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## Lucky Hit Chance: How Does It Work?

Each time you deal damage to an enemy, you have a chance to cause a lucky hit. Each skill have different probability to lucky hit, which you can find on the tooltip. But how does it actually work? Lets use some practical examples. For Necromancer, we have the skills Blighted Corpse Explosion, Bone Spear and Blight.

- Blighted Corpse Explosion, 40% chance to lucky hit and the damage is dealt over 6 seconds.
- Bone Spear, 50% chance to lucky hit and splits into Bone Spear Shards.
- Blight, 40% chance to lucky hit and deals both direct damage and leaves a pool that causes damage over time.

These percentages get increased by having +Lucky Hit Chance% on gear, but these values are the lowest they can have and are often defined as the “Baseline Lucky Hit Chance” of a skill. Conditional +Lucky Hit Chance% does not show up on the tooltip, so you may have a higher chance to lucky hit than the tooltip suggests. The formula to calculate how your +Lucky Hit Chance% affects your chance to lucky hit is as follows:

`[Baseline Lucky Hit Chance%] x [1+(Sum of all +Lucky Hit Chance on gear)] = Tooltip Lucky Hit Chance% for your skill`

For example, if you have +80% Lucky Hit Chance, your Blighted Corpse Explosion will have a **[40%] x [1+(0.8)] = 40% x 1.8 = 72%** chance to Lucky Hit.

You then take the chance you will have to trigger a specific Lucky Hit effect, such as X’fals (50% chance on lucky hit to cause an AoE explosion), and multiply that with your skills Lucky Hit effect. If we use the Blighted Corpse Explosion example above:

`72% x 50% = 36% chance to cause a lucky hit and for that lucky hit to trigger X'fals AoE explosion.`

However, it is not this simple. The tooltip Lucky Hit Chance shows the probability to trigger at least one lucky hit effect in its duration.

In order to know the probability for a damage instance on your screen to trigger a lucky hit effect, you have to understand that not all skills are made equal in terms of lucky hit chance. This section will describe the functionality for the three skills mentioned in the previous post.

### Blighted Corpse Explosion

To understand the probability of each damage instance of Blighted Corpse Explosion (Henceforth BCE), we have to first establish how damage over time affects lucky hit chance. The tooltip Lucky Hit Chance of a damage over time skill looks into the probability that at least one damage instance will be a lucky hit effect. This can be calculated by taking 1 – Probability(No LH) over double the damage over time duration, as each damage over time effect ticks twice per second. To calculate the lucky hit chance of each damage instance, we change the formula around and arrive at the following:

```
1 - (1- Probability(LH per dmg instance))^(12) = Probability(At least 1 LH)
1-Probability(At least 1 LH) = (1- Probability(LH per damage instance))^(12)
(1-Probability(At least 1 LH))^(1/12) = 1- Probability(LH per damage instance)
Probability(LH per damage instance) = 1 - (1-Probability(At least 1 LH))^(1/12)
```

Or, a general formula could be described as:

`1 - (1- Damage Instance LHC%))^(Duration x 2) = Tooltip LHC% --- > 1 - (1- Tooltip LHC%))^(1/(Duration x 2)) = Damage Instance LHC%`

However, it sadly does not end there. Skills like BCE has a unique “tooltip LHC%” which is not shown by the skill. For BCE, **“tooltip LHC%” = 1-(1-Tooltip LHC%)^(1/3)**. So we put this into our original formula and arrive at:

`Damage Instance LHC% for BCE = 1 - (1-(1-(1-Tooltip LHC%)^(1/3)))^(1/12)`

This means that BCE with Baseline LHC% has a** 1-(1-(1-(1-0.25)^(1/3)))^(1/(12))=0.008**, or **0.8% chance** to lucky hit per damage instance. Multiply this by 50% to see X’fals chance.

### Bone Spear

Compared to skills with damage over time effects, skills like Bone Spear are very straight forward. Bone Spear has a baseline 50% chance to lucky hit, which means any effect that triggers from lucky hit effects would have a **[50%] x [1+(Sum of all +Lucky Hit Chance on gear)] x [Lucky Hit Effect]** chance to trigger. For example, Hewed Flesh has a 12% chance to trigger when you lucky hit. This means if you have zero +Lucky Hit Chance% on gear, your probability to trigger Hewed Flesh from a Bone Spear is:

`50% x 12% = 6% chance to trigger Hewed Flesh each cast.`

However, it is important to understand the probability of split abilities such as Enhanced Bone Spear. Each of these shards has a similar “tooltip LHC%” condition as BCE has. In the case of Enhanced Bone Spear, each shard has a “tooltip LHC%” of **1-(1-Tooltip LHC%)^(1/2)**, so **1-(1-0.5)^(1/2) = 29%**. This means that each shard has the following chance to LHC:

`Damage Instance LHC% for Bone Spear Shard = 1-(1-(1-(1-0.5)^(1/2)))^(1/(3)) = 11%.`

So the probability that a Bone Spear Shard would trigger Hewed Flesh would be **11% x 12% = 1.32%**

### Blight

Skills like Blight that has both a direct damage component and damage over time component has their LHC% split between the direct damage and damage over time. This means that there are two calculations we need just to show the Damage Instance LHC%.

`Direct Damage LHC% = 1 - (1-0.4)^(1/2) = 22.54% chance to lucky hit per hit.`

This means that Hewed Flesh would have a **22.54% x 12% = 2.7% **chance to trigger from the direct damage.

`Damage Instance LHC% For Damage over Time = 1-(1-(1-(1-0.4)^(1/2)))^(1/(6x2)) = 2.11% chance to lucky hit per tick`

Which means X’fals would have a **2.11% x 50% = 1.05%** chance to trigger per tick.

This is pretty much universal for any skill that has both a direct hit component and damage over time in the same skill. Some examples of these skills: Firebolt, Meteor, Rupture, Rend, Flay etc.

### Overlapping Damage Over Time Effects

There are two separate mechanics for damage over time effects in regards to LHC; different damage over time effects overlapping, and the same damage over time effects overlapping.

**Different Damage over Time effects overlapping**

When you have multiple sources of damage over time effects overlapping, each of their Damage Instance LHC% is added together into one big sum. For example; if you have Blight AND BCE running on the target at the same time, you would have **2.11% + 0.8% = 2.91%** chance to lucky hit with each tick. In other words, stacking multiple different damage over time effects on the target massively increases the probability of triggering lucky hit effects.

**Same Damage over Time effects overlapping**

When you have the same source of damage over time effects overlapping, each skill has a unique stack cap where eventually applying more of the same damage over time effect has no increase on its Damage Instance LHC%. For example, BCE is capped to the amount of fields you can have on the ground at the same time (which should be 5). Blight is capped to the amount of attack speed and resources you have to throw them out. So, assuming you have 5 BCE overlapping at the same time; your Damage Instance LHC% would be **0.8% x 5 = 4%** chance to lucky hit.

If we apply these two concepts together, we can massively increase our Damage Instance LHC% by applying multiple sources of damage over time effects, and multiple overlapping durations of the same effects.

`2.11% x 3 + 0.81% x 5 = 10.33% chance to lucky hit per damage instance if you have 3 Blights on the target, and 5 overlapping BCE.`

*This mechanic is vital to X’fals builds.*

**Confirmed abilities without an overlap multiplier:**

- Desecrated Ground
- Firebolt Enchantment
- Flame Shield

**Confirmed overlap Multipliers**

### Formulas for Every Ability in the Game

You can find the formulas for every single ability in the game in the calculator. The only class that has not been verified with data gathering is druid. Each formula is color coded based on how much testing has been conducted for it and how certain the conclusions are. If there are any questions regarding the formula, feel free to reach out. All of the testing that resulted into the calculator has been saved (which is over 150 GB of footage). Screenshots from the calculator will be added at the end here just to show the Baseline Lucky Hit Chance% each skill has, and the resulting Damage Instance LHC%. If the calculations changes with patch notes, these images will be removed and uploaded again somewhere in the thread, and linked in this message. As druid has not been verified, it has not been added yet.

These pictures has values instead of “Depends on …. ” as listed above. This is because it was the max total of overlapping damage over time effects that the test character could maintain. Change these caps to whatever your character can maintain on.

### Lucky Hit Effects Causing a Lucky Hit

Abilities or aspects that triggers from a lucky hit tends to not have a lucky hit chance themselves. A reason for this could be to prevent chain proccing of effects; however the following are exceptions to this rule.

- Bursting Venoms aspect; it inherits the Tooltip LHC% from Poison Imbuement, and is calculated as a dot over 3 seconds. The formula for this is estimated to be:

`1-(1-Poison Imbuement Tooltip LHC%)^(1/3)`

- Meteor Enchantment; it inherits full LHC% of the Meteor Skill, and can cause a chain reaction of meteor procs.
- Shattered Stars aspect; the direct damage from the meteorites has no LHC%, but the damage over time does. The formula for this is estimated to be:

`1-(1-(1-(1-(1-(1-Meteor Tooltip LHC%)^(1/2)))^(1/(6))))^(1/3)`

Examples of LHC Interactions that does not have a chance to lucky hit:

- Andariels Visage
- Doombringer
- X’fals

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