That new data point is particularly useful, Maje.

Here are the data points on a graph again:
*graph was incorrect. New graph has been posted below*

I've plotted that new point twice, once assuming critical mass affected the T3 HS chance and the second time assuming it didn't.

This shows two nice things:

• First, the polynomial curve is much closer to the linear curve now. I think this further supports my assumption that the linear pattern is the correct one.
• Second, the point with critical mass not included is closer to the line. It is far too early to say for certain, but this is evidence that critical mass does not affect T3 hot streak chance. We need to test this more. My assumption is that buffs will affect the T3 hot streak chance (as they show up on the character sheet) but target debuffs won't affect T3 hot streak chance. If this is the case, Critical Mass is going to be an interesting one to theorycraft, as it will increase T4 hot streak chance while not affecting T3 hot streaks...

Elimbras:
Wow. You're absolutely correct. The linear/2nd order polynomial pattern is similar to a differential/integral, but the formulas we are seeing are most definitely not related as such. If they were, the linear formula should be y = -0.86875x^2 + 0.8173x + constant
You're also correct about the 2nd/3rd order graphs. I realized the error in the second graph after I posted it - it does match a 3rd order polynomial.
I'm going to go do math penance now for those mistakes... :P

Is there anything confirmed to directly impact T3 HS? I saw the math earlier on the crit chance diminishing return, but is this 100% confirmed in all releases?

Also, anyone know about the pyroblast! v pyroblast dot transfer? Is that going to be going forward that the instant cast doesn't transfer via impact?

Given that the talent description doesn't even say it's affected by crit rate, no it's not confirmed for all versions nor will it ever be. Blizzard can change it however they like without touching the talent description and we wouldn't know about it untill enough tests have been done.

To the point, the above discussion is relevant to the current beta build 13117.

What is the status of Burning Soul? I believe they are in the process of removing most pure pushback reducing talents and making it more generic. Is 3/3 points in Burning Soul overkill from 4.0?

Interesting analysis Shaewyn. However I think you are assuming that current HS is calculated simply as c^2, which I don't believe is quite right. It doesn't account for the previous cast possibly causing hot streak. Apologies for the ascii formatting of formulas below, but this formula was previously posted and verified on EJ:

P(3.x Hot Streak) = c^2 / (1 + c)

At 50% crit rate, the proc chance per cast should be 1/6 not 1/4. One way to derive this formula is:

P(HS) = P(HS | crit) * P(crit) = P(no HS on prev spell | prev spell crit) * P(prev spell crit) * P(current spell crit)

Let Q = P(HS | crit), therefore P(HS) = Q*c = (1 - Q) * c^2

Solving that gives: P(HS) = c^2 / (1 + c) as expected.


Now applying the same idea to the new Hot Streak (combined T3 & T4 chance, assuming T3 resets counter):

P(HS) = P(HS | crit) * P(crit) = P(T4 HS OR T3 HS)

P(T4 HS OR T3 HS) = P(no prev HS AND prev crit AND current crit) + P(T3 HS) - P(no prev HS AND prev crit) * P(current crit AND T3 HS)

Replacing with symbols:

P(HS) = Qc = (1 - Q)*c*c + k*c - (1 - Q)*c*c*k

Solving that:

P(4.x HS) = c (c + k - ck) / (1 + c - ck)

With k=0, that devolves to the old 3.x formula. Substituting your k(c):

P = (1.74c^3 - 1.56c^2 +.82c) / (1.74c^2 + .18c + 1) for c < .47

P = c^2 / (1 + c) for c > .47

The graph for that (which I'm not sure how to post) looks similar to yours below 25% crit, which makes sense since T4 HS is negligible at low crit rates. Above that it is flatter though, hitting 1/6 at 50% crit as expected.

I'm fairly certain the old 3.x formula is correct, hopefully I derived the 4.x formula correctly.

As posted on the Blizzard General Discussion Forum:

Looks like we can't use 6 very important glyphs until they patch/hotfix it. They say it's a priority but no ETA, great.

Assume that it is working, which three would you take?

I'd venture that you would take MA, FB, and Pyro, because of how little LB is of the % of your damage. However, with crits so low, maybe LB would be better than Pyro as it is a constant assured damage?

Blues have updated the broken glyph post. We can use them currently, we just have to use them as Majors.

The listed prime glyphs that are currently incorrectly categorized as major glyphs can still be slotted as majors for the time being.

So our major slot it just getting really crowded

I assume they will correct this asap though, since we kinda rely on being able to use all our glyph slots.

The currently available Major Glyphs for Fire are terrible. This bug will be a small temporary boost to Fire rather than having any negative impact. You can pick and use 5 Prime Glyphs (I'm including Frostfire) so there isn't really a downside.

Maje: Sorry, I mucked up the graph. Here's the correct version:



You're correct, this actually moves the exponential regression further from the linear regression. In addition, according to the R^2 value, the exponential regression is actually the more accurate version.

I'm going to recommend that until we can get some more data, sim writers hold off on implementing either formula. I'll run a couple additional tests, and if anyone else wants to run some, we can add a bunch of points in to get a really good formula. If anyone's going to run a test, please provide: character sheet crit chance, spec (particularly if critical mass is specced, and make sure to not spec t4 HS), and a combat log.


Trel: I've not the time to do the math right now, nor was I the one to originally derive the T4 Hot streak chance formula. The WotLK research you are thinking of is from this thread: Mathematics of dynamic cycles The key thing that has changed in Cataclysm is that Pyroblast itself can proc hot streak. That was the main reason for the formula. Now that Pyroblast can itself proc Hot Streak, that formula must change.

However, and this is one for simulations, Living bomb can no longer proc hot streak. This means that 1 cast every 12 seconds is incapable of causing hot streak, which again alters the DPS value of hot streak. I am solely looking at the proc chance per capable spell, however.

Important:
I haven't discovered this yet, but does the instant "Pyroblast!" proc hot streak? We've been assuming it does, but as it doesn't work with impact, that may not be a given.