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Damage, although depicted as an absolute value of bars, is actually an undisplayed value which is increased or multiplied from its base/current level. Each character starts with a base damage of 3.5 multiplied by a character-specific multiplier. Judas has the largest damage multiplier (1.35) while Eve has the smallest damage multiplier (0.75).
Attack has no maximum value, but there is a "soft cap" due to a square root in the middle of the damage calculations, which causes successive damage upgrades to give smaller increases in damage output. The more damage ups you get throughout one playthrough, not affected by being in the same session, will make other "smaller" damage ups worth less damage by up to 15% less.
Calculating damage in The Binding of Isaac involves several stages of damage: Basic, Effective and Final Damage (which your actual damage output will be).
Stage 1: Basic Damage Calculator
The following items increase Basic Damage. Note, however, that the Basic Damage is not directly related to your Final Damage.
|Item||Icon||Increases Basic Damage by:||Extra Notes:|
|Blood of the Martyr||1|
The value of x starts at 0 and increases by 1 every time you kill an enemy in that room.
The total value of 0.28*x is capped at 2.3 or 9 kills.
Samson's Lock increases Basic Damage by 0.50*x instead of 0.28*x. The effects of Bloody Lust and Samson's Lock stack, but the maximum bonus allowed remains the same, allowing you to reach the capped damage faster.
Multiple uses of Book of Belial/XV The Devil do not stack.
Adds a 1.5X damage multiplier when combined with Blood of the Martyr. Multiplies by 2.0x damage within the first floor and goes down by .25x damage until Necropolis.
|Magic Mushroom||0.3||1.5X damage multiplier.|
1.5X damage multiplier.
Increases knockback of tears.
|Money=Power||0.04 * coins|
|Odd Mushroom (large)||0.3|
|Pentagram||1||+20% chance of a deal with the devil|
x resets to 0 upon entering room and increases by 2 each time you use Razor Blade. Can be used theroectally infinate times.
The Red Patch has a 1/5 chance of increasing x by 3 whenever you get hit.
This effect is applied after the small Odd Mushroom effect.
|Small Rock||1||Small Speed down, Slight tears up, and 1 damage up|
|SMB Super Fan!||0.3|
The value of x depends on how and when the effect was triggered:
x is 2.25 if the effect was triggered via III the Empress,
Special Basic Items
The following items have unique interactions and are calculated in this order - in other words, Odd Mushroom follows all of the other Basic Damage upgrades and precedes Chocolate Milk.
|Item||Icon||Change in Damage||Extra Notes|
|Chemical Peel||2||50% chance for a tear to have increased damage as Cain, instead of a tear with increased damage firing in a fixed pattern of every other tear.|
|Odd Mushroom (small)||Basic Damage is set to Basic Damage * 0.9 - 0.4||Always a 10% damage down on your total damage overall.|
|Chocolate Milk||.234 * Frames Elapsed - 1.56||The game runs at 30 frames per second in optimal conditions; a full charge is gained after 40 frames, or 4/3 seconds.|
Stage 2: Calculating Effective Damage
The Effective Damage is calculated from your Basic Damage as follows:
Effective Damage = 3.5 * (1 + 1.2 * Basic Damage)1/2
Here is a graph on the relationship between Basic and Effective Damage:
Stage 3: Final Touches
In the last stage, a variety of items add to or multiply Effective Damage to turn it into Final Damage:
- If Polyphemus has been obtained:
- If playing as Cain, Effective Damage is multiplied by 1.2
- If playing as ???, Effective Damage is multiplied by 1.05
- If playing as Judas, Effective Damage is multiplied by 1.35
- If playing as Eve, Effective Damage is multiplied by 0.75
- If the Curved Horn has been obtained, Effective Damage is set to Effective Damage + 2
- If Sacred Heart has been obtained, Effective Damage is set to Effective Damage * 2.3 + 1
- For the Technology 2 laser, Effective Damage is multiplied by 0.65
- If this is a tooth shot from Tough Love, Effective Damage is multiplied by 3.2
- If you have at least one of Max’s Head, the Book of Belial / XV the Devil effect with the Blood of the Martyr, or Magic Mushroom, multiply Effective Damage by 1.5
- If Lump of Coal has been obtained and the shot in question is a tear, Effective Damage increases by 0.14 every frame; when the game runs at 30 frames per second, this results in an increase of 4.2 in Effective Damage per second, allowing for a total gain of 21 Effective Damage at maximum.
Additional Info, Special items
Technology laser: Certain items affect the damage of Technology lasers. The Inner Eye and Mutant Spider multiply it by 3, Polyphemus has its usual effect on damage and then multiplies it by 3, and the Lump of Coal adds 2.
Technology 2 laser: Multiply your effective damage by 0.2*x. Every time you fire a tear, x increases by 1, and every time the laser does damage, x is multiplied by 0.8 and increases by 0.2. The laser itself does damage 10 times every second.
Mom's Knife: If the knife touch enemies when it's going forward to them, it deals x6 Tear damage per 0.1 seconds. Otherwise, it deals x2 Tear Damage per 0.1 seconds.
- Isaac's Default Damage : 3.5
- Isaac with MEAT! : 3.5 * (1 + 0.3*1.2)^0.5 = 4.0817
- Isaac with Money=Power and 99 Pennies : 3.5 * (1 + 3.96*1.2)^0.5 = 8.395
- Isaac with Brimstone : 10.5 per hit (you can shoot 2 times per charge.)
- Isaac with Polyphemus : (3.5 + 4) * 2 = 15
- Isaac with Polyphemus & Brimstone : 15 * 3 * 3 = 135 per hit
- Isaac with Polyphemus & Sacred Heart & Brimstone : ((15 * 2.3) +1) * 3 * 3 = 319.5 per hit