I knew the problem and I actually am not 100% sure, if my calculation is right, but yours is defenitily wrong.
The reason for this is, that the Proc chance of Generosity is already the Conditional Probability (P (A if B )) = 0.6 (or in words: 60% chance to trigger if a critical hit occurs)
What we are actually looking for, is P(A and B ) (in words: the probabilty that a crit occurs and Generosity triggers). Thus, we have to convert the formula from_ P(A if B ) = P(A and B ) / P(B )_
into
P(A and B ) = P(A if B ) * P (B )
Given that P(A if B ) is the 60% chance of Generosity to Proc on crit and P(B) your Critchance, this results into my calculation of:
0.6 * 0.5 = 0.3To proof that your calculation must be wrong, just think about what you actually were calculating. You calculated:
P(A if B ) = (P(A) * P(B ) / P(B ) this would always lead to the answer P(A if B ) = P(A), implying that P(A) would be independant from P(B ).
We are both wrong actually. And both right, to an extent.
You are testing for the wrong thing, but since one of the factors (the 60% proc of Generosity) remains constant, testing for concurrence gives the same result as testing for conditional probability. You test for the wrong thing, but get the same result since one of the factors is constant. This would not provide the same results if both probabilities would be dynamic, ultimately yeah, my bad.
Anyway, in a direct comparison, you would need a crit rate of 100% or more to transfer the conditions at a same chance then with purging.
There are two other factors involved here that are significant, one of them is very hard to account for using math, they are:
9s vs 10s cooldown
Transferring condition vs Purging it.
The 9s vs 10s may seem not significant, but after 2/3 checks, we are moving into territory where the negative effects proc on you. In other words, lets say if your crit chance is 70%, then you have a 80.5% chance of 1 transfer in 27 secs vs the 93.6% over 30 seconds (assuming hits at cooldown)
I don’t remember that much from my stats classes to extrapolate probability adjusted for time for both, but Generosity is 10% faster in its checks. Thats significant enough to be fairly effective if your cirt rate is in the 70-80% range imo.
Either way, Generosity requires a significant contribution to Precision to be as effective in its basic function – getting rid of conditions – as Purging.
The second factor that is purely situational is what gets transfered and to whom. Obviously there are so many possibilities here that its hard to even really consider.
And that was my main point – 70-80% crit chance requires serious stat devotion. It is not as clear cut a choice as OP seemed to say IMO, even though I failed at math ;P
EDIT:
Alacrityhas anyone tested if Generosity still “procs” even when there’s no condition to transfer?
In that case Purity might be more desirable, though I’d probably run both at once.
(and I still think that Purity – and Speed – would be more useful as proc-on-swap)
As far as I remember, cool-downs for any sigil proc start after its effect is applied/triggered, by that logic, if there is no effect to apply, there is no effect to trigger.
Or at least that is what would make sense. Stranger things have happened ;P
(edited by silencer.5028)
