Lucky Hit Mechanics

General Functionality

Each time you damage an enemy, you have a chance to cause a Lucky Hit. Each skill has a different Lucky Hit Chance (also known as LHC), which you can find on the tooltip if the Advanced Tooltip option is enabled. But how does Lucky Hit Chance work? Let us look at the base functionality.

If we use Dash as an example, it has a base chance of 25% to cause a Lucky Hit. This percentage will increase if we add any [+]% Lucky Hit to our gear. If we add [+]100% Lucky Hit Chance to our gear, we end up with 25% x (100% + 100%) = 50% Tooltip Lucky Hit %. This means that each time you damage a target with Dash, you have a 50% chance to Lucky hit. But what about skills like Shadow Step that already has a 100% chance to Lucky hit? It functions the same way, you take 100% x (100% + 100%) = 200% chance to Lucky hit. It may not sound intuitive, but Lucky Hit Chance above 100% still helps you, and here is why.

The chance to trigger a Lucky Hit effect has two components, one being the tooltip Lucky Hit%, and the second being the chance to proc the effect itself. These two factors are not capped, so a factor higher than 100% Tooltip Lucky Hit% increases the probability that you will trigger a Lucky Hit effect. Assume that you have Doombringer equipped and you play with Shadow Step.

• With no [+]% Lucky Hit, you will have a 100% x 25% = 25% chance to trigger Doombringer with each cast of Shadow Step.
• If you add [+]100% Lucky Hit, you would have a 200% x 25% = 50% chance to trigger Doombringer.

Season 6 Findings - Internal Cooldown

Before Season 4, the game did not have enough [+]Lucky Hit Chance available for testing to be accurate enough for limit testing of Lucky Hit Chance functionality. However, with the changes to Fists of Fate, more accurate testing could be done to gauge how frequently something procs reliably. On the PTR, effects such as Victimize had no internal cooldown and could occur without any cooldown. As of Season 6, Victimize could not trigger more frequently than roughly every ~0.7 sec regardless of the number of hits done (credits to DiEoxidE for playtesting on this).

It is unclear which effects have an internal cooldown, but the following were tested and verified to not trigger twice within roughly ~0.7 seconds:

• Andariel's Visage
• X'Fal's Corroded Signet
• Victimize

Lucky Hit Effects causing a Lucky Hit

Passives and aspects that trigger from a Lucky Hit are generally unable to generate Lucky Hits themselves. This is in place to prevent a chain of procs from occurring. However, there are some exceptions to this rule such as Bursting Venoms and Meteor. It is unclear whether or not aspects or unique items are supposed to have a chance of causing a Lucky Hit, as it is not communicated in-game

Direct Damage

Direct damage implies that the skill has a single damage component and could be either a single target ability or area of effect (henceforth AoE). Let us use Bone Spear as an example for this section. Bone Spear has a 50% Base Skill Lucky Hit%, meaning that each time you use Bone Spear, you have a 50% chance to cause a Lucky Hit.

If we wonder how many times on average that Bone Spear will trigger the Necromancer passive Hewed Flesh on average, we can calculate it using the formula from the previous section.

Our tooltip Lucky Hit% is 50%, and our chance to trigger Hewed Flesh is 12%. We put these numbers into the formula and calculate that we have a 50% x 12% = 6% chance to trigger Hewed Flesh with each Bone Spear. In other words, this functions the same way as the example we used in the General Functionality section.

Split Lucky Hit%

However, even Direct Damage can have complicated Lucky Hit functionality. Although Bone Spear has a 50% chance of causing a Lucky Hit, can Enhanced Bone Spear Lucky Hit? The answer is yes, but their chance to Lucky Hit is not what you may think. The following information is approximated based on explicit Lucky Hit testing and the formula is subject to change.

"Split Lucky Hit%" is introduced as a concept whenever a skill includes a new damage source to a Direct Damage spell. For Enhanced Bone Spear, we can plug our values into the formula to calculate the probability that a single bone shard will cause a Lucky Hit. This assumes that you create three bone shards per cast of Bone Spear and that Bone Spear has a 50% chance of causing a Lucky Hit.

Each Bone Shard from Enhanced Bone Spear has a 10.9% chance of causing a Lucky Hit in this example. If this was not complicated enough, this is further affected by deciding to use the Paranormal Bone Spear upgrade. That means each time you cause a Critical Strike with Bone Spear, the formula for Lucky Hit of Bone Shard changes to include 5 Bone Shards instead.

As such, adding more Bone Shards does not increase the overall probability. It, instead, reduces the LHC per Bone Shard to compensate for the additional Shards. This is because the Bone Shard formula includes the total amount of Bone Shards.

Damage over Time

Lucky Hit Chance for Damage over Time (henceforth DoT LHC) effects differs from Direct damage. The tooltip of a skill, such as Poison Imbuement, shows the probability of causing at least one Lucky Hit over its duration. See the end of the section for a list of all DoT effects with Lucky Hit. The following formula is used to calculate the probability of a DoT damage instance causing a Lucky Hit.

If we use Poison Imbuement as an example, you change "duration" to 5 and Tooltip Lucky Hit% to 33%. The reason why the duration is doubled is because DoT effects deal damage every 0.5 seconds. Furthermore, it is important to note that if we have Enhanced Poison Imbuement or Tracker, this affects the probability as we have Tooltip Lucky Hit% spread over more damage instances. Let us plug the values into the formula.

Poison Imbuement, without any [+]% Lucky Hit, thus has a 3.9% chance of causing a Lucky Hit per damage instance when using the base duration. If you include duration increases, change the "5" in this calculation to the appropriate number.

Important New Findings

Because this formula has (100% - Tooltip LHC%) as a part of its calculation, it was theorized that you gain no more benefit from Lucky Hit once you reach 100% Tooltip Lucky Hit. Thanks to Fists of Fate's incredibly high [+]Lucky Hit Chance, we could finally investigate the behavior of the formula at 100% Tooltip Lucky Hit Chance.

To disprove this theory, all that was required to do was obtain 100% Tooltip Lucky Hit Chance for a pure DoT ability, such as Poison Imbuement, and observe its behavior. At [+]210% Lucky Hit, 100% Tooltip Lucky Hit was achieved, and the result was 58 procs of X'Fal's Corroded Signet in 792 damage instances from Poison Imbuement. You can reverse engineer the rough Lucky Hit rate of this test by calculating the following:

Damage Instance LHC = Total Effect Triggers / [Total Damage Instances x Effect Chance] = 58 / (792 x 0.75) = 9.76%

If the previous theory was correct, as (100% - Tooltip LHC%) approaches 0, the chance to trigger Lucky Hit effects skyrockets until finally getting to 100% Lucky Hit per tick. At 203.03% Lucky Hit, we would have had 99.99% Tooltip Lucky Hit and an expected proc total of (1-(1-[0.33 x (1+2.03)])^(1/12)) x 0.75 x 792 = 318 X'fals triggers. This was not nearly the case, and similar tests were conducted at other Lucky Hit values to verify this functionality. Further testing has to be conducted, but based on this test, the following was true for Poison Imbuement

DoT Damage Instance LHC = (100% - (100% - 33%)^(1/12)) x  (100% + Sum of [+]Lucky Hit Chance)

Overlapping Damage over Time Effects

When you overlap the DoT effects, the game does not communicate what happens with the Lucky Hit per tick. Does it remain the same? Does it increase? The answer is that it increases, but it has a cap. The only way to get an approximation for these caps is to pay a visit to your friendly Training Dummy and hit it for a very long time while counting Lucky Hit procs. Here are a few caps that have been identified:

• Flay has a cap roughly x2 the DoT LHC%.
• Weapon Expertise 2H Sword has a cap roughly x3 the DoT LHC%.
• Poison Imbuement has a cap roughly x1.5 the DoT LHC%.
• Battle Lunging Strike has a cap roughly x18 the DoT LHC%.

These caps only apply if the DoT is applied to the target. AoE skills differ as they are capped based on the amount you can maintain concurrently. For example, Firewall and Blizzard are both capped based on mana and Attack Speed. Meanwhile, a spell such as Poison Trap is AoE but the damage is connected to the DoT and thus has a cap. Another specific case is Blighted Corpse Explosion, which only has a visual cap on how many can be active at a given time.

What happens if different DoT effects overlap? That question is much easier to answer. When different DoT effects overlap, their DoT LHC% are all "individually" tracked but have their DoT LHC% added together. If we have one DoT effect with 20% DoT LHC%, one with 10%, and one with 23%, we can bunch them together as 20%+10%+23% = 53% chance of causing a Lucky Hit. This is extremely powerful for builds that utilize damage sources such as X'Fal's Corroded Signet.

List of Abilities with DoT LHC%

Below is a complete list of abilities and aspects with a DoT LHC%. This list is subject to change depending on aspects introduced to the game and bug fixes for LHC%.

Direct Damage and Damage over Time

Skills like Blight have both a direct damage component and a damage over time component. These spells use the Split Lucky Hit% formula, but it also means that we have to do two calculations to determine the Lucky Hit Chance of the direct damage and the DoT.

Using Blight as our example, it has 40% Tooltip LHC%. We can plug that into the formula and get 100% - (100% - 40%)^(1/2) = 22.54%. Having done this, we immediately know that the direct damage of Blight has a 22.54% chance of causing a Lucky Hit. To calculate the DoT LHC%, we plug in 22.54% as our new Tooltip LHC% and 6 as our duration.

The DoT LHC% for Blight is 2.11% when you have 40% Tooltip LHC. So if we were wondering what the probability is for Blight to trigger Hewed Flesh, we would have:

• Direct Damage: 22.54% x 12% = 2.7% chance to trigger Hewed Flesh with each cast of Blight.
• DoT Damage: Each tick would have a 2.11% x 12% = 0.25% chance to trigger Hewed Flesh with each DoT tick.

The LHC is calculated with this method for every ability with a direct damage component and a DoT component. Some examples of these abilities are Meteor, Fire Bolt and Rend. However, there are some cases where the formula is altered slightly, such as for Blighted Corpse Explosion.

Instead of following the standard DoT LHC formula, the DoT LHC for Blighted Corpse Explosion first requires you to use the Split Lucky Hit% formula with a twist, in which it is changed to 1/3 at the end instead of 1/2. This means that instead of Blighted Corpse Explosion having a DoT LHC% of: 1-(1-0.25)^(1/12) = 2.368%, it has a DoT LHC% of: 1-(1-(1-(1-0.25)^(1/3)))^(1/12) = 0.79%. This is not communicated in-game, and can only be found through testing.