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Troffel · 04/13/08, 7:13 AM

I think the formula for true fixed-percent procs is wrong.

Calculating the average time to proc ist like flipping a coin and compute how long the average sequence of portraits are.

I assume that the attack is as single attack, which occurres after equal time-periods 1/v.

To have a sequence S(n) with n non-procs and one proc, the probability of occuring this sequence is:
$p(S(n)) = p(1 - p)^n$
The time needed for such a sequence is: $t(S(n)) = \frac{n}{v}$ . (Hit 1 at t=0.)

So the mean of "time to next proc" is
$E(proc) = c + \sum_{i=0}^{\infinity} t(S(i)) p(S(i)) = c + \sum_{i=0}^{\infinity} \frac{i}{v} p (1 - p)^i = c + \frac{1 - p} {v p}$

The main difference is, that you have, if v=1 and p=1, 100% prolongation of the buff and not a gap from 1 sec after the internal cd.

The average uptime U, when c>=D, is
$E(U) = \sum_{i=0}^{\infinity} \frac{D}{c+\frac{i}{v}} p (1-p)^i$

The difference is, that you can not calculate the average as the quotient of the averages.

04/13/08, 7:13 AM	#10 (permalink)
Troffel Von Kaiser Troffel Gnome Warlock Der Rat von Dalaran (EU)	Formula wrong I think the formula for true fixed-percent procs is wrong. Calculating the average time to proc ist like flipping a coin and compute how long the average sequence of portraits are. I assume that the attack is as single attack, which occurres after equal time-periods 1/v. To have a sequence S(n) with n non-procs and one proc, the probability of occuring this sequence is: $p(S(n)) = p(1 - p)^n$ The time needed for such a sequence is: $t(S(n)) = \frac{n}{v}$ . (Hit 1 at t=0.) So the mean of "time to next proc" is $E(proc) = c + \sum_{i=0}^{\infinity} t(S(i)) p(S(i)) = c + \sum_{i=0}^{\infinity} \frac{i}{v} p (1 - p)^i = c + \frac{1 - p} {v p}$ The main difference is, that you have, if v=1 and p=1, 100% prolongation of the buff and not a gap from 1 sec after the internal cd. The average uptime U, when c>=D, is $E(U) = \sum_{i=0}^{\infinity} \frac{D}{c+\frac{i}{v}} p (1-p)^i$ The difference is, that you can not calculate the average as the quotient of the averages. Last edited by Troffel : 04/14/08 at 5:06 PM. Reason: Using the latex-commands. Nice formating of the formulas.