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(→‎Luck Scalar: Emphasis on a common misconceptions.)
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Additionally, luck works with a hidden property called Luck Grade.  While the table below has luck grade colored similar to item rarities, the two properties are not equivalent.<br>
Additionally, luck works with a hidden property called Luck Grade.  While the table below has luck grade colored similar to item rarities, the two properties are not equivalent.<br>
Many loot tables will match Item Rarity one to one with item Luck Grade, but there are many exceptions.  Don't fall into the trap of thinking luck makes higher ''rarities'' more common; see the [[Cave Troll|Cave Troll's quest drops]] for a counterexample.
Many loot tables will match Item Rarity one to one with item Luck Grade, but there are many exceptions.  Don't fall into the trap of thinking luck makes higher ''rarities'' more common; see the [[Cave_Troll#Loot_Tables|Cave Troll's quest drops]] for a counterexample.


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Revision as of 13:38, 31 July 2024

Stats Damage Spell Restoration Luck
Enchantments Health Impact Power Footstep Sound
Movement 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 a container first or deals the killing blow to a monster 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:

Loot Drop Tables and Drop Rate Tables

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

Loot Drop tables list all possible items for a specific drop instance, and for each item therein it associates a Luck Grade.
Drop Rate tables assign a "rate" to each Luck Grade; when normalized, these rates represent the probability of getting a drop of that Luck Grade.

Each Luck Grade's drop rate is split evenly between items that share that Luck Grade. This means that items sharing a Loot Drop table and Luck Grade, will always have the same probability of dropping.
However, be aware that Monsters and Containers can have multiple Loot Drop Tables, each with their own Drop Rate table. See Lich for example.

A Drop can be rolled more than once, but each roll is independent of the others.
The Elite variant of Lich rolls their main gear Loot and Drop tables a total of 3 times, theoretically making it possible (though extremely unlikely) to get 3 identical Artifacts from a single Elite Lich kill.

Luck Scalar

Luck Scalars are 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.

Additionally, luck works with a hidden property called Luck Grade. While the table below has luck grade colored similar to item rarities, the two properties are not equivalent.
Many loot tables will match Item Rarity one to one with item Luck Grade, but there are many exceptions. Don't fall into the trap of thinking luck makes higher rarities more common; see the Cave Troll's quest drops for a counterexample.

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. While the curves are continuous, keep in mind that fractional values of Luck do not exist.

Luck Scalar Graph

LaTeX Formula


Probabilities from Luck

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

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

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

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

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


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


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

Luck Grade Drop Probability at 500 Luck
0
1
2
3
4
5
6
7
8

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.

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