Luck

Lucky crit rolls visualized in a tree diagram.

Luck is a mechanic that rolls an outcome or a number in a range twice, with Lucky rolls applying the best result, and Unlucky rolls applying the worst result.

Modifiers that specify Damage or when Damaging and luck refer specifically to damage ranges after any increased/more modifiers (or "tooltip damage range"), not to the base damage of the weapon/skill. These stats do not affect other mechanics like chance to hit/accuracy or critical hit chance. Additionally, these stats only apply to hit damage, and have no effect on the damage roll of damage over time from damaging ailments, which roll entirely independently of the hit damage's roll.

Lucky and Unlucky modifiers affecting the same stat or mechanic will cancel each other out.

Binary Rolls

Either roll can make the hit critical, so your critical strike chance on the solid line will be increased to the dash-dotted line on lucky rolls.

A binary roll applies to something with only two choices such as chance of hitting, critical strikes, or chance of blocking. The Lucky or Unlucky chance can be calculated from your original chance with the following formulas:

$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}Lucky=2\times Chance-{Chance}^{2}$

$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}Unlucky={Chance}^{2}$

For example, the lucky critical strike chance for a critical strike chance of 40% could be calculated as follows:

$\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}Lucky=2\times 0.4-0.4^{2}=0.8-0.16=0.64$

So a crit chance of 40% will give a lucky crit chance of 64%.

Lucky/unlucky effect on binary rolls

Original chance	Lucky chance	Unlucky chance
10%	19%	1%
25%	43.75%	6.25%
50%	75%	25%
75%	93.75%	56.25%
90%	99%	81%

Note that if a roll has 0% or 100% chance, lucky and unlucky will have no effect.

Damage in a Range

Lucky Damage

Without luck, the average or expected value for a damage roll is $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {min+max}{2}}$.

A lucky roll has expected value $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {min+2\times max}{3}}$.

The extra damage luck adds is a sixth of the range, or $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {max-min}{6}}$.

The average damage is effectively nudged closer toward the max damage, and further from the minimum damage. This means that the larger the range, the more effect luck will have.

Example 1:

You use an attack with a damage range of 600-800, for an average of $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {600+800}{2}}=700$.
The range, or difference between minimum and maximum, is $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}800-600=200$.
The bonus damage will be $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {200}{6}}=33.3$ so your new average damage is $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}700+33.3=733.3$
To calculate how much more damage this is, $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {733.33}{700}}=1.047$ which means a 4.7% increase.

You can calculate how much more damage lucky will provide as a percentage directly as $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {range}{6\times average}}\times 100\%$.

Example 2:

You use a spell with a damage range of 100-1000, for an average of $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {100+1000}{2}}=550$ and range of $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}1000-100=900$.
Adding lucky will give $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {900}{6\times 550}}=0.273\times 100\%=27.3\%$ more damage.

If your minimum damage is 0 this gives a 33% more multiplier. As the minimum damage increases this scales down to a 0% more multiplier when the minimum damage equals the maximum.

Unlucky Damage

Unlucky damage nudges the damage the opposite way, giving an expected value $\color [rgb]{0.6392156862745098,0.5529411764705883,0.42745098039215684}{\frac {2\times min+max}{3}}$, which has subtracted a sixth of the range from the original average.

Making damage unlucky will give a less damage multiplier equal to the more damage multiplier that lucky would give, so the same formula as above can be used.

Related items

Unique items

The following unique items are related to Luck:

Item	Base item		Stats
The Barrow Dweller	Rogue Armour	11	(60-100)% increased Armour and Evasion +(-20--10)% to Fire Resistance +50% to Cold Resistance Damage of Enemies Hitting you is Unlucky while you are on Low Life 50% chance to Avoid Death from Hits
The Burrower	Topaz Ring	32	+(20-30)% to Lightning Resistance-10% to Cold Resistance +(20-30)% to Lightning Resistance (30-50)% increased Mana Regeneration Rate Lightning Damage of Enemies Hitting you is Unlucky
Svalinn	Crucible Tower Shield	84	Grants Skill: Raise Shield Grants Skill: Cast on Block(100-150)% increased Armour -(10-20)% to maximum Block chance Block chance is Lucky

Related passive skills

Passive skills

The following passive skills are related to Luck:

Ascendancy passive skills

The following Ascendancy passive skills are related to Luck:

Keystone passive skills

The following keystone passive skills are related to Luck:

Related modifiers

The following modifiers are related to Luck: No results found