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User:Yodaj007/Sandbox

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Definitions

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  • a: The target AC
  • r: Roll required to confirm critical hit (low end of weapon critical range)
  • b: Bonus damage
  • m: Critical multiplier
  • h: Bonus to hit, including base attack bonus and all applicable modifiers
  • p: Amount of power attack taken from

Chance of hitting

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The roll required to hit is the AC of the target minus the players hit bonus, or . If R is greater than 20, the chance to hit normally 0%. But, it's still possible to hit on a roll of 20, if the player can hit the AC with an assumed roll of 30. If R is less than 1, then any roll other than a 1 will hit. If the required roll is 19, then two values on the die can hit. If it is 15, then 6 values can hit. This can be expressed as:

exists on the interval .

Chance of a critical hit

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In order to get a critical hit, you first have to hit with a die roll greater than or equal to r. To confirm the critical, you just have to hit.

Damage

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The expected damage from hitting is defined as .

The expected damage from critting is defined as .

The expected total damage from an attack is defined as: