What a critical hit adds
A critical hit is a random upgrade to an attack. Each time the attack lands, the game checks a crit chance, and if the check succeeds the damage is multiplied by a crit multiplier. Two numbers describe the whole mechanic: how often it happens, and how much extra it gives.
Games differ in the details. Some apply the multiplier to the base damage only, some to the total after bonuses, and some add a fixed amount instead of multiplying. The maths below assumes the simplest version: a multiplier on the damage of a hit that has already landed. If a game says otherwise, the same method still works with different inputs.
Average damage per hit
The average, or expected value, of an attack is each possible result multiplied by its chance, added together. With a crit chance of p (as a decimal) and a multiplier of m:
Average damage = base × (1 − p) + base × m × p
This simplifies to base × (1 + p × (m − 1)), because the extra damage only comes from the crit share of attacks and equals (m − 1) times the base.
Example with illustrative numbers: a base hit of 100, a 20% crit chance and a 2× multiplier.
- 80% of the time the hit does 100, contributing 80.
- 20% of the time it does 200, contributing 40.
- The average is 120.
Using the shortcut, 1 + 0.2 × (2 − 1) = 1.2, and 100 × 1.2 = 120. Both routes agree.
Chance versus multiplier
Since the average depends on the product p × (m − 1), different builds can have identical averages:
| Crit chance | Multiplier | Bonus factor | Average on base 100 |
|---|---|---|---|
| 20% | 2× | 1 + 0.2 × 1 = 1.2 | 120 |
| 10% | 3× | 1 + 0.1 × 2 = 1.2 | 120 |
| 25% | 1.5× | 1 + 0.25 × 0.5 = 1.125 | 112.5 |
| 30% | 2× | 1 + 0.3 × 1 = 1.3 | 130 |
| 20% | 2.5× | 1 + 0.2 × 1.5 = 1.3 | 130 |
The second row is the useful one: a 10% chance of tripling damage averages out the same as a 20% chance of doubling it. They feel very different in play, though, which is the subject of the next section.
Notice also that the multiplier only helps through (m − 1). Going from 1.5× to 2× adds 0.5 to that term, the same as going from 2× to 2.5×. Each extra step of multiplier is worth the same amount when added, but if a game multiplies several bonuses together, an extra step can be worth more or less depending on what it combines with.
Same average, different spread
Two builds with the same average can produce quite different sessions. Standard deviation measures how far results typically stray from the average.
For the 20% chance and 2× multiplier on a base of 100, the outcomes are 100 (80% of the time) and 200 (20%), with an average of 120.
- Squared distance from average for 100: (100 − 120)² = 400
- Squared distance for 200: (200 − 120)² = 6,400
- Variance: 0.8 × 400 + 0.2 × 6,400 = 320 + 1,280 = 1,600
- Standard deviation: the square root of 1,600, which is 40
For the 10% chance and 3× multiplier, the outcomes are 100 (90%) and 300 (10%), again averaging 120.
- Variance: 0.9 × 400 + 0.1 × 32,400 = 360 + 3,240 = 3,600
- Standard deviation: 60
The rarer, bigger crit has the larger spread, so a short fight can fall further from the average. Over a very long fight the two converge on 120 per hit, which is what the law of large numbers describes, but short encounters are where the difference is felt.
How many crits to expect
If each hit is an independent 20% chance, the average number of crits in 10 hits is 10 × 0.2 = 2. That is an average, not a promise.
- Chance of no crits in 10 hits: 0.8¹⁰ is about 10.7%.
- Chance of exactly 2 crits: 45 × 0.2² × 0.8⁸ is about 30%. The 45 is the number of ways to choose which 2 of the 10 hits are crits, a count from the binomial distribution.
- Chance of at least one crit in 5 hits: 1 − 0.8⁵ = 1 − 0.32768, about 67%.
So roughly one fight in ten of ten hits would contain no crit at all, with nothing wrong with the game. A sequence like that tends to feel more suspicious than it is, and some games adjust the chance after a long run without a crit, which is covered in the article on streak breakers.
Caveats when reading real games
- Stated stats may not be the full picture. Crit chance is sometimes capped, rounded for display or converted from a rating by a formula the game does not show.
- Crits may not be independent. Games with streak adjustments change the chance from hit to hit, so the simple average above is only approximate.
- Other layers matter. Defence, resistances and damage ranges are applied in different orders in different games, and the order changes the result.
- Attack speed is a separate lever. A faster attack gets more rolls per second, which affects both average damage over time and how quickly results settle toward the average.
When two options are close, a Monte Carlo simulation of a few thousand fights is a practical way to see both the average and the spread, instead of relying on a single calculation.