Damage

**Damage** refers to the amount of damage each tear deals to enemies, and is represented by a sword. As damage increases, the size of the tears increases as well. However, tear size is not always a direct indication of how much damage tears will do; for example, items like  and  increase tear size without increasing damage. Tears will grow and shrink when damage changes, but tears of a certain size do not have a specific damage value, and two tears of the same size (in two different runs) are likely to have different damage values.

## Effective Damage

The formula for damage is:

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{\displaystyle \color{white}\mathit{EffectiveDamage} = \mathit{CharBaseDmg} \times \sqrt{\mathit{TotalDmgUps} \times 1.2 + 1} + \mathit{FlatDmgUps}}

where:

* CharBaseDmg = The character's base damage multiplied by their multiplier,
* TotalDmgUps = the total of all regular damage ups collected (not including special exceptions or damage multipliers),
* FlatDmgUps = the total of all damage ups that are excluded from the above (for example,  or ), and
* EffectiveDmg = the approximate damage that can be expected per tear, or per 'tick' when using  or .

This formula makes most damage upgrades less potent the more that Isaac has. For example, a Pentagram on Isaac would make his total damage 3.5 \* (1 \* 1.2 + 1)^0.5 = 3.5 \* 1.48 = 5.19. Another Pentagram increases this to 6.45 (a 1.26 increase instead of a 1.69 increase). The higher a character's base damage, the more effective damage ups will be for that character. Flat damage modifiers and special adjustments like  or  happen after the main formula.

### Character Modifier

The *character base damage* is defined by a base number and a multiplier.

* Eve† and  Tainted Magdalene: 0.75 \* 3.50 = 2.625
* Jacob‡: 1.00 \* 3.5 - 0.75 = 2.75
* Isaac,  Magdalene,  Samson,  Lazarus,  Eden,  Lilith,  The Lost,  Apollyon,  The Soul,  Bethany,  Tainted Isaac,  Tainted Judas,  Tainted ???,  Tainted Samson,  Tainted Lazarus,  Tainted Eden,  Tainted Lilith,  Tainted Keeper,  Tainted Apollyon,  Tainted Bethany and  Tainted Jacob: 1.00 \* 3.50 = 3.50
* ???: 1.05 \* 3.50 = 3.675
* Esau‡: 1.00 \* 3.5 + 0.25 = 3.75
* Keeper,  Cain,  Tainted Cain,  Tainted Eve and  Lazarus Risen: 1.20 \* 3.50 = 4.20
* Judas: 1.35 \* 3.50 = 4.725
* Azazel,  The Forgotten,  Tainted Azazel,  Tainted Forgotten and  Dead Tainted Lazarus: 1.50 \* 3.50 = 5.25
* Lazarus Risen: 1.40 \* 3.50 = 4.90 (+0.5 damage after each death, 6.20 effective damage on the first death)
* Tainted Lost: 1.30 \* 3.50 = 4.55
* Dark Judas: 2 \* 3.50 = 7.00

†:  has the unique effect of increasing Eve's damage modifier from 0.75 to 1.00 when active. This does not apply to other characters, however.

‡: Jacob and Esau have -0.75 and +0.25 flat damage, respectively: their base damage, as far as the damage formula is considered, is still 3.5 with a 1.0 multiplier.

### Damage Multipliers

Some items multiply damage rather than simply adding to it. Damage multipliers do not simply multiply the character's damage once; the damage stat is constantly recalculated and the damage multipliers are multiplied with the end result. This means that if a character starts with 3.50 damage and gets a 2x multiplier, their effective damage will be 3.5\*2 = 7.00. If an item that grants +1 damage is picked up, the character's effective damage will be 3.5\*(1\*1.2+1)^0.5\*2 = 3.5\*(2.2)^0.5\*2 = 3.5\*1.48\*2 = 10.38, and not 7.00 + 1.

Most damage multipliers stack; for example,   and  both provide a 2x multiplier; picking up both will give a total multiplier of 4x. The exception to this is the 1.5x damage multipliers provided by , , and the combination of  and . These multipliers do not stack; for example, picking up both Cricket's Head and Magic Mushroom will result in an overall 1.5x multiplier rather than the expected 2.25x.

### Reverse Formula

Consequently, the reverse formula to determine your damage bonuses from the displayed value is

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{\displaystyle \color{white}\mathit{Bonus} = \frac{1}{1.2}\left[\left(\frac{\mathit{EffectiveDamage}/\mathit{Multipliers} - \mathit{FlatDmgUps}}{\mathit{CharBaseDmg}}\right)^2 - 1\right]}

*Multipliers* is the product of all damage multipliers in effect.

## Items that multiply damage

### Positive Multiplier

Character-specific damage multipliers:

* Eve +  - Raises her damage multiplier from 0.75x to 1x while the whore effect is active. (It does not have this effect for any other character.)
* Judas +  +  +  - 1.4x damage multiplier while the Damocles effect is active.
* Dying with  transforms the player into  Dark Judas, who has a 2x damage multiplier, which is the highest character-based damage multiplier in the game.

Synergy-specific damage multipliers:

* +  - 1.5x damage multiplier. (The multiplier is shared with  and .)
* +  - 1.2x damage multiplier.
* +  - 1.5x damage multiplier.

### Negative Multiplier

* Note that  is not a "real" damage multiplier in that it only affects the increases from other items. For example, if you only had  for a 2x damage multiplier and nothing else, then Odd Mushroom would only grant a flat -0.4 damage (because nothing would be multiplied by 0.9).

## Other

* The Spun transformation increases damage by 2.
* The Conjoined transformation decreases damage by 0.3.
* In co-op, Rage Baby, Revenge Baby, and Belial Baby will occasionally briefly increase damage. Dark Baby will occasionally briefly increase all stats, including damage. Buddy Baby will occasionally briefly grant the  effect, which increases damage. Whore Baby will occasionally briefly grant the  effect, which increases damage.