Expected Damage with Crit Calculator

Understanding the expected damage with crit calculator — concept and principle

Critical hits make damage random: most hits deal base damage, and some deal extra. To compare builds, players need the average, not the best-case number. This calculator combines base damage, critical chance and critical damage bonus into expected damage per hit, then multiplies by attack speed to give damage per second (DPS).

Four crits in ten hits lift the average hit from 100 to 140.

How it is calculated

Crit multiplier = 1 + crit damage bonus ÷ 100. A bonus of 100% doubles a hit; 150% makes it ×2.5.
Expected damage per hit = base × (1 + crit chance × crit bonus), with both as decimals.
DPS = expected damage per hit × attacks per second.

The principle

Expected value is the probability-weighted average of the possible outcomes. A hit is normal with probability (1 − c) and deals D, or critical with probability c and deals D × (1 + b). The average is (1 − c) × D + c × D × (1 + b), which simplifies to D × (1 + c × b). Over many hits the total damage settles close to this average, which is why it is the fair way to compare a crit build with a flat-damage build. Multiplying by attacks per second turns damage per hit into damage per second.

Worked example

Inputs: base damage 100, crit chance 40%, crit bonus 100%, 1.2 attacks per second.
Crit multiplier = 1 + 100 ÷ 100 = 2.
Expected damage per hit = 100 × (1 + 0.40 × 1.00) = 140.
DPS = 140 × 1.2 = 168.

Each point is the calculator re-run with only “Base damage” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Base damage	Expected damage per hit
25	35
50	70
75	105
100	140
125	175
150	210
200	280

How to read the result

The term c × b is the average bonus from crits; here crits add 40% damage on average. Because chance and bonus multiply, raising whichever is relatively lower usually gives more. When one percent of crit chance costs the same as two percent of crit damage, as in a common substat system, expected damage is maximized when the crit damage bonus is about twice the crit chance. Crit chance above 100% normally has no effect, so stop adding it at the cap.

Common mistakes

Entering the total multiplier (200%) in a field that expects the bonus (100%).
Adding crit chance above 100%, which is wasted in most games.
Ignoring that a few big crits matter more than the average against targets with low health or shields, or in short fights.

Keep in mind: The formula assumes each hit crits independently and that crit damage is simply multiplicative. Games with crit damage reduction, guaranteed crits or separate multipliers will differ, so check the game's own formula.

Frequently asked questions

What is a good crit ratio?

In systems where 1% chance and 2% damage cost the same, aim for crit damage about twice crit chance, for example 60% chance and 120% damage.

Does attack speed change expected damage per hit?

No. It only multiplies how many hits land per second.

Is DPS the full story?

No. Armor, resistances, cooldowns and uptime also change real damage over a fight.

Sources: Sheldon M. Ross, A First Course in Probability (expected value)

Checked 8 Nov 2026. Official league / federation formulas where they exist; widely used community formulas otherwise. For fun and analysis — not betting advice.

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