Luck

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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.[1] 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.[2]

Lucky and Unlucky modifiers affecting the same stat or mechanic will cancel each other out.[3]

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:

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

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 .

A lucky roll has expected value .

The extra damage luck adds is a sixth of the range, or .

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 .
The range, or difference between minimum and maximum, is .
The bonus damage will be  so your new average damage is 
To calculate how much more damage this is,  which means a 4.7% increase.

You can calculate how much more damage lucky will provide as a percentage directly as .

Example 2:

You use a spell with a damage range of 100-1000, for an average of  and range of .
Adding lucky will give  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 , 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:

ItemBase itemRequired levelStats
The Barrow DwellerThe Barrow Dweller
Rogue Armour
Armour: 53
Evasion: 43
Requires Level 11, 14 Str, 14 Dex(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
In the mists they dwell,
forever hungry,
forever cold.
Rogue Armour11(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 BurrowerThe Burrower
Topaz Ring
Requires Level 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
It coils deeper and deeper
It slithers between thoughts
It lies beneath the valley
It lies in our minds
Topaz Ring32+(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
SvalinnSvalinn
Crucible Tower Shield
Shield
Chance to Block: 26%
Armour: 110
Requires Level 84, 83 StrGrants Skill: Raise Shield
Grants Skill: Cast on Block
(100-150)% increased Armour
-(10-20)% to maximum Block chance
Block chance is Lucky
The priests found the Great Shield the night it fell to Middengard,
but it was the smiths who delved into the secrets it held.
Crucible Tower Shield84Grants 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: Lua error: Error: Table passive_skills not found..

Ascendancy passive skills

The following Ascendancy passive skills are related to Luck: Lua error: Error: Table passive_skills not found..

Keystone passive skills

The following keystone passive skills are related to Luck: Lua error: Error: Table passive_skills not found..


Related modifiers

The following modifiers are related to Luck: No results found

References