Great, 2 second stun duration and 64 DPS.
Since we have an expected stun rate of 17%, I'll discard the possibility of two stuns in a fight, and focus on the expected damage added given one stun occurs. Since I'm not going to build out a full Markov Chain for you, I'll asume the stun timing is fully stochastic, meaning it's equally likely to occur at any point of the 17 seconds pre-slow.
If it occurs during the malo: the malo phase goes from 5s to <duration of malo cast before stun> + 2 + 5. The stochastic assumption lets us take the midpoint of the cast as the expected time, so it goes from 5s to 2.5 + 2 + 5, or 9.5, adding 4.5 seconds.
If it occurs during a slow, using the same logic, we have it going from 3s to 1.5 + 2 + 3, or 6.5, adding 3.5 seconds.
If it occurs during a recast interval, it's slightly different. We add the 2s stun duration, but subtract time from the recast time; if you get stunned immediately after a resisted slow, the stun will end before the recast duration, adding zero time.
So, if it occurs in the first 4s of a recast, there's zero impact.
If it occurs in the last 2s of a recast duration, the expected duration impact will be 1 second saved from recast duration, plus 2 seconds stunned, or 1 second added.
Over 17 seconds, we have:
5 seconds casting malo, with 4.5 seconds expected added
6 seconds casting slow, with 3.5 seconds expected added
4 seconds in recast duration for the slow, with 0 seconds expected added
2 seconds in recast duration for the slow, with 1 seconds expected added
So the total expected time added will be:
5/17 * 4.5 + 6/17 * 3.5 + 4/17 * 0 + 2/17 * 1
This is an expected time added of 2.68 seconds, which at 64 DPS is 171 expected damage added.
Worst case will be a stun in the last second of a malo, which would be adding a 2 second stun and a 5 second cast, or 448 damage. This will occur 1/17th of the time. Next worst case is in the last second of a slow, which would add a 2 second stun and a 3 second cast, or 320 damage. Since there's three casts in this scenario, there's a total of 3/17th chance of this worst case happening.
So:
There's a 1 in 6 chance of a stun happening pre-slow.
If there's a slow, the expected damage is 171.
There's a 3/17 chance the expected damage is either 320 or 448.
This means the worst case will happen around .1725 * 3/17 or 3% of the time.
Edit: hold on, double-checking math. Ok, satisfied now.
|