This week Jana got quite lucky with gear. She got four new pieces of gear. One was a weapon, which was a huge upgrade. Two were side grades, the same item level as she had before but with better stats. The fourth was one that made me jump up and down excitedly: Cha-Ye’s Essence of Brilliance. Yes, the Thunderforged version.
The commonality of Jana’s upgrades was that they all had critical strike on them (in the case of the trinket, a bucket load of crit). This made me think of a post I did long ago on the optimal use of Inferno Blast and I figured I’d revisit it.
It is now a commonly accepted fact that Inferno Blast should be cast when Heating Up is active in order to trigger a Pyroblast! buff. Back when Mists of Pandaria was in beta, though, it wasn’t clear to me that this would be the case. Inferno Blast offered, as far as I could tell, better DPS than fireball did generally, and I wondered if the dps gain of casting it on cooldown would be more beneficial than using it as a trigger. Then Inferno Blast was nerfed to do less DPS than fireball, but I went through with the calculations because I like to see. The end result was that the differing values of the strategies depended on one’s crit rate, and that at effective crit rates of about 62% or higher, it became better to cast Inferno Blast on cooldown. This, I felt, was unlikely to be achieved in the low-crit post-Wrath era so I really didn’t think too much of it.
Right now, though, self-buffed Jana has a listed crit rate of 40.8%. With the Critical Mass buff, this is an effective crit rate of 53%. But with temporary buffs from trinket and enchanting prods, I’ve seen Jana’s crit rate climb to 53.3%, an effective crit rate of 69.3%. And with Primordius’s 20% crit buff, Jana’s effective crit rate without trinket procs is 79%.
Thus, I think there’s a real possibility that in certain situations, it would be better to cast Inferno Blast on cooldown rather than have it be triggered by a heating up buff. The theory behind this is that when crit rates get so high, the likelihood of a fireball crit after the Inferno Blast cast is such that getting the Pyroblast buff sooner results in enough dps to offset the times when you don’t get that buff.
(Warning: lots of theory craft wonkery ahead. TL;DR: Don’t cast Inferno Blast on Primordius.)
My earlier calculations used numbers as of level 85. I’m going to update them for level 90, but first here’s some definitions:
- F: The DPS value of casting fireball over and over.
- P: The DPS value added by casting pyroblast with a Pyroblast! buff.
- I: The DPS value added by casting Inferno Blast without consideration of any buffs. (This is actually negative.)
- C: The effective crit rate.
- IB(h): The DPS value added by casting Inferno Blast when heating up is active, incorporating the triggering of the Pyroblast! buff and its benefit.
- IB(n): The DPS value added by casting Inferno Blast when heating up is not active, incorporating the triggering of the heating up buff and its benefit.
- L: The length of a fight in seconds.
- S: The cast time of a fireball.
- V(n): The overall value of the strategy of casting Inferno Blast every time it is available.
- V(h): The overal value of the strategy of casting Inferno Blast only when it is available and the heating up buff is active.
If you’ve gotten this far, congratulations. In my prior blog post I calculated the formula for V(n) and V(h) as follows.
- V(n) = (C*((1-C)P + I) + (1-C)*(C*P + I - P*C*C)) * L/8
- V(h) = ((1-C)P+I) * L/(8+S/C-S)
Now let’s get some values for C, P, I, S and L and see how those two values compare. All of these values were taken from Jana’s current gear, self-buffed only. (I may redo this with raid buffed numbers at some point).
A standard fireball hits for about 45.2k, and crits for twice that. Its cast time is 2 seconds. Thus, F is equal to (C*90.4 + (1-C)*45.2)/2, or (90.4C + 45.2 - 45.2C)/2 or (45.2C + 45.2)/2 or 45.2(C+1)/2 or 22.6(C+1).
An inferno blast crits for about 36.1k. (It always crits). It has an effective cast time of 1.34 seconds. Its value over a fireball (I) is equal to 36.1/1.34 - 22.6(C+1) or 27 - 22.6(C+1) or 4.4 - 22.6C.
A pyroblast hits for about 59.6k and will crit for twice that. When buffed, its damage will be increased by 25% to approximately 74.5k on hits and 149k on crits. They will do, on average, 74.5(1+C) damage. It has an effective cast time of 1.34 seconds, so its value is 55.6(1+C), and its value over a fireball is 33(1+C).
Before I go on, there are a few things I am ignoring because I think it would overcomplicate things without adding any visible value. I am ignoring ignite, which as a percentage of all damage should not change the analysis. I am ignoring the DoT portion of the pyroblast. While this is actually quite a bit of damage, because one pyroblast will overwrite and older pyroblast DoT, and the DoT lasts for 18.7 seconds (with Jana’s stats), I assume that the DoT will always be present. At very low values of C this might be a factor but I don’t think it will be with current values.
S is 2 seconds.
L is assumed to be 300 seconds, which represents a 5 minute fight.
Jana’s crit rate is 40.76%. With critical mass’s current 1.3 multiplier, C is 52.99%.
Now we can compute some numbers.
V(n) works out to equal approximately 527.2k. V(h) works out to be equal to approximately 600k.
That’s with Jana’s current crit rate of 40.8. What about other crit rates? Is there a point where V(n) gives us a higher number than V(h)?
Alas, no. This is where the futility of the exercise hits home, as the results I got show that as long as C is below 100%, V(h) will always be greater than V(n). The difference is not terribly large; V(h) has an advantage of between 10-20% over relevant crit ranges, and is smaller as the crit rate gets higher. It is a real advantage, though, and I would be loathe to suggest that an ease of casting Inferno Blast on cooldown could make up for that.
But there was one other thing that I found interesting. At a raw crit rate of 63%, but V(h) and V(n) became negative. This suggests that it’s not worth casting Inferno Blast at all, and that one should just cast fireball and take the Pyroblast crits you get. This makes intuitive sense; when your crit rate gets high enough the value added by the guaranteed crit of Inferno Blast is offset by the reduced damage from the spell itself. And with Jana’s current crit rate of 40.8%, that’s a level which could be achieved during the Primordius fight.
Now, it’s a bit unfair to just assume everything would be equal for Primordius. For one, the fireball cast time is far faster while mutated, and I think one needs to take that into account. Jana’s base haste while mutated is 38%, leading to a fireball cast time of 1.63 seconds. What does this do to V(n) and V(h)?
The results are as suspected: haste does not materially alter the relative values of V(h) or V(n). At a raw crit rate of 63% both V(h) and V(n) are negative. With buffs, Jana is very close to this number, and with enchanting, tailoring or trinket procs, Jana would be over this number. Further, ignoring Inferno Blast during the transformed phase of Primordius makes the rotation far easier to handle. Thus, I think it makes sense at a raw crit rate of 60% with the Primordius buff to ignore Inferno Blast altogether and take what Pyroblast procs you can get.
It wasn’t the finding I expected or even anticipated when I started working on this, but it seems like an interesting and sensible result. I’m going to follow it next time I face Primordius.
(note: it is of course a different matter to consider whether one should use Inferno Blast to spread DoTs from Primordius onto the oozes that are crawling toward him. My feeling is that because it risks giving your melee unhappy buffs, it’s a very bad thing anyway, but now you shouldn’t feel like having to do it to get your pyroblast buffs.)