Crit Chance Expected Damage Multiplier

Compute explicit Bernoulli critical-hit expectation/variance while separating noncrit flat damage; multiplier can model weaker crit variants, no armor, crit dependence or guaranteed damage.

Description

A critical-hit model separates eligible base damage from an unaffected flat amount.

A critical-hit model separates eligible base damage from an unaffected flat amount. The multiplier may be below one if supplied.^[1]

Enter nonnegative base/flat damage and multiplier plus critical probability 0–1. Return expected multiplier, expected damage and variance.

When to use Crit Chance Expected Damage Multiplier

Use Crit Chance Expected Damage Multiplier when you need to evaluate the supplied records under the calculation and evidence rules below. No dice variance, hit chance or mitigation is included.

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.

How to use Crit Chance Expected Damage Multiplier and understand its results

Prepare the supplied game state, observations and explicit variant settings. Follow the card, board, coordinate and state conventions in the calculation rules.
Enter critEligibleBaseDamage, nonCritFlatDamage, callerCritProbability, callerCritDamageMultiplier using the field table and calculation rules, then run the tool.
Read expectedEligibleDamageMultiplier, expectedTotalHitDamage, hitDamageVariance. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
critEligibleBaseDamage	Crit eligible base damage	number	Required
nonCritFlatDamage	Non crit flat damage	number	Required
callerCritProbability	Caller crit probability	number	Required
callerCritDamageMultiplier	Caller crit damage multiplier	number	Required

Enter nonnegative base/flat damage and multiplier plus critical probability 0–1. Return expected multiplier, expected damage and variance.

mean=flat+base×(1+p(multiplier−1)); variance=(base(multiplier−1))²p(1−p)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
expectedEligibleDamageMultiplier	Expected eligible damage multiplier	number
expectedTotalHitDamage	Expected total hit damage	number
hitDamageVariance	Hit damage variance	number

json

{
  "input": {
    "critEligibleBaseDamage": 100,
    "nonCritFlatDamage": 20,
    "callerCritProbability": 0.25,
    "callerCritDamageMultiplier": 2
  },
  "output": {
    "expectedEligibleDamageMultiplier": 1.25,
    "expectedTotalHitDamage": 145,
    "hitDamageVariance": 1875
  }
}

Limitations and assumptions

No dice variance, hit chance or mitigation is included.

Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use DPS Rotation Cycle Calculator: Damage per second over heterogeneous phases is a pooled ratio. Averaging phase DPS values would use different weighting. For a complementary task, use d20 Meet-or-Beat DC Probability: A d20 threshold check counts successful natural faces after a modifier. Advantage and disadvantage select a maximum or minimum of two independent rolls.

References

Crit Chance Expected Damage Multiplier — tool.io

Similar or alternative tools

DPS Rotation Cycle Calculator
Damage per second over heterogeneous phases is a pooled ratio. Averaging phase DPS values would use different weighting.
d20 Meet-or-Beat DC Probability
A d20 threshold check counts successful natural faces after a modifier. Advantage and disadvantage select a maximum or minimum of two independent rolls.