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Originally Posted by Elimbras
I'm sorry if this seems rude, but your statement is plainly wrong from a mathematical point of view.
Assume that BL is popped at a random time. Assume also that you refresh DP exactly every 24s. If dots are auto-updated on buffs, then you gain 40s of BL on your DP. Now, let's see what gain you have if dots are updated on cast. Let X denote the time left on your current DP when BL is cast, and let t=0 be (by convention, up to a shift) the time where BL is cast. At time X, you cast a new DP, hasted with BL. The next DP cast is at X+24. If X was less than 16, we have that X+24 <= 40, and this second DP is also hasted by BL. Otherwise, we have X+24 > 40, and the second DP is not hasted.
Now, BL is cast at a random time, independently of DP cast, and DP is cast exactly every 24s. This means that the remaining time X on the current DP is a uniform random variable on ]0, 24]. So, we have 2/3 chance of having X less than 16, and 1/3 of having X greater than 16. The mean gain of BL on DP is hence 1/3 * 24 + 2/3 * 48 = 40s of hasted DP. That's identical to the case of auto-update. In other words, when there is no auto-update, the potential gain after the end of the buff is exactly the potential loss before the first recast of the dot.
There is no magic value of durations here. This will be always valid, as long as the buff is casted at a random time, independently of the dot casting time. Now, if there is no independence between both, then you could potentially be stucked in a bad synchronization. But with an "equivalent"[*] probability, you could be stucked in a good synchronization. And in fact, you have control of it, and you can ensure in most cases that the synchronization is better that the mean random case.
[*]: I don't mean here the probability of being in a good or bad synchronization are equal. I mean that the expected gain, ie. the expectation of the probability of a synchronization times the gain (or loss) of this synchronization, is fundamentally null.
Unless i missed something, this only true if you're casting nothing but DP. The point he was trying to make was, if you cast other things it would be a dps gain if you just reapplied at the end of the dot.