Damage Formula Reference

Master Formula

Damage = Base × DamageBonus × CRIT × Defense × Resistance × StainVuln × FinalBonus × Special

Each zone is independent — they multiply together. Displayed damage is rounded down. The game caps damage at 9,999,999.

Multiplier zones apply both ways — to characters dealing damage and to enemies dealing damage to characters. Co-op scales enemy stats: enemy Max HP is ×1/1.75/2.5/3.25 for 1/2/3/4 players, ATK is ×1/1.2/1.4/1.6, and Max Break is ×1/2/3/4.

1.1

Base Damage Zone

Base = Σ(DamageMultiplier × CorrespondingStat) + ExtraDamageValue

Skill multipliers default to ATK; some skills add Max HP or DEF multipliers (shown directly on the character stat panel).

Damage Multiplier (with buffs)

DamageMultiplier = OriginalMultiplier × (1 + BoostRate)

ATK composition

ATK = (BaseATK + WeaponATK) × (1 + ATK%) + FlatATK

Same shape for Max HP and DEF. Base stats and weapon ATK are integers; only the % bonuses need precision.

Extra Damage Value currently only appears on Chiz's "Pink Paws Priority Principle" — flat per-Grain bonus damage independent of ATK/HP/DEF.

1.2

Damage Bonus Zone

Bonus = 1 + Universal + DamageType + DamageSource + Other − DamageDealtReduction

Covers every in-game effect labelled Damage Enhancement / Buff / Increase / Bonus. Types include the 6 elements (Lakshana, Anima, Chaos, Psyche, Cosmos, Incantation), plus Normal, Mental, and True. Sources include Normal Attack, Skill, Ultimate, Support Skill, Plunging Attack, Critical Riposte, Buff Damage, Basic Attack Combo, Passive, Esper Cycle, Typeless.

Normal applies to attribute-less damage (e.g. car crashes). Mental ignores defense; True bypasses almost every multiplier zone. Aside from the Nova Esper Cycle, only Fadia's Ultimate currently deals Mental damage.

1.3

CRIT Zone

CRIT = 1 + CRIT_DMG (on critical hit)

CRIT = 1 (otherwise)

Expected (weighted by rate)

ExpectedCRIT = 1 + CRIT_Rate × CRIT_DMG

Character base CRIT Rate is 5%, base CRIT DMG is 50%. Enemies default to 0. Fixed-CRIT-rate effects (Scorch DoT, Adler's skill DoT, Requiem's Nightmare, Bai Zang's DoT) all use a fixed 50% rate.

1.4

Defense Zone

Defense = 1 (if damage is Mental or True)

Defense = AttackerLevelBase / (EffectiveDEF + AttackerLevelBase)

Attacker level base

AttackerLevelBase = 600 + 6 × AttackerLevel

Defender effective DEF (vs enemy attacks)

EffectiveDEF = [BaseDEF × (1 + DEFBoost − DEFShred) + FlatDEF] × (1 − AttackerIgnoreDEF%)

Enemy effective DEF (when characters attack)

EnemyEffectiveDEF = EnemyBaseDEF × (1 − EnemyDEFShred) × (1 − CharacterIgnoreDEF)

Enemies have no DEF-boosting effects. Default enemy base DEF curve: 600 + 6 × EnemyLevel — but in practice enemies are tuned individually (e.g. Beyond the Rails enemies use values equivalent to 10 levels lower).

1.5

Resistance Zone

Resistance = 1 − EsperRes (if EsperRes ≥ 0)

Resistance = 1 − EsperRes / (1 − EsperRes) (if EsperRes < 0)

EsperRes = OriginalRES − IgnoreRES − RESShred

Applies to elemental, Mental, and Normal damage. Enemies have a default 20% RES (some have 28%) to all elements. Weak-element RES is lowered (default 10% or 16%, often 0% in dungeons).

1.6

Stain Vulnerability Zone

StainVuln = 1.2 × [ 1 + (0.2 × CycleIntensity) / (CycleIntensity + 180) ] (when Stain is active)

The base ×1.2 Stain multiplier is multiplied by the intensity curve, not added. The zone approaches ×1.44 as Cycle Intensity → ∞. At CI = 0 the zone is exactly ×1.2.

Stain is the Lakshana + Psyche cycle and only amplifies Lakshana / Psyche damage taken.

1.7

Final Damage Bonus Zone

FinalBonus = 1 + FinalDamageBoost

For effects that increase damage but don't fit the standard Damage Bonus zone (e.g. Sakiri's Scorch enhancement: "DoT damage taken increases by 25% per DoT type on target"). Different Special Multipliers are calculated independently and multiplied together.