade}<235:3.204+0.007\left|L_{uckGrade}-220\right|,235 \le L_{uckGrade}<236:3.309+0.006\left|L_{uckGrade}-235\right|,236 \le L_{uckGrade}<239:3.315+0.007\left|L_{uckGrade}-236\right|,239 \le L_{uckGrade}<240:3.336+0.006\left|L_{uckGrade}-239\right|,240 \le L_{uckGrade}<242:3.342+0.007\left|L_{uckGrade}-240\right|,242 \le L_{uckGrade}<243:3.356+0.006\left|L_{uckGrade}-242\right|,243 \le L_{uckGrade}<244:3.362+0.007\left|L_{uckGrade}-243\right|,244 \le L_{uckGrade}<245:3.369+0.006\left|L_{uckGrade}-244\right|,245 \le L_{uckGrade}<247:3.375+0.007\left|L_{uckGrade}-245\right|,247 \le L_{uckGrade}<249:3.389+0.006\left|L_{uckGrade}-247\right|,249 \le L_{uckGrade}<250:3.401+0.007\left|L_{uckGrade}-249\right|,250 \le L_{uckGrade}<251:3.408+0.006\left|L_{uckGrade}-250\right|,251 \le L_{uckGrade}<252:3.414+0.007\left|L_{uckGrade}-251\right|,252 \le L_{uckGrade}<254:3.421+0.006\left|L_{uckGrade}-252\right|,254 \le L_{uckGrade}<255:3.433+0.007\left|L_{uckGrade}-254\right|,255 \le L_{uckGrade}<258:3.44+0.006\left|L_{uckGrade}-255\right|,258 \le L_{uckGrade}<259:3.458+0.007\left|L_{uckGrade}-258\right|,259 \le L_{uckGrade}<275:3.465+0.006\left|L_{uckGrade}-259\right|,275 \le L_{uckGrade}<276:3.561+0.005\left|L_{uckGrade}-275\right|,276 \le L_{uckGrade}<278:3.566+0.006\left|L_{uckGrade}-276\right|,278 \le L_{uckGrade}<279:3.578+0.005\left|L_{uckGrade}-278\right|,279 \le L_{uckGrade}<281:3.583+0.006\left|L_{uckGrade}-279\right|,281 \le L_{uckGrade}<282:3.595+0.005\left|L_{uckGrade}-281\right|,282 \le L_{uckGrade}<284:3.6+0.006\left|L_{uckGrade}-282\right|,284 \le L_{uckGrade}<285:3.612+0.005\left|L_{uckGrade}-284\right|,285 \le L_{uckGrade}<286:3.617+0.006\left|L_{uckGrade}-285\right|,286 \le L_{uckGrade}<287:3.623+0.005\left|L_{uckGrade}-286\right|,287 \le L_{uckGrade}<288:3.628+0.006\left|L_{uckGrade}-287\right|,288 \le L_{uckGrade}<290:3.634+0.005\left|L_{uckGrade}-288\right|,290 \le L_{uckGrade}<291:3.644+0.006\left|L_{uckGrade}-290\right|,291 \le L_{uckGrade}<293:3.65+0.005\left|L_{uckGrade}-291\right|,293 \le L_{uckGrade}<294:3.66+0.006\left|L_{uckGrade}-293\right|,294 \le L_{uckGrade}<296:3.666+0.005\left|L_{uckGrade}-294\right|,296 \le L_{uckGrade}<297:3.676+0.006\left|L_{uckGrade}-296\right|,297 \le L_{uckGrade}<314:3.682+0.005\left|L_{uckGrade}-297\right|,314 \le L_{uckGrade}<315:3.767+0.004\left|L_{uckGrade}-314\right|,315 \le L_{uckGrade}<318:3.771+0.005\left|L_{uckGrade}-315\right|,318 \le L_{uckGrade}<319:3.786+0.004\left|L_{uckGrade}-318\right|,319 \le L_{uckGrade}<320:3.79+0.005\left|L_{uckGrade}-319\right|,320 \le L_{uckGrade}<321:3.795+0.004\left|L_{uckGrade}-320\right|,321 \le L_{uckGrade}<323:3.799+0.005\left|L_{uckGrade}-321\right|,323 \le L_{uckGrade}<324:3.809+0.004\left|L_{uckGrade}-323\right|,324 \le L_{uckGrade}<325:3.813+0.005\left|L_{uckGrade}-324\right|,325 \le L_{uckGrade}<326:3.818+0.004\left|L_{uckGrade}-325\right|,326 \le L_{uckGrade}<327:3.822+0.005\left|L_{uckGrade}-326\right|,327 \le L_{uckGrade}<329:3.827+0.004\left|L_{uckGrade}-327\right|,329 \le L_{uckGrade}<330:3.835+0.005\left|L_{uckGrade}-329\right|,330 \le L_{uckGrade}<331:3.84+0.004\left|L_{uckGrade}-330\right|,331 \le L_{uckGrade}<332:3.844+0.005\left|L_{uckGrade}-331\right|,332 \le L_{uckGrade}<335:3.849+0.004\left|L_{uckGrade}-332\right|,335 \le L_{uckGrade}<336:3.861+0.005\left|L_{uckGrade}-335\right|,336 \le L_{uckGrade}<342:3.866+0.004\left|L_{uckGrade}-336\right|,342 \le L_{uckGrade}<343:3.89+0.005\left|L_{uckGrade}-342\right|,343 \le L_{uckGrade}<346:3.895+0.004\left|L_{uckGrade}-343\right|,346 \le L_{uckGrade}<347:3.907+0.003\left|L_{uckGrade}-346\right|,347 \le L_{uckGrade}<353:3.91+0.004\left|L_{uckGrade}-347\right|,353 \le L_{uckGrade}<354:3.934+0.003\left|L_{uckGrade}-353\right|,354 \le L_{uckGrade}<357:3.937+0.004\left|L_{uckGrade}-354\right|,357 \le L_{uckGrade}<358:3.949+0.003\left|L_{uckGrade}-357\right|,358 \le L_{uckGrade}<359:3.952+0.004\left|L_{uckGrade}-358\right|,359 \le L_{uckGrade}<360:3.956+0.003\left|L_{uckGrade}-359\right|,360 \le L_{uckGrade}<362:3.959+0.004\left|L_{uckGrade}-360\right|,362 \le L_{uckGrade}<363:3.967+0.003\left|L_{uckGrade}-362\right|,363 \le L_{uckGrade}<364:3.97+0.004\left|L_{uckGrade}-363\right|,364 \le L_{uckGrade}<365:3.974+0.003\left|L_{uckGrade}-364\right|,365 \le L_{uckGrade}<366:3.977+0.004\left|L_{uckGrade}-365\right|,366 \le L_{uckGrade}<367:3.981+0.003\left|L_{uckGrade}-366\right|,367 \le L_{uckGrade}<368:3.984+0.004\left|L_{uckGrade}-367\right|,368 \le L_{uckGrade}<370:3.988+0.003\left|L_{uckGrade}-368\right|,370 \le L_{uckGrade}<371:3.994+0.004\left|L_{uckGrade}-370\right|,371 \le L_{uckGrade}<374:3.998+0.003\left|L_{uckGrade}-371\right|,374 \le L_{uckGrade}<375:4.007+0.004\left|L_{uckGrade}-374\right|,375 \le L_{uckGrade}<380:4.011+0.003\left|L_{uckGrade}-375\right|,380 \le L_{uckGrade}<381:4.026+0.004\left|L_{uckGrade}-380\right|,381 \le L_{uckGrade}<386:4.03+0.003\left|L_{uckGrade}-381\right|,386 \le L_{uckGrade}<387:4.045+0.002\left|L_{uckGrade}-386\right|,387 \le L_{uckGrade}<392:4.047+0.003\left|L_{uckGrade}-387\right|,392 \le L_{uckGrade}<393:4.062+0.002\left|L_{uckGrade}-392\right|,393 \le L_{uckGrade}<396:4.064+0.003\left|L_{uckGrade}-393\right|,396 \le L_{uckGrade}<397:4.073+0.002\left|L_{uckGrade}-396\right|,397 \le L_{uckGrade}<399:4.075+0.003\left|L_{uckGrade}-397\right|,399 \le L_{uckGrade}<400:4.081+0.002\left|L_{uckGrade}-399\right|,400 \le L_{uckGrade}<401:4.083+0.003\left|L_{uckGrade}-400\right|,401 \le L_{uckGrade}<402:4.086+0.002\left|L_{uckGrade}-401\right|,402 \le L_{uckGrade}<403:4.088+0.003\left|L_{uckGrade}-402\right|,403 \le L_{uckGrade}<404:4.091+0.002\left|L_{uckGrade}-403\right|,404 \le L_{uckGrade}<405:4.093+0.003\left|L_{uckGrade}-404\right|,405 \le L_{uckGrade}<406:4.096+0.002\left|L_{uckGrade}-405\right|,406 \le L_{uckGrade}<407:4.098+0.003\left|L_{uckGrade}-406\right|,407 \le L_{uckGrade}<409:4.101+0.002\left|L_{uckGrade}-407\right|,409 \le L_{uckGrade}<410:4.105+0.003\left|L_{uckGrade}-409\right|,410 \le L_{uckGrade}<413:4.108+0.002\left|L_{uckGrade}-410\right|,413 \le L_{uckGrade}<414:4.114+0.003\left|L_{uckGrade}-413\right|,414 \le L_{uckGrade}<419:4.117+0.002\left|L_{uckGrade}-414\right|,419 \le L_{uckGrade}<420:4.127+0.003\left|L_{uckGrade}-419\right|,420 \le L_{uckGrade}<425:4.13+0.002\left|L_{uckGrade}-420\right|,425 \le L_{uckGrade}<426:4.14+0.001\left|L_{uckGrade}-425\right|,426 \le L_{uckGrade}<431:4.141+0.002\left|L_{uckGrade}-426\right|,431 \le L_{uckGrade}<432:4.151+0.001\left|L_{uckGrade}-431\right|,432 \le L_{uckGrade}<435:4.152+0.002\left|L_{uckGrade}-432\right|,435 \le L_{uckGrade}<436:4.158+0.001\left|L_{uckGrade}-435\right|,436 \le L_{uckGrade}<438:4.159+0.002\left|L_{uckGrade}-436\right|,438 \le L_{uckGrade}<439:4.163+0.001\left|L_{uckGrade}-438\right|,439 \le L_{uckGrade}<440:4.164+0.002\left|L_{uckGrade}-439\right|,440 \le L_{uckGrade}<441:4.166+0.001\left|L_{uckGrade}-440\right|,441 \le L_{uckGrade}<442:4.167+0.002\left|L_{uckGrade}-441\right|,442 \le L_{uckGrade}<443:4.169+0.001\left|L_{uckGrade}-442\right|,443 \le L_{uckGrade}<444:4.17+0.002\left|L_{uckGrade}-443\right|,444 \le L_{uckGrade}<445:4.172+0.001\left|L_{uckGrade}-444\right|,445 \le L_{uckGrade}<446:4.173+0.002\left|L_{uckGrade}-445\right|,446 \le L_{uckGrade}<448:4.175+0.001\left|L_{uckGrade}-446\right|,448 \le L_{uckGrade}<449:4.177+0.002\left|L_{uckGrade}-448\right|,449 \le L_{uckGrade}<452:4.179+0.001\left|L_{uckGrade}-449\right|,452 \le L_{uckGrade}<453:4.182+0.002\left|L_{uckGrade}-452\right|,453 \le L_{uckGrade}<457:4.184+0.001\left|L_{uckGrade}-453\right|,457 \le L_{uckGrade}<458:4.188+0.002\left|L_{uckGrade}-457\right|,458 \le L_{uckGrade}<465:4.19+0.001\left|L_{uckGrade}-458\right|,465 \le L_{uckGrade}<466:4.197+0\left|L_{uckGrade}-465\right|,466 \le L_{uckGrade}<471:4.197+0.001\left|L_{uckGrade}-466\right|,471 \le L_{uckGrade}<472:4.202+0\left|L_{uckGrade}-471\right|,472 \le L_{uckGrade}<474:4.202+0.001\left|L_{uckGrade}-472\right|,474 \le L_{uckGrade}<475:4.204+0\left|L_{uckGrade}-474\right|,475 \le L_{uckGrade}<477:4.204+0.001\left|L_{uckGrade}-475\right|,477 \le L_{uckGrade}<478:4.206+0\left|L_{uckGrade}-477\right|,478 \le L_{uckGrade}<479:4.206+0.001\left|L_{uckGrade}-478\right|,479 \le L_{uckGrade}<480:4.207+0\left|L_{uckGrade}-479\right|,480 \le L_{uckGrade}<481:4.207+0.001\left|L_{uckGrade}-480\right|,481 \le L_{uckGrade}<482:4.208+0\left|L_{uckGrade}-481\right|,482 \le L_{uckGrade}<483:4.208+0.001\left|L_{uckGrade}-482\right|,483 \le L_{uckGrade}<484:4.209+0\left|L_{uckGrade}-483\right|,484 \le L_{uckGrade}<485:4.209+0.001\left|L_{uckGrade}-484\right|,485 \le L_{uckGrade}<487:4.21+0\left|L_{uckGrade}-485\right|,487 \le L_{uckGrade}<488:4.21+0.001\left|L_{uckGrade}-487\right|,488 \le L_{uckGrade}<490:4.211+0\left|L_{uckGrade}-488\right|,490 \le L_{uckGrade}<491:4.211+0.001\left|L_{uckGrade}-490\right|,491 \le L_{uckGrade}<496:4.212+0\left|L_{uckGrade}-491\right|,496 \le L_{uckGrade}<497:4.212+0.001\left|L_{uckGrade}-496\right|,497 \le L_{uckGrade}<500:4.213+0\left|L_{uckGrade}-497\right|\right\}

See Example for how to use.

If the Luck Scalar Graph doesn't cover a Scalar value you wish to see please reference the desmos graph.
The desmos graph displays the LaTeX equations.

Probabilities from Luck

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

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

Example last updated on Patch:6.5#Hotfix 53. Figures may be outdated, but the math and concepts remain the same.

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

Luck Grade	Drop Rate
0	220
1	250
2	200
3	150
4	100
5	50
6	20
7	10
8	0

Every monster with a quest drop uses this Drop Rate table, however, depending on the monster's Loot Table, most of the Luck Grades will be associated with dropping nothing.
And in other instances, like Dire Wolf, a Luck Grade's rate may be split between two or more Loot drops.
This will not affect the calculations below, but they will determine an individual item's probability.

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

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

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

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White} {\color[RGB]{50, 50, 50}1.000 \cdot \textbf{220} } + {\color[RGB]{100, 100, 100}1.000 \cdot \textbf{250} } + {\color[RGB]{222, 222, 222}1.000 \cdot \textbf{200} } + {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{150} } + {\color[RGB]{74, 155, 209}1.000 \cdot \textbf{100} } + {\color[RGB]{173, 90, 255}1.000 \cdot \textbf{50} } + {\color[RGB]{247, 162, 45}1.000 \cdot \textbf{20} } + {\color[RGB]{227, 216, 140}1.000 \cdot \textbf{10} } + {\color[RGB]{227, 216, 140}1.000 \cdot \textbf{0} } = {\color{violet}1000} }

Luck Grade	Drop Probability at 0 Luck
0	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{50, 50, 50}1.000 \cdot \textbf{220} } }{ {\color{violet}1000} }=22\%}
1	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {250}}}{\color {violet}1000}}=25\%$
2	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {200}}}{\color {violet}1000}}=20\%$
3	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1000}}=15\%$
4	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {100}}}{\color {violet}1000}}=10\%$
5	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {50}}}{\color {violet}1000}}=5\%$
6	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {20}}}{\color {violet}1000}}=2\%$
7	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {10}}}{\color {violet}1000}}=1\%$
8	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}{\color {violet}1000}}=0\%$

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

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {220}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {250}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {200}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {100}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.125\cdot {\textbf {50}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {20}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {10}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}={\color {violet}1227.42}$

Luck Grade	Drop Probability at 250 Luck
0	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {220}}}{\color {violet}1227.42}}=13.443\%$
1	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {250}}}{\color {violet}1227.42}}=15.276\%$
2	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {200}}}{\color {violet}1227.42}}=14.258\%$
3	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1227.42}}=12.221\%$
4	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {100}}}{\color {violet}1227.42}}=23.448\%$
5	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.125\cdot {\textbf {50}}}{\color {violet}1227.42}}=12.868\%$
6	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {20}}}{\color {violet}1227.42}}=5.607\%$
7	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {10}}}{\color {violet}1227.42}}=2.880\%$
8	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}{\color {violet}1227.42}}=0\%$

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

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {220}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {250}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {200}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}3.505\cdot {\textbf {100}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {50}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {20}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {10}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {0}}}={\color {violet}1208.51}$

Luck Grade	Drop Probability at 500 Luck
0	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {220}}}{\color {violet}1208.51}}=9.102\%$
1	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {250}}}{\color {violet}1208.51}}=10.343\%$
2	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {200}}}{\color {violet}1208.51}}=12.412\%$
3	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1208.51}}=12.412\%$
4	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}3.505\cdot {\textbf {100}}}{\color {violet}1208.51}}=29.003\%$
5	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {50}}}{\color {violet}1208.51}}=16.057\%$
6	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {20}}}{\color {violet}1208.51}}=7.045\%$
7	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {10}}}{\color {violet}1208.51}}=3.626\%$
8	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {0}}}{\color {violet}1208.51}}=0\%$

Example last updated on Patch:6.5#Hotfix 53. Figures may be outdated, but the math and concepts remain the same.

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

Luck Grade	Drop Rate
0	99900
1	0
2	100
3	0
4	0
5	0
6	0
7	0
8	0

The Loot Table for the Gold Coin Chest is rather simple. At Luck Grade 0 you get nothing. At Luck Grade 2 you get 1 Gold Coin Chest.

Notice that despite the Gold Coin Chest's item rarity being 7, its Luck Grade is actually 2.
Despite the being equal for most items, Item Rarity does not equal Luck Grade.

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

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

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {99900}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {100}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}={\color {violet}100000}$

Luck Grade	Drop Probability at 0 Luck
0	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {99900}}}{\color {violet}100000}}=99.9\%$
1	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
2	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {100}}}{\color {violet}100000}}=0.1\%$
3	$\color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
4	$\color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
5	$\color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
6	$\color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
7	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$
8	$\color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%$

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

$\color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {99900}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {0}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {100}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {0}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.159\cdot {\textbf {0}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}={\color {violet}75012.5}$

Luck Grade	Drop Probability at 250 Luck
0	$\color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {99900}}}{\color {violet}75012.5}}=99.883\%$
1	$\color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%$
2	$\color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {100}}}{\color {violet}75012.5}}=0.117\%$
3	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}
4	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{74, 155, 209}2.878 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}
5	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{173, 90, 255}3.159 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}
6	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{247, 162, 45}3.441 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}
7	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}
8	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{227, 216, 140}3.535 \cdot \textbf{0} } }{ {\color{violet}75012.5} }=0\%}

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

Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White} {\color[RGB]{50, 50, 50}0.500 \cdot \textbf{99900} } + {\color[RGB]{100, 100, 100}0.500 \cdot \textbf{0} } + {\color[RGB]{222, 222, 222}0.750 \cdot \textbf{100} } + {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } + {\color[RGB]{74, 155, 209}3.505 \cdot \textbf{0} } + {\color[RGB]{173, 90, 255}3.881 \cdot \textbf{0} } + {\color[RGB]{247, 162, 45}4.257 \cdot \textbf{0} } + {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } + {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } = {\color{violet}50025} }

Luck Grade	Drop Probability at 500 Luck
0	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{50, 50, 50}0.500 \cdot \textbf{99900} } }{ {\color{violet}50025} }=99.850\%}
1	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{100, 100, 100}0.500 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
2	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{222, 222, 222}0.750 \cdot \textbf{100} } }{ {\color{violet}50025} }=0.150\%}
3	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{98, 190, 11}1.000 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
4	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{74, 155, 209}3.505 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
5	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{173, 90, 255}3.881 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
6	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{247, 162, 45}4.257 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
7	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}
8	Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White}\frac{ {\color[RGB]{227, 216, 140}4.382 \cdot \textbf{0} } }{ {\color{violet}50025} }=0\%}

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.

How to Use Wiki Tables and Graphs

On loose loot, monster, and prop pages the wiki displays graphs and tables showcasing the effect of luck on specific luck grades and loot tables.
The meaning of these graphs can be obtuse so we will walk through an example using the graphs and (partial) tables of the Inferno Treasure Hoard.

The following tables for illustrative purposes only. They are not updated to match the current patch so only use them for learning purposes. The concepts remain the same.

Graphs

For each luck value "X" the graph displays the ratio between the probability of a specific luck grade at X luck over the probability of that same luck grade at 0 luck.
Not only does this visualize the effect luck has on probabilities, these ratios can be used to calculate probabilities of specific items and luck grades.

To see how probabilities at X luck are calculated see the following section: Probabilities from Luck.

Note that you can choose which luck grades are displayed by toggling the luck grade in the legend. Simply click on them to disable and enable the luck grade curve.

Tables

Loot Summaries

Loot Summaries present basic sums of probabilities in loot table grouped by rarities and item types.
They ignore properties like luck grades, however, so beware that you cannot always use the ratios in the luck effect graph to get specific probabilities for a rarity/type.

In the case of the TreasureHoardHR3, however, rarity matches luck grade one to one, so we can go between luck 0 summaries and luck 150 summaries simply by applying the proper ratios.
Applying the ratio for luck 150 to the legend rarity we get: Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White} 1.43386 \cdot 2.5\% = 3.58465\%} , which matches the tables below.

Loot Summary at 0 Luck

Type Rarity	Misc 100%
Common 15%	15.0%
Uncommon 20.5%	20.5%
Rare 45%	45.0%
Epic 17%	17.0%
Legend 2.5%	2.5%

Loot Summary at 150 Luck

Type Rarity	Misc 100%
Common 7.48%	7.4821%
Uncommon 11.05%	11.0546%
Rare 55.25%	55.254%
Epic 22.62%	22.6247%
Legend 3.58%	3.5846%

Loot Table

Loot Tables are sorted alphanumerically by item name.
These tables only display items that can drop, they won't display entries for dropping nothing.
In cases where a table can drop nothing it is best to look at the luck effect graph and loot summary to see if there are any "nothing" drops.

Loot Table

Name	Type	Luck GradeLuck Grades present on the graph but missing in the column below are associated with dropping nothing.	Rarity	Item Count	Probability
Ancient Scroll	Misc	2	Common	1	0.5%
	Misc	3	Uncommon	1	0.6833%
	Misc	4	Rare	1	1.5%
	Misc	5	Epic	1	0.5667%
	Misc	6	Legendary	1	0.0833%
Blue Sapphire	Misc	2	Common	1	0.5%
	Misc	3	Uncommon	1	0.6833%
	Misc	4	Rare	1	1.5%
	Misc	5	Epic	1	0.5667%
	Misc	6	Legendary	1	0.0833%
Ceremonial Dagger	Misc	2	Common	1	0.5%
	Misc	3	Uncommon	1	0.6833%
	Misc	4	Rare	1	1.5%
	Misc	5	Epic	1	0.5667%
	Misc	6	Legendary	1	0.0833%
Diamond	Misc	2	Common	1	0.5%
	Misc	3	Uncommon	1	0.6833%
	Misc	4	Rare	1	1.5%
	Misc	5	Epic	1	0.5667%
	Misc	6	Legendary	1	0.0833%
...

Drop Source Table

Drop Source Tables are displayed on item pages. The drop source table for Viola is shown below.

If an item has any drop source from loose loot, monsters, or props, the table will show them, otherwise it will instead say that nothing drops that item.
The table rows are sorted by total expected value per source, i.e. the sum of count * probability * loot table rolls for each source's subrow.

Drop source table at 0 luck

NameSorted by total expected value in descending order TEV = Sum of all (Probability of 1 drop * Item count per roll * Roll count)	Type	Item count	Probability of 1+ drops per instance1-(1-probability per roll)(loot table roll count) Some loot tables are rolled multiple times per instance (i.e. monster kill/container interaction/loose loot generation). For further information, please reference the loot tables on the associated source page.
Frost Wyvern#Elite	Monster	1-3	0.2498%
Weapon FrozenRoom	Loose Loot	1	0.0714%
DualBossWeapon-Global#HR	Loose Loot	1	0.0038%

Example: Royal Diamond at 150 Luck

Suppose we are interested in the Royal Diamond and we want to calculate the probability for 150 luck.
We only need three pieces of information to calculate this: the luck grade, the probability at luck 0, and the probability ratio at luck 150.

First, we find the luck grade of the Royal Diamond: 6.
Next, since the loot table presents probabilities at luck 0, we simply look up the probability for the Royal Diamond: 0.0833%.
And lastly, we look at the graph for luck grade 6 at luck 150: 1.43386.

Combining all of this, we find that the probability of the Royal Diamond at 150 luck becomes Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \color{White} 1.43386 \cdot 0.0833\% = 0.1194\%}