Damage

OutdatedThis article or section contains information that is **out of date**.**Reason:** 0.6 changed calculation of enhancements and growth for multi-attack weapons and added new modifiers
Please replace the old information with up to date information.
**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.

## Calculating damage

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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{\displaystyle 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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{\displaystyle randAttackDamage = attackDamage - random(max((attackDamage \cdot 0.1), 2)) + random(max((attackDamage \cdot 0.2), 4)
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`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.

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{\displaystyle totalDamage = round(randAttackDamage \cdot damageMod)
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`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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{\displaystyle totalWeaponDamage = ((0.2 + blacksmithsGearBonus) \cdot weaponEnhancements + weaponDamage + 0.02 \cdot playerLevel)
 }

`totalWeaponDamage = ((0.2 + blacksmithsGearBonus) * weaponEnhancements + weaponDamage + 0.02 * playerLevel)`
Damage 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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{\displaystyle 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%) * ...`
There are some additional character abilities that modify weapon damage in the same manner as any of the modifiers above. Each of these abilities only has specific weapons they can modify.

List of additional abilities that modify weaponDamage
Elite Cooking
Broken Dreams
Eldritch Horror
 1. ↑ EN's Curse Lvl 7 has a 10% damage boost that stacks multiplicatively with itself every time the attack chains.

## 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 modifier and all ATK bonuses from items and the character's skills. ATK bonuses stack additively.

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{\displaystyle totalATK = baseATK + (bonus1 + bonus2 + bonus3 + \ldots)
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`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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{\displaystyle damageMod = \left(1 + \frac{totalCritMod}{100%}\right) \cdot bonusDamageTaken \cdot DB\cdot DR\cdot DevilHat
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`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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{\displaystyle totalCritMod = baseCritMod + (critMod1 + critMod2 + critMod3 + \ldots)
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`totalCritMod = baseCritMod + (critMod1 + critMod2 + critMod3 + ...)`

List of effects that modify critical damage
 ATK Up Stamp | Stamp

### Bonus damage taken

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

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{\displaystyle bonusDamageTaken = 1+\frac{bonus1 + bonus2 + bonus3 + \ldots}{100%}
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`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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{\displaystyle DB = 1 + (bonus1-1) + (bonus2-1) \ldots
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`DB = 1 + (bonus1-1) + (bonus2-1) ...`

List of affects that modify DB
 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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{\displaystyle DR = \left(1-\frac{reduction1}{100%}\right) \cdot \left(1-\frac{reduction2}{100%}\right) \cdot \left(1-\frac{reduction3}{100%}\right) \cdot \ldots
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`DR = (1 - reduction1/100%) * (1 - reduction2/100%) * (1 - reduction3/100%) * ...`

### Devil Hat

Devil Hat is a unique multiplier to the Devil Hat item that deals with proximity to the target. If the target is within 130px, the multiplier is 0.9. If they are 130px or further from the character, then the multiplier is 1.2/1.4/1.6, depending on its level.

It is worth noting that Kusogaki Shackles only lessens the penalty multiplier from being within 150px but it does not change the range requirement for switching to the positive multiplier.

## Other

There are a few adjustments to damage that don't fit neatly into the other categories. Some of these are due to bugs in the game's code while others are one off abilities that only affect a single damage source or a single character. The table below lists these unique damage situations, and more information about each one can be found on the individual pages of those effects.

1. ↑ 1.0 1.1 1.2 /u/ctom42. Holocure Damage Formula Deep Dive.