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7DS ORIGIN APPCommunity Database
Mechanics

Damage Formula

How damage is actually calculated in Seven Deadly Sins: Origin — datamined from the game files and validated in combat.

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Limitations

This page is a reconstructed estimate, not an official value. Keep these limits in mind:

  • ◆This is an estimate: rounding creates a margin of a few points.
  • ◆Team buffs and synergies are not included in the base formula.
  • ◆The constant K varies slightly with the attacker's defense penetration.
  • ◆The damage formula runs on Netmarble's server — the client datamine only ships the input stats, not the formula. Our model is empirically validated up to ~116 % boss Crit Damage Resist (Corrupted Ancient Dragon). Beyond that (Abyss-tier raids), a server-side cap or normalization may make the predictions diverge.

The first documented formula

This is how Seven Deadly Sins: Origin actually computes damage. Every term was extracted from the game files and verified in combat. The elemental advantage term (see Validation below) was confirmed via blind prediction within <0.5% of measured. The critical term has been empirically verified across 8 independent tests from UI 85% up to UI 248%, confirming `1 + (UI − boss's crit damage resistance)` linearly with no observed cap.

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.

Damage =
Attacker side
Attack (+ Elemental ATK)ATK + elem. ATKSkill coefficient× Coeff.Attack-type bonus× (1 + Bonus)Critical× Crit.
×multiplied by
Target side
Defense mitigation× K / (K + DEF)Elemental resistance× (1 − Resist)Elemental advantage× (1 + Weakness)

ATK = (Base ATK + Equipment ATK) × (1 + Attack increase). Elemental ATK adds to this total, but only for your character's element.

Each term explained

  1. 1
    Attack (+ Elemental ATK)

    Your total attack. Elemental attack (e.g. Dark Attack) adds to it, but only for your character's element.

  2. 2
    Skill coefficient

    The percentage of attack dealt by the move used (auto-attack, skill, ultimate…).

  3. 3
    Attack-type bonus

    'Normal attack / skill / ultimate damage increase' applies depending on the type of hit.

  4. 4
    Defense mitigation

    K / (K + target Defense). The more defense the target has, the less it takes. K is an attacker-side constant.

  5. 5
    Elemental resistance

    A flat reduction of elemental damage, specific to the target. Bosses gain more as the world level rises.

  6. 6
    Elemental advantage

    Hitting a weakness raises damage (the green arrow); hitting a resistance lowers it. Signed: +2000 weakness = +20%.

  7. 7
    Critical

    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.

  8. 8
    DistanceDatamined · pending

    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.

Three elemental stats — don't mix them up

The element-vs-target interaction has three separate pieces, often confused:

Weakness / advantage

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.

Elemental resistance (%)

A flat percentage reduction of elemental damage on the target. On bosses it rises with the world level.

Flat elemental defense

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.

Bursts & elemental advantage

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.

Stacking & cap

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.

Base hit (on a neutral target)6 906
× Defense mitigation (DEF 3,372)× 0,6274 330
× Elemental resistance (15%)× 0,853 681
× Elemental advantage (Earth weakness +2000)× 1,24 417

Estimated: 4,417. Measured in-game: 4,425 — a 0.2% gap.

💡 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.

Datamined constants

The fixed values pulled from the game files, for theorycrafters.

Apparent crit rate ceiling
Every mob has 10% baseline Crit Resistance (DB-confirmed — field bosses 10%, some elites 15%). UI 100% → 90% observed = emergent effect. Bypassable via debuffs (Daisy Electromagnet −20% Crit Resistance).
90%
Constant K (defense mitigation)
Varies slightly with defense penetration
≈ 5 500–5 700
Elemental advantage scale
Per point of weakness
+1% / 100
Minimum damage reduction
Floor on incoming damage
5%
Elemental advantage cap
Total sum (target + burst + gear) caps here → ×6.00 max on the advantage term
+500%
Crit Chance UI cap
`battle_max_critical_rate = 10000` (100 %) — the hero stat panel clamps to 100 % displayed. The underlying stat might exceed it via stack-exploit (see patch 1.5 Clotho+Merlin), but the UI clamps at 100 %.
100%
Boss CDR effective cap (suspected)
Linear model empirically validated up to ~116 % (Corrupted Ancient Dragon). Beyond (Taranis raw 222.4 %), community observations suggest a ~120 % cap or server-side soft cap. Not verifiable from the datamine — the real formula lives in Netmarble's server code.
≈ 120% ?

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 weaknessPredicted damageActual damageGap
+20004,4174,425+0.2%
03,5993,600+0.0%
−10003,2493,250+0.0%
−20002,6642,652−0.5%

Average error below 0.5%. The elemental-advantage term is thus confirmed across the full spectrum, advantage and disadvantage alike.

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. Many buffs/debuffs are fully independent × (1 + X%) multipliers that stack on top of everything. Two datamined 'damage taken' debuff examples: King's Mark of the Forest = +2% per stack up to ×1.20 at 10 stacks; Slader's Deep Wound (Bloody Arc) = +25% damage taken (×1.25) for 15s. Each multiplies the base hit, on top of crit/weakness/etc.

Q.Am I overstacking my critical damage?

Short answer: no, **within the tested range**. Across 8 tests from UI 85 % to UI 248 % on Storm Bird WL4 (resist 27.8 %), the multiplier is strictly `1 + (UI − boss crit resist)`. No cap observed on that range. But the validation stops at 27.8 % boss resist. On bosses with high Crit Damage Resistance (Corrupted Ancient Dragon 116.1 %, Taranis 222.4 % raw datamine), community observations suggest a cap or normalization that our linear model doesn't capture — most likely computed server-side at Netmarble, invisible to client datamining. Stack freely, but treat the calculator's output as an approximation on those tiers.

Q.Why does my crit chance seem capped at 90 %?

Every mob has 10 % baseline Crit Resistance — DB-confirmed (field bosses 10 %, some elites 15 %). 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 damage formula runs on Netmarble's server — client sends the action, server computes, client displays. The datamine only gives us the **inputs** (boss stats, skill nominal multipliers), not the formula. Our model reverse-engineers the behavior from Halfmind's 8 blind-prediction tests (gap < 0.5 %) and works very well in the validated range (boss CDR ≤ 116 %). Beyond that: possibly a server cap on effective CDR (~120 % suspected from Taranis observations), a soft cap with diminishing returns, or normalization by raid tier. Undetermined from datamine alone — the real formula is in the server code.