Calculating Average Value of Damage w/ 30% Crit Chance

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Discussion Overview

The discussion revolves around calculating the average value of damage in a scenario where there is a 30% chance of a critical hit that deals 150% damage. Participants explore the relationship between critical hit probability and damage outcomes, considering the implications of these factors in a general context.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant suggests that the problem may relate to the binomial distribution due to the fixed probability of success and the nature of critical hits.
  • Another participant proposes a formula for the expected value of damage, indicating it involves a weighted average based on the probabilities of critical and normal hits.
  • There is clarification on the components of the proposed formula, with participants confirming the interpretation of the probabilities and damage multipliers.

Areas of Agreement / Disagreement

Participants generally agree on the structure of the calculation involving probabilities and damage multipliers, but the discussion does not resolve whether the proposed method is the only or best approach.

Contextual Notes

Participants mention a random number that affects the base damage, but there is a preference to keep the discussion in general terms without incorporating this variability into the calculations.

benorin
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How do I calculate the average value of some damage values where there is say a 30% chance of critical hit and on a crit 150% damage is done? I run into this problem often, if I had to guess I'd say it's likely related to the binomial distribution because there's either a crit or not, fixed probability of success, and presumably a fixed number of trials. I should mention that what value a crit does 150% of is based on a fixed number ##\theta D## where ##\theta\in\left\{ .88, 1.12\right\}## is a random number but please try not to use that fact in the calulation if at all possible I'd like it in general terms please. Thanks!
 
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It is the expected value of the damage roll times 0.3*1.5+0.7*1.0
 
So 0.3 from the crit rate, 1.5 from the 150% dmg, I'm assuming the 0.7=1-0.3 and 1.0 for normal or 100% dmg, correct?
 
benorin said:
So 0.3 from the crit rate, 1.5 from the 150% dmg, I'm assuming the 0.7=1-0.3 and 1.0 for normal or 100% dmg, correct?
Yes, it is a weighted average.
 

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