From Dark and Darker Wiki
| Stats | Damage | Spell Restoration | Luck |
| Enchantments | Health | Impact Power | Footstep Sound |
| Healing | Action/Interaction/Cast Speed | Silence | |
| Shield | Looted Handled Supplied | Experience | |
| Spells |
Loot is rolled when you open the container or kill the mob.
Whoever opens the loot first or kills the mob first is the person whose luck is used to calculate the drops.
(It is not confirmed if Bard's Unchained Harmony rolls the loot table when it opens the containers.)
Luck is capped at 500.
It is possible to reach the Luck cap:
Each drop instance makes use of three pieces of information: the Loot Drop table, the Drop Rate table, and the player's Luck.
Loot Drop tables list all possible items for a specific drop instance, and for each item therein it associates a Luck Grade.
Drop Rate tables assign a "rate" to each Luck Grade; when normalized, these rates represent the probability of getting a drop of that Luck Grade.
Each Luck Grade's drop rate is split evenly between items that share that Luck Grade. This means that items sharing a Loot Drop table and Luck Grade, will always have the same probability of dropping.
However, be aware that Monsters and Containers can have multiple Loot Drop Tables, each with their own Drop Rate table. See Lich for example.
A Drop can be rolled more than once, but each roll is independent of the others.
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 Scalars are one piece of information needed to calculate drop probability at X Luck.
The calculation is not a simple multiplication, so do not expect Uniques to be 4.382 times more common at 500 Luck.
The true effect of Luck varies depending on Drop Rate tables.
See the Luck/Probabilities from Luck subsection for an in-depth explanation of how Luck Scalars affect probabilities of drops.
Luck Scalar Table
| Luck Grade | Luck | ||||||||||
| 0 | 50 | 100 | 150 | 200 | 250 | 300 | 350 | 400 | 450 | 500 | |
| 0 | 1.000 | 0.950 | 0.900 | 0.850 | 0.800 | 0.750 | 0.700 | 0.650 | 0.600 | 0.550 | 0.500 |
| 1 | 1.000 | 0.950 | 0.900 | 0.850 | 0.800 | 0.750 | 0.700 | 0.650 | 0.600 | 0.550 | 0.500 |
| 2 | 1.000 | 0.975 | 0.950 | 0.925 | 0.900 | 0.875 | 0.850 | 0.825 | 0.800 | 0.775 | 0.750 |
| 3 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
| 4 | 1.000 | 1.476 | 1.901 | 2.277 | 2.602 | 2.878 | 3.103 | 3.279 | 3.404 | 3.480 | 3.505 |
| 5 | 1.000 | 1.547 | 2.036 | 2.468 | 2.842 | 3.159 | 3.418 | 3.620 | 3.765 | 3.851 | 3.881 |
| 6 | 1.000 | 1.618 | 2.171 | 2.659 | 3.083 | 3.441 | 3.734 | 3.962 | 4.125 | 4.223 | 4.257 |
| 7 | 1.000 | 1.642 | 2.216 | 2.723 | 3.163 | 3.535 | 3.839 | 4.076 | 4.245 | 4.347 | 4.382 |
| 8 | 1.000 | 1.642 | 2.216 | 2.723 | 3.163 | 3.535 | 3.839 | 4.076 | 4.245 | 4.347 | 4.382 |
If the Luck Scalar Table and Graph don't cover a Scalar value you wish to see, use the desmos graph. The desmos graph displays the LaTeX equations which are continuous curves, but keep in mind that fractional values of Luck do not exist.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade00}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade01}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade02}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<10:1+0\left|L_{uckGrade}-0\right|,10 \le L_{uckGrade}<20:1+0\left|L_{uckGrade}-10\right|,20 \le L_{uckGrade}<30:0.999+0\left|L_{uckGrade}-20\right|,30 \le L_{uckGrade}<40:0.999+0\left|L_{uckGrade}-30\right|,40 \le L_{uckGrade}<50:0.998+0\left|L_{uckGrade}-40\right|,50 \le L_{uckGrade}<60:0.998+0\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<70:0.997+0\left|L_{uckGrade}-60\right|,70 \le L_{uckGrade}<80:0.997+0\left|L_{uckGrade}-70\right|,80 \le L_{uckGrade}<90:0.996+0\left|L_{uckGrade}-80\right|,90 \le L_{uckGrade}<100:0.996+0\left|L_{uckGrade}-90\right|,100 \le L_{uckGrade}<110:0.995+0\left|L_{uckGrade}-100\right|,110 \le L_{uckGrade}<120:0.995+0\left|L_{uckGrade}-110\right|,120 \le L_{uckGrade}<130:0.994+0\left|L_{uckGrade}-120\right|,130 \le L_{uckGrade}<140:0.994+0\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<150:0.993+0\left|L_{uckGrade}-140\right|,150 \le L_{uckGrade}<160:0.993+0\left|L_{uckGrade}-150\right|,160 \le L_{uckGrade}<170:0.992+0\left|L_{uckGrade}-160\right|,170 \le L_{uckGrade}<180:0.992+0\left|L_{uckGrade}-170\right|,180 \le L_{uckGrade}<190:0.991+0\left|L_{uckGrade}-180\right|,190 \le L_{uckGrade}<200:0.991+0\left|L_{uckGrade}-190\right|,200 \le L_{uckGrade}<210:0.99+0\left|L_{uckGrade}-200\right|,210 \le L_{uckGrade}<220:0.99+0\left|L_{uckGrade}-210\right|,220 \le L_{uckGrade}<230:0.989+0\left|L_{uckGrade}-220\right|,230 \le L_{uckGrade}<240:0.989+0\left|L_{uckGrade}-230\right|,240 \le L_{uckGrade}<250:0.988+0\left|L_{uckGrade}-240\right|,250 \le L_{uckGrade}<260:0.988+0\left|L_{uckGrade}-250\right|,260 \le L_{uckGrade}<270:0.987+0\left|L_{uckGrade}-260\right|,270 \le L_{uckGrade}<280:0.987+0\left|L_{uckGrade}-270\right|,280 \le L_{uckGrade}<290:0.986+0\left|L_{uckGrade}-280\right|,290 \le L_{uckGrade}<300:0.986+0\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<310:0.985+0\left|L_{uckGrade}-300\right|,310 \le L_{uckGrade}<320:0.985+0\left|L_{uckGrade}-310\right|,320 \le L_{uckGrade}<330:0.984+0\left|L_{uckGrade}-320\right|,330 \le L_{uckGrade}<340:0.984+0\left|L_{uckGrade}-330\right|,340 \le L_{uckGrade}<350:0.983+0\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<360:0.983+0\left|L_{uckGrade}-350\right|,360 \le L_{uckGrade}<370:0.982+0\left|L_{uckGrade}-360\right|,370 \le L_{uckGrade}<380:0.982+0\left|L_{uckGrade}-370\right|,380 \le L_{uckGrade}<390:0.981+0\left|L_{uckGrade}-380\right|,390 \le L_{uckGrade}<400:0.981+0\left|L_{uckGrade}-390\right|,400 \le L_{uckGrade}<410:0.98+0\left|L_{uckGrade}-400\right|,410 \le L_{uckGrade}<420:0.98+0\left|L_{uckGrade}-410\right|,420 \le L_{uckGrade}<430:0.979+0\left|L_{uckGrade}-420\right|,430 \le L_{uckGrade}<440:0.979+0\left|L_{uckGrade}-430\right|,440 \le L_{uckGrade}<450:0.978+0\left|L_{uckGrade}-440\right|,450 \le L_{uckGrade}<460:0.978+0\left|L_{uckGrade}-450\right|,460 \le L_{uckGrade}<470:0.977+0\left|L_{uckGrade}-460\right|,470 \le L_{uckGrade}<480:0.977+0\left|L_{uckGrade}-470\right|,480 \le L_{uckGrade}<490:0.976+0\left|L_{uckGrade}-480\right|,490 \le L_{uckGrade}<500:0.976+0\left|L_{uckGrade}-490\right|,500 \le L_{uckGrade}<510:0.975+0\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<520:0.975+0\left|L_{uckGrade}-510\right|,520 \le L_{uckGrade}<530:0.974+0\left|L_{uckGrade}-520\right|,530 \le L_{uckGrade}<540:0.974+0\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<550:0.973+0\left|L_{uckGrade}-540\right|,550 \le L_{uckGrade}<560:0.973+0\left|L_{uckGrade}-550\right|,560 \le L_{uckGrade}<570:0.972+0\left|L_{uckGrade}-560\right|,570 \le L_{uckGrade}<580:0.972+0\left|L_{uckGrade}-570\right|,580 \le L_{uckGrade}<590:0.971+0\left|L_{uckGrade}-580\right|,590 \le L_{uckGrade}<600:0.971+0\left|L_{uckGrade}-590\right|,600 \le L_{uckGrade}<610:0.97+0\left|L_{uckGrade}-600\right|,610 \le L_{uckGrade}<620:0.97+0\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<630:0.969+0\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<640:0.969+0\left|L_{uckGrade}-630\right|,640 \le L_{uckGrade}<650:0.968+0\left|L_{uckGrade}-640\right|,650 \le L_{uckGrade}<660:0.968+0\left|L_{uckGrade}-650\right|,660 \le L_{uckGrade}<670:0.967+0\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<680:0.967+0\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<690:0.966+0\left|L_{uckGrade}-680\right|,690 \le L_{uckGrade}<700:0.966+0\left|L_{uckGrade}-690\right|,700 \le L_{uckGrade}<710:0.965+0\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<720:0.965+0\left|L_{uckGrade}-710\right|,720 \le L_{uckGrade}<730:0.964+0\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<740:0.964+0\left|L_{uckGrade}-730\right|,740 \le L_{uckGrade}<750:0.963+0\left|L_{uckGrade}-740\right|,750 \le L_{uckGrade}<760:0.963+0\left|L_{uckGrade}-750\right|,760 \le L_{uckGrade}<770:0.962+0\left|L_{uckGrade}-760\right|,770 \le L_{uckGrade}<780:0.962+0\left|L_{uckGrade}-770\right|,780 \le L_{uckGrade}<790:0.961+0\left|L_{uckGrade}-780\right|,790 \le L_{uckGrade}<800:0.961+0\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<810:0.96+0\left|L_{uckGrade}-800\right|,810 \le L_{uckGrade}<820:0.96+0\left|L_{uckGrade}-810\right|,820 \le L_{uckGrade}<830:0.959+0\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<840:0.959+0\left|L_{uckGrade}-830\right|,840 \le L_{uckGrade}<850:0.958+0\left|L_{uckGrade}-840\right|,850 \le L_{uckGrade}<860:0.958+0\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<870:0.957+0\left|L_{uckGrade}-860\right|,870 \le L_{uckGrade}<880:0.957+0\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<890:0.956+0\left|L_{uckGrade}-880\right|,890 \le L_{uckGrade}<900:0.956+0\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<910:0.955+0\left|L_{uckGrade}-900\right|,910 \le L_{uckGrade}<920:0.955+0\left|L_{uckGrade}-910\right|,920 \le L_{uckGrade}<930:0.954+0\left|L_{uckGrade}-920\right|,930 \le L_{uckGrade}<940:0.954+0\left|L_{uckGrade}-930\right|,940 \le L_{uckGrade}<950:0.953+0\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<960:0.953+0\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<970:0.952+0\left|L_{uckGrade}-960\right|,970 \le L_{uckGrade}<980:0.952+0\left|L_{uckGrade}-970\right|,980 \le L_{uckGrade}<990:0.951+0\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1000:0.951+0\left|L_{uckGrade}-990\right|,1000 \le L_{uckGrade}<1010:0.95+0\left|L_{uckGrade}-1000\right|,1010 \le L_{uckGrade}<1020:0.95+0\left|L_{uckGrade}-1010\right|,1020 \le L_{uckGrade}<1030:0.949+0\left|L_{uckGrade}-1020\right|,1030 \le L_{uckGrade}<1040:0.949+0\left|L_{uckGrade}-1030\right|,1040 \le L_{uckGrade}<1050:0.948+0\left|L_{uckGrade}-1040\right|,1050 \le L_{uckGrade}<1060:0.948+0\left|L_{uckGrade}-1050\right|,1060 \le L_{uckGrade}<1070:0.947+0\left|L_{uckGrade}-1060\right|,1070 \le L_{uckGrade}<1080:0.947+0\left|L_{uckGrade}-1070\right|,1080 \le L_{uckGrade}<1090:0.946+0\left|L_{uckGrade}-1080\right|,1090 \le L_{uckGrade}<1100:0.946+0\left|L_{uckGrade}-1090\right|,1100 \le L_{uckGrade}<1110:0.945+0\left|L_{uckGrade}-1100\right|,1110 \le L_{uckGrade}<1120:0.945+0\left|L_{uckGrade}-1110\right|,1120 \le L_{uckGrade}<1130:0.944+0\left|L_{uckGrade}-1120\right|,1130 \le L_{uckGrade}<1140:0.944+0\left|L_{uckGrade}-1130\right|,1140 \le L_{uckGrade}<1150:0.943+0\left|L_{uckGrade}-1140\right|,1150 \le L_{uckGrade}<1160:0.943+0\left|L_{uckGrade}-1150\right|,1160 \le L_{uckGrade}<1170:0.942+0\left|L_{uckGrade}-1160\right|,1170 \le L_{uckGrade}<1180:0.942+0\left|L_{uckGrade}-1170\right|,1180 \le L_{uckGrade}<1190:0.941+0\left|L_{uckGrade}-1180\right|,1190 \le L_{uckGrade}<1200:0.941+0\left|L_{uckGrade}-1190\right|,1200 \le L_{uckGrade}<1210:0.94+0\left|L_{uckGrade}-1200\right|,1210 \le L_{uckGrade}<1220:0.94+0\left|L_{uckGrade}-1210\right|,1220 \le L_{uckGrade}<1230:0.939+0\left|L_{uckGrade}-1220\right|,1230 \le L_{uckGrade}<1240:0.939+0\left|L_{uckGrade}-1230\right|,1240 \le L_{uckGrade}<1250:0.938+0\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1260:0.938+0\left|L_{uckGrade}-1250\right|,1260 \le L_{uckGrade}<1270:0.937+0\left|L_{uckGrade}-1260\right|,1270 \le L_{uckGrade}<1280:0.937+0\left|L_{uckGrade}-1270\right|,1280 \le L_{uckGrade}<1290:0.936+0\left|L_{uckGrade}-1280\right|,1290 \le L_{uckGrade}<1300:0.936+0\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1310:0.935+0\left|L_{uckGrade}-1300\right|,1310 \le L_{uckGrade}<1320:0.935+0\left|L_{uckGrade}-1310\right|,1320 \le L_{uckGrade}<1330:0.934+0\left|L_{uckGrade}-1320\right|,1330 \le L_{uckGrade}<1340:0.934+0\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1350:0.933+0\left|L_{uckGrade}-1340\right|,1350 \le L_{uckGrade}<1360:0.933+0\left|L_{uckGrade}-1350\right|,1360 \le L_{uckGrade}<1370:0.932+0\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1380:0.932+0\left|L_{uckGrade}-1370\right|,1380 \le L_{uckGrade}<1390:0.931+0\left|L_{uckGrade}-1380\right|,1390 \le L_{uckGrade}<1400:0.931+0\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1410:0.93+0\left|L_{uckGrade}-1400\right|,1410 \le L_{uckGrade}<1420:0.93+0\left|L_{uckGrade}-1410\right|,1420 \le L_{uckGrade}<1430:0.929+0\left|L_{uckGrade}-1420\right|,1430 \le L_{uckGrade}<1440:0.929+0\left|L_{uckGrade}-1430\right|,1440 \le L_{uckGrade}<1450:0.928+0\left|L_{uckGrade}-1440\right|,1450 \le L_{uckGrade}<1460:0.928+0\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1470:0.927+0\left|L_{uckGrade}-1460\right|,1470 \le L_{uckGrade}<1480:0.927+0\left|L_{uckGrade}-1470\right|,1480 \le L_{uckGrade}<1490:0.926+0\left|L_{uckGrade}-1480\right|,1490 \le L_{uckGrade}<1500:0.926+0\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1510:0.925+0\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:0.925+0\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1530:0.924+0\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1540:0.924+0\left|L_{uckGrade}-1530\right|,1540 \le L_{uckGrade}<1550:0.923+0\left|L_{uckGrade}-1540\right|,1550 \le L_{uckGrade}<1560:0.923+0\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1570:0.922+0\left|L_{uckGrade}-1560\right|,1570 \le L_{uckGrade}<1580:0.922+0\left|L_{uckGrade}-1570\right|,1580 \le L_{uckGrade}<1590:0.921+0\left|L_{uckGrade}-1580\right|,1590 \le L_{uckGrade}<1600:0.921+0\left|L_{uckGrade}-1590\right|,1600 \le L_{uckGrade}<1610:0.92+0\left|L_{uckGrade}-1600\right|,1610 \le L_{uckGrade}<1620:0.92+0\left|L_{uckGrade}-1610\right|,1620 \le L_{uckGrade}<1630:0.919+0\left|L_{uckGrade}-1620\right|,1630 \le L_{uckGrade}<1640:0.919+0\left|L_{uckGrade}-1630\right|,1640 \le L_{uckGrade}<1650:0.918+0\left|L_{uckGrade}-1640\right|,1650 \le L_{uckGrade}<1660:0.918+0\left|L_{uckGrade}-1650\right|,1660 \le L_{uckGrade}<1670:0.917+0\left|L_{uckGrade}-1660\right|,1670 \le L_{uckGrade}<1680:0.917+0\left|L_{uckGrade}-1670\right|,1680 \le L_{uckGrade}<1690:0.916+0\left|L_{uckGrade}-1680\right|,1690 \le L_{uckGrade}<1700:0.916+0\left|L_{uckGrade}-1690\right|,1700 \le L_{uckGrade}<1710:0.915+0\left|L_{uckGrade}-1700\right|,1710 \le L_{uckGrade}<1720:0.915+0\left|L_{uckGrade}-1710\right|,1720 \le L_{uckGrade}<1730:0.914+0\left|L_{uckGrade}-1720\right|,1730 \le L_{uckGrade}<1740:0.914+0\left|L_{uckGrade}-1730\right|,1740 \le L_{uckGrade}<1750:0.913+0\left|L_{uckGrade}-1740\right|,1750 \le L_{uckGrade}<1760:0.913+0\left|L_{uckGrade}-1750\right|,1760 \le L_{uckGrade}<1770:0.912+0\left|L_{uckGrade}-1760\right|,1770 \le L_{uckGrade}<1780:0.912+0\left|L_{uckGrade}-1770\right|,1780 \le L_{uckGrade}<1790:0.911+0\left|L_{uckGrade}-1780\right|,1790 \le L_{uckGrade}<1800:0.911+0\left|L_{uckGrade}-1790\right|,1800 \le L_{uckGrade}<1810:0.91+0\left|L_{uckGrade}-1800\right|,1810 \le L_{uckGrade}<1820:0.91+0\left|L_{uckGrade}-1810\right|,1820 \le L_{uckGrade}<1830:0.909+0\left|L_{uckGrade}-1820\right|,1830 \le L_{uckGrade}<1840:0.909+0\left|L_{uckGrade}-1830\right|,1840 \le L_{uckGrade}<1850:0.908+0\left|L_{uckGrade}-1840\right|,1850 \le L_{uckGrade}<1860:0.908+0\left|L_{uckGrade}-1850\right|,1860 \le L_{uckGrade}<1870:0.907+0\left|L_{uckGrade}-1860\right|,1870 \le L_{uckGrade}<1880:0.907+0\left|L_{uckGrade}-1870\right|,1880 \le L_{uckGrade}<1890:0.906+0\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1900:0.906+0\left|L_{uckGrade}-1890\right|,1900 \le L_{uckGrade}<1910:0.905+0\left|L_{uckGrade}-1900\right|,1910 \le L_{uckGrade}<1920:0.905+0\left|L_{uckGrade}-1910\right|,1920 \le L_{uckGrade}<1930:0.904+0\left|L_{uckGrade}-1920\right|,1930 \le L_{uckGrade}<1940:0.904+0\left|L_{uckGrade}-1930\right|,1940 \le L_{uckGrade}<1950:0.903+0\left|L_{uckGrade}-1940\right|,1950 \le L_{uckGrade}<1960:0.903+0\left|L_{uckGrade}-1950\right|,1960 \le L_{uckGrade}<1970:0.902+0\left|L_{uckGrade}-1960\right|,1970 \le L_{uckGrade}<1980:0.902+0\left|L_{uckGrade}-1970\right|,1980 \le L_{uckGrade}<1990:0.901+0\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2000:0.901+0\left|L_{uckGrade}-1990\right|,2000 \le L_{uckGrade}<2010:0.9+0\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2020:0.9+0\left|L_{uckGrade}-2010\right|,2020 \le L_{uckGrade}<2030:0.899+0\left|L_{uckGrade}-2020\right|,2030 \le L_{uckGrade}<2040:0.899+0\left|L_{uckGrade}-2030\right|,2040 \le L_{uckGrade}<2050:0.898+0\left|L_{uckGrade}-2040\right|,2050 \le L_{uckGrade}<2060:0.898+0\left|L_{uckGrade}-2050\right|,2060 \le L_{uckGrade}<2070:0.897+0\left|L_{uckGrade}-2060\right|,2070 \le L_{uckGrade}<2080:0.897+0\left|L_{uckGrade}-2070\right|,2080 \le L_{uckGrade}<2090:0.896+0\left|L_{uckGrade}-2080\right|,2090 \le L_{uckGrade}<2100:0.896+0\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2110:0.895+0\left|L_{uckGrade}-2100\right|,2110 \le L_{uckGrade}<2120:0.895+0\left|L_{uckGrade}-2110\right|,2120 \le L_{uckGrade}<2130:0.894+0\left|L_{uckGrade}-2120\right|,2130 \le L_{uckGrade}<2140:0.894+0\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2150:0.893+0\left|L_{uckGrade}-2140\right|,2150 \le L_{uckGrade}<2160:0.893+0\left|L_{uckGrade}-2150\right|,2160 \le L_{uckGrade}<2170:0.892+0\left|L_{uckGrade}-2160\right|,2170 \le L_{uckGrade}<2180:0.892+0\left|L_{uckGrade}-2170\right|,2180 \le L_{uckGrade}<2190:0.891+0\left|L_{uckGrade}-2180\right|,2190 \le L_{uckGrade}<2200:0.891+0\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2210:0.89+0\left|L_{uckGrade}-2200\right|,2210 \le L_{uckGrade}<2220:0.89+0\left|L_{uckGrade}-2210\right|,2220 \le L_{uckGrade}<2230:0.889+0\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2240:0.889+0\left|L_{uckGrade}-2230\right|,2240 \le L_{uckGrade}<2250:0.888+0\left|L_{uckGrade}-2240\right|,2250 \le L_{uckGrade}<2260:0.888+0\left|L_{uckGrade}-2250\right|,2260 \le L_{uckGrade}<2270:0.887+0\left|L_{uckGrade}-2260\right|,2270 \le L_{uckGrade}<2280:0.887+0\left|L_{uckGrade}-2270\right|,2280 \le L_{uckGrade}<2290:0.886+0\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2300:0.886+0\left|L_{uckGrade}-2290\right|,2300 \le L_{uckGrade}<2310:0.885+0\left|L_{uckGrade}-2300\right|,2310 \le L_{uckGrade}<2320:0.885+0\left|L_{uckGrade}-2310\right|,2320 \le L_{uckGrade}<2330:0.884+0\left|L_{uckGrade}-2320\right|,2330 \le L_{uckGrade}<2340:0.884+0\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2350:0.883+0\left|L_{uckGrade}-2340\right|,2350 \le L_{uckGrade}<2360:0.883+0\left|L_{uckGrade}-2350\right|,2360 \le L_{uckGrade}<2370:0.882+0\left|L_{uckGrade}-2360\right|,2370 \le L_{uckGrade}<2380:0.882+0\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2390:0.881+0\left|L_{uckGrade}-2380\right|,2390 \le L_{uckGrade}<2400:0.881+0\left|L_{uckGrade}-2390\right|,2400 \le L_{uckGrade}<2410:0.88+0\left|L_{uckGrade}-2400\right|,2410 \le L_{uckGrade}<2420:0.88+0\left|L_{uckGrade}-2410\right|,2420 \le L_{uckGrade}<2430:0.879+0\left|L_{uckGrade}-2420\right|,2430 \le L_{uckGrade}<2440:0.879+0\left|L_{uckGrade}-2430\right|,2440 \le L_{uckGrade}<2450:0.878+0\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2460:0.878+0\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2470:0.877+0\left|L_{uckGrade}-2460\right|,2470 \le L_{uckGrade}<2480:0.877+0\left|L_{uckGrade}-2470\right|,2480 \le L_{uckGrade}<2490:0.876+0\left|L_{uckGrade}-2480\right|,2490 \le L_{uckGrade}<2500:0.876+0\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2510:0.875+0\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:0.875+0\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2530:0.874+0\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2540:0.874+0\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2550:0.873+0\left|L_{uckGrade}-2540\right|,2550 \le L_{uckGrade}<2560:0.873+0\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2570:0.872+0\left|L_{uckGrade}-2560\right|,2570 \le L_{uckGrade}<2580:0.872+0\left|L_{uckGrade}-2570\right|,2580 \le L_{uckGrade}<2590:0.871+0\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2600:0.871+0\left|L_{uckGrade}-2590\right|,2600 \le L_{uckGrade}<2610:0.87+0\left|L_{uckGrade}-2600\right|,2610 \le L_{uckGrade}<2620:0.87+0\left|L_{uckGrade}-2610\right|,2620 \le L_{uckGrade}<2630:0.869+0\left|L_{uckGrade}-2620\right|,2630 \le L_{uckGrade}<2640:0.869+0\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2650:0.868+0\left|L_{uckGrade}-2640\right|,2650 \le L_{uckGrade}<2660:0.868+0\left|L_{uckGrade}-2650\right|,2660 \le L_{uckGrade}<2670:0.867+0\left|L_{uckGrade}-2660\right|,2670 \le L_{uckGrade}<2680:0.867+0\left|L_{uckGrade}-2670\right|,2680 \le L_{uckGrade}<2690:0.866+0\left|L_{uckGrade}-2680\right|,2690 \le L_{uckGrade}<2700:0.866+0\left|L_{uckGrade}-2690\right|,2700 \le L_{uckGrade}<2710:0.865+0\left|L_{uckGrade}-2700\right|,2710 \le L_{uckGrade}<2720:0.865+0\left|L_{uckGrade}-2710\right|,2720 \le L_{uckGrade}<2730:0.864+0\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2740:0.864+0\left|L_{uckGrade}-2730\right|,2740 \le L_{uckGrade}<2750:0.863+0\left|L_{uckGrade}-2740\right|,2750 \le L_{uckGrade}<2760:0.863+0\left|L_{uckGrade}-2750\right|,2760 \le L_{uckGrade}<2770:0.862+0\left|L_{uckGrade}-2760\right|,2770 \le L_{uckGrade}<2780:0.862+0\left|L_{uckGrade}-2770\right|,2780 \le L_{uckGrade}<2790:0.861+0\left|L_{uckGrade}-2780\right|,2790 \le L_{uckGrade}<2800:0.861+0\left|L_{uckGrade}-2790\right|,2800 \le L_{uckGrade}<2810:0.86+0\left|L_{uckGrade}-2800\right|,2810 \le L_{uckGrade}<2820:0.86+0\left|L_{uckGrade}-2810\right|,2820 \le L_{uckGrade}<2830:0.859+0\left|L_{uckGrade}-2820\right|,2830 \le L_{uckGrade}<2840:0.859+0\left|L_{uckGrade}-2830\right|,2840 \le L_{uckGrade}<2850:0.858+0\left|L_{uckGrade}-2840\right|,2850 \le L_{uckGrade}<2860:0.858+0\left|L_{uckGrade}-2850\right|,2860 \le L_{uckGrade}<2870:0.857+0\left|L_{uckGrade}-2860\right|,2870 \le L_{uckGrade}<2880:0.857+0\left|L_{uckGrade}-2870\right|,2880 \le L_{uckGrade}<2890:0.856+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2900:0.856+0\left|L_{uckGrade}-2890\right|,2900 \le L_{uckGrade}<2910:0.855+0\left|L_{uckGrade}-2900\right|,2910 \le L_{uckGrade}<2920:0.855+0\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2930:0.854+0\left|L_{uckGrade}-2920\right|,2930 \le L_{uckGrade}<2940:0.854+0\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2950:0.853+0\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2960:0.853+0\left|L_{uckGrade}-2950\right|,2960 \le L_{uckGrade}<2970:0.852+0\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<2980:0.852+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<2990:0.851+0\left|L_{uckGrade}-2980\right|,2990 \le L_{uckGrade}<3000:0.851+0\left|L_{uckGrade}-2990\right|,3000 \le L_{uckGrade}<3010:0.85+0\left|L_{uckGrade}-3000\right|,3010 \le L_{uckGrade}<3020:0.85+0\left|L_{uckGrade}-3010\right|,3020 \le L_{uckGrade}<3030:0.849+0\left|L_{uckGrade}-3020\right|,3030 \le L_{uckGrade}<3040:0.849+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3050:0.848+0\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3060:0.848+0\left|L_{uckGrade}-3050\right|,3060 \le L_{uckGrade}<3070:0.847+0\left|L_{uckGrade}-3060\right|,3070 \le L_{uckGrade}<3080:0.847+0\left|L_{uckGrade}-3070\right|,3080 \le L_{uckGrade}<3090:0.846+0\left|L_{uckGrade}-3080\right|,3090 \le L_{uckGrade}<3100:0.846+0\left|L_{uckGrade}-3090\right|,3100 \le L_{uckGrade}<3110:0.845+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3120:0.845+0\left|L_{uckGrade}-3110\right|,3120 \le L_{uckGrade}<3130:0.844+0\left|L_{uckGrade}-3120\right|,3130 \le L_{uckGrade}<3140:0.844+0\left|L_{uckGrade}-3130\right|,3140 \le L_{uckGrade}<3150:0.843+0\left|L_{uckGrade}-3140\right|,3150 \le L_{uckGrade}<3160:0.843+0\left|L_{uckGrade}-3150\right|,3160 \le L_{uckGrade}<3170:0.842+0\left|L_{uckGrade}-3160\right|,3170 \le L_{uckGrade}<3180:0.842+0\left|L_{uckGrade}-3170\right|,3180 \le L_{uckGrade}<3190:0.841+0\left|L_{uckGrade}-3180\right|,3190 \le L_{uckGrade}<3200:0.841+0\left|L_{uckGrade}-3190\right|,3200 \le L_{uckGrade}<3210:0.84+0\left|L_{uckGrade}-3200\right|,3210 \le L_{uckGrade}<3220:0.84+0\left|L_{uckGrade}-3210\right|,3220 \le L_{uckGrade}<3230:0.839+0\left|L_{uckGrade}-3220\right|,3230 \le L_{uckGrade}<3240:0.839+0\left|L_{uckGrade}-3230\right|,3240 \le L_{uckGrade}<3250:0.838+0\left|L_{uckGrade}-3240\right|,3250 \le L_{uckGrade}<3260:0.838+0\left|L_{uckGrade}-3250\right|,3260 \le L_{uckGrade}<3270:0.837+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3280:0.837+0\left|L_{uckGrade}-3270\right|,3280 \le L_{uckGrade}<3290:0.836+0\left|L_{uckGrade}-3280\right|,3290 \le L_{uckGrade}<3300:0.836+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3310:0.835+0\left|L_{uckGrade}-3300\right|,3310 \le L_{uckGrade}<3320:0.835+0\left|L_{uckGrade}-3310\right|,3320 \le L_{uckGrade}<3330:0.834+0\left|L_{uckGrade}-3320\right|,3330 \le L_{uckGrade}<3340:0.834+0\left|L_{uckGrade}-3330\right|,3340 \le L_{uckGrade}<3350:0.833+0\left|L_{uckGrade}-3340\right|,3350 \le L_{uckGrade}<3360:0.833+0\left|L_{uckGrade}-3350\right|,3360 \le L_{uckGrade}<3370:0.832+0\left|L_{uckGrade}-3360\right|,3370 \le L_{uckGrade}<3380:0.832+0\left|L_{uckGrade}-3370\right|,3380 \le L_{uckGrade}<3390:0.831+0\left|L_{uckGrade}-3380\right|,3390 \le L_{uckGrade}<3400:0.831+0\left|L_{uckGrade}-3390\right|,3400 \le L_{uckGrade}<3410:0.83+0\left|L_{uckGrade}-3400\right|,3410 \le L_{uckGrade}<3420:0.83+0\left|L_{uckGrade}-3410\right|,3420 \le L_{uckGrade}<3430:0.829+0\left|L_{uckGrade}-3420\right|,3430 \le L_{uckGrade}<3440:0.829+0\left|L_{uckGrade}-3430\right|,3440 \le L_{uckGrade}<3450:0.828+0\left|L_{uckGrade}-3440\right|,3450 \le L_{uckGrade}<3460:0.828+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3470:0.827+0\left|L_{uckGrade}-3460\right|,3470 \le L_{uckGrade}<3480:0.827+0\left|L_{uckGrade}-3470\right|,3480 \le L_{uckGrade}<3490:0.826+0\left|L_{uckGrade}-3480\right|,3490 \le L_{uckGrade}<3500:0.826+0\left|L_{uckGrade}-3490\right|,3500 \le L_{uckGrade}<3510:0.825+0\left|L_{uckGrade}-3500\right|,3510 \le L_{uckGrade}<3520:0.825+0\left|L_{uckGrade}-3510\right|,3520 \le L_{uckGrade}<3530:0.824+0\left|L_{uckGrade}-3520\right|,3530 \le L_{uckGrade}<3540:0.824+0\left|L_{uckGrade}-3530\right|,3540 \le L_{uckGrade}<3550:0.823+0\left|L_{uckGrade}-3540\right|,3550 \le L_{uckGrade}<3560:0.823+0\left|L_{uckGrade}-3550\right|,3560 \le L_{uckGrade}<3570:0.822+0\left|L_{uckGrade}-3560\right|,3570 \le L_{uckGrade}<3580:0.822+0\left|L_{uckGrade}-3570\right|,3580 \le L_{uckGrade}<3590:0.821+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3600:0.821+0\left|L_{uckGrade}-3590\right|,3600 \le L_{uckGrade}<3610:0.82+0\left|L_{uckGrade}-3600\right|,3610 \le L_{uckGrade}<3620:0.82+0\left|L_{uckGrade}-3610\right|,3620 \le L_{uckGrade}<3630:0.819+0\left|L_{uckGrade}-3620\right|,3630 \le L_{uckGrade}<3640:0.819+0\left|L_{uckGrade}-3630\right|,3640 \le L_{uckGrade}<3650:0.818+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3660:0.818+0\left|L_{uckGrade}-3650\right|,3660 \le L_{uckGrade}<3670:0.817+0\left|L_{uckGrade}-3660\right|,3670 \le L_{uckGrade}<3680:0.817+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3690:0.816+0\left|L_{uckGrade}-3680\right|,3690 \le L_{uckGrade}<3700:0.816+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3710:0.815+0\left|L_{uckGrade}-3700\right|,3710 \le L_{uckGrade}<3720:0.815+0\left|L_{uckGrade}-3710\right|,3720 \le L_{uckGrade}<3730:0.814+0\left|L_{uckGrade}-3720\right|,3730 \le L_{uckGrade}<3740:0.814+0\left|L_{uckGrade}-3730\right|,3740 \le L_{uckGrade}<3750:0.813+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3760:0.813+0\left|L_{uckGrade}-3750\right|,3760 \le L_{uckGrade}<3770:0.812+0\left|L_{uckGrade}-3760\right|,3770 \le L_{uckGrade}<3780:0.812+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3790:0.811+0\left|L_{uckGrade}-3780\right|,3790 \le L_{uckGrade}<3800:0.811+0\left|L_{uckGrade}-3790\right|,3800 \le L_{uckGrade}<3810:0.81+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<3820:0.81+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3830:0.809+0\left|L_{uckGrade}-3820\right|,3830 \le L_{uckGrade}<3840:0.809+0\left|L_{uckGrade}-3830\right|,3840 \le L_{uckGrade}<3850:0.808+0\left|L_{uckGrade}-3840\right|,3850 \le L_{uckGrade}<3860:0.808+0\left|L_{uckGrade}-3850\right|,3860 \le L_{uckGrade}<3870:0.807+0\left|L_{uckGrade}-3860\right|,3870 \le L_{uckGrade}<3880:0.807+0\left|L_{uckGrade}-3870\right|,3880 \le L_{uckGrade}<3890:0.806+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3900:0.806+0\left|L_{uckGrade}-3890\right|,3900 \le L_{uckGrade}<3910:0.805+0\left|L_{uckGrade}-3900\right|,3910 \le L_{uckGrade}<3920:0.805+0\left|L_{uckGrade}-3910\right|,3920 \le L_{uckGrade}<3930:0.804+0\left|L_{uckGrade}-3920\right|,3930 \le L_{uckGrade}<3940:0.804+0\left|L_{uckGrade}-3930\right|,3940 \le L_{uckGrade}<3950:0.803+0\left|L_{uckGrade}-3940\right|,3950 \le L_{uckGrade}<3960:0.803+0\left|L_{uckGrade}-3950\right|,3960 \le L_{uckGrade}<3970:0.802+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3980:0.802+0\left|L_{uckGrade}-3970\right|,3980 \le L_{uckGrade}<3990:0.801+0\left|L_{uckGrade}-3980\right|,3990 \le L_{uckGrade}<4000:0.801+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4010:0.8+0\left|L_{uckGrade}-4000\right|,4010 \le L_{uckGrade}<4020:0.8+0\left|L_{uckGrade}-4010\right|,4020 \le L_{uckGrade}<4030:0.799+0\left|L_{uckGrade}-4020\right|,4030 \le L_{uckGrade}<4040:0.799+0\left|L_{uckGrade}-4030\right|,4040 \le L_{uckGrade}<4050:0.798+0\left|L_{uckGrade}-4040\right|,4050 \le L_{uckGrade}<4060:0.798+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4070:0.797+0\left|L_{uckGrade}-4060\right|,4070 \le L_{uckGrade}<4080:0.797+0\left|L_{uckGrade}-4070\right|,4080 \le L_{uckGrade}<4090:0.796+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4100:0.796+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4110:0.795+0\left|L_{uckGrade}-4100\right|,4110 \le L_{uckGrade}<4120:0.795+0\left|L_{uckGrade}-4110\right|,4120 \le L_{uckGrade}<4130:0.794+0\left|L_{uckGrade}-4120\right|,4130 \le L_{uckGrade}<4140:0.794+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4150:0.793+0\left|L_{uckGrade}-4140\right|,4150 \le L_{uckGrade}<4160:0.793+0\left|L_{uckGrade}-4150\right|,4160 \le L_{uckGrade}<4170:0.792+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4180:0.792+0\left|L_{uckGrade}-4170\right|,4180 \le L_{uckGrade}<4190:0.791+0\left|L_{uckGrade}-4180\right|,4190 \le L_{uckGrade}<4200:0.791+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4210:0.79+0\left|L_{uckGrade}-4200\right|,4210 \le L_{uckGrade}<4220:0.79+0\left|L_{uckGrade}-4210\right|,4220 \le L_{uckGrade}<4230:0.789+0\left|L_{uckGrade}-4220\right|,4230 \le L_{uckGrade}<4240:0.789+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4250:0.788+0\left|L_{uckGrade}-4240\right|,4250 \le L_{uckGrade}<4260:0.788+0\left|L_{uckGrade}-4250\right|,4260 \le L_{uckGrade}<4270:0.787+0\left|L_{uckGrade}-4260\right|,4270 \le L_{uckGrade}<4280:0.787+0\left|L_{uckGrade}-4270\right|,4280 \le L_{uckGrade}<4290:0.786+0\left|L_{uckGrade}-4280\right|,4290 \le L_{uckGrade}<4300:0.786+0\left|L_{uckGrade}-4290\right|,4300 \le L_{uckGrade}<4310:0.785+0\left|L_{uckGrade}-4300\right|,4310 \le L_{uckGrade}<4320:0.785+0\left|L_{uckGrade}-4310\right|,4320 \le L_{uckGrade}<4330:0.784+0\left|L_{uckGrade}-4320\right|,4330 \le L_{uckGrade}<4340:0.784+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4350:0.783+0\left|L_{uckGrade}-4340\right|,4350 \le L_{uckGrade}<4360:0.783+0\left|L_{uckGrade}-4350\right|,4360 \le L_{uckGrade}<4370:0.782+0\left|L_{uckGrade}-4360\right|,4370 \le L_{uckGrade}<4380:0.782+0\left|L_{uckGrade}-4370\right|,4380 \le L_{uckGrade}<4390:0.781+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4400:0.781+0\left|L_{uckGrade}-4390\right|,4400 \le L_{uckGrade}<4410:0.78+0\left|L_{uckGrade}-4400\right|,4410 \le L_{uckGrade}<4420:0.78+0\left|L_{uckGrade}-4410\right|,4420 \le L_{uckGrade}<4430:0.779+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4440:0.779+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4450:0.778+0\left|L_{uckGrade}-4440\right|,4450 \le L_{uckGrade}<4460:0.778+0\left|L_{uckGrade}-4450\right|,4460 \le L_{uckGrade}<4470:0.777+0\left|L_{uckGrade}-4460\right|,4470 \le L_{uckGrade}<4480:0.777+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4490:0.776+0\left|L_{uckGrade}-4480\right|,4490 \le L_{uckGrade}<4500:0.776+0\left|L_{uckGrade}-4490\right|,4500 \le L_{uckGrade}<4510:0.775+0\left|L_{uckGrade}-4500\right|,4510 \le L_{uckGrade}<4520:0.775+0\left|L_{uckGrade}-4510\right|,4520 \le L_{uckGrade}<4530:0.774+0\left|L_{uckGrade}-4520\right|,4530 \le L_{uckGrade}<4540:0.774+0\left|L_{uckGrade}-4530\right|,4540 \le L_{uckGrade}<4550:0.773+0\left|L_{uckGrade}-4540\right|,4550 \le L_{uckGrade}<4560:0.773+0\left|L_{uckGrade}-4550\right|,4560 \le L_{uckGrade}<4570:0.772+0\left|L_{uckGrade}-4560\right|,4570 \le L_{uckGrade}<4580:0.772+0\left|L_{uckGrade}-4570\right|,4580 \le L_{uckGrade}<4590:0.771+0\left|L_{uckGrade}-4580\right|,4590 \le L_{uckGrade}<4600:0.771+0\left|L_{uckGrade}-4590\right|,4600 \le L_{uckGrade}<4610:0.77+0\left|L_{uckGrade}-4600\right|,4610 \le L_{uckGrade}<4620:0.77+0\left|L_{uckGrade}-4610\right|,4620 \le L_{uckGrade}<4630:0.769+0\left|L_{uckGrade}-4620\right|,4630 \le L_{uckGrade}<4640:0.769+0\left|L_{uckGrade}-4630\right|,4640 \le L_{uckGrade}<4650:0.768+0\left|L_{uckGrade}-4640\right|,4650 \le L_{uckGrade}<4660:0.768+0\left|L_{uckGrade}-4650\right|,4660 \le L_{uckGrade}<4670:0.767+0\left|L_{uckGrade}-4660\right|,4670 \le L_{uckGrade}<4680:0.767+0\left|L_{uckGrade}-4670\right|,4680 \le L_{uckGrade}<4690:0.766+0\left|L_{uckGrade}-4680\right|,4690 \le L_{uckGrade}<4700:0.766+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4710:0.765+0\left|L_{uckGrade}-4700\right|,4710 \le L_{uckGrade}<4720:0.765+0\left|L_{uckGrade}-4710\right|,4720 \le L_{uckGrade}<4730:0.764+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4740:0.764+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4750:0.763+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4760:0.763+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4770:0.762+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4780:0.762+0\left|L_{uckGrade}-4770\right|,4780 \le L_{uckGrade}<4790:0.761+0\left|L_{uckGrade}-4780\right|,4790 \le L_{uckGrade}<4800:0.761+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4810:0.76+0\left|L_{uckGrade}-4800\right|,4810 \le L_{uckGrade}<4820:0.76+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4830:0.759+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4840:0.759+0\left|L_{uckGrade}-4830\right|,4840 \le L_{uckGrade}<4850:0.758+0\left|L_{uckGrade}-4840\right|,4850 \le L_{uckGrade}<4860:0.758+0\left|L_{uckGrade}-4850\right|,4860 \le L_{uckGrade}<4870:0.757+0\left|L_{uckGrade}-4860\right|,4870 \le L_{uckGrade}<4880:0.757+0\left|L_{uckGrade}-4870\right|,4880 \le L_{uckGrade}<4890:0.756+0\left|L_{uckGrade}-4880\right|,4890 \le L_{uckGrade}<4900:0.756+0\left|L_{uckGrade}-4890\right|,4900 \le L_{uckGrade}<4910:0.755+0\left|L_{uckGrade}-4900\right|,4910 \le L_{uckGrade}<4920:0.755+0\left|L_{uckGrade}-4910\right|,4920 \le L_{uckGrade}<4930:0.754+0\left|L_{uckGrade}-4920\right|,4930 \le L_{uckGrade}<4940:0.754+0\left|L_{uckGrade}-4930\right|,4940 \le L_{uckGrade}<4950:0.753+0\left|L_{uckGrade}-4940\right|,4950 \le L_{uckGrade}<4960:0.753+0\left|L_{uckGrade}-4950\right|,4960 \le L_{uckGrade}<4970:0.752+0\left|L_{uckGrade}-4960\right|,4970 \le L_{uckGrade}<4980:0.752+0\left|L_{uckGrade}-4970\right|,4980 \le L_{uckGrade}<4990:0.751+0\left|L_{uckGrade}-4980\right|,4990 \le L_{uckGrade}<5000:0.751+0\left|L_{uckGrade}-4990\right|\right\}
See Example for how to use.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade03}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<5000:1+0\left|L_{uckGrade}-0\right|\right\}
See Example for how to use.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade04}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<70:1+0.001\left|L_{uckGrade}-0\right|,70 \le L_{uckGrade}<80:1.07+0.001\left|L_{uckGrade}-70\right|,80 \le L_{uckGrade}<120:1.079+0.001\left|L_{uckGrade}-80\right|,120 \le L_{uckGrade}<130:1.119+0.001\left|L_{uckGrade}-120\right|,130 \le L_{uckGrade}<160:1.128+0.001\left|L_{uckGrade}-130\right|,160 \le L_{uckGrade}<170:1.158+0.001\left|L_{uckGrade}-160\right|,170 \le L_{uckGrade}<190:1.167+0.001\left|L_{uckGrade}-170\right|,190 \le L_{uckGrade}<200:1.187+0.001\left|L_{uckGrade}-190\right|,200 \le L_{uckGrade}<210:1.196+0.001\left|L_{uckGrade}-200\right|,210 \le L_{uckGrade}<220:1.206+0.001\left|L_{uckGrade}-210\right|,220 \le L_{uckGrade}<230:1.215+0.001\left|L_{uckGrade}-220\right|,230 \le L_{uckGrade}<240:1.225+0.001\left|L_{uckGrade}-230\right|,240 \le L_{uckGrade}<260:1.234+0.001\left|L_{uckGrade}-240\right|,260 \le L_{uckGrade}<280:1.254+0.001\left|L_{uckGrade}-260\right|,280 \le L_{uckGrade}<290:1.272+0.001\left|L_{uckGrade}-280\right|,290 \le L_{uckGrade}<300:1.282+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<310:1.291+0.001\left|L_{uckGrade}-300\right|,310 \le L_{uckGrade}<330:1.301+0.001\left|L_{uckGrade}-310\right|,330 \le L_{uckGrade}<340:1.319+0.001\left|L_{uckGrade}-330\right|,340 \le L_{uckGrade}<360:1.329+0.001\left|L_{uckGrade}-340\right|,360 \le L_{uckGrade}<370:1.347+0.001\left|L_{uckGrade}-360\right|,370 \le L_{uckGrade}<400:1.357+0.001\left|L_{uckGrade}-370\right|,400 \le L_{uckGrade}<410:1.384+0.001\left|L_{uckGrade}-400\right|,410 \le L_{uckGrade}<490:1.394+0.001\left|L_{uckGrade}-410\right|,490 \le L_{uckGrade}<500:1.466+0.001\left|L_{uckGrade}-490\right|,500 \le L_{uckGrade}<510:1.476+0.001\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<520:1.485+0.001\left|L_{uckGrade}-510\right|,520 \le L_{uckGrade}<600:1.493+0.001\left|L_{uckGrade}-520\right|,600 \le L_{uckGrade}<610:1.565+0.001\left|L_{uckGrade}-600\right|,610 \le L_{uckGrade}<640:1.573+0.001\left|L_{uckGrade}-610\right|,640 \le L_{uckGrade}<650:1.6+0.001\left|L_{uckGrade}-640\right|,650 \le L_{uckGrade}<670:1.608+0.001\left|L_{uckGrade}-650\right|,670 \le L_{uckGrade}<680:1.626+0.001\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<700:1.634+0.001\left|L_{uckGrade}-680\right|,700 \le L_{uckGrade}<710:1.652+0.001\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<720:1.66+0.001\left|L_{uckGrade}-710\right|,720 \le L_{uckGrade}<730:1.669+0.001\left|L_{uckGrade}-720\right|,730 \le L_{uckGrade}<750:1.677+0.001\left|L_{uckGrade}-730\right|,750 \le L_{uckGrade}<770:1.695+0.001\left|L_{uckGrade}-750\right|,770 \le L_{uckGrade}<780:1.711+0.001\left|L_{uckGrade}-770\right|,780 \le L_{uckGrade}<790:1.72+0.001\left|L_{uckGrade}-780\right|,790 \le L_{uckGrade}<800:1.728+0.001\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<810:1.737+0.001\left|L_{uckGrade}-800\right|,810 \le L_{uckGrade}<820:1.745+0.001\left|L_{uckGrade}-810\right|,820 \le L_{uckGrade}<840:1.754+0.001\left|L_{uckGrade}-820\right|,840 \le L_{uckGrade}<850:1.77+0.001\left|L_{uckGrade}-840\right|,850 \le L_{uckGrade}<880:1.779+0.001\left|L_{uckGrade}-850\right|,880 \le L_{uckGrade}<890:1.803+0.001\left|L_{uckGrade}-880\right|,890 \le L_{uckGrade}<930:1.812+0.001\left|L_{uckGrade}-890\right|,930 \le L_{uckGrade}<940:1.844+0.001\left|L_{uckGrade}-930\right|,940 \le L_{uckGrade}<1070:1.853+0.001\left|L_{uckGrade}-940\right|,1070 \le L_{uckGrade}<1080:1.957+0.001\left|L_{uckGrade}-1070\right|,1080 \le L_{uckGrade}<1120:1.964+0.001\left|L_{uckGrade}-1080\right|,1120 \le L_{uckGrade}<1130:1.996+0.001\left|L_{uckGrade}-1120\right|,1130 \le L_{uckGrade}<1160:2.003+0.001\left|L_{uckGrade}-1130\right|,1160 \le L_{uckGrade}<1170:2.027+0.001\left|L_{uckGrade}-1160\right|,1170 \le L_{uckGrade}<1190:2.034+0.001\left|L_{uckGrade}-1170\right|,1190 \le L_{uckGrade}<1200:2.05+0.001\left|L_{uckGrade}-1190\right|,1200 \le L_{uckGrade}<1210:2.057+0.001\left|L_{uckGrade}-1200\right|,1210 \le L_{uckGrade}<1220:2.065+0.001\left|L_{uckGrade}-1210\right|,1220 \le L_{uckGrade}<1230:2.072+0.001\left|L_{uckGrade}-1220\right|,1230 \le L_{uckGrade}<1240:2.08+0.001\left|L_{uckGrade}-1230\right|,1240 \le L_{uckGrade}<1260:2.087+0.001\left|L_{uckGrade}-1240\right|,1260 \le L_{uckGrade}<1280:2.103+0.001\left|L_{uckGrade}-1260\right|,1280 \le L_{uckGrade}<1290:2.117+0.001\left|L_{uckGrade}-1280\right|,1290 \le L_{uckGrade}<1300:2.125+0.001\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1310:2.132+0.001\left|L_{uckGrade}-1300\right|,1310 \le L_{uckGrade}<1330:2.14+0.001\left|L_{uckGrade}-1310\right|,1330 \le L_{uckGrade}<1340:2.154+0.001\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1360:2.162+0.001\left|L_{uckGrade}-1340\right|,1360 \le L_{uckGrade}<1370:2.176+0.001\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1400:2.184+0.001\left|L_{uckGrade}-1370\right|,1400 \le L_{uckGrade}<1410:2.205+0.001\left|L_{uckGrade}-1400\right|,1410 \le L_{uckGrade}<1490:2.213+0.001\left|L_{uckGrade}-1410\right|,1490 \le L_{uckGrade}<1500:2.269+0.001\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1510:2.277+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:2.284+0.001\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1600:2.29+0.001\left|L_{uckGrade}-1520\right|,1600 \le L_{uckGrade}<1610:2.346+0.001\left|L_{uckGrade}-1600\right|,1610 \le L_{uckGrade}<1640:2.352+0.001\left|L_{uckGrade}-1610\right|,1640 \le L_{uckGrade}<1650:2.373+0.001\left|L_{uckGrade}-1640\right|,1650 \le L_{uckGrade}<1670:2.379+0.001\left|L_{uckGrade}-1650\right|,1670 \le L_{uckGrade}<1680:2.393+0.001\left|L_{uckGrade}-1670\right|,1680 \le L_{uckGrade}<1700:2.399+0.001\left|L_{uckGrade}-1680\right|,1700 \le L_{uckGrade}<1710:2.413+0.001\left|L_{uckGrade}-1700\right|,1710 \le L_{uckGrade}<1720:2.419+0.001\left|L_{uckGrade}-1710\right|,1720 \le L_{uckGrade}<1730:2.426+0.001\left|L_{uckGrade}-1720\right|,1730 \le L_{uckGrade}<1750:2.432+0.001\left|L_{uckGrade}-1730\right|,1750 \le L_{uckGrade}<1770:2.446+0.001\left|L_{uckGrade}-1750\right|,1770 \le L_{uckGrade}<1780:2.458+0.001\left|L_{uckGrade}-1770\right|,1780 \le L_{uckGrade}<1790:2.465+0.001\left|L_{uckGrade}-1780\right|,1790 \le L_{uckGrade}<1800:2.471+0.001\left|L_{uckGrade}-1790\right|,1800 \le L_{uckGrade}<1810:2.478+0.001\left|L_{uckGrade}-1800\right|,1810 \le L_{uckGrade}<1820:2.484+0.001\left|L_{uckGrade}-1810\right|,1820 \le L_{uckGrade}<1840:2.491+0.001\left|L_{uckGrade}-1820\right|,1840 \le L_{uckGrade}<1850:2.503+0.001\left|L_{uckGrade}-1840\right|,1850 \le L_{uckGrade}<1880:2.51+0.001\left|L_{uckGrade}-1850\right|,1880 \le L_{uckGrade}<1890:2.528+0.001\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1930:2.535+0.001\left|L_{uckGrade}-1890\right|,1930 \le L_{uckGrade}<1940:2.559+0.001\left|L_{uckGrade}-1930\right|,1940 \le L_{uckGrade}<2070:2.566+0.001\left|L_{uckGrade}-1940\right|,2070 \le L_{uckGrade}<2080:2.644+0\left|L_{uckGrade}-2070\right|,2080 \le L_{uckGrade}<2120:2.649+0.001\left|L_{uckGrade}-2080\right|,2120 \le L_{uckGrade}<2130:2.673+0\left|L_{uckGrade}-2120\right|,2130 \le L_{uckGrade}<2160:2.678+0.001\left|L_{uckGrade}-2130\right|,2160 \le L_{uckGrade}<2170:2.696+0\left|L_{uckGrade}-2160\right|,2170 \le L_{uckGrade}<2190:2.701+0.001\left|L_{uckGrade}-2170\right|,2190 \le L_{uckGrade}<2200:2.713+0\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2210:2.718+0.001\left|L_{uckGrade}-2200\right|,2210 \le L_{uckGrade}<2220:2.724+0\left|L_{uckGrade}-2210\right|,2220 \le L_{uckGrade}<2230:2.729+0.001\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2240:2.735+0.001\left|L_{uckGrade}-2230\right|,2240 \le L_{uckGrade}<2260:2.74+0.001\left|L_{uckGrade}-2240\right|,2260 \le L_{uckGrade}<2280:2.752+0.001\left|L_{uckGrade}-2260\right|,2280 \le L_{uckGrade}<2290:2.762+0.001\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2300:2.768+0.001\left|L_{uckGrade}-2290\right|,2300 \le L_{uckGrade}<2310:2.773+0.001\left|L_{uckGrade}-2300\right|,2310 \le L_{uckGrade}<2330:2.779+0.001\left|L_{uckGrade}-2310\right|,2330 \le L_{uckGrade}<2340:2.789+0.001\left|L_{uckGrade}-2330\right|,2340 \le L_{uckGrade}<2360:2.795+0.001\left|L_{uckGrade}-2340\right|,2360 \le L_{uckGrade}<2370:2.805+0.001\left|L_{uckGrade}-2360\right|,2370 \le L_{uckGrade}<2400:2.811+0.001\left|L_{uckGrade}-2370\right|,2400 \le L_{uckGrade}<2410:2.826+0.001\left|L_{uckGrade}-2400\right|,2410 \le L_{uckGrade}<2490:2.832+0.001\left|L_{uckGrade}-2410\right|,2490 \le L_{uckGrade}<2500:2.872+0.001\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2510:2.878+0\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:2.883+0\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2600:2.887+0.001\left|L_{uckGrade}-2520\right|,2600 \le L_{uckGrade}<2610:2.927+0\left|L_{uckGrade}-2600\right|,2610 \le L_{uckGrade}<2640:2.931+0.001\left|L_{uckGrade}-2610\right|,2640 \le L_{uckGrade}<2650:2.946+0\left|L_{uckGrade}-2640\right|,2650 \le L_{uckGrade}<2670:2.95+0\left|L_{uckGrade}-2650\right|,2670 \le L_{uckGrade}<2680:2.96+0\left|L_{uckGrade}-2670\right|,2680 \le L_{uckGrade}<2700:2.964+0.001\left|L_{uckGrade}-2680\right|,2700 \le L_{uckGrade}<2710:2.974+0\left|L_{uckGrade}-2700\right|,2710 \le L_{uckGrade}<2720:2.978+0\left|L_{uckGrade}-2710\right|,2720 \le L_{uckGrade}<2730:2.983+0\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2750:2.987+0\left|L_{uckGrade}-2730\right|,2750 \le L_{uckGrade}<2770:2.997+0\left|L_{uckGrade}-2750\right|,2770 \le L_{uckGrade}<2780:3.005+0\left|L_{uckGrade}-2770\right|,2780 \le L_{uckGrade}<2790:3.01+0\left|L_{uckGrade}-2780\right|,2790 \le L_{uckGrade}<2800:3.014+0.001\left|L_{uckGrade}-2790\right|,2800 \le L_{uckGrade}<2810:3.019+0\left|L_{uckGrade}-2800\right|,2810 \le L_{uckGrade}<2820:3.023+0\left|L_{uckGrade}-2810\right|,2820 \le L_{uckGrade}<2840:3.028+0\left|L_{uckGrade}-2820\right|,2840 \le L_{uckGrade}<2850:3.036+0\left|L_{uckGrade}-2840\right|,2850 \le L_{uckGrade}<2880:3.041+0\left|L_{uckGrade}-2850\right|,2880 \le L_{uckGrade}<2890:3.053+0\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2930:3.058+0\left|L_{uckGrade}-2890\right|,2930 \le L_{uckGrade}<2940:3.074+0.001\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<3070:3.079+0\left|L_{uckGrade}-2940\right|,3070 \le L_{uckGrade}<3080:3.131+0\left|L_{uckGrade}-3070\right|,3080 \le L_{uckGrade}<3120:3.134+0\left|L_{uckGrade}-3080\right|,3120 \le L_{uckGrade}<3130:3.15+0\left|L_{uckGrade}-3120\right|,3130 \le L_{uckGrade}<3160:3.153+0\left|L_{uckGrade}-3130\right|,3160 \le L_{uckGrade}<3170:3.165+0\left|L_{uckGrade}-3160\right|,3170 \le L_{uckGrade}<3190:3.168+0\left|L_{uckGrade}-3170\right|,3190 \le L_{uckGrade}<3200:3.176+0\left|L_{uckGrade}-3190\right|,3200 \le L_{uckGrade}<3210:3.179+0\left|L_{uckGrade}-3200\right|,3210 \le L_{uckGrade}<3220:3.183+0\left|L_{uckGrade}-3210\right|,3220 \le L_{uckGrade}<3230:3.186+0\left|L_{uckGrade}-3220\right|,3230 \le L_{uckGrade}<3240:3.19+0\left|L_{uckGrade}-3230\right|,3240 \le L_{uckGrade}<3260:3.193+0\left|L_{uckGrade}-3240\right|,3260 \le L_{uckGrade}<3280:3.201+0\left|L_{uckGrade}-3260\right|,3280 \le L_{uckGrade}<3290:3.207+0\left|L_{uckGrade}-3280\right|,3290 \le L_{uckGrade}<3300:3.211+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3310:3.214+0\left|L_{uckGrade}-3300\right|,3310 \le L_{uckGrade}<3330:3.218+0\left|L_{uckGrade}-3310\right|,3330 \le L_{uckGrade}<3340:3.224+0\left|L_{uckGrade}-3330\right|,3340 \le L_{uckGrade}<3360:3.228+0\left|L_{uckGrade}-3340\right|,3360 \le L_{uckGrade}<3370:3.234+0\left|L_{uckGrade}-3360\right|,3370 \le L_{uckGrade}<3400:3.238+0\left|L_{uckGrade}-3370\right|,3400 \le L_{uckGrade}<3410:3.247+0\left|L_{uckGrade}-3400\right|,3410 \le L_{uckGrade}<3490:3.251+0\left|L_{uckGrade}-3410\right|,3490 \le L_{uckGrade}<3500:3.275+0\left|L_{uckGrade}-3490\right|,3500 \le L_{uckGrade}<3510:3.279+0\left|L_{uckGrade}-3500\right|,3510 \le L_{uckGrade}<3520:3.282+0\left|L_{uckGrade}-3510\right|,3520 \le L_{uckGrade}<3600:3.284+0\left|L_{uckGrade}-3520\right|,3600 \le L_{uckGrade}<3610:3.308+0\left|L_{uckGrade}-3600\right|,3610 \le L_{uckGrade}<3640:3.31+0\left|L_{uckGrade}-3610\right|,3640 \le L_{uckGrade}<3650:3.319+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3670:3.321+0\left|L_{uckGrade}-3650\right|,3670 \le L_{uckGrade}<3680:3.327+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3700:3.329+0\left|L_{uckGrade}-3680\right|,3700 \le L_{uckGrade}<3710:3.335+0\left|L_{uckGrade}-3700\right|,3710 \le L_{uckGrade}<3720:3.337+0\left|L_{uckGrade}-3710\right|,3720 \le L_{uckGrade}<3730:3.34+0\left|L_{uckGrade}-3720\right|,3730 \le L_{uckGrade}<3750:3.342+0\left|L_{uckGrade}-3730\right|,3750 \le L_{uckGrade}<3770:3.348+0\left|L_{uckGrade}-3750\right|,3770 \le L_{uckGrade}<3780:3.352+0\left|L_{uckGrade}-3770\right|,3780 \le L_{uckGrade}<3790:3.355+0\left|L_{uckGrade}-3780\right|,3790 \le L_{uckGrade}<3800:3.357+0\left|L_{uckGrade}-3790\right|,3800 \le L_{uckGrade}<3810:3.36+0\left|L_{uckGrade}-3800\right|,3810 \le L_{uckGrade}<3820:3.362+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3840:3.365+0\left|L_{uckGrade}-3820\right|,3840 \le L_{uckGrade}<3850:3.369+0\left|L_{uckGrade}-3840\right|,3850 \le L_{uckGrade}<3880:3.372+0\left|L_{uckGrade}-3850\right|,3880 \le L_{uckGrade}<3890:3.378+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3930:3.381+0\left|L_{uckGrade}-3890\right|,3930 \le L_{uckGrade}<3940:3.389+0\left|L_{uckGrade}-3930\right|,3940 \le L_{uckGrade}<4070:3.392+0\left|L_{uckGrade}-3940\right|,4070 \le L_{uckGrade}<4080:3.418+0\left|L_{uckGrade}-4070\right|,4080 \le L_{uckGrade}<4120:3.419+0\left|L_{uckGrade}-4080\right|,4120 \le L_{uckGrade}<4130:3.427+0\left|L_{uckGrade}-4120\right|,4130 \le L_{uckGrade}<4160:3.428+0\left|L_{uckGrade}-4130\right|,4160 \le L_{uckGrade}<4170:3.434+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4190:3.435+0\left|L_{uckGrade}-4170\right|,4190 \le L_{uckGrade}<4200:3.439+0\left|L_{uckGrade}-4190\right|,4200 \le L_{uckGrade}<4210:3.44+0\left|L_{uckGrade}-4200\right|,4210 \le L_{uckGrade}<4220:3.442+0\left|L_{uckGrade}-4210\right|,4220 \le L_{uckGrade}<4230:3.443+0\left|L_{uckGrade}-4220\right|,4230 \le L_{uckGrade}<4240:3.445+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4260:3.446+0\left|L_{uckGrade}-4240\right|,4260 \le L_{uckGrade}<4280:3.45+0\left|L_{uckGrade}-4260\right|,4280 \le L_{uckGrade}<4290:3.452+0\left|L_{uckGrade}-4280\right|,4290 \le L_{uckGrade}<4300:3.454+0\left|L_{uckGrade}-4290\right|,4300 \le L_{uckGrade}<4310:3.455+0\left|L_{uckGrade}-4300\right|,4310 \le L_{uckGrade}<4330:3.457+0\left|L_{uckGrade}-4310\right|,4330 \le L_{uckGrade}<4340:3.459+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4360:3.461+0\left|L_{uckGrade}-4340\right|,4360 \le L_{uckGrade}<4370:3.463+0\left|L_{uckGrade}-4360\right|,4370 \le L_{uckGrade}<4400:3.465+0\left|L_{uckGrade}-4370\right|,4400 \le L_{uckGrade}<4410:3.468+0\left|L_{uckGrade}-4400\right|,4410 \le L_{uckGrade}<4490:3.47+0\left|L_{uckGrade}-4410\right|,4490 \le L_{uckGrade}<4500:3.478+0\left|L_{uckGrade}-4490\right|,4500 \le L_{uckGrade}<4510:3.48+0\left|L_{uckGrade}-4500\right|,4510 \le L_{uckGrade}<4520:3.481+0\left|L_{uckGrade}-4510\right|,4520 \le L_{uckGrade}<4600:3.481+0\left|L_{uckGrade}-4520\right|,4600 \le L_{uckGrade}<4610:3.489+0\left|L_{uckGrade}-4600\right|,4610 \le L_{uckGrade}<4640:3.489+0\left|L_{uckGrade}-4610\right|,4640 \le L_{uckGrade}<4650:3.492+0\left|L_{uckGrade}-4640\right|,4650 \le L_{uckGrade}<4670:3.492+0\left|L_{uckGrade}-4650\right|,4670 \le L_{uckGrade}<4680:3.494+0\left|L_{uckGrade}-4670\right|,4680 \le L_{uckGrade}<4700:3.494+0\left|L_{uckGrade}-4680\right|,4700 \le L_{uckGrade}<4710:3.496+0\left|L_{uckGrade}-4700\right|,4710 \le L_{uckGrade}<4720:3.496+0\left|L_{uckGrade}-4710\right|,4720 \le L_{uckGrade}<4730:3.497+0\left|L_{uckGrade}-4720\right|,4730 \le L_{uckGrade}<4750:3.497+0\left|L_{uckGrade}-4730\right|,4750 \le L_{uckGrade}<4770:3.499+0\left|L_{uckGrade}-4750\right|,4770 \le L_{uckGrade}<4780:3.499+0\left|L_{uckGrade}-4770\right|,4780 \le L_{uckGrade}<4790:3.5+0\left|L_{uckGrade}-4780\right|,4790 \le L_{uckGrade}<4800:3.5+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4810:3.501+0\left|L_{uckGrade}-4800\right|,4810 \le L_{uckGrade}<4820:3.501+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4840:3.502+0\left|L_{uckGrade}-4820\right|,4840 \le L_{uckGrade}<4850:3.502+0\left|L_{uckGrade}-4840\right|,4850 \le L_{uckGrade}<4880:3.503+0\left|L_{uckGrade}-4850\right|,4880 \le L_{uckGrade}<4890:3.503+0\left|L_{uckGrade}-4880\right|,4890 \le L_{uckGrade}<4930:3.504+0\left|L_{uckGrade}-4890\right|,4930 \le L_{uckGrade}<4940:3.504+0\left|L_{uckGrade}-4930\right|,4940 \le L_{uckGrade}<5000:3.505+0\left|L_{uckGrade}-4940\right|\right\}
See Example for how to use.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade05}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<10:1+0.001\left|L_{uckGrade}-0\right|,10 \le L_{uckGrade}<30:1.012+0.001\left|L_{uckGrade}-10\right|,30 \le L_{uckGrade}<40:1.034+0.001\left|L_{uckGrade}-30\right|,40 \le L_{uckGrade}<50:1.046+0.001\left|L_{uckGrade}-40\right|,50 \le L_{uckGrade}<60:1.057+0.001\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<80:1.069+0.001\left|L_{uckGrade}-60\right|,80 \le L_{uckGrade}<90:1.091+0.001\left|L_{uckGrade}-80\right|,90 \le L_{uckGrade}<120:1.103+0.001\left|L_{uckGrade}-90\right|,120 \le L_{uckGrade}<130:1.136+0.001\left|L_{uckGrade}-120\right|,130 \le L_{uckGrade}<180:1.148+0.001\left|L_{uckGrade}-130\right|,180 \le L_{uckGrade}<190:1.203+0.001\left|L_{uckGrade}-180\right|,190 \le L_{uckGrade}<260:1.215+0.001\left|L_{uckGrade}-190\right|,260 \le L_{uckGrade}<270:1.292+0.001\left|L_{uckGrade}-260\right|,270 \le L_{uckGrade}<320:1.302+0.001\left|L_{uckGrade}-270\right|,320 \le L_{uckGrade}<330:1.357+0.001\left|L_{uckGrade}-320\right|,330 \le L_{uckGrade}<360:1.367+0.001\left|L_{uckGrade}-330\right|,360 \le L_{uckGrade}<370:1.4+0.001\left|L_{uckGrade}-360\right|,370 \le L_{uckGrade}<380:1.41+0.001\left|L_{uckGrade}-370\right|,380 \le L_{uckGrade}<390:1.421+0.001\left|L_{uckGrade}-380\right|,390 \le L_{uckGrade}<410:1.431+0.001\left|L_{uckGrade}-390\right|,410 \le L_{uckGrade}<420:1.453+0.001\left|L_{uckGrade}-410\right|,420 \le L_{uckGrade}<430:1.463+0.001\left|L_{uckGrade}-420\right|,430 \le L_{uckGrade}<440:1.474+0.001\left|L_{uckGrade}-430\right|,440 \le L_{uckGrade}<450:1.484+0.001\left|L_{uckGrade}-440\right|,450 \le L_{uckGrade}<460:1.495+0.001\left|L_{uckGrade}-450\right|,460 \le L_{uckGrade}<470:1.505+0.001\left|L_{uckGrade}-460\right|,470 \le L_{uckGrade}<490:1.516+0.001\left|L_{uckGrade}-470\right|,490 \le L_{uckGrade}<500:1.536+0.001\left|L_{uckGrade}-490\right|,500 \le L_{uckGrade}<510:1.547+0.001\left|L_{uckGrade}-500\right|,510 \le L_{uckGrade}<520:1.557+0.001\left|L_{uckGrade}-510\right|,520 \le L_{uckGrade}<550:1.568+0.001\left|L_{uckGrade}-520\right|,550 \le L_{uckGrade}<560:1.598+0.001\left|L_{uckGrade}-550\right|,560 \le L_{uckGrade}<610:1.609+0.001\left|L_{uckGrade}-560\right|,610 \le L_{uckGrade}<620:1.659+0.001\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<690:1.67+0.001\left|L_{uckGrade}-620\right|,690 \le L_{uckGrade}<700:1.74+0.001\left|L_{uckGrade}-690\right|,700 \le L_{uckGrade}<750:1.749+0.001\left|L_{uckGrade}-700\right|,750 \le L_{uckGrade}<760:1.799+0.001\left|L_{uckGrade}-750\right|,760 \le L_{uckGrade}<790:1.808+0.001\left|L_{uckGrade}-760\right|,790 \le L_{uckGrade}<800:1.838+0.001\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<820:1.847+0.001\left|L_{uckGrade}-800\right|,820 \le L_{uckGrade}<830:1.867+0.001\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<840:1.876+0.001\left|L_{uckGrade}-830\right|,840 \le L_{uckGrade}<850:1.886+0.001\left|L_{uckGrade}-840\right|,850 \le L_{uckGrade}<860:1.895+0.001\left|L_{uckGrade}-850\right|,860 \le L_{uckGrade}<870:1.905+0.001\left|L_{uckGrade}-860\right|,870 \le L_{uckGrade}<880:1.914+0.001\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<890:1.924+0.001\left|L_{uckGrade}-880\right|,890 \le L_{uckGrade}<900:1.933+0.001\left|L_{uckGrade}-890\right|,900 \le L_{uckGrade}<910:1.943+0.001\left|L_{uckGrade}-900\right|,910 \le L_{uckGrade}<920:1.952+0.001\left|L_{uckGrade}-910\right|,920 \le L_{uckGrade}<940:1.962+0.001\left|L_{uckGrade}-920\right|,940 \le L_{uckGrade}<950:1.98+0.001\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<970:1.99+0.001\left|L_{uckGrade}-950\right|,970 \le L_{uckGrade}<980:2.008+0.001\left|L_{uckGrade}-970\right|,980 \le L_{uckGrade}<1010:2.018+0.001\left|L_{uckGrade}-980\right|,1010 \le L_{uckGrade}<1020:2.045+0.001\left|L_{uckGrade}-1010\right|,1020 \le L_{uckGrade}<1160:2.055+0.001\left|L_{uckGrade}-1020\right|,1160 \le L_{uckGrade}<1170:2.181+0.001\left|L_{uckGrade}-1160\right|,1170 \le L_{uckGrade}<1210:2.189+0.001\left|L_{uckGrade}-1170\right|,1210 \le L_{uckGrade}<1220:2.225+0.001\left|L_{uckGrade}-1210\right|,1220 \le L_{uckGrade}<1240:2.233+0.001\left|L_{uckGrade}-1220\right|,1240 \le L_{uckGrade}<1250:2.251+0.001\left|L_{uckGrade}-1240\right|,1250 \le L_{uckGrade}<1260:2.259+0.001\left|L_{uckGrade}-1250\right|,1260 \le L_{uckGrade}<1270:2.268+0.001\left|L_{uckGrade}-1260\right|,1270 \le L_{uckGrade}<1290:2.276+0.001\left|L_{uckGrade}-1270\right|,1290 \le L_{uckGrade}<1300:2.294+0.001\left|L_{uckGrade}-1290\right|,1300 \le L_{uckGrade}<1310:2.302+0.001\left|L_{uckGrade}-1300\right|,1310 \le L_{uckGrade}<1320:2.311+0.001\left|L_{uckGrade}-1310\right|,1320 \le L_{uckGrade}<1330:2.319+0.001\left|L_{uckGrade}-1320\right|,1330 \le L_{uckGrade}<1350:2.328+0.001\left|L_{uckGrade}-1330\right|,1350 \le L_{uckGrade}<1360:2.344+0.001\left|L_{uckGrade}-1350\right|,1360 \le L_{uckGrade}<1370:2.353+0.001\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1380:2.361+0.001\left|L_{uckGrade}-1370\right|,1380 \le L_{uckGrade}<1410:2.37+0.001\left|L_{uckGrade}-1380\right|,1410 \le L_{uckGrade}<1420:2.394+0.001\left|L_{uckGrade}-1410\right|,1420 \le L_{uckGrade}<1450:2.403+0.001\left|L_{uckGrade}-1420\right|,1450 \le L_{uckGrade}<1460:2.427+0.001\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1590:2.436+0.001\left|L_{uckGrade}-1460\right|,1590 \le L_{uckGrade}<1600:2.54+0.001\left|L_{uckGrade}-1590\right|,1600 \le L_{uckGrade}<1640:2.547+0.001\left|L_{uckGrade}-1600\right|,1640 \le L_{uckGrade}<1650:2.579+0.001\left|L_{uckGrade}-1640\right|,1650 \le L_{uckGrade}<1670:2.586+0.001\left|L_{uckGrade}-1650\right|,1670 \le L_{uckGrade}<1680:2.602+0.001\left|L_{uckGrade}-1670\right|,1680 \le L_{uckGrade}<1700:2.609+0.001\left|L_{uckGrade}-1680\right|,1700 \le L_{uckGrade}<1710:2.625+0.001\left|L_{uckGrade}-1700\right|,1710 \le L_{uckGrade}<1720:2.632+0.001\left|L_{uckGrade}-1710\right|,1720 \le L_{uckGrade}<1730:2.64+0.001\left|L_{uckGrade}-1720\right|,1730 \le L_{uckGrade}<1740:2.647+0.001\left|L_{uckGrade}-1730\right|,1740 \le L_{uckGrade}<1750:2.655+0.001\left|L_{uckGrade}-1740\right|,1750 \le L_{uckGrade}<1760:2.662+0.001\left|L_{uckGrade}-1750\right|,1760 \le L_{uckGrade}<1770:2.67+0.001\left|L_{uckGrade}-1760\right|,1770 \le L_{uckGrade}<1780:2.677+0.001\left|L_{uckGrade}-1770\right|,1780 \le L_{uckGrade}<1800:2.685+0.001\left|L_{uckGrade}-1780\right|,1800 \le L_{uckGrade}<1810:2.699+0.001\left|L_{uckGrade}-1800\right|,1810 \le L_{uckGrade}<1830:2.707+0.001\left|L_{uckGrade}-1810\right|,1830 \le L_{uckGrade}<1840:2.721+0.001\left|L_{uckGrade}-1830\right|,1840 \le L_{uckGrade}<1860:2.729+0.001\left|L_{uckGrade}-1840\right|,1860 \le L_{uckGrade}<1870:2.743+0.001\left|L_{uckGrade}-1860\right|,1870 \le L_{uckGrade}<2050:2.751+0.001\left|L_{uckGrade}-1870\right|,2050 \le L_{uckGrade}<2060:2.877+0.001\left|L_{uckGrade}-2050\right|,2060 \le L_{uckGrade}<2090:2.883+0.001\left|L_{uckGrade}-2060\right|,2090 \le L_{uckGrade}<2100:2.904+0.001\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2120:2.91+0.001\left|L_{uckGrade}-2100\right|,2120 \le L_{uckGrade}<2130:2.924+0.001\left|L_{uckGrade}-2120\right|,2130 \le L_{uckGrade}<2140:2.93+0.001\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2150:2.937+0.001\left|L_{uckGrade}-2140\right|,2150 \le L_{uckGrade}<2160:2.943+0.001\left|L_{uckGrade}-2150\right|,2160 \le L_{uckGrade}<2170:2.95+0.001\left|L_{uckGrade}-2160\right|,2170 \le L_{uckGrade}<2180:2.956+0.001\left|L_{uckGrade}-2170\right|,2180 \le L_{uckGrade}<2190:2.963+0.001\left|L_{uckGrade}-2180\right|,2190 \le L_{uckGrade}<2200:2.969+0.001\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2210:2.976+0.001\left|L_{uckGrade}-2200\right|,2210 \le L_{uckGrade}<2220:2.982+0.001\left|L_{uckGrade}-2210\right|,2220 \le L_{uckGrade}<2230:2.989+0.001\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2240:2.995+0.001\left|L_{uckGrade}-2230\right|,2240 \le L_{uckGrade}<2260:3.002+0.001\left|L_{uckGrade}-2240\right|,2260 \le L_{uckGrade}<2270:3.014+0.001\left|L_{uckGrade}-2260\right|,2270 \le L_{uckGrade}<2300:3.021+0.001\left|L_{uckGrade}-2270\right|,2300 \le L_{uckGrade}<2310:3.039+0.001\left|L_{uckGrade}-2300\right|,2310 \le L_{uckGrade}<2480:3.046+0.001\left|L_{uckGrade}-2310\right|,2480 \le L_{uckGrade}<2490:3.148+0\left|L_{uckGrade}-2480\right|,2490 \le L_{uckGrade}<2520:3.153+0.001\left|L_{uckGrade}-2490\right|,2520 \le L_{uckGrade}<2530:3.171+0.001\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2550:3.176+0.001\left|L_{uckGrade}-2530\right|,2550 \le L_{uckGrade}<2560:3.188+0\left|L_{uckGrade}-2550\right|,2560 \le L_{uckGrade}<2570:3.193+0.001\left|L_{uckGrade}-2560\right|,2570 \le L_{uckGrade}<2580:3.199+0.001\left|L_{uckGrade}-2570\right|,2580 \le L_{uckGrade}<2600:3.204+0.001\left|L_{uckGrade}-2580\right|,2600 \le L_{uckGrade}<2610:3.216+0\left|L_{uckGrade}-2600\right|,2610 \le L_{uckGrade}<2620:3.221+0.001\left|L_{uckGrade}-2610\right|,2620 \le L_{uckGrade}<2630:3.227+0.001\left|L_{uckGrade}-2620\right|,2630 \le L_{uckGrade}<2640:3.232+0.001\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2660:3.238+0.001\left|L_{uckGrade}-2640\right|,2660 \le L_{uckGrade}<2670:3.248+0.001\left|L_{uckGrade}-2660\right|,2670 \le L_{uckGrade}<2690:3.254+0\left|L_{uckGrade}-2670\right|,2690 \le L_{uckGrade}<2700:3.264+0.001\left|L_{uckGrade}-2690\right|,2700 \le L_{uckGrade}<2720:3.27+0\left|L_{uckGrade}-2700\right|,2720 \le L_{uckGrade}<2730:3.28+0.001\left|L_{uckGrade}-2720\right|,2730 \le L_{uckGrade}<2780:3.286+0\left|L_{uckGrade}-2730\right|,2780 \le L_{uckGrade}<2790:3.311+0.001\left|L_{uckGrade}-2780\right|,2790 \le L_{uckGrade}<2870:3.317+0.001\left|L_{uckGrade}-2790\right|,2870 \le L_{uckGrade}<2880:3.357+0\left|L_{uckGrade}-2870\right|,2880 \le L_{uckGrade}<2930:3.361+0\left|L_{uckGrade}-2880\right|,2930 \le L_{uckGrade}<2940:3.386+0\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2970:3.39+0\left|L_{uckGrade}-2940\right|,2970 \le L_{uckGrade}<2980:3.405+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<2990:3.409+0.001\left|L_{uckGrade}-2980\right|,2990 \le L_{uckGrade}<3000:3.414+0\left|L_{uckGrade}-2990\right|,3000 \le L_{uckGrade}<3020:3.418+0\left|L_{uckGrade}-3000\right|,3020 \le L_{uckGrade}<3030:3.428+0\left|L_{uckGrade}-3020\right|,3030 \le L_{uckGrade}<3040:3.432+0\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3050:3.437+0\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3060:3.441+0.001\left|L_{uckGrade}-3050\right|,3060 \le L_{uckGrade}<3070:3.446+0\left|L_{uckGrade}-3060\right|,3070 \le L_{uckGrade}<3080:3.45+0\left|L_{uckGrade}-3070\right|,3080 \le L_{uckGrade}<3100:3.455+0\left|L_{uckGrade}-3080\right|,3100 \le L_{uckGrade}<3110:3.463+0\left|L_{uckGrade}-3100\right|,3110 \le L_{uckGrade}<3130:3.468+0\left|L_{uckGrade}-3110\right|,3130 \le L_{uckGrade}<3140:3.476+0\left|L_{uckGrade}-3130\right|,3140 \le L_{uckGrade}<3160:3.481+0\left|L_{uckGrade}-3140\right|,3160 \le L_{uckGrade}<3170:3.489+0.001\left|L_{uckGrade}-3160\right|,3170 \le L_{uckGrade}<3230:3.494+0\left|L_{uckGrade}-3170\right|,3230 \le L_{uckGrade}<3240:3.518+0.001\left|L_{uckGrade}-3230\right|,3240 \le L_{uckGrade}<3290:3.523+0\left|L_{uckGrade}-3240\right|,3290 \le L_{uckGrade}<3300:3.543+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3360:3.546+0\left|L_{uckGrade}-3300\right|,3360 \le L_{uckGrade}<3370:3.57+0\left|L_{uckGrade}-3360\right|,3370 \le L_{uckGrade}<3400:3.573+0\left|L_{uckGrade}-3370\right|,3400 \le L_{uckGrade}<3410:3.585+0\left|L_{uckGrade}-3400\right|,3410 \le L_{uckGrade}<3420:3.588+0\left|L_{uckGrade}-3410\right|,3420 \le L_{uckGrade}<3430:3.592+0\left|L_{uckGrade}-3420\right|,3430 \le L_{uckGrade}<3450:3.595+0\left|L_{uckGrade}-3430\right|,3450 \le L_{uckGrade}<3460:3.603+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3470:3.606+0\left|L_{uckGrade}-3460\right|,3470 \le L_{uckGrade}<3480:3.61+0\left|L_{uckGrade}-3470\right|,3480 \le L_{uckGrade}<3490:3.613+0\left|L_{uckGrade}-3480\right|,3490 \le L_{uckGrade}<3500:3.617+0\left|L_{uckGrade}-3490\right|,3500 \le L_{uckGrade}<3510:3.62+0\left|L_{uckGrade}-3500\right|,3510 \le L_{uckGrade}<3520:3.624+0\left|L_{uckGrade}-3510\right|,3520 \le L_{uckGrade}<3530:3.627+0\left|L_{uckGrade}-3520\right|,3530 \le L_{uckGrade}<3550:3.631+0\left|L_{uckGrade}-3530\right|,3550 \le L_{uckGrade}<3560:3.637+0\left|L_{uckGrade}-3550\right|,3560 \le L_{uckGrade}<3590:3.641+0\left|L_{uckGrade}-3560\right|,3590 \le L_{uckGrade}<3600:3.65+0\left|L_{uckGrade}-3590\right|,3600 \le L_{uckGrade}<3640:3.654+0\left|L_{uckGrade}-3600\right|,3640 \le L_{uckGrade}<3650:3.666+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3760:3.67+0\left|L_{uckGrade}-3650\right|,3760 \le L_{uckGrade}<3770:3.703+0\left|L_{uckGrade}-3760\right|,3770 \le L_{uckGrade}<3810:3.705+0\left|L_{uckGrade}-3770\right|,3810 \le L_{uckGrade}<3820:3.717+0\left|L_{uckGrade}-3810\right|,3820 \le L_{uckGrade}<3840:3.719+0\left|L_{uckGrade}-3820\right|,3840 \le L_{uckGrade}<3850:3.725+0\left|L_{uckGrade}-3840\right|,3850 \le L_{uckGrade}<3870:3.727+0\left|L_{uckGrade}-3850\right|,3870 \le L_{uckGrade}<3880:3.733+0\left|L_{uckGrade}-3870\right|,3880 \le L_{uckGrade}<3890:3.735+0\left|L_{uckGrade}-3880\right|,3890 \le L_{uckGrade}<3900:3.738+0\left|L_{uckGrade}-3890\right|,3900 \le L_{uckGrade}<3910:3.74+0\left|L_{uckGrade}-3900\right|,3910 \le L_{uckGrade}<3920:3.743+0\left|L_{uckGrade}-3910\right|,3920 \le L_{uckGrade}<3930:3.745+0\left|L_{uckGrade}-3920\right|,3930 \le L_{uckGrade}<3940:3.748+0\left|L_{uckGrade}-3930\right|,3940 \le L_{uckGrade}<3950:3.75+0\left|L_{uckGrade}-3940\right|,3950 \le L_{uckGrade}<3960:3.753+0\left|L_{uckGrade}-3950\right|,3960 \le L_{uckGrade}<3970:3.755+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3990:3.758+0\left|L_{uckGrade}-3970\right|,3990 \le L_{uckGrade}<4000:3.762+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4030:3.765+0\left|L_{uckGrade}-4000\right|,4030 \le L_{uckGrade}<4040:3.771+0\left|L_{uckGrade}-4030\right|,4040 \le L_{uckGrade}<4090:3.774+0\left|L_{uckGrade}-4040\right|,4090 \le L_{uckGrade}<4100:3.784+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4170:3.787+0\left|L_{uckGrade}-4100\right|,4170 \le L_{uckGrade}<4180:3.801+0\left|L_{uckGrade}-4170\right|,4180 \le L_{uckGrade}<4230:3.802+0\left|L_{uckGrade}-4180\right|,4230 \le L_{uckGrade}<4240:3.812+0\left|L_{uckGrade}-4230\right|,4240 \le L_{uckGrade}<4270:3.813+0\left|L_{uckGrade}-4240\right|,4270 \le L_{uckGrade}<4280:3.819+0\left|L_{uckGrade}-4270\right|,4280 \le L_{uckGrade}<4300:3.82+0\left|L_{uckGrade}-4280\right|,4300 \le L_{uckGrade}<4310:3.824+0\left|L_{uckGrade}-4300\right|,4310 \le L_{uckGrade}<4320:3.825+0\left|L_{uckGrade}-4310\right|,4320 \le L_{uckGrade}<4330:3.827+0\left|L_{uckGrade}-4320\right|,4330 \le L_{uckGrade}<4340:3.828+0\left|L_{uckGrade}-4330\right|,4340 \le L_{uckGrade}<4350:3.83+0\left|L_{uckGrade}-4340\right|,4350 \le L_{uckGrade}<4360:3.831+0\left|L_{uckGrade}-4350\right|,4360 \le L_{uckGrade}<4370:3.833+0\left|L_{uckGrade}-4360\right|,4370 \le L_{uckGrade}<4380:3.834+0\left|L_{uckGrade}-4370\right|,4380 \le L_{uckGrade}<4390:3.836+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4400:3.837+0\left|L_{uckGrade}-4390\right|,4400 \le L_{uckGrade}<4420:3.839+0\left|L_{uckGrade}-4400\right|,4420 \le L_{uckGrade}<4430:3.841+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4450:3.843+0\left|L_{uckGrade}-4430\right|,4450 \le L_{uckGrade}<4460:3.845+0\left|L_{uckGrade}-4450\right|,4460 \le L_{uckGrade}<4500:3.847+0\left|L_{uckGrade}-4460\right|,4500 \le L_{uckGrade}<4510:3.851+0\left|L_{uckGrade}-4500\right|,4510 \le L_{uckGrade}<4630:3.853+0\left|L_{uckGrade}-4510\right|,4630 \le L_{uckGrade}<4640:3.865+0\left|L_{uckGrade}-4630\right|,4640 \le L_{uckGrade}<4680:3.865+0\left|L_{uckGrade}-4640\right|,4680 \le L_{uckGrade}<4690:3.869+0\left|L_{uckGrade}-4680\right|,4690 \le L_{uckGrade}<4710:3.869+0\left|L_{uckGrade}-4690\right|,4710 \le L_{uckGrade}<4720:3.871+0\left|L_{uckGrade}-4710\right|,4720 \le L_{uckGrade}<4740:3.871+0\left|L_{uckGrade}-4720\right|,4740 \le L_{uckGrade}<4750:3.873+0\left|L_{uckGrade}-4740\right|,4750 \le L_{uckGrade}<4760:3.873+0\left|L_{uckGrade}-4750\right|,4760 \le L_{uckGrade}<4770:3.874+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4780:3.874+0\left|L_{uckGrade}-4770\right|,4780 \le L_{uckGrade}<4790:3.875+0\left|L_{uckGrade}-4780\right|,4790 \le L_{uckGrade}<4800:3.875+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4810:3.876+0\left|L_{uckGrade}-4800\right|,4810 \le L_{uckGrade}<4820:3.876+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4830:3.877+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4840:3.877+0\left|L_{uckGrade}-4830\right|,4840 \le L_{uckGrade}<4860:3.878+0\left|L_{uckGrade}-4840\right|,4860 \le L_{uckGrade}<4870:3.878+0\left|L_{uckGrade}-4860\right|,4870 \le L_{uckGrade}<4900:3.879+0\left|L_{uckGrade}-4870\right|,4900 \le L_{uckGrade}<4910:3.879+0\left|L_{uckGrade}-4900\right|,4910 \le L_{uckGrade}<4950:3.88+0\left|L_{uckGrade}-4910\right|,4950 \le L_{uckGrade}<4960:3.88+0\left|L_{uckGrade}-4950\right|,4960 \le L_{uckGrade}<5000:3.881+0\left|L_{uckGrade}-4960\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}<60:1+0.001\left|L_{uckGrade}-0\right|,60 \le L_{uckGrade}<70:1.078+0.001\left|L_{uckGrade}-60\right|,70 \le L_{uckGrade}<110:1.09+0.001\left|L_{uckGrade}-70\right|,110 \le L_{uckGrade}<120:1.142+0.001\left|L_{uckGrade}-110\right|,120 \le L_{uckGrade}<140:1.154+0.001\left|L_{uckGrade}-120\right|,140 \le L_{uckGrade}<150:1.18+0.001\left|L_{uckGrade}-140\right|,150 \le L_{uckGrade}<160:1.192+0.001\left|L_{uckGrade}-150\right|,160 \le L_{uckGrade}<170:1.205+0.001\left|L_{uckGrade}-160\right|,170 \le L_{uckGrade}<190:1.217+0.001\left|L_{uckGrade}-170\right|,190 \le L_{uckGrade}<200:1.243+0.001\left|L_{uckGrade}-190\right|,200 \le L_{uckGrade}<210:1.255+0.001\left|L_{uckGrade}-200\right|,210 \le L_{uckGrade}<230:1.268+0.001\left|L_{uckGrade}-210\right|,230 \le L_{uckGrade}<240:1.292+0.001\left|L_{uckGrade}-230\right|,240 \le L_{uckGrade}<250:1.305+0.001\left|L_{uckGrade}-240\right|,250 \le L_{uckGrade}<260:1.317+0.001\left|L_{uckGrade}-250\right|,260 \le L_{uckGrade}<290:1.33+0.001\left|L_{uckGrade}-260\right|,290 \le L_{uckGrade}<300:1.366+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<340:1.379+0.001\left|L_{uckGrade}-300\right|,340 \le L_{uckGrade}<350:1.427+0.001\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<430:1.44+0.001\left|L_{uckGrade}-350\right|,430 \le L_{uckGrade}<440:1.536+0.001\left|L_{uckGrade}-430\right|,440 \le L_{uckGrade}<480:1.547+0.001\left|L_{uckGrade}-440\right|,480 \le L_{uckGrade}<490:1.595+0.001\left|L_{uckGrade}-480\right|,490 \le L_{uckGrade}<520:1.606+0.001\left|L_{uckGrade}-490\right|,520 \le L_{uckGrade}<530:1.642+0.001\left|L_{uckGrade}-520\right|,530 \le L_{uckGrade}<540:1.653+0.001\left|L_{uckGrade}-530\right|,540 \le L_{uckGrade}<550:1.665+0.001\left|L_{uckGrade}-540\right|,550 \le L_{uckGrade}<570:1.676+0.001\left|L_{uckGrade}-550\right|,570 \le L_{uckGrade}<580:1.7+0.001\left|L_{uckGrade}-570\right|,580 \le L_{uckGrade}<590:1.711+0.001\left|L_{uckGrade}-580\right|,590 \le L_{uckGrade}<610:1.723+0.001\left|L_{uckGrade}-590\right|,610 \le L_{uckGrade}<620:1.745+0.001\left|L_{uckGrade}-610\right|,620 \le L_{uckGrade}<630:1.757+0.001\left|L_{uckGrade}-620\right|,630 \le L_{uckGrade}<640:1.768+0.001\left|L_{uckGrade}-630\right|,640 \le L_{uckGrade}<660:1.78+0.001\left|L_{uckGrade}-640\right|,660 \le L_{uckGrade}<670:1.802+0.001\left|L_{uckGrade}-660\right|,670 \le L_{uckGrade}<710:1.814+0.001\left|L_{uckGrade}-670\right|,710 \le L_{uckGrade}<720:1.858+0.001\left|L_{uckGrade}-710\right|,720 \le L_{uckGrade}<830:1.87+0.001\left|L_{uckGrade}-720\right|,830 \le L_{uckGrade}<840:1.991+0.001\left|L_{uckGrade}-830\right|,840 \le L_{uckGrade}<870:2.001+0.001\left|L_{uckGrade}-840\right|,870 \le L_{uckGrade}<880:2.034+0.001\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<910:2.044+0.001\left|L_{uckGrade}-880\right|,910 \le L_{uckGrade}<920:2.077+0.001\left|L_{uckGrade}-910\right|,920 \le L_{uckGrade}<930:2.087+0.001\left|L_{uckGrade}-920\right|,930 \le L_{uckGrade}<940:2.098+0.001\left|L_{uckGrade}-930\right|,940 \le L_{uckGrade}<950:2.108+0.001\left|L_{uckGrade}-940\right|,950 \le L_{uckGrade}<960:2.119+0.001\left|L_{uckGrade}-950\right|,960 \le L_{uckGrade}<970:2.129+0.001\left|L_{uckGrade}-960\right|,970 \le L_{uckGrade}<980:2.14+0.001\left|L_{uckGrade}-970\right|,980 \le L_{uckGrade}<990:2.15+0.001\left|L_{uckGrade}-980\right|,990 \le L_{uckGrade}<1000:2.161+0.001\left|L_{uckGrade}-990\right|,1000 \le L_{uckGrade}<1010:2.171+0.001\left|L_{uckGrade}-1000\right|,1010 \le L_{uckGrade}<1030:2.182+0.001\left|L_{uckGrade}-1010\right|,1030 \le L_{uckGrade}<1040:2.202+0.001\left|L_{uckGrade}-1030\right|,1040 \le L_{uckGrade}<1060:2.213+0.001\left|L_{uckGrade}-1040\right|,1060 \le L_{uckGrade}<1070:2.233+0.001\left|L_{uckGrade}-1060\right|,1070 \le L_{uckGrade}<1130:2.244+0.001\left|L_{uckGrade}-1070\right|,1130 \le L_{uckGrade}<1140:2.304+0.001\left|L_{uckGrade}-1130\right|,1140 \le L_{uckGrade}<1180:2.315+0.001\left|L_{uckGrade}-1140\right|,1180 \le L_{uckGrade}<1190:2.355+0.001\left|L_{uckGrade}-1180\right|,1190 \le L_{uckGrade}<1250:2.364+0.001\left|L_{uckGrade}-1190\right|,1250 \le L_{uckGrade}<1260:2.424+0.001\left|L_{uckGrade}-1250\right|,1260 \le L_{uckGrade}<1280:2.433+0.001\left|L_{uckGrade}-1260\right|,1280 \le L_{uckGrade}<1290:2.453+0.001\left|L_{uckGrade}-1280\right|,1290 \le L_{uckGrade}<1310:2.462+0.001\left|L_{uckGrade}-1290\right|,1310 \le L_{uckGrade}<1320:2.482+0.001\left|L_{uckGrade}-1310\right|,1320 \le L_{uckGrade}<1330:2.491+0.001\left|L_{uckGrade}-1320\right|,1330 \le L_{uckGrade}<1340:2.501+0.001\left|L_{uckGrade}-1330\right|,1340 \le L_{uckGrade}<1350:2.51+0.001\left|L_{uckGrade}-1340\right|,1350 \le L_{uckGrade}<1360:2.52+0.001\left|L_{uckGrade}-1350\right|,1360 \le L_{uckGrade}<1370:2.529+0.001\left|L_{uckGrade}-1360\right|,1370 \le L_{uckGrade}<1380:2.539+0.001\left|L_{uckGrade}-1370\right|,1380 \le L_{uckGrade}<1390:2.548+0.001\left|L_{uckGrade}-1380\right|,1390 \le L_{uckGrade}<1410:2.558+0.001\left|L_{uckGrade}-1390\right|,1410 \le L_{uckGrade}<1420:2.576+0.001\left|L_{uckGrade}-1410\right|,1420 \le L_{uckGrade}<1440:2.586+0.001\left|L_{uckGrade}-1420\right|,1440 \le L_{uckGrade}<1450:2.604+0.001\left|L_{uckGrade}-1440\right|,1450 \le L_{uckGrade}<1500:2.614+0.001\left|L_{uckGrade}-1450\right|,1500 \le L_{uckGrade}<1510:2.659+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1580:2.669+0.001\left|L_{uckGrade}-1510\right|,1580 \le L_{uckGrade}<1590:2.732+0.001\left|L_{uckGrade}-1580\right|,1590 \le L_{uckGrade}<1630:2.74+0.001\left|L_{uckGrade}-1590\right|,1630 \le L_{uckGrade}<1640:2.776+0.001\left|L_{uckGrade}-1630\right|,1640 \le L_{uckGrade}<1670:2.784+0.001\left|L_{uckGrade}-1640\right|,1670 \le L_{uckGrade}<1680:2.811+0.001\left|L_{uckGrade}-1670\right|,1680 \le L_{uckGrade}<1700:2.819+0.001\left|L_{uckGrade}-1680\right|,1700 \le L_{uckGrade}<1710:2.837+0.001\left|L_{uckGrade}-1700\right|,1710 \le L_{uckGrade}<1720:2.845+0.001\left|L_{uckGrade}-1710\right|,1720 \le L_{uckGrade}<1730:2.854+0.001\left|L_{uckGrade}-1720\right|,1730 \le L_{uckGrade}<1740:2.862+0.001\left|L_{uckGrade}-1730\right|,1740 \le L_{uckGrade}<1750:2.871+0.001\left|L_{uckGrade}-1740\right|,1750 \le L_{uckGrade}<1760:2.879+0.001\left|L_{uckGrade}-1750\right|,1760 \le L_{uckGrade}<1780:2.888+0.001\left|L_{uckGrade}-1760\right|,1780 \le L_{uckGrade}<1790:2.904+0.001\left|L_{uckGrade}-1780\right|,1790 \le L_{uckGrade}<1810:2.913+0.001\left|L_{uckGrade}-1790\right|,1810 \le L_{uckGrade}<1820:2.929+0.001\left|L_{uckGrade}-1810\right|,1820 \le L_{uckGrade}<1850:2.938+0.001\left|L_{uckGrade}-1820\right|,1850 \le L_{uckGrade}<1860:2.962+0.001\left|L_{uckGrade}-1850\right|,1860 \le L_{uckGrade}<2000:2.971+0.001\left|L_{uckGrade}-1860\right|,2000 \le L_{uckGrade}<2010:3.083+0.001\left|L_{uckGrade}-2000\right|,2010 \le L_{uckGrade}<2040:3.09+0.001\left|L_{uckGrade}-2010\right|,2040 \le L_{uckGrade}<2050:3.114+0.001\left|L_{uckGrade}-2040\right|,2050 \le L_{uckGrade}<2070:3.121+0.001\left|L_{uckGrade}-2050\right|,2070 \le L_{uckGrade}<2080:3.137+0.001\left|L_{uckGrade}-2070\right|,2080 \le L_{uckGrade}<2090:3.144+0.001\left|L_{uckGrade}-2080\right|,2090 \le L_{uckGrade}<2100:3.152+0.001\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2110:3.159+0.001\left|L_{uckGrade}-2100\right|,2110 \le L_{uckGrade}<2120:3.167+0.001\left|L_{uckGrade}-2110\right|,2120 \le L_{uckGrade}<2130:3.174+0.001\left|L_{uckGrade}-2120\right|,2130 \le L_{uckGrade}<2140:3.182+0.001\left|L_{uckGrade}-2130\right|,2140 \le L_{uckGrade}<2150:3.189+0.001\left|L_{uckGrade}-2140\right|,2150 \le L_{uckGrade}<2160:3.197+0.001\left|L_{uckGrade}-2150\right|,2160 \le L_{uckGrade}<2170:3.204+0.001\left|L_{uckGrade}-2160\right|,2170 \le L_{uckGrade}<2190:3.212+0.001\left|L_{uckGrade}-2170\right|,2190 \le L_{uckGrade}<2200:3.226+0.001\left|L_{uckGrade}-2190\right|,2200 \le L_{uckGrade}<2230:3.234+0.001\left|L_{uckGrade}-2200\right|,2230 \le L_{uckGrade}<2240:3.255+0.001\left|L_{uckGrade}-2230\right|,2240 \le L_{uckGrade}<2390:3.263+0.001\left|L_{uckGrade}-2240\right|,2390 \le L_{uckGrade}<2400:3.368+0.001\left|L_{uckGrade}-2390\right|,2400 \le L_{uckGrade}<2430:3.374+0.001\left|L_{uckGrade}-2400\right|,2430 \le L_{uckGrade}<2440:3.395+0.001\left|L_{uckGrade}-2430\right|,2440 \le L_{uckGrade}<2450:3.401+0.001\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2460:3.408+0.001\left|L_{uckGrade}-2450\right|,2460 \le L_{uckGrade}<2480:3.414+0.001\left|L_{uckGrade}-2460\right|,2480 \le L_{uckGrade}<2490:3.428+0.001\left|L_{uckGrade}-2480\right|,2490 \le L_{uckGrade}<2500:3.434+0.001\left|L_{uckGrade}-2490\right|,2500 \le L_{uckGrade}<2510:3.441+0.001\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2520:3.447+0.001\left|L_{uckGrade}-2510\right|,2520 \le L_{uckGrade}<2530:3.454+0.001\left|L_{uckGrade}-2520\right|,2530 \le L_{uckGrade}<2540:3.46+0.001\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2560:3.467+0.001\left|L_{uckGrade}-2540\right|,2560 \le L_{uckGrade}<2570:3.479+0.001\left|L_{uckGrade}-2560\right|,2570 \le L_{uckGrade}<2590:3.486+0.001\left|L_{uckGrade}-2570\right|,2590 \le L_{uckGrade}<2600:3.498+0.001\left|L_{uckGrade}-2590\right|,2600 \le L_{uckGrade}<2640:3.505+0.001\left|L_{uckGrade}-2600\right|,2640 \le L_{uckGrade}<2650:3.529+0.001\left|L_{uckGrade}-2640\right|,2650 \le L_{uckGrade}<2740:3.536+0.001\left|L_{uckGrade}-2650\right|,2740 \le L_{uckGrade}<2750:3.59+0.001\left|L_{uckGrade}-2740\right|,2750 \le L_{uckGrade}<2790:3.595+0.001\left|L_{uckGrade}-2750\right|,2790 \le L_{uckGrade}<2800:3.619+0\left|L_{uckGrade}-2790\right|,2800 \le L_{uckGrade}<2830:3.624+0.001\left|L_{uckGrade}-2800\right|,2830 \le L_{uckGrade}<2840:3.642+0\left|L_{uckGrade}-2830\right|,2840 \le L_{uckGrade}<2850:3.647+0.001\left|L_{uckGrade}-2840\right|,2850 \le L_{uckGrade}<2860:3.653+0\left|L_{uckGrade}-2850\right|,2860 \le L_{uckGrade}<2870:3.658+0.001\left|L_{uckGrade}-2860\right|,2870 \le L_{uckGrade}<2880:3.664+0\left|L_{uckGrade}-2870\right|,2880 \le L_{uckGrade}<2890:3.669+0.001\left|L_{uckGrade}-2880\right|,2890 \le L_{uckGrade}<2900:3.675+0.001\left|L_{uckGrade}-2890\right|,2900 \le L_{uckGrade}<2910:3.68+0.001\left|L_{uckGrade}-2900\right|,2910 \le L_{uckGrade}<2920:3.686+0\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2930:3.691+0.001\left|L_{uckGrade}-2920\right|,2930 \le L_{uckGrade}<2940:3.697+0\left|L_{uckGrade}-2930\right|,2940 \le L_{uckGrade}<2950:3.702+0.001\left|L_{uckGrade}-2940\right|,2950 \le L_{uckGrade}<2980:3.708+0\left|L_{uckGrade}-2950\right|,2980 \le L_{uckGrade}<2990:3.723+0.001\left|L_{uckGrade}-2980\right|,2990 \le L_{uckGrade}<3030:3.729+0.001\left|L_{uckGrade}-2990\right|,3030 \le L_{uckGrade}<3040:3.749+0.001\left|L_{uckGrade}-3030\right|,3040 \le L_{uckGrade}<3120:3.755+0.001\left|L_{uckGrade}-3040\right|,3120 \le L_{uckGrade}<3130:3.795+0\left|L_{uckGrade}-3120\right|,3130 \le L_{uckGrade}<3180:3.799+0\left|L_{uckGrade}-3130\right|,3180 \le L_{uckGrade}<3190:3.824+0\left|L_{uckGrade}-3180\right|,3190 \le L_{uckGrade}<3210:3.828+0.001\left|L_{uckGrade}-3190\right|,3210 \le L_{uckGrade}<3220:3.838+0\left|L_{uckGrade}-3210\right|,3220 \le L_{uckGrade}<3240:3.842+0\left|L_{uckGrade}-3220\right|,3240 \le L_{uckGrade}<3250:3.852+0\left|L_{uckGrade}-3240\right|,3250 \le L_{uckGrade}<3260:3.856+0.001\left|L_{uckGrade}-3250\right|,3260 \le L_{uckGrade}<3270:3.861+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3280:3.865+0\left|L_{uckGrade}-3270\right|,3280 \le L_{uckGrade}<3290:3.87+0\left|L_{uckGrade}-3280\right|,3290 \le L_{uckGrade}<3300:3.874+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3320:3.879+0\left|L_{uckGrade}-3300\right|,3320 \le L_{uckGrade}<3330:3.887+0\left|L_{uckGrade}-3320\right|,3330 \le L_{uckGrade}<3350:3.892+0\left|L_{uckGrade}-3330\right|,3350 \le L_{uckGrade}<3360:3.9+0\left|L_{uckGrade}-3350\right|,3360 \le L_{uckGrade}<3390:3.905+0\left|L_{uckGrade}-3360\right|,3390 \le L_{uckGrade}<3400:3.917+0.001\left|L_{uckGrade}-3390\right|,3400 \le L_{uckGrade}<3530:3.922+0\left|L_{uckGrade}-3400\right|,3530 \le L_{uckGrade}<3540:3.974+0\left|L_{uckGrade}-3530\right|,3540 \le L_{uckGrade}<3580:3.977+0\left|L_{uckGrade}-3540\right|,3580 \le L_{uckGrade}<3590:3.993+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3610:3.996+0\left|L_{uckGrade}-3590\right|,3610 \le L_{uckGrade}<3620:4.004+0\left|L_{uckGrade}-3610\right|,3620 \le L_{uckGrade}<3630:4.007+0\left|L_{uckGrade}-3620\right|,3630 \le L_{uckGrade}<3640:4.011+0\left|L_{uckGrade}-3630\right|,3640 \le L_{uckGrade}<3650:4.014+0\left|L_{uckGrade}-3640\right|,3650 \le L_{uckGrade}<3660:4.018+0\left|L_{uckGrade}-3650\right|,3660 \le L_{uckGrade}<3670:4.021+0\left|L_{uckGrade}-3660\right|,3670 \le L_{uckGrade}<3680:4.025+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3690:4.028+0\left|L_{uckGrade}-3680\right|,3690 \le L_{uckGrade}<3710:4.032+0\left|L_{uckGrade}-3690\right|,3710 \le L_{uckGrade}<3720:4.038+0\left|L_{uckGrade}-3710\right|,3720 \le L_{uckGrade}<3740:4.042+0\left|L_{uckGrade}-3720\right|,3740 \le L_{uckGrade}<3750:4.048+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3780:4.052+0\left|L_{uckGrade}-3750\right|,3780 \le L_{uckGrade}<3790:4.061+0\left|L_{uckGrade}-3780\right|,3790 \le L_{uckGrade}<3910:4.065+0\left|L_{uckGrade}-3790\right|,3910 \le L_{uckGrade}<3920:4.101+0\left|L_{uckGrade}-3910\right|,3920 \le L_{uckGrade}<3960:4.103+0\left|L_{uckGrade}-3920\right|,3960 \le L_{uckGrade}<3970:4.115+0\left|L_{uckGrade}-3960\right|,3970 \le L_{uckGrade}<3990:4.117+0\left|L_{uckGrade}-3970\right|,3990 \le L_{uckGrade}<4000:4.123+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4010:4.125+0\left|L_{uckGrade}-4000\right|,4010 \le L_{uckGrade}<4020:4.128+0\left|L_{uckGrade}-4010\right|,4020 \le L_{uckGrade}<4030:4.13+0\left|L_{uckGrade}-4020\right|,4030 \le L_{uckGrade}<4040:4.133+0\left|L_{uckGrade}-4030\right|,4040 \le L_{uckGrade}<4050:4.135+0\left|L_{uckGrade}-4040\right|,4050 \le L_{uckGrade}<4060:4.138+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4070:4.14+0\left|L_{uckGrade}-4060\right|,4070 \le L_{uckGrade}<4080:4.143+0\left|L_{uckGrade}-4070\right|,4080 \le L_{uckGrade}<4090:4.145+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4110:4.148+0\left|L_{uckGrade}-4090\right|,4110 \le L_{uckGrade}<4120:4.152+0\left|L_{uckGrade}-4110\right|,4120 \le L_{uckGrade}<4150:4.155+0\left|L_{uckGrade}-4120\right|,4150 \le L_{uckGrade}<4160:4.161+0\left|L_{uckGrade}-4150\right|,4160 \le L_{uckGrade}<4320:4.164+0\left|L_{uckGrade}-4160\right|,4320 \le L_{uckGrade}<4330:4.196+0\left|L_{uckGrade}-4320\right|,4330 \le L_{uckGrade}<4350:4.197+0\left|L_{uckGrade}-4330\right|,4350 \le L_{uckGrade}<4360:4.201+0\left|L_{uckGrade}-4350\right|,4360 \le L_{uckGrade}<4380:4.202+0\left|L_{uckGrade}-4360\right|,4380 \le L_{uckGrade}<4390:4.206+0\left|L_{uckGrade}-4380\right|,4390 \le L_{uckGrade}<4400:4.207+0\left|L_{uckGrade}-4390\right|,4400 \le L_{uckGrade}<4410:4.209+0\left|L_{uckGrade}-4400\right|,4410 \le L_{uckGrade}<4430:4.21+0\left|L_{uckGrade}-4410\right|,4430 \le L_{uckGrade}<4450:4.214+0\left|L_{uckGrade}-4430\right|,4450 \le L_{uckGrade}<4460:4.216+0\left|L_{uckGrade}-4450\right|,4460 \le L_{uckGrade}<4470:4.218+0\left|L_{uckGrade}-4460\right|,4470 \le L_{uckGrade}<4480:4.219+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4500:4.221+0\left|L_{uckGrade}-4480\right|,4500 \le L_{uckGrade}<4510:4.223+0\left|L_{uckGrade}-4500\right|,4510 \le L_{uckGrade}<4540:4.225+0\left|L_{uckGrade}-4510\right|,4540 \le L_{uckGrade}<4550:4.228+0\left|L_{uckGrade}-4540\right|,4550 \le L_{uckGrade}<4690:4.23+0\left|L_{uckGrade}-4550\right|,4690 \le L_{uckGrade}<4700:4.244+0\left|L_{uckGrade}-4690\right|,4700 \le L_{uckGrade}<4730:4.244+0\left|L_{uckGrade}-4700\right|,4730 \le L_{uckGrade}<4740:4.247+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4760:4.247+0\left|L_{uckGrade}-4740\right|,4760 \le L_{uckGrade}<4770:4.249+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4780:4.249+0\left|L_{uckGrade}-4770\right|,4780 \le L_{uckGrade}<4790:4.25+0\left|L_{uckGrade}-4780\right|,4790 \le L_{uckGrade}<4810:4.25+0\left|L_{uckGrade}-4790\right|,4810 \le L_{uckGrade}<4820:4.252+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4830:4.252+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4850:4.253+0\left|L_{uckGrade}-4830\right|,4850 \le L_{uckGrade}<4860:4.253+0\left|L_{uckGrade}-4850\right|,4860 \le L_{uckGrade}<4880:4.254+0\left|L_{uckGrade}-4860\right|,4880 \le L_{uckGrade}<4890:4.254+0\left|L_{uckGrade}-4880\right|,4890 \le L_{uckGrade}<4910:4.255+0\left|L_{uckGrade}-4890\right|,4910 \le L_{uckGrade}<4920:4.255+0\left|L_{uckGrade}-4910\right|,4920 \le L_{uckGrade}<4990:4.256+0\left|L_{uckGrade}-4920\right|,4990 \le L_{uckGrade}<5000:4.256+0\left|L_{uckGrade}-4990\right|\right\}
See Example for how to use.
LaTeX Formula
Can be pasted into Desmos or other LaTeX editors for quick use of the equation.
Triple click to select all. Note: Some browsers will add an extra return carriage (line end) after the formula. Remove it before pasting for best results.
L_{uckGrade07}(L_{uckGrade})=\left\{0 \le L_{uckGrade}<10:1+0.001\left|L_{uckGrade}-0\right|,10 \le L_{uckGrade}<30:1.014+0.001\left|L_{uckGrade}-10\right|,30 \le L_{uckGrade}<40:1.04+0.001\left|L_{uckGrade}-30\right|,40 \le L_{uckGrade}<50:1.054+0.001\left|L_{uckGrade}-40\right|,50 \le L_{uckGrade}<60:1.067+0.001\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<80:1.081+0.001\left|L_{uckGrade}-60\right|,80 \le L_{uckGrade}<90:1.107+0.001\left|L_{uckGrade}-80\right|,90 \le L_{uckGrade}<130:1.121+0.001\left|L_{uckGrade}-90\right|,130 \le L_{uckGrade}<140:1.173+0.001\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<240:1.187+0.001\left|L_{uckGrade}-140\right|,240 \le L_{uckGrade}<250:1.317+0.001\left|L_{uckGrade}-240\right|,250 \le L_{uckGrade}<290:1.329+0.001\left|L_{uckGrade}-250\right|,290 \le L_{uckGrade}<300:1.381+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<320:1.393+0.001\left|L_{uckGrade}-300\right|,320 \le L_{uckGrade}<330:1.419+0.001\left|L_{uckGrade}-320\right|,330 \le L_{uckGrade}<340:1.431+0.001\left|L_{uckGrade}-330\right|,340 \le L_{uckGrade}<350:1.444+0.001\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<370:1.456+0.001\left|L_{uckGrade}-350\right|,370 \le L_{uckGrade}<390:1.482+0.001\left|L_{uckGrade}-370\right|,390 \le L_{uckGrade}<400:1.506+0.001\left|L_{uckGrade}-390\right|,400 \le L_{uckGrade}<410:1.519+0.001\left|L_{uckGrade}-400\right|,410 \le L_{uckGrade}<420:1.531+0.001\left|L_{uckGrade}-410\right|,420 \le L_{uckGrade}<440:1.544+0.001\left|L_{uckGrade}-420\right|,440 \le L_{uckGrade}<450:1.568+0.001\left|L_{uckGrade}-440\right|,450 \le L_{uckGrade}<470:1.581+0.001\left|L_{uckGrade}-450\right|,470 \le L_{uckGrade}<480:1.605+0.001\left|L_{uckGrade}-470\right|,480 \le L_{uckGrade}<640:1.618+0.001\left|L_{uckGrade}-480\right|,640 \le L_{uckGrade}<650:1.81+0.001\left|L_{uckGrade}-640\right|,650 \le L_{uckGrade}<670:1.821+0.001\left|L_{uckGrade}-650\right|,670 \le L_{uckGrade}<680:1.845+0.001\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<700:1.856+0.001\left|L_{uckGrade}-680\right|,700 \le L_{uckGrade}<710:1.88+0.001\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<730:1.891+0.001\left|L_{uckGrade}-710\right|,730 \le L_{uckGrade}<740:1.915+0.001\left|L_{uckGrade}-730\right|,740 \le L_{uckGrade}<750:1.926+0.001\left|L_{uckGrade}-740\right|,750 \le L_{uckGrade}<770:1.938+0.001\left|L_{uckGrade}-750\right|,770 \le L_{uckGrade}<780:1.96+0.001\left|L_{uckGrade}-770\right|,780 \le L_{uckGrade}<790:1.972+0.001\left|L_{uckGrade}-780\right|,790 \le L_{uckGrade}<800:1.983+0.001\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<820:1.995+0.001\left|L_{uckGrade}-800\right|,820 \le L_{uckGrade}<830:2.017+0.001\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<870:2.029+0.001\left|L_{uckGrade}-830\right|,870 \le L_{uckGrade}<880:2.073+0.001\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<990:2.085+0.001\left|L_{uckGrade}-880\right|,990 \le L_{uckGrade}<1000:2.206+0.001\left|L_{uckGrade}-990\right|,1000 \le L_{uckGrade}<1030:2.216+0.001\left|L_{uckGrade}-1000\right|,1030 \le L_{uckGrade}<1040:2.249+0.001\left|L_{uckGrade}-1030\right|,1040 \le L_{uckGrade}<1060:2.259+0.001\left|L_{uckGrade}-1040\right|,1060 \le L_{uckGrade}<1070:2.281+0.001\left|L_{uckGrade}-1060\right|,1070 \le L_{uckGrade}<1090:2.291+0.001\left|L_{uckGrade}-1070\right|,1090 \le L_{uckGrade}<1100:2.313+0.001\left|L_{uckGrade}-1090\right|,1100 \le L_{uckGrade}<1110:2.323+0.001\left|L_{uckGrade}-1100\right|,1110 \le L_{uckGrade}<1120:2.334+0.001\left|L_{uckGrade}-1110\right|,1120 \le L_{uckGrade}<1130:2.344+0.001\left|L_{uckGrade}-1120\right|,1130 \le L_{uckGrade}<1140:2.355+0.001\left|L_{uckGrade}-1130\right|,1140 \le L_{uckGrade}<1150:2.365+0.001\left|L_{uckGrade}-1140\right|,1150 \le L_{uckGrade}<1170:2.376+0.001\left|L_{uckGrade}-1150\right|,1170 \le L_{uckGrade}<1180:2.396+0.001\left|L_{uckGrade}-1170\right|,1180 \le L_{uckGrade}<1210:2.407+0.001\left|L_{uckGrade}-1180\right|,1210 \le L_{uckGrade}<1220:2.437+0.001\left|L_{uckGrade}-1210\right|,1220 \le L_{uckGrade}<1270:2.448+0.001\left|L_{uckGrade}-1220\right|,1270 \le L_{uckGrade}<1280:2.498+0.001\left|L_{uckGrade}-1270\right|,1280 \le L_{uckGrade}<1320:2.509+0.001\left|L_{uckGrade}-1280\right|,1320 \le L_{uckGrade}<1330:2.549+0.001\left|L_{uckGrade}-1320\right|,1330 \le L_{uckGrade}<1390:2.558+0.001\left|L_{uckGrade}-1330\right|,1390 \le L_{uckGrade}<1400:2.618+0.001\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1420:2.627+0.001\left|L_{uckGrade}-1400\right|,1420 \le L_{uckGrade}<1430:2.647+0.001\left|L_{uckGrade}-1420\right|,1430 \le L_{uckGrade}<1450:2.656+0.001\left|L_{uckGrade}-1430\right|,1450 \le L_{uckGrade}<1460:2.676+0.001\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1470:2.685+0.001\left|L_{uckGrade}-1460\right|,1470 \le L_{uckGrade}<1480:2.695+0.001\left|L_{uckGrade}-1470\right|,1480 \le L_{uckGrade}<1490:2.704+0.001\left|L_{uckGrade}-1480\right|,1490 \le L_{uckGrade}<1500:2.714+0.001\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1510:2.723+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:2.733+0.001\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1530:2.742+0.001\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1550:2.752+0.001\left|L_{uckGrade}-1530\right|,1550 \le L_{uckGrade}<1560:2.77+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1590:2.78+0.001\left|L_{uckGrade}-1560\right|,1590 \le L_{uckGrade}<1600:2.807+0.001\left|L_{uckGrade}-1590\right|,1600 \le L_{uckGrade}<1740:2.817+0.001\left|L_{uckGrade}-1600\right|,1740 \le L_{uckGrade}<1750:2.943+0.001\left|L_{uckGrade}-1740\right|,1750 \le L_{uckGrade}<1780:2.951+0.001\left|L_{uckGrade}-1750\right|,1780 \le L_{uckGrade}<1790:2.978+0.001\left|L_{uckGrade}-1780\right|,1790 \le L_{uckGrade}<1810:2.986+0.001\left|L_{uckGrade}-1790\right|,1810 \le L_{uckGrade}<1820:3.004+0.001\left|L_{uckGrade}-1810\right|,1820 \le L_{uckGrade}<1830:3.012+0.001\left|L_{uckGrade}-1820\right|,1830 \le L_{uckGrade}<1840:3.021+0.001\left|L_{uckGrade}-1830\right|,1840 \le L_{uckGrade}<1850:3.029+0.001\left|L_{uckGrade}-1840\right|,1850 \le L_{uckGrade}<1860:3.038+0.001\left|L_{uckGrade}-1850\right|,1860 \le L_{uckGrade}<1870:3.046+0.001\left|L_{uckGrade}-1860\right|,1870 \le L_{uckGrade}<1880:3.055+0.001\left|L_{uckGrade}-1870\right|,1880 \le L_{uckGrade}<1890:3.063+0.001\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1900:3.072+0.001\left|L_{uckGrade}-1890\right|,1900 \le L_{uckGrade}<1910:3.08+0.001\left|L_{uckGrade}-1900\right|,1910 \le L_{uckGrade}<1930:3.089+0.001\left|L_{uckGrade}-1910\right|,1930 \le L_{uckGrade}<1940:3.105+0.001\left|L_{uckGrade}-1930\right|,1940 \le L_{uckGrade}<1980:3.114+0.001\left|L_{uckGrade}-1940\right|,1980 \le L_{uckGrade}<1990:3.146+0.001\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2090:3.155+0.001\left|L_{uckGrade}-1990\right|,2090 \le L_{uckGrade}<2100:3.235+0.001\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2140:3.242+0.001\left|L_{uckGrade}-2100\right|,2140 \le L_{uckGrade}<2150:3.274+0.001\left|L_{uckGrade}-2140\right|,2150 \le L_{uckGrade}<2170:3.281+0.001\left|L_{uckGrade}-2150\right|,2170 \le L_{uckGrade}<2180:3.297+0.001\left|L_{uckGrade}-2170\right|,2180 \le L_{uckGrade}<2200:3.304+0.001\left|L_{uckGrade}-2180\right|,2200 \le L_{uckGrade}<2210:3.32+0.001\left|L_{uckGrade}-2200\right|,2210 \le L_{uckGrade}<2220:3.327+0.001\left|L_{uckGrade}-2210\right|,2220 \le L_{uckGrade}<2230:3.335+0.001\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2240:3.342+0.001\left|L_{uckGrade}-2230\right|,2240 \le L_{uckGrade}<2250:3.35+0.001\left|L_{uckGrade}-2240\right|,2250 \le L_{uckGrade}<2260:3.357+0.001\left|L_{uckGrade}-2250\right|,2260 \le L_{uckGrade}<2280:3.365+0.001\left|L_{uckGrade}-2260\right|,2280 \le L_{uckGrade}<2290:3.379+0.001\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2310:3.387+0.001\left|L_{uckGrade}-2290\right|,2310 \le L_{uckGrade}<2320:3.401+0.001\left|L_{uckGrade}-2310\right|,2320 \le L_{uckGrade}<2370:3.409+0.001\left|L_{uckGrade}-2320\right|,2370 \le L_{uckGrade}<2380:3.444+0.001\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2440:3.452+0.001\left|L_{uckGrade}-2380\right|,2440 \le L_{uckGrade}<2450:3.494+0.001\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2500:3.5+0.001\left|L_{uckGrade}-2450\right|,2500 \le L_{uckGrade}<2510:3.535+0.001\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2530:3.541+0.001\left|L_{uckGrade}-2510\right|,2530 \le L_{uckGrade}<2540:3.555+0.001\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2560:3.561+0.001\left|L_{uckGrade}-2540\right|,2560 \le L_{uckGrade}<2570:3.575+0.001\left|L_{uckGrade}-2560\right|,2570 \le L_{uckGrade}<2580:3.581+0.001\left|L_{uckGrade}-2570\right|,2580 \le L_{uckGrade}<2590:3.588+0.001\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2600:3.594+0.001\left|L_{uckGrade}-2590\right|,2600 \le L_{uckGrade}<2610:3.601+0.001\left|L_{uckGrade}-2600\right|,2610 \le L_{uckGrade}<2620:3.607+0.001\left|L_{uckGrade}-2610\right|,2620 \le L_{uckGrade}<2630:3.614+0.001\left|L_{uckGrade}-2620\right|,2630 \le L_{uckGrade}<2640:3.62+0.001\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2660:3.627+0.001\left|L_{uckGrade}-2640\right|,2660 \le L_{uckGrade}<2670:3.639+0.001\left|L_{uckGrade}-2660\right|,2670 \le L_{uckGrade}<2700:3.646+0.001\left|L_{uckGrade}-2670\right|,2700 \le L_{uckGrade}<2710:3.664+0.001\left|L_{uckGrade}-2700\right|,2710 \le L_{uckGrade}<2860:3.671+0.001\left|L_{uckGrade}-2710\right|,2860 \le L_{uckGrade}<2870:3.761+0\left|L_{uckGrade}-2860\right|,2870 \le L_{uckGrade}<2900:3.766+0.001\left|L_{uckGrade}-2870\right|,2900 \le L_{uckGrade}<2910:3.784+0.001\left|L_{uckGrade}-2900\right|,2910 \le L_{uckGrade}<2920:3.789+0.001\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2930:3.795+0\left|L_{uckGrade}-2920\right|,2930 \le L_{uckGrade}<2950:3.8+0.001\left|L_{uckGrade}-2930\right|,2950 \le L_{uckGrade}<2960:3.812+0.001\left|L_{uckGrade}-2950\right|,2960 \le L_{uckGrade}<2970:3.817+0.001\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<2980:3.823+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<2990:3.828+0.001\left|L_{uckGrade}-2980\right|,2990 \le L_{uckGrade}<3010:3.834+0\left|L_{uckGrade}-2990\right|,3010 \le L_{uckGrade}<3020:3.844+0.001\left|L_{uckGrade}-3010\right|,3020 \le L_{uckGrade}<3040:3.85+0\left|L_{uckGrade}-3020\right|,3040 \le L_{uckGrade}<3050:3.86+0.001\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3080:3.866+0\left|L_{uckGrade}-3050\right|,3080 \le L_{uckGrade}<3090:3.881+0.001\left|L_{uckGrade}-3080\right|,3090 \le L_{uckGrade}<3220:3.887+0\left|L_{uckGrade}-3090\right|,3220 \le L_{uckGrade}<3230:3.952+0\left|L_{uckGrade}-3220\right|,3230 \le L_{uckGrade}<3260:3.956+0.001\left|L_{uckGrade}-3230\right|,3260 \le L_{uckGrade}<3270:3.971+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3290:3.975+0\left|L_{uckGrade}-3270\right|,3290 \le L_{uckGrade}<3300:3.985+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3310:3.989+0.001\left|L_{uckGrade}-3300\right|,3310 \le L_{uckGrade}<3320:3.994+0\left|L_{uckGrade}-3310\right|,3320 \le L_{uckGrade}<3340:3.998+0\left|L_{uckGrade}-3320\right|,3340 \le L_{uckGrade}<3360:4.008+0\left|L_{uckGrade}-3340\right|,3360 \le L_{uckGrade}<3370:4.016+0\left|L_{uckGrade}-3360\right|,3370 \le L_{uckGrade}<3380:4.021+0\left|L_{uckGrade}-3370\right|,3380 \le L_{uckGrade}<3390:4.025+0\left|L_{uckGrade}-3380\right|,3390 \le L_{uckGrade}<3410:4.03+0\left|L_{uckGrade}-3390\right|,3410 \le L_{uckGrade}<3420:4.038+0\left|L_{uckGrade}-3410\right|,3420 \le L_{uckGrade}<3450:4.043+0\left|L_{uckGrade}-3420\right|,3450 \le L_{uckGrade}<3460:4.055+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3580:4.06+0\left|L_{uckGrade}-3460\right|,3580 \le L_{uckGrade}<3590:4.108+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3630:4.111+0\left|L_{uckGrade}-3590\right|,3630 \le L_{uckGrade}<3640:4.127+0\left|L_{uckGrade}-3630\right|,3640 \le L_{uckGrade}<3660:4.13+0\left|L_{uckGrade}-3640\right|,3660 \le L_{uckGrade}<3670:4.138+0\left|L_{uckGrade}-3660\right|,3670 \le L_{uckGrade}<3680:4.141+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3690:4.145+0\left|L_{uckGrade}-3680\right|,3690 \le L_{uckGrade}<3700:4.148+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3710:4.152+0\left|L_{uckGrade}-3700\right|,3710 \le L_{uckGrade}<3720:4.155+0\left|L_{uckGrade}-3710\right|,3720 \le L_{uckGrade}<3730:4.159+0\left|L_{uckGrade}-3720\right|,3730 \le L_{uckGrade}<3740:4.162+0\left|L_{uckGrade}-3730\right|,3740 \le L_{uckGrade}<3750:4.166+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3760:4.169+0\left|L_{uckGrade}-3750\right|,3760 \le L_{uckGrade}<3790:4.173+0\left|L_{uckGrade}-3760\right|,3790 \le L_{uckGrade}<3800:4.182+0\left|L_{uckGrade}-3790\right|,3800 \le L_{uckGrade}<3830:4.186+0\left|L_{uckGrade}-3800\right|,3830 \le L_{uckGrade}<3840:4.195+0\left|L_{uckGrade}-3830\right|,3840 \le L_{uckGrade}<3940:4.199+0\left|L_{uckGrade}-3840\right|,3940 \le L_{uckGrade}<3950:4.229+0\left|L_{uckGrade}-3940\right|,3950 \le L_{uckGrade}<3990:4.231+0\left|L_{uckGrade}-3950\right|,3990 \le L_{uckGrade}<4000:4.243+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4020:4.245+0\left|L_{uckGrade}-4000\right|,4020 \le L_{uckGrade}<4030:4.251+0\left|L_{uckGrade}-4020\right|,4030 \le L_{uckGrade}<4050:4.253+0\left|L_{uckGrade}-4030\right|,4050 \le L_{uckGrade}<4060:4.259+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4070:4.261+0\left|L_{uckGrade}-4060\right|,4070 \le L_{uckGrade}<4080:4.264+0\left|L_{uckGrade}-4070\right|,4080 \le L_{uckGrade}<4090:4.266+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4100:4.269+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4110:4.271+0\left|L_{uckGrade}-4100\right|,4110 \le L_{uckGrade}<4130:4.274+0\left|L_{uckGrade}-4110\right|,4130 \le L_{uckGrade}<4140:4.278+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4160:4.281+0\left|L_{uckGrade}-4140\right|,4160 \le L_{uckGrade}<4170:4.285+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4210:4.288+0\left|L_{uckGrade}-4170\right|,4210 \le L_{uckGrade}<4220:4.296+0\left|L_{uckGrade}-4210\right|,4220 \le L_{uckGrade}<4310:4.299+0\left|L_{uckGrade}-4220\right|,4310 \le L_{uckGrade}<4320:4.317+0\left|L_{uckGrade}-4310\right|,4320 \le L_{uckGrade}<4360:4.318+0\left|L_{uckGrade}-4320\right|,4360 \le L_{uckGrade}<4370:4.326+0\left|L_{uckGrade}-4360\right|,4370 \le L_{uckGrade}<4390:4.327+0\left|L_{uckGrade}-4370\right|,4390 \le L_{uckGrade}<4400:4.331+0\left|L_{uckGrade}-4390\right|,4400 \le L_{uckGrade}<4420:4.332+0\left|L_{uckGrade}-4400\right|,4420 \le L_{uckGrade}<4430:4.336+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4440:4.337+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4450:4.339+0\left|L_{uckGrade}-4440\right|,4450 \le L_{uckGrade}<4460:4.34+0\left|L_{uckGrade}-4450\right|,4460 \le L_{uckGrade}<4470:4.342+0\left|L_{uckGrade}-4460\right|,4470 \le L_{uckGrade}<4480:4.343+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4500:4.345+0\left|L_{uckGrade}-4480\right|,4500 \le L_{uckGrade}<4510:4.347+0\left|L_{uckGrade}-4500\right|,4510 \le L_{uckGrade}<4530:4.349+0\left|L_{uckGrade}-4510\right|,4530 \le L_{uckGrade}<4540:4.351+0\left|L_{uckGrade}-4530\right|,4540 \le L_{uckGrade}<4580:4.353+0\left|L_{uckGrade}-4540\right|,4580 \le L_{uckGrade}<4590:4.357+0\left|L_{uckGrade}-4580\right|,4590 \le L_{uckGrade}<4670:4.359+0\left|L_{uckGrade}-4590\right|,4670 \le L_{uckGrade}<4680:4.367+0\left|L_{uckGrade}-4670\right|,4680 \le L_{uckGrade}<4730:4.367+0\left|L_{uckGrade}-4680\right|,4730 \le L_{uckGrade}<4740:4.372+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4760:4.372+0\left|L_{uckGrade}-4740\right|,4760 \le L_{uckGrade}<4770:4.374+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4790:4.374+0\left|L_{uckGrade}-4770\right|,4790 \le L_{uckGrade}<4800:4.376+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4810:4.376+0\left|L_{uckGrade}-4800\right|,4810 \le L_{uckGrade}<4820:4.377+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4830:4.377+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4840:4.378+0\left|L_{uckGrade}-4830\right|,4840 \le L_{uckGrade}<4850:4.378+0\left|L_{uckGrade}-4840\right|,4850 \le L_{uckGrade}<4870:4.379+0\left|L_{uckGrade}-4850\right|,4870 \le L_{uckGrade}<4880:4.379+0\left|L_{uckGrade}-4870\right|,4880 \le L_{uckGrade}<4900:4.38+0\left|L_{uckGrade}-4880\right|,4900 \le L_{uckGrade}<4910:4.38+0\left|L_{uckGrade}-4900\right|,4910 \le L_{uckGrade}<4960:4.381+0\left|L_{uckGrade}-4910\right|,4960 \le L_{uckGrade}<4970:4.381+0\left|L_{uckGrade}-4960\right|,4970 \le L_{uckGrade}<5000:4.382+0\left|L_{uckGrade}-4970\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}<10:1+0.001\left|L_{uckGrade}-0\right|,10 \le L_{uckGrade}<30:1.014+0.001\left|L_{uckGrade}-10\right|,30 \le L_{uckGrade}<40:1.04+0.001\left|L_{uckGrade}-30\right|,40 \le L_{uckGrade}<50:1.054+0.001\left|L_{uckGrade}-40\right|,50 \le L_{uckGrade}<60:1.067+0.001\left|L_{uckGrade}-50\right|,60 \le L_{uckGrade}<80:1.081+0.001\left|L_{uckGrade}-60\right|,80 \le L_{uckGrade}<90:1.107+0.001\left|L_{uckGrade}-80\right|,90 \le L_{uckGrade}<130:1.121+0.001\left|L_{uckGrade}-90\right|,130 \le L_{uckGrade}<140:1.173+0.001\left|L_{uckGrade}-130\right|,140 \le L_{uckGrade}<240:1.187+0.001\left|L_{uckGrade}-140\right|,240 \le L_{uckGrade}<250:1.317+0.001\left|L_{uckGrade}-240\right|,250 \le L_{uckGrade}<290:1.329+0.001\left|L_{uckGrade}-250\right|,290 \le L_{uckGrade}<300:1.381+0.001\left|L_{uckGrade}-290\right|,300 \le L_{uckGrade}<320:1.393+0.001\left|L_{uckGrade}-300\right|,320 \le L_{uckGrade}<330:1.419+0.001\left|L_{uckGrade}-320\right|,330 \le L_{uckGrade}<340:1.431+0.001\left|L_{uckGrade}-330\right|,340 \le L_{uckGrade}<350:1.444+0.001\left|L_{uckGrade}-340\right|,350 \le L_{uckGrade}<370:1.456+0.001\left|L_{uckGrade}-350\right|,370 \le L_{uckGrade}<390:1.482+0.001\left|L_{uckGrade}-370\right|,390 \le L_{uckGrade}<400:1.506+0.001\left|L_{uckGrade}-390\right|,400 \le L_{uckGrade}<410:1.519+0.001\left|L_{uckGrade}-400\right|,410 \le L_{uckGrade}<420:1.531+0.001\left|L_{uckGrade}-410\right|,420 \le L_{uckGrade}<440:1.544+0.001\left|L_{uckGrade}-420\right|,440 \le L_{uckGrade}<450:1.568+0.001\left|L_{uckGrade}-440\right|,450 \le L_{uckGrade}<470:1.581+0.001\left|L_{uckGrade}-450\right|,470 \le L_{uckGrade}<480:1.605+0.001\left|L_{uckGrade}-470\right|,480 \le L_{uckGrade}<640:1.618+0.001\left|L_{uckGrade}-480\right|,640 \le L_{uckGrade}<650:1.81+0.001\left|L_{uckGrade}-640\right|,650 \le L_{uckGrade}<670:1.821+0.001\left|L_{uckGrade}-650\right|,670 \le L_{uckGrade}<680:1.845+0.001\left|L_{uckGrade}-670\right|,680 \le L_{uckGrade}<700:1.856+0.001\left|L_{uckGrade}-680\right|,700 \le L_{uckGrade}<710:1.88+0.001\left|L_{uckGrade}-700\right|,710 \le L_{uckGrade}<730:1.891+0.001\left|L_{uckGrade}-710\right|,730 \le L_{uckGrade}<740:1.915+0.001\left|L_{uckGrade}-730\right|,740 \le L_{uckGrade}<750:1.926+0.001\left|L_{uckGrade}-740\right|,750 \le L_{uckGrade}<770:1.938+0.001\left|L_{uckGrade}-750\right|,770 \le L_{uckGrade}<780:1.96+0.001\left|L_{uckGrade}-770\right|,780 \le L_{uckGrade}<790:1.972+0.001\left|L_{uckGrade}-780\right|,790 \le L_{uckGrade}<800:1.983+0.001\left|L_{uckGrade}-790\right|,800 \le L_{uckGrade}<820:1.995+0.001\left|L_{uckGrade}-800\right|,820 \le L_{uckGrade}<830:2.017+0.001\left|L_{uckGrade}-820\right|,830 \le L_{uckGrade}<870:2.029+0.001\left|L_{uckGrade}-830\right|,870 \le L_{uckGrade}<880:2.073+0.001\left|L_{uckGrade}-870\right|,880 \le L_{uckGrade}<990:2.085+0.001\left|L_{uckGrade}-880\right|,990 \le L_{uckGrade}<1000:2.206+0.001\left|L_{uckGrade}-990\right|,1000 \le L_{uckGrade}<1030:2.216+0.001\left|L_{uckGrade}-1000\right|,1030 \le L_{uckGrade}<1040:2.249+0.001\left|L_{uckGrade}-1030\right|,1040 \le L_{uckGrade}<1060:2.259+0.001\left|L_{uckGrade}-1040\right|,1060 \le L_{uckGrade}<1070:2.281+0.001\left|L_{uckGrade}-1060\right|,1070 \le L_{uckGrade}<1090:2.291+0.001\left|L_{uckGrade}-1070\right|,1090 \le L_{uckGrade}<1100:2.313+0.001\left|L_{uckGrade}-1090\right|,1100 \le L_{uckGrade}<1110:2.323+0.001\left|L_{uckGrade}-1100\right|,1110 \le L_{uckGrade}<1120:2.334+0.001\left|L_{uckGrade}-1110\right|,1120 \le L_{uckGrade}<1130:2.344+0.001\left|L_{uckGrade}-1120\right|,1130 \le L_{uckGrade}<1140:2.355+0.001\left|L_{uckGrade}-1130\right|,1140 \le L_{uckGrade}<1150:2.365+0.001\left|L_{uckGrade}-1140\right|,1150 \le L_{uckGrade}<1170:2.376+0.001\left|L_{uckGrade}-1150\right|,1170 \le L_{uckGrade}<1180:2.396+0.001\left|L_{uckGrade}-1170\right|,1180 \le L_{uckGrade}<1210:2.407+0.001\left|L_{uckGrade}-1180\right|,1210 \le L_{uckGrade}<1220:2.437+0.001\left|L_{uckGrade}-1210\right|,1220 \le L_{uckGrade}<1270:2.448+0.001\left|L_{uckGrade}-1220\right|,1270 \le L_{uckGrade}<1280:2.498+0.001\left|L_{uckGrade}-1270\right|,1280 \le L_{uckGrade}<1320:2.509+0.001\left|L_{uckGrade}-1280\right|,1320 \le L_{uckGrade}<1330:2.549+0.001\left|L_{uckGrade}-1320\right|,1330 \le L_{uckGrade}<1390:2.558+0.001\left|L_{uckGrade}-1330\right|,1390 \le L_{uckGrade}<1400:2.618+0.001\left|L_{uckGrade}-1390\right|,1400 \le L_{uckGrade}<1420:2.627+0.001\left|L_{uckGrade}-1400\right|,1420 \le L_{uckGrade}<1430:2.647+0.001\left|L_{uckGrade}-1420\right|,1430 \le L_{uckGrade}<1450:2.656+0.001\left|L_{uckGrade}-1430\right|,1450 \le L_{uckGrade}<1460:2.676+0.001\left|L_{uckGrade}-1450\right|,1460 \le L_{uckGrade}<1470:2.685+0.001\left|L_{uckGrade}-1460\right|,1470 \le L_{uckGrade}<1480:2.695+0.001\left|L_{uckGrade}-1470\right|,1480 \le L_{uckGrade}<1490:2.704+0.001\left|L_{uckGrade}-1480\right|,1490 \le L_{uckGrade}<1500:2.714+0.001\left|L_{uckGrade}-1490\right|,1500 \le L_{uckGrade}<1510:2.723+0.001\left|L_{uckGrade}-1500\right|,1510 \le L_{uckGrade}<1520:2.733+0.001\left|L_{uckGrade}-1510\right|,1520 \le L_{uckGrade}<1530:2.742+0.001\left|L_{uckGrade}-1520\right|,1530 \le L_{uckGrade}<1550:2.752+0.001\left|L_{uckGrade}-1530\right|,1550 \le L_{uckGrade}<1560:2.77+0.001\left|L_{uckGrade}-1550\right|,1560 \le L_{uckGrade}<1590:2.78+0.001\left|L_{uckGrade}-1560\right|,1590 \le L_{uckGrade}<1600:2.807+0.001\left|L_{uckGrade}-1590\right|,1600 \le L_{uckGrade}<1740:2.817+0.001\left|L_{uckGrade}-1600\right|,1740 \le L_{uckGrade}<1750:2.943+0.001\left|L_{uckGrade}-1740\right|,1750 \le L_{uckGrade}<1780:2.951+0.001\left|L_{uckGrade}-1750\right|,1780 \le L_{uckGrade}<1790:2.978+0.001\left|L_{uckGrade}-1780\right|,1790 \le L_{uckGrade}<1810:2.986+0.001\left|L_{uckGrade}-1790\right|,1810 \le L_{uckGrade}<1820:3.004+0.001\left|L_{uckGrade}-1810\right|,1820 \le L_{uckGrade}<1830:3.012+0.001\left|L_{uckGrade}-1820\right|,1830 \le L_{uckGrade}<1840:3.021+0.001\left|L_{uckGrade}-1830\right|,1840 \le L_{uckGrade}<1850:3.029+0.001\left|L_{uckGrade}-1840\right|,1850 \le L_{uckGrade}<1860:3.038+0.001\left|L_{uckGrade}-1850\right|,1860 \le L_{uckGrade}<1870:3.046+0.001\left|L_{uckGrade}-1860\right|,1870 \le L_{uckGrade}<1880:3.055+0.001\left|L_{uckGrade}-1870\right|,1880 \le L_{uckGrade}<1890:3.063+0.001\left|L_{uckGrade}-1880\right|,1890 \le L_{uckGrade}<1900:3.072+0.001\left|L_{uckGrade}-1890\right|,1900 \le L_{uckGrade}<1910:3.08+0.001\left|L_{uckGrade}-1900\right|,1910 \le L_{uckGrade}<1930:3.089+0.001\left|L_{uckGrade}-1910\right|,1930 \le L_{uckGrade}<1940:3.105+0.001\left|L_{uckGrade}-1930\right|,1940 \le L_{uckGrade}<1980:3.114+0.001\left|L_{uckGrade}-1940\right|,1980 \le L_{uckGrade}<1990:3.146+0.001\left|L_{uckGrade}-1980\right|,1990 \le L_{uckGrade}<2090:3.155+0.001\left|L_{uckGrade}-1990\right|,2090 \le L_{uckGrade}<2100:3.235+0.001\left|L_{uckGrade}-2090\right|,2100 \le L_{uckGrade}<2140:3.242+0.001\left|L_{uckGrade}-2100\right|,2140 \le L_{uckGrade}<2150:3.274+0.001\left|L_{uckGrade}-2140\right|,2150 \le L_{uckGrade}<2170:3.281+0.001\left|L_{uckGrade}-2150\right|,2170 \le L_{uckGrade}<2180:3.297+0.001\left|L_{uckGrade}-2170\right|,2180 \le L_{uckGrade}<2200:3.304+0.001\left|L_{uckGrade}-2180\right|,2200 \le L_{uckGrade}<2210:3.32+0.001\left|L_{uckGrade}-2200\right|,2210 \le L_{uckGrade}<2220:3.327+0.001\left|L_{uckGrade}-2210\right|,2220 \le L_{uckGrade}<2230:3.335+0.001\left|L_{uckGrade}-2220\right|,2230 \le L_{uckGrade}<2240:3.342+0.001\left|L_{uckGrade}-2230\right|,2240 \le L_{uckGrade}<2250:3.35+0.001\left|L_{uckGrade}-2240\right|,2250 \le L_{uckGrade}<2260:3.357+0.001\left|L_{uckGrade}-2250\right|,2260 \le L_{uckGrade}<2280:3.365+0.001\left|L_{uckGrade}-2260\right|,2280 \le L_{uckGrade}<2290:3.379+0.001\left|L_{uckGrade}-2280\right|,2290 \le L_{uckGrade}<2310:3.387+0.001\left|L_{uckGrade}-2290\right|,2310 \le L_{uckGrade}<2320:3.401+0.001\left|L_{uckGrade}-2310\right|,2320 \le L_{uckGrade}<2370:3.409+0.001\left|L_{uckGrade}-2320\right|,2370 \le L_{uckGrade}<2380:3.444+0.001\left|L_{uckGrade}-2370\right|,2380 \le L_{uckGrade}<2440:3.452+0.001\left|L_{uckGrade}-2380\right|,2440 \le L_{uckGrade}<2450:3.494+0.001\left|L_{uckGrade}-2440\right|,2450 \le L_{uckGrade}<2500:3.5+0.001\left|L_{uckGrade}-2450\right|,2500 \le L_{uckGrade}<2510:3.535+0.001\left|L_{uckGrade}-2500\right|,2510 \le L_{uckGrade}<2530:3.541+0.001\left|L_{uckGrade}-2510\right|,2530 \le L_{uckGrade}<2540:3.555+0.001\left|L_{uckGrade}-2530\right|,2540 \le L_{uckGrade}<2560:3.561+0.001\left|L_{uckGrade}-2540\right|,2560 \le L_{uckGrade}<2570:3.575+0.001\left|L_{uckGrade}-2560\right|,2570 \le L_{uckGrade}<2580:3.581+0.001\left|L_{uckGrade}-2570\right|,2580 \le L_{uckGrade}<2590:3.588+0.001\left|L_{uckGrade}-2580\right|,2590 \le L_{uckGrade}<2600:3.594+0.001\left|L_{uckGrade}-2590\right|,2600 \le L_{uckGrade}<2610:3.601+0.001\left|L_{uckGrade}-2600\right|,2610 \le L_{uckGrade}<2620:3.607+0.001\left|L_{uckGrade}-2610\right|,2620 \le L_{uckGrade}<2630:3.614+0.001\left|L_{uckGrade}-2620\right|,2630 \le L_{uckGrade}<2640:3.62+0.001\left|L_{uckGrade}-2630\right|,2640 \le L_{uckGrade}<2660:3.627+0.001\left|L_{uckGrade}-2640\right|,2660 \le L_{uckGrade}<2670:3.639+0.001\left|L_{uckGrade}-2660\right|,2670 \le L_{uckGrade}<2700:3.646+0.001\left|L_{uckGrade}-2670\right|,2700 \le L_{uckGrade}<2710:3.664+0.001\left|L_{uckGrade}-2700\right|,2710 \le L_{uckGrade}<2860:3.671+0.001\left|L_{uckGrade}-2710\right|,2860 \le L_{uckGrade}<2870:3.761+0\left|L_{uckGrade}-2860\right|,2870 \le L_{uckGrade}<2900:3.766+0.001\left|L_{uckGrade}-2870\right|,2900 \le L_{uckGrade}<2910:3.784+0.001\left|L_{uckGrade}-2900\right|,2910 \le L_{uckGrade}<2920:3.789+0.001\left|L_{uckGrade}-2910\right|,2920 \le L_{uckGrade}<2930:3.795+0\left|L_{uckGrade}-2920\right|,2930 \le L_{uckGrade}<2950:3.8+0.001\left|L_{uckGrade}-2930\right|,2950 \le L_{uckGrade}<2960:3.812+0.001\left|L_{uckGrade}-2950\right|,2960 \le L_{uckGrade}<2970:3.817+0.001\left|L_{uckGrade}-2960\right|,2970 \le L_{uckGrade}<2980:3.823+0\left|L_{uckGrade}-2970\right|,2980 \le L_{uckGrade}<2990:3.828+0.001\left|L_{uckGrade}-2980\right|,2990 \le L_{uckGrade}<3010:3.834+0\left|L_{uckGrade}-2990\right|,3010 \le L_{uckGrade}<3020:3.844+0.001\left|L_{uckGrade}-3010\right|,3020 \le L_{uckGrade}<3040:3.85+0\left|L_{uckGrade}-3020\right|,3040 \le L_{uckGrade}<3050:3.86+0.001\left|L_{uckGrade}-3040\right|,3050 \le L_{uckGrade}<3080:3.866+0\left|L_{uckGrade}-3050\right|,3080 \le L_{uckGrade}<3090:3.881+0.001\left|L_{uckGrade}-3080\right|,3090 \le L_{uckGrade}<3220:3.887+0\left|L_{uckGrade}-3090\right|,3220 \le L_{uckGrade}<3230:3.952+0\left|L_{uckGrade}-3220\right|,3230 \le L_{uckGrade}<3260:3.956+0.001\left|L_{uckGrade}-3230\right|,3260 \le L_{uckGrade}<3270:3.971+0\left|L_{uckGrade}-3260\right|,3270 \le L_{uckGrade}<3290:3.975+0\left|L_{uckGrade}-3270\right|,3290 \le L_{uckGrade}<3300:3.985+0\left|L_{uckGrade}-3290\right|,3300 \le L_{uckGrade}<3310:3.989+0.001\left|L_{uckGrade}-3300\right|,3310 \le L_{uckGrade}<3320:3.994+0\left|L_{uckGrade}-3310\right|,3320 \le L_{uckGrade}<3340:3.998+0\left|L_{uckGrade}-3320\right|,3340 \le L_{uckGrade}<3360:4.008+0\left|L_{uckGrade}-3340\right|,3360 \le L_{uckGrade}<3370:4.016+0\left|L_{uckGrade}-3360\right|,3370 \le L_{uckGrade}<3380:4.021+0\left|L_{uckGrade}-3370\right|,3380 \le L_{uckGrade}<3390:4.025+0\left|L_{uckGrade}-3380\right|,3390 \le L_{uckGrade}<3410:4.03+0\left|L_{uckGrade}-3390\right|,3410 \le L_{uckGrade}<3420:4.038+0\left|L_{uckGrade}-3410\right|,3420 \le L_{uckGrade}<3450:4.043+0\left|L_{uckGrade}-3420\right|,3450 \le L_{uckGrade}<3460:4.055+0\left|L_{uckGrade}-3450\right|,3460 \le L_{uckGrade}<3580:4.06+0\left|L_{uckGrade}-3460\right|,3580 \le L_{uckGrade}<3590:4.108+0\left|L_{uckGrade}-3580\right|,3590 \le L_{uckGrade}<3630:4.111+0\left|L_{uckGrade}-3590\right|,3630 \le L_{uckGrade}<3640:4.127+0\left|L_{uckGrade}-3630\right|,3640 \le L_{uckGrade}<3660:4.13+0\left|L_{uckGrade}-3640\right|,3660 \le L_{uckGrade}<3670:4.138+0\left|L_{uckGrade}-3660\right|,3670 \le L_{uckGrade}<3680:4.141+0\left|L_{uckGrade}-3670\right|,3680 \le L_{uckGrade}<3690:4.145+0\left|L_{uckGrade}-3680\right|,3690 \le L_{uckGrade}<3700:4.148+0\left|L_{uckGrade}-3690\right|,3700 \le L_{uckGrade}<3710:4.152+0\left|L_{uckGrade}-3700\right|,3710 \le L_{uckGrade}<3720:4.155+0\left|L_{uckGrade}-3710\right|,3720 \le L_{uckGrade}<3730:4.159+0\left|L_{uckGrade}-3720\right|,3730 \le L_{uckGrade}<3740:4.162+0\left|L_{uckGrade}-3730\right|,3740 \le L_{uckGrade}<3750:4.166+0\left|L_{uckGrade}-3740\right|,3750 \le L_{uckGrade}<3760:4.169+0\left|L_{uckGrade}-3750\right|,3760 \le L_{uckGrade}<3790:4.173+0\left|L_{uckGrade}-3760\right|,3790 \le L_{uckGrade}<3800:4.182+0\left|L_{uckGrade}-3790\right|,3800 \le L_{uckGrade}<3830:4.186+0\left|L_{uckGrade}-3800\right|,3830 \le L_{uckGrade}<3840:4.195+0\left|L_{uckGrade}-3830\right|,3840 \le L_{uckGrade}<3940:4.199+0\left|L_{uckGrade}-3840\right|,3940 \le L_{uckGrade}<3950:4.229+0\left|L_{uckGrade}-3940\right|,3950 \le L_{uckGrade}<3990:4.231+0\left|L_{uckGrade}-3950\right|,3990 \le L_{uckGrade}<4000:4.243+0\left|L_{uckGrade}-3990\right|,4000 \le L_{uckGrade}<4020:4.245+0\left|L_{uckGrade}-4000\right|,4020 \le L_{uckGrade}<4030:4.251+0\left|L_{uckGrade}-4020\right|,4030 \le L_{uckGrade}<4050:4.253+0\left|L_{uckGrade}-4030\right|,4050 \le L_{uckGrade}<4060:4.259+0\left|L_{uckGrade}-4050\right|,4060 \le L_{uckGrade}<4070:4.261+0\left|L_{uckGrade}-4060\right|,4070 \le L_{uckGrade}<4080:4.264+0\left|L_{uckGrade}-4070\right|,4080 \le L_{uckGrade}<4090:4.266+0\left|L_{uckGrade}-4080\right|,4090 \le L_{uckGrade}<4100:4.269+0\left|L_{uckGrade}-4090\right|,4100 \le L_{uckGrade}<4110:4.271+0\left|L_{uckGrade}-4100\right|,4110 \le L_{uckGrade}<4130:4.274+0\left|L_{uckGrade}-4110\right|,4130 \le L_{uckGrade}<4140:4.278+0\left|L_{uckGrade}-4130\right|,4140 \le L_{uckGrade}<4160:4.281+0\left|L_{uckGrade}-4140\right|,4160 \le L_{uckGrade}<4170:4.285+0\left|L_{uckGrade}-4160\right|,4170 \le L_{uckGrade}<4210:4.288+0\left|L_{uckGrade}-4170\right|,4210 \le L_{uckGrade}<4220:4.296+0\left|L_{uckGrade}-4210\right|,4220 \le L_{uckGrade}<4310:4.299+0\left|L_{uckGrade}-4220\right|,4310 \le L_{uckGrade}<4320:4.317+0\left|L_{uckGrade}-4310\right|,4320 \le L_{uckGrade}<4360:4.318+0\left|L_{uckGrade}-4320\right|,4360 \le L_{uckGrade}<4370:4.326+0\left|L_{uckGrade}-4360\right|,4370 \le L_{uckGrade}<4390:4.327+0\left|L_{uckGrade}-4370\right|,4390 \le L_{uckGrade}<4400:4.331+0\left|L_{uckGrade}-4390\right|,4400 \le L_{uckGrade}<4420:4.332+0\left|L_{uckGrade}-4400\right|,4420 \le L_{uckGrade}<4430:4.336+0\left|L_{uckGrade}-4420\right|,4430 \le L_{uckGrade}<4440:4.337+0\left|L_{uckGrade}-4430\right|,4440 \le L_{uckGrade}<4450:4.339+0\left|L_{uckGrade}-4440\right|,4450 \le L_{uckGrade}<4460:4.34+0\left|L_{uckGrade}-4450\right|,4460 \le L_{uckGrade}<4470:4.342+0\left|L_{uckGrade}-4460\right|,4470 \le L_{uckGrade}<4480:4.343+0\left|L_{uckGrade}-4470\right|,4480 \le L_{uckGrade}<4500:4.345+0\left|L_{uckGrade}-4480\right|,4500 \le L_{uckGrade}<4510:4.347+0\left|L_{uckGrade}-4500\right|,4510 \le L_{uckGrade}<4530:4.349+0\left|L_{uckGrade}-4510\right|,4530 \le L_{uckGrade}<4540:4.351+0\left|L_{uckGrade}-4530\right|,4540 \le L_{uckGrade}<4580:4.353+0\left|L_{uckGrade}-4540\right|,4580 \le L_{uckGrade}<4590:4.357+0\left|L_{uckGrade}-4580\right|,4590 \le L_{uckGrade}<4670:4.359+0\left|L_{uckGrade}-4590\right|,4670 \le L_{uckGrade}<4680:4.367+0\left|L_{uckGrade}-4670\right|,4680 \le L_{uckGrade}<4730:4.367+0\left|L_{uckGrade}-4680\right|,4730 \le L_{uckGrade}<4740:4.372+0\left|L_{uckGrade}-4730\right|,4740 \le L_{uckGrade}<4760:4.372+0\left|L_{uckGrade}-4740\right|,4760 \le L_{uckGrade}<4770:4.374+0\left|L_{uckGrade}-4760\right|,4770 \le L_{uckGrade}<4790:4.374+0\left|L_{uckGrade}-4770\right|,4790 \le L_{uckGrade}<4800:4.376+0\left|L_{uckGrade}-4790\right|,4800 \le L_{uckGrade}<4810:4.376+0\left|L_{uckGrade}-4800\right|,4810 \le L_{uckGrade}<4820:4.377+0\left|L_{uckGrade}-4810\right|,4820 \le L_{uckGrade}<4830:4.377+0\left|L_{uckGrade}-4820\right|,4830 \le L_{uckGrade}<4840:4.378+0\left|L_{uckGrade}-4830\right|,4840 \le L_{uckGrade}<4850:4.378+0\left|L_{uckGrade}-4840\right|,4850 \le L_{uckGrade}<4870:4.379+0\left|L_{uckGrade}-4850\right|,4870 \le L_{uckGrade}<4880:4.379+0\left|L_{uckGrade}-4870\right|,4880 \le L_{uckGrade}<4900:4.38+0\left|L_{uckGrade}-4880\right|,4900 \le L_{uckGrade}<4910:4.38+0\left|L_{uckGrade}-4900\right|,4910 \le L_{uckGrade}<4960:4.381+0\left|L_{uckGrade}-4910\right|,4960 \le L_{uckGrade}<4970:4.381+0\left|L_{uckGrade}-4960\right|,4970 \le L_{uckGrade}<5000:4.382+0\left|L_{uckGrade}-4970\right|\right\}
See Example for how to use.
To calculate the drop rate at X Luck there are three steps.
The table below is the Drop Rate table of Quest Drops.
Every monster with a quest drop uses the Drop Rate table.
However, depending on the monster's Loot Drop Table, many of the Luck Grade rates will be associated with dropping nothing.
And in other instances, like Demon Centaur, a Luck Grade's rate may be split between two Loot Drops.
This will not affect the calculations below, but they will determine an individual item's probability.
| Luck Grade | Drop Rate |
| Junk | 220 |
| Poor | 250 |
| Common | 200 |
| Uncommon | 150 |
| Rare | 100 |
| Epic | 50 |
| Legendary | 20 |
| Unique | 10 |
Click expand to see the calculations for 0 and 250 Luck.
Drop Rate tables generally sum to a power of ten. Since the Luck Scalars are simply 1 at 0 Luck, the probability calculation is trivial.
Using the Luck Scalars at 0 Luck, the dot product is
![{\displaystyle \color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {220}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {250}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {200}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {100}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {50}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {20}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {10}}}={\color {violet}1000}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/10b7388e197831c8fd6d0f267b2bd6c14ca5a945)
| Luck Grade | Drop Probability at 0 Luck |
| Junk | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {220}}}{\color {violet}1000}}=22\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ead68e396c591d89cc51046793332c89c258d18f)
|
| Poor | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {250}}}{\color {violet}1000}}=25\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f933a58a26d396e6a49ff2cda4af7ba9878faaa3)
|
| Common | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {200}}}{\color {violet}1000}}=20\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/965f88463b0fb9c06690ff7ba7ea6414f62b13d1)
|
| Uncommon | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1000}}=15\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b37f8521cc36aa172c8926b47d0b6719e2ba708b)
|
| Rare | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {100}}}{\color {violet}1000}}=10\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54b5680bdcf8777ce50ee03789b81ca0afa34721)
|
| Epic | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {50}}}{\color {violet}1000}}=5\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9b5e9ceada70b9e762028869647bd866beb5fcd4)
|
| Legendary | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {20}}}{\color {violet}1000}}=2\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/49ec0d3fc6e0bf88d44bb8c08144673182d9b2e4)
|
| Unique | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {10}}}{\color {violet}1000}}=1\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cae551306eb138f857033ead909c3504d83d097a)
|
Using the Luck Scalars at 250 Luck, the dot product is
![{\displaystyle \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 {violet}1227.42}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/03ff28f35f6cb3a407d75594713ecd412d253eee)
| Luck Grade | Drop Probability at 250 Luck |
| Junk | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {220}}}{\color {violet}1227.42}}=13.443\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6778f4b90201b07a250130410c92283928f7bd33)
|
| Poor | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {250}}}{\color {violet}1227.42}}=15.276\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/12bb0a2a71c6ebb0c4c3fab1a69e8522616b5c27)
|
| Common | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {200}}}{\color {violet}1227.42}}=14.258\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c8e9722ff81d0f84a58d5f6d1fbf83078ed3dd0d)
|
| Uncommon | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1227.42}}=12.221\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/951556c3bcbb5624e90e24701641a2986cb36cb9)
|
| Rare | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {100}}}{\color {violet}1227.42}}=23.448\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b96b0c71369ce08731c3c37e8449bf3d0b094484)
|
| Epic | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.125\cdot {\textbf {50}}}{\color {violet}1227.42}}=12.868\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6ec11d3641d283592c512fb694bb478bd7a81fd9)
|
| Legendary | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {20}}}{\color {violet}1227.42}}=5.607\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e4968f94c9f4e90deff8f63bf4ccf9f239bb610f)
|
| Unique | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {10}}}{\color {violet}1227.42}}=2.880\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5e26d3f29781d1836967cb780f0e672fa0f8f074)
|
Using the Luck Scalars at 500 Luck, the dot product is
![{\displaystyle \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 {violet}1208.51}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d972971aa388e800f4ac1e3eafbfc2c0038b2601)
| Luck Grade | Drop Probability at 500 Luck |
| Junk | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {220}}}{\color {violet}1208.51}}=9.102\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/efe75157f2f7d8997fc9442a2f102739079ecec7)
|
| Poor | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {250}}}{\color {violet}1208.51}}=10.343\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60804fc4fe761796becbd34db764dba970963a1d)
|
| Common | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {200}}}{\color {violet}1208.51}}=12.412\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38f6ccb8397db926ef064b2b609fb878b06da8fb)
|
| Uncommon | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {150}}}{\color {violet}1208.51}}=12.412\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c573238a4cee96101a3db4fe2144990b27c239aa)
|
| Rare | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}3.505\cdot {\textbf {100}}}{\color {violet}1208.51}}=29.003\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2ef8aa3727f0ca78de7fee9c804d2e277e16f5ec)
|
| Epic | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {50}}}{\color {violet}1208.51}}=16.057\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d7b21b79c675dc0080ed85321895b7e77b7b195e)
|
| Legendary | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {20}}}{\color {violet}1208.51}}=7.045\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/37489ca7f5897f2a79ae5c80d8807bbc69d3e20a)
|
| Unique | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {10}}}{\color {violet}1208.51}}=3.626\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2be8dc1cfc0199a7a6824cacbc8198e1008408b4)
|
The table below is the Drop Rate table of the Gold Coin Chest.
The Loot Drop table is rather simple. At Luck Grade 0, "Junk", you get nothing. At Luck Grade 2, "Common", you get 1x Gold Coin Chest.
Notice that despite the Gold Coin Chest's item rarity being unique, its Luck Grade is actually Common.
Item Rarity does not equal Luck Grade, despite the two being equal for most items.
| Luck Grade | Drop Rate |
| Junk | 99900 |
| Poor | 0 |
| Common | 100 |
| Uncommon | 0 |
| Rare | 0 |
| Epic | 0 |
| Legendary | 0 |
| Unique | 0 |
Click expand to see the calculations for 0 and 250 Luck.
Using the Luck Scalars at 0 Luck, the dot product is
![{\displaystyle \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 {violet}100000}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/52c55dc9b966b1f885e2f96f9f871cfcf3769c50)
| Luck Grade | Drop Probability at 0 Luck |
| Junk | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}1.000\cdot {\textbf {99900}}}{\color {violet}100000}}=99.9\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3244bb589efe7b3a2e088ccf29c70eda02221786)
|
| Poor | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b185a5a2a46c837866d1c8b76b9f26740202bf00)
|
| Common | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}1.000\cdot {\textbf {100}}}{\color {violet}100000}}=0.1\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1a7210f0d34ef4d30d2131bf148ec2d052e04efb)
|
| Uncommon | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/52a16cd2bb4120372dcc13f4d7970c5947930a78)
|
| Rare | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/137df6b1d231dac078c09e16bcd9d7e3cad4e61d)
|
| Epic | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0a23ac5e5bc7162143663316df0ef7046b0b0698)
|
| Legendary | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/015b362de95c1d498fc2f5b6e70373ef10ca067d)
|
| Unique | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}1.000\cdot {\textbf {0}}}{\color {violet}100000}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1cfbe2a8d7bffc939247ca3015d2fb936748645b)
|
Using the Luck Scalars at 250 Luck, the dot product is
![{\displaystyle \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 {violet}75012.5}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd66bebf3a8f7e8e858026aa611898ed99a0a4b)
| Luck Grade | Drop Probability at 250 Luck |
| Junk | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.750\cdot {\textbf {99900}}}{\color {violet}75012.5}}=99.883\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/25da508bdf77e2b514f4f3e4d494f2b1e8e634e6)
|
| Poor | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.750\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/931becd69ecdf761e2e658005a69888f7b550501)
|
| Common | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.875\cdot {\textbf {100}}}{\color {violet}75012.5}}=0.117\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4afa810db1c229726b00d6645960b2e50cd63741)
|
| Uncommon | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/12d3344098cf5eb2ce323026da57a921cf750246)
|
| Rare | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}2.878\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54ba17993874ae4d1de07e7123080eda1f957591)
|
| Epic | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.159\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dd7e36dd6e1f7bb6defc8800ccffef7408c93c84)
|
| Legendary | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}3.441\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4f67dd7cf99d542f679e74188b7fa12ec4da312d)
|
| Unique | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}3.535\cdot {\textbf {0}}}{\color {violet}75012.5}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/55b69a3c027487b53898662c6a0b1612902f6e71)
|
Using the Luck Scalars at 500 Luck, the dot product is
![{\displaystyle \color {White}{\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {99900}}}+{\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {0}}}+{\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {100}}}+{\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}+{\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}3.505\cdot {\textbf {0}}}+{\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {0}}}+{\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {0}}}+{\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {0}}}={\color {violet}50025}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/18cee5bc9a76b13f6c99561cb6baf939d9358d7e)
| Luck Grade | Drop Probability at 500 Luck |
| Junk | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.19607843137254902,0.19607843137254902,0.19607843137254902}0.500\cdot {\textbf {99900}}}{\color {violet}50025}}=99.850\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/02700ebd3cb00999448d7e7a6eb3ef83d8de5e6d)
|
| Poor | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.39215686274509803,0.39215686274509803,0.39215686274509803}0.500\cdot {\textbf {0}}}{\color {violet}50025}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/41b76f7a3a9b6827097bd88ea82be735f2ca4994)
|
| Common | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8705882352941177,0.8705882352941177,0.8705882352941177}0.750\cdot {\textbf {100}}}{\color {violet}50025}}=0.150\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/385c99ede37ca7d0a5f0f3fff6e525446943c1c6)
|
| Uncommon | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.3843137254901961,0.7450980392156863,0.043137254901960784}1.000\cdot {\textbf {0}}}{\color {violet}50025}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b1d9cbbaf57195d1221d8f903bc16ecf479c885d)
|
| Rare | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.2901960784313726,0.6078431372549019,0.8196078431372549}3.505\cdot {\textbf {0}}}{\color {violet}50025}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/dfc21a2f23ffad40211c78e1a25086812086314b)
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| Epic | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.6784313725490196,0.35294117647058826,1}3.881\cdot {\textbf {0}}}{\color {violet}50025}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/be9399b2797240c1d1c454c5cb69ad570046b8fa)
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| Legendary | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.9686274509803922,0.6352941176470588,0.17647058823529413}4.257\cdot {\textbf {0}}}{\color {violet}50025}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b6ef359a5d1c2e571d444101f1c09f5cfb55887)
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| Unique | ![{\displaystyle \color {White}{\frac {\color [rgb]{0.8901960784313725,0.8470588235294118,0.5490196078431373}4.382\cdot {\textbf {0}}}{\color {violet}50025}}=0\%}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b5ac47fa0096e0deccab15de3ef4d6e81f72347a)
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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.