- Thrash (bear) now deals much more damage (and note that it is not exclusive with thrash (cat));
- Mangle (bear) and thrash (bear) no longer cost rage, and hence will not consume clearcasts.
Therefore, let me attempt a new estimate. Since thrash (bear) now outdamages mangle (bear), I will use it instead and consider the following 4.5-second sequence: shift to bear form; thrash (bear); shift to cat form. As discussed in my earlier post, this sort of sequence results, at typical haste values, in the replacement of 5 cat-form swings with 2 bear-form swings. (This is complicated slightly by the fact that bear form now scales haste rating by 1.5, but this effect is small and I will neglect it.)
The clearcast analysis is slightly different now, however: instead of consuming clearcasts, the sequence only prevents us from spending them (since we are in bear form). As before, I will assume that if a clearcast is triggered by the (cat) swing immediately prior to shifting, then we do not react to it in time and still shift. Thus, 6 (cat form) clearcast chances would have occured during the sequence, and these are replaced by 1 cat-form clearcast chance and 2 bear-form clearcast chances, with the caveat that at most one clearcast can happen in this duration. Since clearcast chance is normalized to weapon speed, the expected number of clearcasts triggered in cat or bear form is the same, and so we really only need to consider the chance that we trigger more than one clearcast. Given that the cat-form clearcast chance is 3.5/60 and the bear-form clearcast chance 3.5/24, we have a 2*3.5/60*3.5/24+(3.5/24)^2 chance to trigger at least 2 clearcasts and a 3.5/60*(3.5/24)^2 chance to trigger 3. Thus, the expected number of lost clearcasts is 2*3.5/60*3.5/24+(3.5/24)^2+3.5/60*(3.5/24)^2 ~= 0.040.
Let's assume a clearcast is worth roughly the damage of a shred. This is a slight underestimate since we ought to consider the combo points, but it should be close enough. Now the damage gain from this sequence is roughly
where M = thrash (bear) damage; S = swing (bear) damage; s = swing (cat) damage; and m = shred damage. Now plugging in some rough values from my own character -- M = 86611; S = 17843; s = 18556; m = 58841 -- we obtain a damage gain of about 27k. If this sequence were performed every 16 seconds -- the duration of thrash (bear) -- it would earn about 1700 dps. Of course, that is only an upper limit; realistically we are not likely to find the requisite 4-5 free global cooldowns so often.
Using thrash (bear) and maul
A small improvement to that sequence might be to add maul. Maul is off the global cooldown, so it does not cost any additional time; the difficulty is that it costs rage. Because of the rage cost, we are only able to maul after the first bear-form swing if it crits; otherwise we need to wait until the second swing. Also, maul will consume clearcasts, so it should be aborted if a clearcast occurs and there is time to react.
Assume a (bear form) crit rate of t. The first swing crits with probability t; if it does, then we have a (1-3.5/60)(1-3.5/24) chance to maul, since that is the probability that a clearcast did not occur beforehand. If the first swing does not crit (probability 1-t), then the analysis is slightly more complicated. The problem is that the second swing occurs immediately before the cat form shift, so if that swing triggers a clearcast then there is no time to react: we have to maul anyway. We again have a (1-3.5/60)(1-3.5/24) chance to maul, but there is now also a loss of (1-3.5/60)(1-3.5/24)3.5/24 ~= 0.117 clearcasts. Overall, then, we gain (1-3.5/60)(1-3.5/24) ~= 0.80 mauls and lose 0.117*(1-t) clearcasts, and the estimated damage gain from the revised sequence is
where L = maul damage. Taking t = .35 and L = 24660, again rough example values from my own character, we obtain a damage gain around 42k -- a substantial improvement.
Using thrash (bear), mangle (bear), and maul
Another possible improvement might be to add mangle (bear), since we are already in bear form. It's interesting to note that, by a similar analysis to that made in the previous post, at low enough haste values (<1% unbuffed in bear form) this does not even cost any additional cat-form swings. At more realistic haste values (~5% unbuffed in bear form) it has about a 20% chance to cost an additional 2.5 cat swings (replacing them with 1 bear swing). Of course, this addition also raises the duration of the overall sequence to 6 seconds, making it substantially more unwieldy.
For brevity, I'll not walk through the full analysis in this case. We gain a mangle (bear), lose 2.5*0.2=0.5 cat swings, gain 0.2 bear swings, and lose 0.2*(1-(1-3.5/60)(1-3.5/24)^2)*3.5/24 ~= 0.009 clearcasts. Because of the longer time spent in bear form, there is also sufficient time to react to a clearcast and avoid casting maul, so the "-0.117*(1-t)m" term changes to "-0.117*(1-t)L". The estimated damage gain from this new sequence is now
where K = mangle (bear) damage. Taking K = 52310 (again an example value from my own character), this produces a damage gain around 91k. Now that is a rather large improvement; the caveat is that we have extended the sequence from 4.5 seconds to 6 seconds, making it substantially more likely to interfere with the cat-form rotation.
A closing remark
I've established that the insertion of bear-form abilities into a DPS rotation is likely to yield a significant damage gain if it does not interfere with the cat-form rotation. The obvious objection is that maybe it is not possible to insert a bear-form sequence without damaging the cat-form rotation. This is a more difficult thing to decide by an elementary study such is this one. My own suspicion is that it would be quite difficult to find an opportunity to insert a bear-form sequence into a DoC rotation (due to the additional global cooldowns it requires), but into a HotW/NV rotation should not be so hard.