# Damage Formula

DMG Formula Parts
Phys (PWR/ATK)
Phys (SPD/ATK)
Phys (INT/M.AT)
Magical

The following is the damage formula given in the official Another Eden World Ultimania book.  This is separate from the Healing Formula. Also rechecked and updated with all new game features and additions to formula by wiki team.

# Damage Formula

## Base Formula:

### Main Formula:

$TotalDamage=(BaseDamage \times ElementalModifier + DamageSpread) \times EnemyResistance$ • ※The minimum allowed value of (BaseDamage * ElementalModifier) is 1 if EnemyDEF exceeds ATK by 2 times for normal hits (or 4 times for critical hits).

### Skill Multipliers:

$\times SkillMultiplier \times SkillDmgUpMultipliers$ ### Buffs, Debuffs Multipliers:

$\times StanceMultiplier \times ResistanceDebuffsTotal \times TypeDMGBuffsTotal$ ### Grasta, Weapons Multipliers:

$\times DmgUpWeaponsAndGrastaTotal \times P\&P\ GrastaMultipliers$ ## Critical Hit Chance

$CriticalHitChance = LCK / 16$ ※By default, only physical attacks are capable of critical hits.

※However, magic attacks can deal critical hits if a character uses an ability or equipment which adds critical rate. For instance, a Power of Sorcery Mind Grasta can be equipped to add a 40% critical hit rate to all magic attacks, while AS Mighty's Meditation skill provides him with guaranteed critical hits for three magic attacks.

## Base Damage

### Physical (PWR/ATK dependent)

Characters who do not use a staff weapon will deal physical damage based on their PWR and ATK.

$BaseDamage =$ $\underbrace{ \left(ATK_{\times pwr\%} - \frac{EnemyDEF}{\dbinom{2_{\ norm}}{4_{\;crit\;\;}}}\right) \times \left(\frac{PWR_{base}}{32} + 1\right) \times \dbinom{1.75_{\ norm}}{3.25_{\;crit\;\;}}}_{BaseDMG}$ ### Physical (INT/M.AT dependent)

Characters who use a staff weapon will deal physical damage based on their INT and M.ATK. Excluding Staff Slam - basic attack skill.

$BaseDamage =$ $\underbrace{ \left(M.ATK_{\times int\%} - \frac{EnemyDEF}{\dbinom{2_{\ norm}}{4_{\;crit\;\;}}}\right) \times \left(\frac{INT_{base}}{32} + 1\right) \times \dbinom{1.75_{\ norm}}{3.25_{\;crit\;\;}}}_{BaseDMG}$ ### Magical

All magic attacks, regardless of weapon, are based on INT and M.ATK. Examples include Joker's Megidolaon skill.

$BaseDamage =$ $\underbrace{ \left(M.ATK_{\times int\%} - \frac{EnemyM.DEF}{\dbinom{2_{\ norm}}{4_{\;crit\;\;}}}\right) \times \left(\frac{INT_{base}}{32} + 1\right) \times \dbinom{1.75_{\ norm}}{3.25_{\;crit\;\;}}}_{BaseDMG}$ ## Elemental Modifier

The Element Modifier is equal to 1 for Null element attacks, otherwise refer to the formulas below. Also, please note that Intelligence buffs have no effect on Element Modifiers.

### Physical (PWR/ATK dependent)

$ElementalModifier =$ $\times \underbrace{\left(\frac{\sqrt{M.AT_{base} * 10 + 16} - 4}{64} + 1\right)}_{ElementalMOD}$ ### Physical (INT/M.AT dependent)

$ElementalModifier =$ $\times \underbrace{\left(\frac{\sqrt{INT_{base} * 10 + 16} - 4}{64} + 1\right)}_{ElementalMOD}$ ### Magical

$ElementalModifier =$ $\times \underbrace{\left(\frac{\sqrt{INT_{base} * 10 + 16} - 4}{64} + 1\right)}_{ElementalMOD}$ ### Physical (PWR/ATK dependent)

$DamageSpread =$ $+ \underbrace{\frac{ATK_{\times pwr\%} * (\overbrace{16\sim47}^{Random})}{25.6}}_{DMG\ Spread}$ ### Physical (INT/M.AT dependent)

$DamageSpread =$ $+ \underbrace{\frac{M.ATK_{\times int\%} * (\overbrace{16\sim47}^{Random})}{25.6}}_{DMG\ Spread}$ ### Magical

$DamageSpread =$ $+ \underbrace{\frac{M.ATK_{\times int\%} * (\overbrace{32\sim94}^{Random})}{25.6}}_{DMG\ Spread}$ ## Skill Multiplier

$\times \underbrace{ \left( \frac{SkillMOD\%}{100\%}\right) }_{Skill\ Multiplier}$ The following are standard multipliers on character skills, they apply to character total damage.:

Single Hit Skills
Basic attack Physical Non-Elemental 100%
Skill Target Skill Type Element Skill S M L XL
Single Target Physical Non-Elemental 150% 170% 190% 210%
Elemental 140% 160% 180% 200%
Magical Non-Elemental 140% 160% 180% 200%
Elemental 130% 150% 170% 190%
AoE Physical Non-Elemental 110% 130% 150% 170%
Elemental 100% 120% 140% 160%
Magical Non-Elemental 100% 120% 140% 160%
Elemental 90% 110% 130% 150%
• Multi-hit skill modifiers when summed up are equivalent to their single hit skill modifiers.
• eg. A non-elemental physical single target skill (150%) multi-hit skill will have a multiplier on each attack of 75% x2 or 50% x3.
• If the number of hits divides unevenly, round the multiplier up.
• eg. Foran's Lightning Stab has a 190% multiplier, but 3 hits = 63.3333...%. This rounds up to 64% x3.
• Some characters have non standard multipliers. Example Tsubame, Elga
• Some characters have double attack skills, as example Single Target XL, plus AoE M Hozuki, Melina with manifest. Or when additional attacks are added from some stacking mechanic: Suzette AS, Akane AS
• In such case each additional attack uses full damage formula with own multipliers, like if several skills were used.

## Enemy Resistance

• When attacking an enemy Weak to your attack,
• Value is 2.0 for magical attacks.
• Value is $\left(\mathrm{M.AT} + \sqrt{2 \cdot \mathrm{M.AT}}\right)\!\!/512 + 1.85$ for Str-based Physical attacks.
• Value is $\left(\mathrm{INT} + \sqrt{2 \cdot \mathrm{INT}}\right)\!\!/512 + 1.85$ for Int-based Physical attacks.
• When attacking a Resistant enemy, value is 0.25.
• When attacking a Absorptive enemy, value is -0.5 (skill heals rather than dealing damage).
• During Another Force, the value is 0.
• When attacking an Ineffective enemy, value is 0.
• When attacking normal enemies, value is 1.

## Other Multipliers of Damage Formula

Every multiplier applies to total damage.

$\times \underbrace{ \left( 1+\frac{SkillEffect\%1}{100\%}\right )\times...\times \left( 1+\frac{SkillEffect\%N}{100\%}\right ) }_{Skill\ DMG+\ Multipliers}$ $\times \underbrace{ \left( 1+\frac{Stance\ DMG\%(+/-)}{100\%} \right )}_{Stance(Zone)\ Multiplier}$ $\times \underbrace{\left(1+\frac{TypeDebuffsDiminished\%}{100\%}+\frac{PhysDebuffsDiminished\%}{100\%}\right) }_{Debuff\ Groups}$ $\times \underbrace{\overbrace{\left(1+\frac{BuffsDiminsished\%}{100\%}\right)}^{Group1}\times...\times \overbrace{\left(1+\frac{BuffsDiminished\%}{100\%}\right)}^{GroupN}}_{Buff\ Groups}$ $\times \underbrace{ \left( 1+\frac{Weapon\ Dmg\%+}{100\%}+ \frac{Grasta1\ Dmg\%+}{100\%} + ... + \frac{Grasta3\ Dmg\%+}{100\%} \right) }_{DMG+\ Weapons,Grasta}$ $\times \underbrace{ \underbrace{\overbrace{1.3}^{Poison1}}_{Pain1}\times...\times \underbrace{\overbrace{1.3}^{Poison3}}_{Pain3} }_{Poison,Pain\ Grasta}$ • Buffs or Debuffs of the same group, stack with diminishing returns:
Formula for Diminished returns is: 1 + A% + (A x B%) + (A x B% x C%), where A is the highest value.
• Same group isBuffs or Debuffs with same name of effect.
• Fire resistance debuff of 1 char and Fire resistance debuff of 2nd char
• PWR Buff + PWR Buff..
• Additional groups of same type:
• Type resistance Buff, + Fire\Wind\Water\Earth res Buffs. Also they all decrease Null magic damage.
• Type resistance Debuff + Fire\Wind\Water\Earth res Debuffs. Also they all increase Null magic damage.
• Type damage Buff + Fire\Wind\Water\Earth damage Buffs.
• Physical resistance Buff + Pierce\Blunt\Slash res Buffs
• Physical resistance Debuff + Pierce\Blunt\Slash res Debuffs.
• Buffs\Debuffs with stacks (30% max stack: x3-5). Usually stack base+half+half... ex. 30+15+15=60%. There are exceptions: Lovely
• Combining stacked Buff\Debuff with Buff\Debuff of same group results it's total number to be used in diminishing returns formula. (60% from above ex.)
• Crit damage up buffs stack additively: 50% + 30% + 50% = +130% = x2.3 Multiplier
• Skill effect multipliers: Possible effects present on skills divide to:
• Effect with Icon are Buffs and Debuffs, they can affect damage from other skills of characters.
• Icon on party members, it adds to Buff Multiplier of that specific Buff type.
• Icon on enemies,it adds to Debuff Multiplierof that specific Debuff type.
• Effect without Icon, present only in description, it affects this skill only. It is Skill Effect Multiplier
• Buffs, Debuffs, Skills Effects are 3 different multipliers, that are multiplicative with each other.
• Example of calculation:
• Water Zone in Effect +50% water damage.
• Myunfa uses Crit DMG +50% VC
• Dewey with manifest(unreleased) uses Mist Blast Crit DMG +50%.
• Shanie (Another Style) uses Wasserfall with one stack, that increases her Normal damage +100%, and Crit damage +100% from normal. Also she has Water Type damage Buff +30% on her. She Crits with this attack.
• Damage Calculation here is only for Multipliers, doesn't include Base formula, elemental mod, etc.
• 200%(XL ST) x ~2.25 (critical) x 2 (skill effect: normal damage) x2 (skill effect: critical damage) x 2 (buffs: ) x 1.5 (zone) x 1.3 (buffs: water damage) = ~7020% damage