What DPS is and what it hides
Damage per second is a rate: the average damage you deal divided by the time it takes to deal it. Every game that shows a DPS number computes the same product - an average hit multiplied by how often you hit - and the differences between games are entirely in which modifiers apply and in what order. Get the structure right and the same calculation serves an ARPG, an MMO, a shooter and a tower defence game.
The number is an average, and that is both its strength and its blind spot. Over a long fight against a single target, average damage is what determines the outcome, and DPS predicts it well. Over three seconds it does not: a slow weapon with a huge hit and a 25% crit chance has enormous variance, so its actual damage in a short window is frequently far below its DPS. This is why burst damage and sustained damage are tracked separately in serious theorycrafting, and why a build's DPS figure alone never settles an argument about which weapon feels better.
DPS also assumes you are attacking continuously. Real damage output is DPS multiplied by uptime, and uptime is eroded by movement, target switching, resource costs, cast times, animation locks and mechanics that force you to stop. A build with 10% higher DPS and 20% worse uptime is a downgrade, and no sheet number will tell you that.
The formula, factor by factor
Average base hit. Weapons with a damage range roll uniformly between the ends, so the average is the midpoint, (min + max) / 2. A 80-120 weapon averages 100.
Critical strike factor. A fraction c of hits deal m times damage and the rest deal normal damage, so the expected multiple is c x m + (1 - c) x 1, which simplifies to 1 + c(m - 1). At 25% chance and a 2.0x multiplier that is 1 + 0.25 = 1.25. Getting the multiplier's definition right is where most errors enter: some games quote a total multiplier (2.0x means double) and others quote bonus critical damage (+100% means the same thing, +150% means 2.5x). This calculator wants the total multiple.
Damage bonuses. Additive increases from passives and buffs are summed and applied once: three sources of +20% give a single x1.60, not x1.728. Multiplicative sources - the ones a game usually calls "more" damage rather than "increased" damage - are applied separately, so fold them into this field only if they genuinely stack additively in your game.
Attacks per second. Attack speed bonuses divide the attack time rather than adding to the rate: a base attack time of 1.40 s with +25% speed gives 1.25 / 1.40 = 0.8929 attacks per second, equivalent to an attack every 1.12 s. That inversion is why attack speed has diminishing absolute returns in one direction and compounding returns in the other.
Mitigation and hit chance. Both are straightforward multipliers on the result: mitigation removes a fraction of each landed hit, and hit chance removes a fraction of the attacks. Neither changes the average hit itself, which is why the calculator reports the pre-mitigation and post-mitigation figures separately - the pre-mitigation number is what your character sheet shows, and the post-mitigation number is what the target actually loses.
Worked example: an 80-120 weapon against a 30% mitigation target
Take a weapon dealing 80-120 damage on a 1.40 s base attack time, with +25% attack speed, 25% crit chance at a 2.0x multiplier, +40% increased damage, 95% chance to hit, against a target with 25,000 health and 30% damage reduction.
- Average base hit. (80 + 120) / 2 = 100.
- Critical strike factor. 1 + 0.25 x (2.0 - 1) = 1.25. So the average hit before bonuses is 125.
- Damage bonuses. 125 x 1.40 = 175. This is the average hit your sheet would show.
- Target mitigation. 175 x (1 - 0.30) = 122.5 damage actually removed per landed hit.
- Attacks per second. (1 + 0.25) / 1.40 = 1.25 / 1.40 = 0.8929 attacks per second, one attack every 1.12 seconds.
- Damage per second. 0.8929 x 122.5 x 0.95 = 103.91 DPS.
- Time to kill. 25,000 / 103.91 = 240.6 seconds, or just over four minutes.
Now test an upgrade. Raising crit chance from 25% to 40% changes the factor from 1.25 to 1.40, which is a 12% increase in every downstream figure: DPS goes to 116.38 and time to kill falls to 214.8 seconds. Raising the crit multiplier from 2.0x to 2.6x instead changes the factor to 1 + 0.25 x 1.6 = 1.40 - exactly the same result. That equivalence is not a coincidence, and the next section explains when to prefer which.
Which stat to buy next
Differentiate the crit factor and the comparison becomes exact. With f = 1 + c(m - 1), an extra point of crit chance adds (m - 1) to the factor while an extra point of multiplier adds c. So crit chance is worth more than crit damage exactly when (m - 1) exceeds c - that is, when your bonus critical damage percentage is larger than your critical strike chance percentage. At 25% chance and 2.0x multiplier, (m-1) = 100% against c = 25%, so chance is worth four times as much per point. Keep buying chance until the two converge, then alternate. This is the whole of the classic "balance crit chance and crit damage" advice, stated exactly.
Attack speed and flat damage compare just as cleanly, because both enter the product linearly: a 10% increase in either raises DPS by 10%. What separates them in practice is everything the formula omits. Attack speed improves resource generation, on-hit effects and reaction time but worsens damage-per-hit thresholds and can be capped by animation. Flat damage improves burst and overkill efficiency. When two upgrades give the same DPS, take the one that better matches how you actually play.
Compare builds on effective DPS against the target you actually fight, never on the sheet number. Mitigation is the reason: a build with high flat damage per hit and one with many small hits are affected very differently by flat damage reduction, and by armour formulas where mitigation scales with the size of the incoming hit. The effective health pool calculator handles the defensive side of the same arithmetic, converting armour and resistances into the health total your DPS is really chewing through.
Critical strike damage multiplier by chance and multiplier
| Crit chance | 1.5x multiplier | 2.0x multiplier | 2.5x multiplier | 3.0x multiplier |
|---|---|---|---|---|
| 0% | 1.000 | 1.000 | 1.000 | 1.000 |
| 10% | 1.050 | 1.100 | 1.150 | 1.200 |
| 20% | 1.100 | 1.200 | 1.300 | 1.400 |
| 30% | 1.150 | 1.300 | 1.450 | 1.600 |
| 40% | 1.200 | 1.400 | 1.600 | 1.800 |
| 50% | 1.250 | 1.500 | 1.750 | 2.000 |
| 60% | 1.300 | 1.600 | 1.900 | 2.200 |
| 70% | 1.350 | 1.700 | 2.050 | 2.400 |
| 80% | 1.400 | 1.800 | 2.200 | 2.600 |
| 90% | 1.450 | 1.900 | 2.350 | 2.800 |
| 100% | 1.500 | 2.000 | 2.500 | 3.000 |
Read the columns as total multipliers. If your game quotes bonus critical damage instead, add 100%: +100% bonus is the 2.0x column and +200% bonus is the 3.0x column.
Where a DPS number stops being honest
- Uptime is not included. Real output is DPS multiplied by the fraction of the fight you spend attacking. Movement, target switching and animation locks routinely cost 20% or more, and no sheet accounts for them.
- Additive and multiplicative bonuses are not the same. Two +50% additive sources give x2.00; two separate multiplicative sources give x2.25. Putting a multiplicative modifier into the additive field understates your damage.
- Damage over time, procs and pets are separate calculations. This models direct hits only. Anything that ticks on its own schedule must be computed on that schedule and added.
- Mitigation formulas vary. Some games apply flat reduction before percentage reduction, some scale armour effectiveness against attacker level, and some have diminishing returns curves. Convert your target's defences to a single effective percentage before entering it.
- Overkill is wasted. Against small targets a large hit spills damage that the DPS figure counts and the fight does not. Time to kill is the more honest measure whenever the target dies in a handful of hits.
- Attack speed is often capped or quantised. Server tick rates and animation frames can round your real attack rate down, so the last few percent of attack speed sometimes does nothing at all.
Check what your game means by crit multiplier
The single most common error in DPS arithmetic is mixing the two conventions for critical damage. A total multiplier of 2.0x and a bonus of +100% describe the same crit; a bonus of +200% is a total multiplier of 3.0x. If you enter 2.0 when your game means +200% bonus, your crit factor at 50% chance comes out as 1.50 instead of 2.00 and every downstream figure is a third too low. The rule is simple: this calculator wants the number a critical hit is multiplied by, so a crit that hits twice as hard is 2.0.
Where DPS fits among the other numbers
DPS is one of three quantities that decide a fight. The second is effective health - how much damage you can absorb - and the third is uptime, the fraction of the fight in which either of the first two matters. Optimising DPS in isolation is the classic theorycrafting mistake, because a build that dies in four seconds has an effective DPS of zero for the rest of the fight. Balance the three by computing time to kill against time to be killed, using the effective health pool calculator for the defensive half.
The probability machinery underneath DPS is the same as in tabletop combat: a chance to hit multiplied by an average damage roll. The dice probability calculator makes that structure explicit and gives the full distribution rather than just the average, which is what you want when a single roll decides an encounter. For the acquisition side of the loop, the drop rate calculator tells you how many runs a specific upgrade will take and the gacha pull calculator handles banner systems with pity.
If you want to go further than a single-target rate, the next steps are a damage-over-time model that tracks each effect on its own timer, a rotation simulator that respects cooldowns and resources, and finally a full combat simulation that samples the actual distribution rather than its mean. Each layer adds accuracy at a large cost in complexity, and each one still rests on the average-hit-times-rate product computed here. Get this number right first, because every more sophisticated model is built from it.
Key terms
- Base attack time
- Seconds per attack before any speed bonus, a property of the weapon. Its reciprocal is the base attacks per second, so a 1.40 s weapon starts at 0.714 attacks per second.
- Critical strike factor
- The expected damage multiple per hit, 1 + c(m - 1). It is the single number that summarises both crit stats, and it is what you compare when weighing crit gear.
- Effective DPS
- Damage per second after the target's mitigation and your miss chance. It is what the enemy health bar loses, as opposed to the pre-mitigation figure a character sheet usually shows.
- Time to kill
- Target health divided by effective DPS. It is a more honest comparison than DPS whenever the target dies quickly, because it exposes overkill and burst effects that an average rate hides.