Damage Formula
How damage is actually calculated in Seven Deadly Sins: Origin — datamined from the game files and validated in combat.
The damage formula, measured
Every term below was extracted from the game files, then tested against real combat: eight damage values predicted and sealed before being filmed, all landing within ±0.014%. What this page claims, it proves — and what it hasn't proven yet carries its badge.
The full formula
A hit's damage is the product of several factors: your attack, the skill's coefficient, then a chain of target-side multipliers (defense, resistance, weakness) and the critical hit.
ATK = (Base ATK + Equipment ATK) × (1 + Attack increase). Elemental ATK adds to this total, but only for your character's element.
The proof
Sealed-prediction campaign (2026-08-20). The strongest test on this page: the eight values below were predicted and committed to git BEFORE the hits were filmed, then read frame by frame from the recording (training dummy: zero defense, no weakness, no resistances). All eight bands landed within ±0.014%.
| Hit | Predicted damage | Actual damage |
|---|---|---|
| Auto 1 — normal | 5,876.8 | 5,877 |
| Auto 1 — critical | 14,107.4 | 14,108 |
| Autos 2-3 — normal | 3,503.5 | 3,504 |
| Autos 2-3 — critical | 8,410.2 | 8,411 |
| Auto 4 — normal | 11,753.7 | 11,754 |
| Auto 4 — critical | 28,214.7 | 28,215 |
| Skill (E) — normal | 61,782.1 | 61,783 |
| Skill (E) — critical | 148,308.0 | 148,309 |
Diane, potential 8, stats read by probe. The measured crit multiplier is exactly ×(1 + Crit Damage) on all four pairs — the crit law is validated from 0% to 188% crit damage resistance.
How it was established▼
The elemental advantage term was confirmed via blind prediction: a single character (Diane Earth) hitting 4 bosses of different weakness at WL4, predictions computed before in-game measurement. The critical term was verified across 8 independent tests from UI 85% to UI 248% — perfectly linear within 0.1pp, formula confirmed.
| Elemental weakness | Predicted damage | Actual damage | Gap |
|---|---|---|---|
| +2000 | 4,417 | 4,425 | +0.2% |
| 0 | 3,599 | 3,600 | +0.0% |
| −1000 | 3,249 | 3,250 | +0.0% |
| −2000 | 2,664 | 2,652 | −0.5% |
Average error below 0.5%. The elemental-advantage term is thus confirmed across the full spectrum, advantage and disadvantage alike.
💡 Crit & ATK% beat elemental attack
Elemental attack is additive: it adds a fixed amount to your attack pool, which dilutes as you grow stronger. Critical rate, critical damage and attack% increase are multiplicative: they amplify your whole kit and never dilute. That's why a weapon with a critical-damage substat almost always beats one with elemental attack, even on a character of the matching element. It's not a bug — it's a stat hierarchy.
Each term explained
- 1Attack (+ Elemental ATK)Measured
Your total attack. Elemental attack (e.g. Dark Attack) adds to it, but only for your character's element.
- 2Skill coefficientMeasured
The percentage of attack dealt by the move used (auto-attack, skill, ultimate…).
- 3Attack-type bonusDatamined
'Normal attack / skill / ultimate damage increase' applies depending on the type of hit.
- 4Defense mitigationMeasured
K / (K + target's Defense), with K = 5,128 measured in-game (2026-08-20). The more defense the target has, the less damage it takes.
- 5Elemental resistanceDatamined
A flat reduction of elemental damage, specific to the target. Bosses gain more as the world level rises.
- 6Elemental advantageMeasured
Hitting a weakness raises damage (the green arrow); hitting a resistance lowers it. Signed: +2000 weakness = +20%.
- 7CriticalMeasured
On a critical hit, the multiplier is `1 + (UI Crit Damage − target's crit damage resistance)`. The UI value on your character sheet is used directly — no hidden additive above it. Rarity baselines (+15 SR / +25 SSR) are already inside your UI value.
- 8DistanceUntested
Damage falls off with distance: 100% within ~500 units, 50% at 500–1000, 10% beyond. It's the only positional modifier — there's no random per-hit roll, damage is deterministic.
Element, burst & stacking
The element-vs-target interaction has three separate pieces, often confused:
A target's signed weakness/resistance to an element (the up/down arrow). Positive = it takes more damage. Multiple sources feed it — the target's innate weakness, your Burst's debuff, and 'elemental damage' bonuses on your gear — all summed into the same total.
A flat percentage reduction of elemental damage on the target. On bosses it rises with the world level.
The 'Fire / Wind / Dark Defence' rows on your character sheet (plus 'All-Element Defence'). These reduce the elemental damage YOU take — a defensive stat, not an offensive one.
The elemental-advantage term is a sum: the target's weakness, the debuff your Burst applies, and the 'elemental damage' bonuses on your gear all add up, then the total runs through × (1 + sum / 10000). Activating an elemental Burst applies a big weakness debuff on the target — Dark +25% (15s), every other element +15% (30s). Because everything adds, a Burst (+25%) plus a gear bonus (+2%) gives +27% (×1.27), not the two multiplied.
The formula chains all its multipliers. For critical damage, all sources are already summed into the 'Crit Damage' % shown on your character sheet: rarity baseline (+15 SR / +25 SSR), mastery, gear substats, set bonuses, engraving passives, active buffs. The formula uses this UI value directly: `1 + (UI − boss's crit damage resistance)`, no hidden additive. Linearity has been empirically verified from UI 85% up to UI 248% with no observed cap — each additional % translates directly into +1pp on the multiplier.
Empirical observation (8 independent tests): between UI 85.83% and UI 248.68% against the same target (constant crit resistance at 27.8%), the observed multiplier is strictly `1 + (UI − 27.8%)` within 0.1pp. The constant `ga_criticalpowerper_rate_range_max = 20000` (200%) present in DefineTable appears to be obsolete post-1.4 (like `ga_default_criticalpowerper_rate = 12000` before it) — no cap activates within the tested range. Stack freely.
Worked example
Diane (Earth) hits the Red Demon — weak to Earth — at world level 4. Starting from a neutral base hit, we apply the target-side multipliers.
Estimated: 4,417. Measured in-game: 4,425 — a 0.2% gap.
Datamined constants
The fixed values pulled from the game files, for theorycrafters.
FAQ
Q.Is weapon elemental damage bugged?▼
No. Elemental ATK is a weak additive stat next to multiplicative ones (crit, ATK%). A crit weapon often beats an elemental one, even on the matching element — it's a stat hierarchy, not a bug.
Q.Crit or ATK%?▼
Both are multiplicative and excellent. Crit (rate × damage) shines most when your rate is high — secure a solid crit rate first, then stack crit damage.
Q.How much is elemental advantage worth?▼
It depends on the target's weakness: a +2000 weakness means +20% damage. Hitting a resistance lowers it by the same logic.
Q.Why does my damage sometimes change?▼
Damage is deterministic — the same hit gives the same number. If it changes, it's either distance (damage falls off past ~500 units) or the known bug where a unit's ATK differs between teams until you re-equip its gear. It is not a random roll.
Q.How do I estimate crit on average (DPS)?▼
Our crit term gives the multiplier of a single critical hit. For average DPS, use the expected value: 1 + Crit Rate × Crit Damage. E.g. 60% crit rate and +140% crit damage → 1 + 0.60 × 1.40 = 1.84.
Q.How do team buffs and debuffs count?▼
The base formula models a single hit, excluding team synergies. 'Damage taken' effects land in the SAME sum as your own damage % bonuses — measured in game, not inferred. Datamined values: King's Mark of the Forest = +2% per stack, i.e. +20% at 10 stacks; Slader's Deep Wound (Bloody Arc) = +25% for 15s, only if the target is Bleeding; First Strike (weapon passive) = +20% to +50% depending on tier. Some are gated by skill category: Tioreh's raises only Normal Skill damage taken. The counter-intuitive part: these debuffs have diminishing returns against your own bucket. Slader's +25% is worth +25% on a bare sheet, but +12.5% if you already have +100% damage, and +8.3% at +200%. In the calculator, enter them under 'Damage Modifier %' — it is the same term.
Q.Am I overstacking my critical damage?▼
Short answer: no, as long as you stay above the target's crit resistance. The multiplier is strictly `1 + (Crit Damage − target crit damage resistance)`, measurement-validated from 0% to 188% resistance (exact pairs ×2.4005 / ×1.5465 / ×1.2731, 2026-08-20 campaign). Below the target's resistance the ×1.00 floor applies: a crit equals a normal hit, and every extra point of Crit Damage pays nothing until you climb back above it. Against Taranis (222.4%), your crits are normal hits — full stop.
Q.Why does my crit chance seem capped at 90 %?▼
Every mob has 10 % baseline Crit Resistance — DB-confirmed (that 10 % is the BASE stat — difficulty and world-level scaling add a flat on top, so elites and field bosses read 15 % in WL3/WL4 and dungeon tiers 15-20 %). At UI 100 % Crit Chance, your effective rate = 100 % − 10 % = 90 % (linear model). The calculator defaults boss Crit Resist to 10 %, and the boss preset adjusts if needed. Server-side caveat: a formal 90 % cap may also exist in the server code. The datamine has `ga_critical_rate_max = 9000` (90 %) AND `battle_max_critical_rate = 10000` (100 % UI display cap). Indistinguishable empirically without Daisy (Electromagnet −20 % Crit Resistance brings a boss to 0 %): if observed crit = 100 % at UI 100 % → no formal cap; still 90 % → server-side cap active.
Q.Why can the calculator diverge from in-game damage?▼
The formula runs on Netmarble's servers — the client sends the action, the server computes, the client displays. The datamine only ships the inputs. Our model is now calibrated by direct measurement (2026-08-20 video campaign: eight bands predicted within ±0.014% on a neutral target, crit law validated from 0 to 188% resistance, defense constant K measured). Remaining gaps come from content mechanics — some bosses carry invisible spawn buffs (the junction Golem: +80% DEF), each target has its own elemental weaknesses — and per-hero kits (passives, per-skill substats). The old "suspected ~120% server cap" is resolved: it was the ×1.00 floor of the crit multiplier.
Scope & honesty
What this page does not cover yet. The formula is measured — these limits describe its edges, not its reliability:
- ◆This is an estimate: rounding creates a margin of a few points.
- ◆Team buffs and synergies are not included in the base formula.
- ◆The defense constant K is now measured in-game (defense plateaus, 2026-08-20); the K/(K+DEF) form remains an approximation outside the measured range.
- ◆The damage formula runs on Netmarble's servers — the client datamine only ships input stats. The crit term is measurement-validated from 0% to 188% crit damage resistance (six points): above your Crit Damage, the multiplier sits on its ×1.00 floor and further Crit Damage pays nothing.
● Defaults = Diane P8, measured within ±0.01%
Set everything to 0 to simulate a training dummy.
| Skill | Mult | Pot | Dmg+ | Dummy | Boss | Net Dmg% | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| No crit | Crit | Avg | No crit | Crit | Avg | ||||||
| 2,260 | 5,425 | 3,969 | 2,260 | 4,796 | 3,376 | 0.0% | |||||
| 86,305 | 207,132 | 151,551 | 86,305 | 183,139 | 128,912 | 39.3% | |||||
| 39,361 | 94,466 | 69,117 | 39,361 | 83,523 | 58,792 | 39.3% | |||||
| 124,805 | 299,531 | 219,157 | 124,805 | 264,835 | 186,418 | 89.3% | |||||
- ◆Aim for a 1:2 CC:CD ratio — for every 1% Crit Chance, target 2% Crit Damage.
- ◆Crit Chance substats are worth ~2x Crit Damage substats in Netmarble's roll weighting.
- ◆Balance your Damage% bucket and Crit Damage — the closer the two values, the less diminishing returns.
?How to use this calculator▼
Model calibrated by direct measurement (2026-08-20 campaign). Defense mitigation K/(K+DEF), K = 5,128, is included via the Defense field. Team synergies and conditional passives are out of scope.