Damage Formula

The **Damage Formula** is a part of the core game mechanics of *Octopath Traveler*.

## Simplified Formulas

The various skill pages of this wiki display simplified formulas that include only information that vary between each skill, such as its base damage or how much of the opponents defense it ignores. Various other information, such as your character level, is listed below in Other Multipliers.

### Damage

Damage formulas are displayed using the following template:

Damage = **[Base Damage Multiplier]** x [*Attacker Atk* - (*Target Def* x **[Defense Multiplier]**)]
**Boost**: Damage increases by **+[Boost Bonus]%** per boost
This is a simplified damage formula that provides only four key pieces of information:

1. Base Damage Multiplier: This is a constant value for each skill.
2. Whether the attacker increases the damage in proportion to their Physical Attack stat or Elemental Attack stat; likewise, whether the target decreases the damage in proportion to their Physical Defense stat or their Elemental Defense Stat. Damaging Skills are categorized as either Physical Attacks or Elemental Attacks, with the former applying Physical Attack and Elemental Defense and the latter applying Elemental Attack and Elemental Defense. Healing Skills increase the healing in proportion to the Healers Elemental Defense.
3. Defense Multiplier: This is a constant value for each skill, and determines how much of the targets defensive stat (either Physical Defense or Elemental Defense) actually reduces the damage of the ability.
4. Boost Bonus: This determines how much the damage of the ability increases for each level of boost. This is expressed as a percentage, and it stacks additively with itself to form a sort of damage multiplier. For instance, a skill with a +90% Boost Bonus does 100%/190%/280%/370% damage at boost level none/x2/x3/Max. Note that due to bugs, some skills gain slightly more or less damage at various boost levels.

This does not factor in additional multipliers (see Other Multipliers).

### Standard Attacks

Standard attacks are made with +20 hit ratio over standard attacks and deal the following damage:

Damage = **0.8** x [*Attacker P.Atk* - (*Target P.Def* x **0.5**)]
**Boost**: Make **+1 attack** per boost, hitting an additional time.
Thus, an attacker with 400 physical attack striking a foe with 300 physical defense with a standard attack deals 0.8 x [400 - (300 x 0.5)] = 200 base damage per hit. This is additionally scaled by a number of damage multipliers.

Counterattacks (such as from  or the Counterattack buff), as well as followup attacks (such as from ) also use the Standard Attack formula.

### Healing Formula

This is used specifically for Recovery Skills, whose healing depends on the skill users Elemental Defense stat; Items and Concoctions, on the other hand, restore a specific amount (usually a flat value) which is dependent upon the item used.

Healing = **[Base Healing Multiplier]** x *Healer E.Def*
**Boost**: Healing increases by **+[Boost Bonus]%** per boost
This template includes three key pieces of information:

1. Base Healing Multiplier: Unique value for each healing skill.
2. Healer Elemental Defense: All healing skills scale the amount healed based on the healers Elemental Defense. This does **not** include Increased Elemental Defense, as that skill does not directly increase Elemental Defense.
3. Boost Bonus: An amount unique to each boost bonus. This is expressed as a percentage, and it additively increases the healing of the skill. For instance, a skill with a +30% boost bonus heals 100%/130%/160%/190% at boost level none/x2/x3/Max.

## Other Multipliers

### Damage Multipliers

The following multipliers apply to all kinds of damage, whether from skills, talents, or what have you.

* Crit Multiplier: Equal to x1.0 by default, but if the attack is a critical hit, it becomes x1.25.
	+ Chance of critical hit is derived from your Critical stat (see Critical Hit)
	+ guarantees critical hits for elemental attacks
	+ guarantees critical hits for standard attacks and physical attack skills
* Weakness Multiplier: Damage bonuses received for striking using an attack type the target is weak to, or for striking broken targets (Broken multiplier overrides and replaces Weakness multiplier)
	+ Broken Target: x2.0
	+ Weakness vs. Unbroken Target: x1.3 (or x1.5 if the attacking character has )
	+ None of the above: x1.0
	+ Note: Use the highest value that applies
* Level Scaling Multiplier: Varies between x0.5625 and x1.4063 based on the attackers level; see Level Multiplier for a table.
* Support Skill Multiplier: All the multipliers provided by all relevant Support Skills, for example:
	+ : up to x3 damage at 1 HP
	+ : x1.5 for all skills that use the attackers Elemental Attack
	+ : x1.2 for all skills that use the attackers Elemental Attack
	+ Note: if more than one applies, all such values stack multiplicatively with each other
* Buff/Debuff Multipliers: Various buffs and debuffs that modify damage. These buffs do not increase your stats, but rather are factored in explicitly as multipliers.
	+ Increased Physical Attack and Increased Elemental Attack on attacker: x3/2 (x1.5)
	+ Decreased Physical Attack and Decreased Elemental Attack on attacker: x2/3 (x0.66..)
	+ Increased Physical Defense and Increased Elemental Defense on target: x2/3 (x0.66..)
	+ Decreased Physical Defense and Decreased Elemental Defense on target: x3/2 (x1.5)
	+ Note: if more than one applies, all such values stack multiplicatively with each other
* Elemental Bonuses: This is the multiplier that is provided by equipment which increase/decrease the damage of elemental attacks. The equipment indicates whether it applies to damage you inflict or damage you receive.
	+ "greatly reduces damage taken" on accessory/armor = x0.01 (e.g. )
	+ "reduces damage taken" on accessory/armor = x0.5 (e.g. )
	+ "slightly reduces damage taken" on armor = x0.75 (e.g. )
	+ "increases damage dealt" on weapon = x1.3, or x1.6 if two are equipped (e.g )
	+ "decreases damage dealt" on weapon = x?? (e.g. )
	+ Note: It is unknown whether multiple damage-reducing accessories for the same element stack together
* Random Multiplier: This is a random number between x0.98 and x1.02; essentially, all skills randomly deal between 98% and 102% of damage.

### Healing Multipliers

The following multipliers apply to various sources of healing.

* Level Scaling Multiplier: Varies between x0.5625 and x1.4063 based on the healers level; see Level Multiplier for a table. Applies only to HP recovery skills.
* Support Skill Multiplier:
	+ x1.3 if Heightened Healing is equipped (applies to *all* sources of healing, including SP healing and from items).
	+ x1.0 otherwise
* Random Multiplier: This is a random number between x0.98 and x1.02; essentially, all HP healing skills randomly heal between 98% and 102% of damage. Applies only to HP recovery skills.

## Full Damage Formula

The full damage formula used within the code of Octopath Traveler has been simplified in this wiki and need not be learned. For reference, it is as follows.

Damage = (*Attack Value* - [*Defense Value* x *Defense Ratio* / 2] ) x (*Invocation Ratio* / 100) x (*Ability Ratio* / 100) x *Other Multipliers*

Note that the simplified damage formula rearranges and precalculates various values. See Other Multipliers for the remainder of the multipliers.

### Attack Value

If the attack is a standard attack or Physical Attack Skill, this is the attackers **Physical Attack** stat. Conversely, if it is an Elemental Attack Skill, it is the attackers **Elemental Attack** stat.

### Defense Value and Defense Ratio

[*Defense Value* x *Defense Ratio* / 2]
* Defense Value: This is the corresponding defense counterpart of the target, similar to *Attack Value*; for physical attacks, it's **Physical Defense**, while for elemental attacks, it's **Elemental Defense**.

* Defense Ratio: This varies based on the skill being used; most skills modify the effective defense value of the target, with more powerful single-target skills penetrating more defense. For instance, 's defense ratio is 0.8, as in only 80% of the targets physical defense is applied; the remaining 20% is ignored. Some skills have a defense ratio of *above* 1.0, causing them to treat enemy defense as if it were higher than normal. For instance,  has a defense ratio of 1.25.

Note also the division by 2 in the above formula; this has the effect of causing all skills to ignore half the enemies defense by default. In the simplified damage formula used within the skill descriptions of this wiki, this division by two is already combined with the defense ratio; for instance,  is listed as having a defense multiplier of 0.4 (because 0.8 x 0.5 = 0.4). Similarly,  is listed as having a defense multiplier of 0.625 (because 1.25 x 0.5 = 0.625).

### Invocation Ratio

(Invocation Ratio/100)
This is a value that depends on the skill being used, and is roughly analogous to the "base damage multiplier" of a skill. This is then divided by 100.

On each skill page, this (along with **Ability Ratio**) is already combined into a single "Base Damage" value. For instance, the skill  has an Invocation Ratio of 150 and an Ability Ratio of 100 while unboosted; this is listed on the wiki as having a 1.5 base damage multiplier (because 150/100 x 100/100 = 1.5).

### Ability Ratio

(Ability Ratio / 100)
This is a value that depends on the skill being used, and is roughly analogous to the "boost multiplier" of a skill. It is divided by 100, much like Invocation Ratio. It increases by a specific amount each level of boost. While the vast majority of skills increase by a constant amount, due to bugs/typos by the developers a small handful of skills increase by different amounts. For instance,  has an Ability Ratio of 80/152/226/298 at boost levels None/x2/x3/Max, respectively; this is an increase of +72/+74/+72, which translates to +90%/+92.5%/+90% of the base Ability Ratio of 80. The vast majority of multi-attack skills increase by 90% per boost, so the lv 3 value appears to be some kind of typo or mistake.

On each skill page, this (along with **Ability Ratio**) is simplified into the "Base Damage Multiplier" and "Boost Bonus" values, which are already precalculated assuming the division by 100. For instance,  has an Invocation Ratio of 80 and an Ability Ratio of 80/110/140/170 at boost levels None/x2/x3/Max, respectively, (i.e. base of 80, +30 per boost); this is simplified into a base damage of 80/100 x 80/100 = 0.64 and a boost bonus of 30/80 = +37.5% on the associated skill page.