Elitist Jerks - View Single Post

Troffel · 04/14/08, 4:54 PM

Originally Posted by Aldriana

I disagree. That attempts to answer the question "if I pick an interval between two procs at random, on average what is the expected uptime of buff during that interval" - which is related to, but not identical to, the question we actually want to know the answer to, namely "If I pick a random instant of time, what is the probability that the buff is up". The relevant distinction is that when we choose an instant of time at random, we are not equally likely to wind up in any interval; we are slightly more likely to pick one of the longer ones, and slightly less likely to pick one of the shorter ones.

Thus, my logic is as follows:

Let the average interval between procs be $I$ . Thus, by definition over the course of some long segment of time $T$ , there will be, on average, $\frac{T}{I}$ procs, and thus $\frac{DT}{I}$ total uptime. Hence, if we pick a time at random during this period of time, the probability that the buff is active is the total amount of time when the buff is active divided by the length of our interval, that is, $\frac{\frac{DT}{I}}{T}=\frac{D}{I}$ .

But the same problem remains. The expected value of the number of procs in a long time segment is not the quotient of the the time segment divided by the expected value of the time between procs. But i think the approximation can be used, if the proc chance is high enough. Try it for yourself, generate a large enough sequence $(I_i)_{i=1..n}$ and calculate $\frac{T}{n}\sum^n_{i=1} \frac{1}{I_i}$ as the expected value of the number of procs and $\frac{T}{\frac{1}{n}\sum^n_i I_i}$ . You will find a hugh difference depending of the generation (distibution) of the sequence...

Originally Posted by Aldriana

Besides which, even if there is a flaw in my logic (and I'm not going to say for certain that there isn't): it's a far more useful formula than the one you present; even if it is slightly off (and I don't think it is), it's certainly close enough to give good approximations in real world cases, and has the distinct advantage of not requiring the evaluation of infinite sums, which is going to make it much more useful to most members of this community in practice, as my suspicion is that most people here don't necessarily remember how to evaluate an infinite sum.

The question is, what we do practice or want we do theorycrafting. For practice are simple rules of thumb sufficient and often used for raiding. But my understanding is, that this is elitist jerks and the elite are not afraid of infinity sums nor Illidan either. So my target is to discuss how far the model reach and when/what approximations are useful.

The problem with theorycrafting is, that, if it is often too inexactly, it is not worth to do it for raiding, since equiment and skill makes a lot of more difference. 10% calculation error in dps means much and my experience is, that the carefully and precise calculation is worth the time. So lets discuss the approximations later and try to achive a model, which fits best. The usefulness of a formula is: How exact it covers the "reality" and not how easy it is to calculate. By the way i think that the infinite sum has closed analyical form, but i was to lazy to calculate it yesterday.