How the game works out a hit

GODDESS OF VICTORY: NIKKE damage formula

A critical hit, a core hit, the weapon's range bonus and Full Burst don't multiply each other. They add into one bonus, so all four at once deal 3.3 times a plain hit, not 5.85. Element advantage and charge multiply on top of that.

The formula

damage = (ATK - DEF) × skill or shot ratio
       × (100% + crit + core + range + Full Burst)
       × element × charge
       × (100% + damage up)
       × (100% - target's damage reduction)

The first line is the hit before bonuses: the Nikke's ATK minus the target's DEF, times the shot's or skill's ratio, split across its pellets or projectiles. True Damage skips the DEF part.

Each bracket is a sum, and only the brackets multiply. A buff to Critical Damage or core damage makes its term bigger inside the first bracket, which already holds the others, so it adds less than its number suggests. Attack Damage, Pierce Damage, Parts Damage, True Damage and Sustained Damage buffs all share the second bracket in the same way. A hit always deals at least 1.

The bonus bracket

BonusAddsWhen it applies

Critical hitAdds: +50%When it applies: 15% of hits by default. Critical Rate buffs raise the chance and Critical Damage buffs the bonus.
Core hitAdds: +100%When it applies: Hitting a Rapture's core. 12 SMGs add +150% instead (listed below), and core damage buffs add on top.
Range bonusAdds: +30%When it applies: Firing from inside the weapon's best range. Each Nikke has her own band, set by her weapon.
Full BurstAdds: +50%When it applies: While Full Burst is up, 10s for most Nikkes. Burst stages I to III add nothing on their own.

Core hits add +150% for Aigis, Miranda, Soline, Crow, Epinel, Mica: Snow Buddy, Alice: Wonderland Bunny, Clay, Quency: Escape Queen, Little Mermaid, Chisato Nishikigi and E.H.

Element

Every Nikke and every Rapture has a code. Hitting the code yours beats multiplies damage by 110%, and Elemental Advantage Damage buffs add to that 10% rather than multiplying it. There's no penalty the other way: hitting a code that beats yours deals normal damage.

The cycle runs Water beats Fire beats Wind beats Iron beats Electric, which beats Water.

CodeStrong againstWeak to

FireStrong against: WindWeak to: Water
WaterStrong against: FireWeak to: Electric
WindStrong against: IronWeak to: Fire
ElectricStrong against: WaterWeak to: Iron
IronStrong against: ElectricWeak to: Wind

Weapons

Sniper Rifles and Rocket Launchers charge: a full charge multiplies the hit (by 250% for most), and Charge Damage buffs raise that multiplier. The others fire as long as you hold. The usual numbers for each weapon type:

WeaponAmmoReloadChargeFull charge

Assault RifleAmmo: 60 (9 to 90)Reload: 1sCharge: None
SMGAmmo: 120Reload: 1sCharge: None
ShotgunAmmo: 9 (5 to 9)Reload: 1.5sCharge: None
Sniper RifleAmmo: 6Reload: 2sCharge: 1sFull charge: 250%
Rocket LauncherAmmo: 6 (6 to 120)Reload: 2sCharge: 1sFull charge: 250%
Machine GunAmmo: 300Reload: 2.5sCharge: None