Quote:
Originally Posted by Duik
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And we have a finite number of events. While i do not understand fully the math i can grasp there is a difference because our fights take a finite number of random or percentage inputs.
I also understand all of us will not get this subtle difference.
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Oh this subtle nuance makes absolutely no real-world difference. But since DSM is utterly incapable of admitting he is ever wrong, he's in an all-out fight over whether his Scourge proc does 2.2DPS or 0.75DPS while spamming JBB. Utterly irrelevant.
But to close the loop on the simplified example we started yesterday:
If there's only one proc, and it's on the t=0 swing, the probability is 10.4 * 89.6 * 89.6, or 8.35%, and does 112 damage
If there's only one proc, and it's on the t=8 swing, the probability is 89.6 * 10.4 * 89.6, or 8.35%, and does 88 damage
If there's only one proc, and it's on the t=16 swing, the probability is 89.6 * 89.6 * 10.4, or 8.35%, and does 64 damage
If there's no proc, damage is 0, the probability is 89.6 * 89.6 * 89.6, 71.9%, and does zero damage
If there's two procs at t=0 and t=8, the probability is 10.4 * 10.4 * 89.6, or 0.97%, and does 152 damage
If there's two procs at t=0 and t=16, the probability is 10.4 * 89.6 * 10.4, or 0.97%, and does 152 damage
If there's two procs at t=8 and t=16, the probability is 89.6 * 10.4 * 10.4, or 0.97%, and does 112 damage
If there's a proc on all three swings, the probability is 10.4 * 10.4 * 10.4, or 0.11%, and does 192 damage
The sum of probabilities is 100% after compensating for rounding: 8.35 + 8.35 + 8.35 + 71.9 + 0.97 + 0.97 + 0.97 + 0.11 = 99.97
The expected value is equal to the sum of all the possible outcomes, each weighted by the probability of that outcome occurring.
112 * .0835 + 88 * .0835 + 64 * .0835 + 0 * .719 + 152 * .0097 + 152 * .0097 + 112 * .0097 + 192 * .0011 = 26.29
So the expected damage is 26.29 over an 18 second fight, or 1.46 DPS.
This calculation will provide a different DPS value for a 132 second fight, but the principle behind the calculation is the same. I did this calculation
here, and came up with 0.75DPS