Damage

Damage is the means of depleting a unit's health. The damage from an attack - weapon, Special Attack or skill - depends on the character's or target's attack/weapon strength and various damage modifiers, such as ATK stat and damage taken debuffs.

Overview

The amount of damage dealt is calculated via the following procedure:

First, the base damage is calculated from the weapon damage and the character's ATK:

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$attackDamage=10\cdot totalWeaponDamage\cdot \frac{totalATK}{100\%}$

attackDamage = 10 * totalWeaponDamage * totalATK/100%

Then randomization is added to the base damage if the base damage is greater than 2. This will result in the new value being within ±10% range of the base value if the base damage is higher than 20 or ±2 damage if base damage is less than 20:

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$randAttackDamage=attackDamage-random(max((attackDamage\cdot 0.1),2))+random(max((attackDamage\cdot 0.2),4)$

randAttackDamage = attackDamage - random(max((attackDamage * 0.1), 2)) + random(max((attackDamage * 0.2), 4)

Lastly the value is multiplied by damage modifiers and rounded to closest integer. In the case of a result that ends in .5 the rounding is to the nearest even integer.

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$totalDamage=round(randAttackDamage\cdot damageMod)$

totalDamage = round(randAttackDamage * damageMod)

Weapon damage

The damage dealt by a weapon or an attack depends on its base damage modifier, enhancements applied to a weapon beyond its max level and the Growth bonus to the character's main weapon or special attack.

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$totalWeaponDamage=weaponDamage+enhancementBonus+growthBonus$

totalWeaponDamage = weaponDamage + enhancementBonus + growthBonus

Weapon damage bonuses

Some attacks have effects that add directly to the base weapon damage of that attack.

List of effects that add to baseweaponDamage

Effect	Type	Weapon Specific	Character
Knight's Dance	Skill	Knight's Dance	Shirogane Noel
Rocket Launcher Awakened	Weapon	Rocket Launcher Awakened	Usada Pekora

Weapon damage bonuses, such as level up, stamp and enchantment bonuses, are multiplied directly to weapon's base damage. The bonuses from Level Ups stack multiplicatively with each other and the base weapon damage. The bonuses from stamps and enchantments are also applied to the base weapon damage.

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$weaponDamage=\frac{baseWeaponDamage}{100\%}\cdot (1+\frac{attackStampBonus}{100\%})\cdot (1+\frac{soloStampBonus}{100\%})\cdot (1+\frac{attackEnchantmentBonus1}{100\%})\cdot (1+\frac{attackEnchantmentBonus2}{100\%})\cdot (1+\frac{levelBonus1}{100\%})\cdot (1+\frac{levelBonus2}{100\%})\cdot (1+\frac{levelBonus3}{100\%})\cdot \dots$

weaponDamage = baseWeaponDamage/100% * (1 + attackStampBonus/100%) * (1 + soloStampBonus/100%) * (1 + attackEnchantmentBonus1/100%) * (1 + attackEnchantmentBonus2/100%) * (1 + levelBonus1/100%) * (1 + levelBonus2/100%) * (1 + levelBonus3/100%) * ...

Enhancement bonus

Enhancement bonus is a flat damage bonus applied to weapons using an Anvil's "Upgrade" option on a max level weapon, increasing the weapon's base damage for each successful enhancement. The bonus are split based on the number of attacks in the weapon's main attack sequence, including additional projectiles Projectile Up Stamp, Klutz, or the +1 Projectile enchantment. This value is referred to as splitCount

Some weapons have a custom splitCount that is hard coded which ignore extra projectiles and projectile count. Below is a table of these weapons and their splitCounts

Additionally, levels 2 and 3 of Blacksmith's Gear provide a multiplier to the enhancement bonus

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$enhancementBonus=\frac{(0.2+\frac{max(1,blacksmithsGearLevel)-1}{20})\cdot weaponEnhancements}{splitCount}$

enhancementBonus = (0.2 + ( max(1, blacksmithsGearLevel) - 1) / 20) * weaponEnhancements) / splitCount

Growth bonus

Growth is flat damage bonus that only applies to the character's main weapon's or Special Attack's damage. Similarly to enhancements, the bonus is divided by the number of the attacks in the weapon's attack sequence. Additionally, if the attack's hit cooldown is less than 20, the growth bonus is gradually reduced to a minimum of 20%.

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$growthBonus=\frac{0.01\cdot growthLevel\cdot playerLevel\cdot \frac{min(20,max(4,hitCD))}{20}}{splitCount}$

growthBonus = (0.01 * growthLevel * playerLevel * min(20, max(4, hitCD))/20) / splitCount

ATK

The damage dealt by a character is most notably modified by their ATK-stat. The characters total ATK is the sum of their base ATK stat and all ATK bonuses from items and the character's skills. ATK bonuses stack additively.

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$totalATK=baseATK+(bonus1+bonus2+bonus3+\dots )$

totalATK = baseATK + (bonus1 + bonus2 + bonus3 + ...)

Damage modifiers

Damage modifiers are multipliers to the attack's damage. Damage modifiers generally stack multiplicatively with each other and additively with other effects of the same type.

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$damageMod=(1+\frac{totalCritMod}{100\%}\cdot BonusCritDamage)\cdot bonusDamageTaken\cdot DB\cdot SkillDamage\cdot DR$

damageMod = (1 + totalCritMod/100% * BonusCritDamage) * bonusDamageTaken * DB * SkillDamage * DR

Critical hits

Critical hits multiply the damage dealt based on their critical damage modifier, if triggered. By default each character's critical damage modifier is 50%, meaning that their critical hits deal 1.5x damage. Some abilities can change the character's or the weapon's critical hit modifier.

Critical damage modifiers from different sources stack additively with each other. Critical damage modifiers that effect all damage are summed together as CRT Damage in the pause menu. CRT Damage does not include baseCritMod.

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$totalCritMod=baseCritMod+(critMod1+critMod2+critMod3+\dots )$

totalCritMod = baseCritMod + (critMod1 + critMod2 + critMod3 + ...)

totalCritMod is only relevant to the damage calculation if your hit is a critical hit. On a regular hit, totalCritMod is 0. If you are looking for average damage you can multiply totalCritMod by CRT/100% before using it in the damageMod calcualation.

List of effects that modify critical damage

Effect	Type	Character
The Ame Way	Skill	Amelia Watson
Rat's Ninja Way	Skill	Hakos Baelz
Chocotto Cooking	Skill	Yuzuki Choco
Lady Of The Peafowl	Skill	Pavolia Reine
The Reaper	Special Attack	Mori Calliope
Axe Swing Awakened	Weapon	Hoshimachi Suisei
Hope Soda	Item	-
ATK Up Stamp	Stamp	-
Crit Damage +10%	Enhancement	-

Bonus Crit Damage

When a player character gains CRT above 100% the excess is converted to Bonus Crit Damage.

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$BonusCritDamage=1+(\frac{Crit\%-100}{200})$

BonusCritDamage = 1 + ((Crit% - 100)/200)

Bonus damage taken

Bonus damage taken modifiers are applied by debuffs. Bonuses of this type stack additively with each other.

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$bonusDamageTaken=1+\frac{bonus1+bonus2+bonus3+\dots }{100\%}$

bonusDamageTaken = 1+((bonus1 + bonus2 + bonus3 + ...) / 100%)

Damage bonus

Damage bonus (DB) is a separate variable from bonus damage taken. Instead of being based on debuffs on enemies, these effects directly boost the character damage. Currently, all effects that modify DB are expressed in a multiplier form in the game text, rather than a percentage form, with the exception of Slumber. These modifiers stack additively with each other.

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$DB=1+(bonus1-1)+(bonus2-1)\dots$

DB = 1 + (bonus1-1) + (bonus2-1) ...

List of effects that modify DB

Effect	Type	Character
Slumber	Skill	Anya Melfissa
Holy Fire	Weapon	-
Gorilla's Paw	Item	-
Face Mask	Item	-
Candy Kingdom Sweets	Item	-

Skill Damage

Several effects in the game boost damage for skills. These effects are additive with each other and serve as a multiplier on damage for valid skills. Skills that copy damage from another source do not work with skill damage.

List of effects that Skill Damage

Effect	Type	Character
GWS Pill	Item	-
Super Injection Type Asacoco	Item	-
Skill Up	Upgrade	-
Fan Letters	Fan Letter	-

Damage reduction

The damage reduction modifier is comprised of the various reductions to the damage the target receives from the attacker. This type of modifiers exceptionally stack multiplicatively with each other. Currently only damage dealt to the player is impacted by this modifier but since the game uses the same formula for dealing damage to the player as it does for dealing damage to enemies, this variable is included.

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$DR=(1-\frac{reduction1}{100\%})\cdot (1-\frac{reduction2}{100\%})\cdot (1-\frac{reduction3}{100\%})\cdot \dots$

DR = (1 - reduction1/100%) * (1 - reduction2/100%) * (1 - reduction3/100%) * ...

List of effects that modify damage received

Effect	Type	Character
Endurance	Skill	Inugami Korone
Worldwide Strongest Idol	Skill	Akai Haato
Hoshinova & Moona	Skill	Moona Hoshinova
Slumber	Skill	Anya Melfissa
Muscle	Skill	Shirogane Noel
Hatotaurus	Special Attack	Ookami Mio
Body Pillow	Item	-
Membership	Item	-
Breastplate	Item	-
Face Mask	Item	-
Defense Up	Upgrade	-

On-hit damage

Some sources apply damage as an on-hit effect. These on-hit effects are all multipliers that are applied after totalDamage is calculated. Some of these effects have their own rounding or flooring of the damage that they apply, so the order in which the effects are applied in the damage formula makes a difference. The order in which on-hit effects are applied is non-deterministic.

After all applicable on-hit affects are applied the final damage is rounded one last time. All rounding both by on-hit effects and by this last step follows the same rule for numbers ending in .5.

List of effects that apply on-hit damage

Effect	Type	Character	Rounding Type
The Forbidden Wah	Skill	Ninomae Ina'nis	-
Cheerful Laugh	Skill	Ookami Mio	Floor
Duck Whisper	Skill	Oozora Subaru	Floor
Cleaning Maid	Skill	Minato Aqua	-
No Pressure	Skill	Kaela Kovalskia	Round
Secret Agent	Skill	Vestia Zeta	-
GMMF	Skill	Kiryu Coco	?
Apex Shooter	Skill	Tokoyami Towa	?
Cleaning Broom Awakened	Weapon	Minato Aqua	-
Beetle	Item	-	Floor
Devil Hat	Item	-	Floor
Ninja Headband	Item	-	Floor
Piki Piki Piman	Item	-	Floor
Unit Stamp	Stamp	-	Round

Direct damage

A few effects in this game deal damage directly rather than going through the full damage calculation. Most of these effects copy damage from a triggering source and modify it in some manner. In the case of direct damage all of the steps of the damage calculation are skipped except for on-hit effects.