Proc Uptime

[Rhaegal]

I found a cool formula that helps you figure out how useful a proc will be for you, if you can find the following information on it:

D = Duration of the buff
P = Chance the buff procs on any given attack
V = Number of attacks that can trigger the proc in a given second
c = Internal cooldown of the proc
u = uptime

u=D/(c+(1/VP)) *** This is wrong. See below for correct formula***

For a 2h weapon, V is easy, but it's less straightforward if you DW. For DW, V = AB/(A+B)

For example, take [Shard of Contempt]. The proc lasts 20 seconds, has a 10% chance to proc, and has a 45 second internal cooldown. I DW two 2.6 speed weapons, so for me, V = 2.6*2.6/(2.6+2.6) = 6.76/5.2 = 1.3. If I want to add Stormstrike hits into that, add in ~2/12 = 0.17 (2 hits every 12 seconds, worst-case average). Add in WF: based on some old WWS reports I have an average of ~0.2 WF hits per second. Both of those combined bring V up to 1.67 hits per second.

u = 20 / (45 + (1 / (1.67*0.10) ) ) = 0.39

Thus, you can expect the proc to be up for ~40% of the time, which means the proc is worth an average of 40% of 230 AP, or 92 AP.

[unomas]

Nice. My proc uptime goodness checking was for more ghetto and annoying. i like equations.

ps FUCK OFF MY SHARD

[Rhaegal]

So, there's an error in the formula that myself and someone else caught independently. V is actually the inverse of what it should be. Instead of being "hits per second," the formula above is "time between hits." The net result is that if you do the calculations for different weapon speeds, as written, uptime actually decreases as you hit faster. That's clearly wrong. Fortunately, this can be fixed by changing the (1/VP) term to (V/P)

u=D/(c+(V/P)

I'll recalculate mine, this time accounting for the fact that Flurry is up basically 100% of the time for me, making my attacks actually 1.82 speed. V becomes 0.909, so:

u = 20 / (45 + (0.909/0.10)) = 0.37

Proc uptime for me should be 37%. This isn't entirely true if my assumption above was accurate, that specials (e.g., Windfury, Stormstrike) can proc the effect. Working on a way to include them that doesn't make the algebra horrendous.

[mageofundead]

So, there's an error in the formula that myself and someone else caught independently.

And that is the reason why I denounce Maths!

[Rhaegal]

New formula:

u = D / (c + (1/(P/V + PA)))

uptime.JPG (2.66 KiB) Viewed 997 times

(First is useful for calculating with a scientific or graphing calculator, second might help visualize how the terms interact instead of having to interpret parentheses.)

Cleaned up the algebra as much as possible. It actually makes sense this way, too. Adding in WF and SS, I obtained an uptime of 44%, as opposed to 37% without those extra hits factored in.