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

Weapon damage bonuses, such as level up, stamp and enchantment bonuses, are applied 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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$weaponDamage={\frac {baseWeaponDamage}{100\%}}\cdot \left(1+{\frac {attackStampBonus}{100\%}}\right)\cdot \left(1+{\frac {soloStampBonus}{100\%}}\right)\cdot \left(1+{\frac {attackEnchantmentBonus1}{100\%}}\right)\cdot \left(1+{\frac {attackEnchantmentBonus2}{100\%}}\right)\cdot \left(1+{\frac {levelBonus1}{100\%}}\right)\cdot \left(1+{\frac {levelBonus2}{100\%}}\right)\cdot \left(1+{\frac {levelBonus3}{100\%}}\right)\cdot \ldots$

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

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$enhancementBonus={\frac {0.2+{\frac {MAX(1,blacksmithsGearLevel)-1}{2}})\cdot weaponEnhancements}{splitCount}}$

enhancementBonus = ((0.2 + (blacksmithsGearLevel - 1) / 2) * 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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$growtBonus={\frac {0.01\cdot growthLevel\cdot playerLevel\cdot {\frac {max(4,hitCD)}{20}}}{splitCount}}$

growtBonus = (0.01 * growthLevel * playerLevel * 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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$totalATK=baseATK+(bonus1+bonus2+bonus3+\ldots )$

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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$damageMod=\left(1+{\frac {totalCritMod}{100\%}}\right)\cdot bonusDamageTaken\cdot DB\cdot DR\cdot DevilHat$

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

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.

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

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

Bonus damage taken

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

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

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 give DB are expressed in a multiplier form in the game text, rather than a percentage form. These modifiers stack additively with each other.

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

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

List of affects that modify DB

Effect	Type	Character
Gorilla's Paw	Item	-
Face Mask	Item	-
Candy Kingdom Sweets	Item	-

Damage reduction

Damage reduction (or damage received) 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.

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

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
Slumber	Skill	Anya Melfissa
Hatotaurus	Special Attack	Ookami Mio
Body Pillow	Item	-
Membership	Item	-
Breastplate	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. Currently the exact order in which the game applies these effects is unknown but the table below lists them in the order in which they appear in the game code which is the current best guess as to the order they are applied.

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 applying On-Hit Damage

Effect	Type	Character	Rounding Type
Unit Stamp	Stamp	-	Round
The Forbidden Wah	Skill	Ninomae Ina'nis
Cleaning Broom Awakened	Weapon	Minato Aqua
Klutz	Skill	Minato Aqua
Duck Whisper	Skill	Oozora Subaru	Floor
Piki Piki Piman	Item	-	Floor
No Pressure	Skill	Kaela Kovalskia	Round
Ninja Headband	Item	-	Floor
Beetle	Item	-	Floor
Secret Agent	Skill	-
Cheerful Laugh	Skill	Ookami Mio	Floor
Devil Hat	Item	-	Floor

External links

• Damage calculator for Update 0.6 by ctom42