Fire Cataclysm Discussion: OP Updated for Release - Page 20

Maje · 10/10/10, 7:59 AM

The scorches that hit for less than 6k are not critical (iscritical=0), the log I posted is raw since I wanted all the information to be available.

Also note that at 00:44:46.703 when Ignite is removed and than applied some of the previous bank is actually resolved, I'm guessing it's because of how events are sent in relation to the real calculations.

EDIT: One more thing, unrelated to the script but to make some things clearer; at 00:44:42.250 when the scorch crits and Ignite isn't applied in the log if you ignore that crit, the bank that you have at that point (5649.2) is in fact resolved to 0 after the 3 ticks of 1883, so like I said in my post in this case the clculations weren't buggy it's just that that Scorch wasn't taken into account at all. [Dosn't mean that Ignite isn't bugged in other ways as well.]

Maje · 10/10/10, 5:32 PM

Did a little more testing at l80 after I noticed that T3 does in fact work for my l85 mage.

Spec: Talent Calculator - World of Warcraft
No glyphs, no buffs, no target debuffs; vs l80 testing dummy.

l80:
184 int
0 crit rating
2.01% crit

1955 scorches
44 crits (2.25% crit)
34 hs procs (77.27% proc chance)
108 Impact procs (5.5% proc chance, seems bugged to me)

l80:
2052 int
1463 crit rating
45.13% crit

2109 scorches
982 crits (46.56% crit)
11 hs procs (1.12% proc chance, with such a 'high' proc chance no wonder I thought it was bugged)
98 Impact procs (4.64% proc chance, certainly bugged)

I'll run another test with around 20% crit chance and only one point in Impact, first to get another datapoint for T3 HS and secondly to see if the second point in Impact actually does anything.

EDIT: Ok another run;
Same spec as above except with one point in Impact.

l80:
1381 int
624 crit rating
22.81% crit

1945 scorches
513 crits (26.37% crit)
67 hs procs (10.73% proc chance)
73 Impact procs (3.75% proc chance)

and yet another 1 point in Impact.

l80:
861 int
276 crit rating
12.10% crit

3249 scorches
357 crits (10.98% crit)
97 hs procs (27.17% proc chance)
99 Impact procs (3.04% proc chance)

In conclusion T3 HS proc chance scales inversely (exponentially) with crit chance and hits a 0 at around 45-50% crit. Subjectively it seems quite low, assuming around 20% crit (buffs only, not debuffs) we'll have about 10% T3 proc chance. Much much lower than what we're seeing now. The fact that Blizzard is not specifying clearly how T3 proc works is extremely annoying and will undoubtedly be a source of many stealth changes.

Impact is quite definitely not 5% per point, it seems closer to 2.5% per point.

I tried checking how Combustion works but that too doesn't seem to work as advertised, there are various things at play that differ by dot type and various coefficients, again, extremely annoying.

I should probably wrap all the data in a pretty table, though I have no idea how to do that.

Shaewyn · 10/10/10, 11:49 PM

Ok, taking the data from Maje's tests and having fun with math:

Crit Chance	Scorches	Crits	HS procs	Crit %	HS per Crit	HS %
0.0201	1955	44	34	0.022506394	0.772727273	0.017391304
0.121	3249	357	97	0.109879963	0.271708683	0.02985534
0.2281	1945	513	67	0.263753213	0.130604288	0.034447301
0.4513	2109	982	11	0.465623518	0.011201629	0.005215742

Graphing this and looking for an exponential regression:

A formula that fits Maje's data (exponential regression) is:

y=0.9472e^(-9.134x)

Now we can use the formula we found earlier in this thread:
$P = P(\text{T3 HS}) + P(\text{T4 HS}) - P(\text{T3 and T4 HS}) = k*c + c^2 - k*c^2$

Using the exponential formula from Maje's data, we know $k=0.9472e^{-9.134c}$

so: $P(\text{T3 HS})=0.9472e^{-9.134c}*c$

Here's the trouble. If T3 HS does not reset T4 HS, then:
$P(\text{T4 HS})=c^2$

if T3 does reset the T4 HS counter (as I suspect), then:
$P(\text{T4 HS})=(c-(0.9472e^{-9.134c}*c))^2$

So, this gives us these graphs:

Particularly interesting:

As we can see, the 20% crit line is where the T4 Hot streak becomes more valuable than the T3 hot streak.

Notes:
* the exponential formula will not be quite correct, due to the nature of binomial distributions and crit chances. It is likely, however, to be close.
* The relative value of T3 and T4 HS depends on the exact "resetting" nature of the two procs. (i.e. does a T3 HS proc reset the counter for the T4 HS?)

Tyfon · 10/11/10, 2:07 AM

Is it possible that Maje's data on Impact proc % is low because the log only tracks new procs, not refreshes?

Maje · 10/11/10, 3:19 AM

It bloody hell does, my appologies for botching the queries up, the updated numbers in a nicer table courtesy of Shaewyn, the numbers that changed where HS and Impact procs:

Hot Streak:

Crit Chance	Scorches	Crits	HS procs	Crit %	HS per Crit	HS %
0.0201	1955	44	40	0.022506394	0.909090909	0.02046035
0.121	3249	357	211	0.109879963	0.591036414	0.06494306
0.2281	1945	513	158	0.263753213	0.307992203	0.08123393
0.4513	2109	982	12	0.465623518	0.012219959	0.00568990

It still drops do 0 at the same percentage of crits however it is much higher at lower percentages.

Impact

Scorches	Points In Impact	Procs	Impact %
1955	2	193	9.87
2109	2	192	9.10
1945	1	112	5.76
3249	1	161	4.96

We can all relax it is indeed 5% per point.

Again apologies for broken data in the previous post. Perhaps if Shaewyn redid the graphs we'll be good to go.

Zaldinar · 10/11/10, 5:01 AM

Maje, do you still have the raw combat logs for this?

Maje · 10/11/10, 5:34 AM

Yes, I have 4 separate logs, I changed the files slightly so I can read them as a csv-s but that's it, each has the amount of crit in the file name so it should be easy to match them.

I'll send you the link in a PM if anybody else wants them PM me, since the upload service is limited I don't want it to get capped by random downloads.

EDIT: the best fitting regression function I found was actually a polynom, and we can safely flatten it from around 47% crit where it 0.

y = 3.536191224*x^2 - 3.755802532*x + 0.9861411843

gogetass2 · 10/11/10, 8:22 AM

Regarding combustion, it seems to be double dipping atleast from haste, and I kinda suspect if for other stats aswell.

Here's an sample in FoS on the last boss with ub 2066 int, 2405 sp 561 haste (17,11%) 1135 crit rating (41,07%) and 20.57 mastery (51%)

Had ele shaman (10% sp 5% haste + bloodlust), a warlock (8% spell damage) a prot paladin (kings) and a priest as healer.

Having all the max single target talents + 2/3 haste 3/3 crit and berserking from trolls I got following total combustion damage

Which is 22 tics, where I could max get 18 hits outside lust (including BM).

Weather it double dips from mastery or not and how crit effects it I don't know.

Seems to be a dot that combines all the damage into a new that you essicially apply then modify it again with certain things like haste.

Edit: yes missing the T10 2 set bonus.

• ash2ash · 10/11/10, 9:45 AM

Originally Posted by gogetass2

Regarding combustion, it seems to be double dipping atleast from haste, and I kinda suspect if for other stats aswell.

1.1711(rating)*1.05(WoA)*1.02(NWP)*1.20(Zerking)*1.3(BL) = 1.956, so you should be getting 10 extra ticks with the buffs you typed. Are you sure you're not missing 4pT10 (12% haste), because that would bring it to 2.19, or 22 ticks.

Elimbras · 10/11/10, 11:49 AM

Originally Posted by Shaewyn

Here's the trouble. If T3 HS does not reset T4 HS, then:
$P(\text{T4 HS})=c^2$

if T3 does reset the T4 HS counter (as I suspect), then:
$P(\text{T4 HS})=(c-(0.9472e^{-9.134c}*c))^2$

To make it more explicit (because I'm not sure of which formula you used for which graphs), here are the final formulas, assuming that HS can proc of Fireball and Pyroblast.
1/ If T3 HS reset the counter, we have:
$P(\text{T4 HS}) = P(\text{spell } n-1 \text{ crit and did not proc T3 HS}) \times P(\text{spell } n \text{ crit}) = c^2 (1-k(c))$
and the final formula is:
$P(\text{HS}) = k(c) c + c^2(1-k(c))^2$

2/ If T3 HS does not reset the counter (that's easier to deal with):
$P(\text{HS}) = k(c) c + c^2 (1 - k(c))$

Shaewyn · 10/11/10, 2:43 PM

Alrighty. The updated data from Maje makes for some really interesting math.

The exponential regression is no longer a good fit. Here's the data with polynomial and linear regression lines:

The polynomial curve is a better fit to the data that Maje provided, however, I think that the linear line is probably the correct explanation. The linear model is simpler to manage and implement, and the integral of the linear model is a very nice parabola which nicely balances the T4 Hot streak chance - I would postulate that Blizzard actually started with the integral (per-cast chance) and then applied that to the T3 per-crit chance. Examine these graphs:

When you graph the per cast chance of the two models (i.e. taking the integral of the per-crit function), the linear model gives you a nice parabola with a (relatively) simple formula, and a vertex at 23% crit, 9.1% per cast hot streak chance.

Assuming a linear function for per-crit hot streak chance of: $k(c)=-1.7106c+.7893$

we can get these graphs:

Explicitly, the formulas I've used are:
$k(c)=-1.7106c+.7893$
$P(\text{T3 HS})=k(c)*c$
$P(\text{T4 HS})= c^2 (1-k(c))^2$
$P(\text{HS}) = k(c) c + c^2(1-k(c))^2$

I've use that formula for the T4 HS chance because it gives the net benefit from T4 HS. That is, it gives you:
$P(\text{T4 HS}) = P(\text{spell } n-1 \text{ crit and did not proc T3 HS}) \times P(\text{spell } n \text{ crit and did not proc T3 HS})$

Notable observations from the graphs:

T3 HS gives you no benefit above 47% crit.
With the linear formula, T3 and T4 cross over at about 34% crit chance. That is, below 34% crit, T3 is more valuable, above that point T4 is more valuable.
Below 19% crit, T4 HS gives you less than 1% chance per cast for a HS proc, if you have T3 HS.
Below 9% crit, T4 HS gives you less than 0.1% chance per cast for a HS proc, if you have T3 HS.

I'm not sure of exact DPS % increases per point of T4 HS, but below 19% fully-buffed crit, T4 hot streak is terrible.

Tyrian · 10/11/10, 3:27 PM

I'm not sure of exact DPS % increases per point of T4 HS, but below 19% fully-buffed crit, T4 hot streak is terrible

This immediately made me wonder whether there's any niche builds for fresh 85 mages with low Combat Ratings, which intentionally skip T4 Hot Streak. It appears the answer is no, outside of unrealistic situational encounters.

Talent Calculator - World of Warcraft - This has an easy job reaching Improved Blink and taking full Burning Soul. But losing T4 Hot Streak while at low levels of gear to do this (even if the % chance proc is so low) is not worth it, perhaps only in very specific encounter situations where Imp Blink could shine. (Can anyone think of some precedents where Imp Blink really could be this important or useful? Razorgore in Blackwing Lair could be one. Veteran mages will know the mage strat i'm referring to. Ossirian the Unscarred, Buru, Battleguard Sartura, Ouro submerge phases?)

Talent Calculator - World of Warcraft - The more likely option, but very situational. I removed a point from Piercing Ice, but depending on encounter type you could remove the point from Pyromaniac or Improved Flamestrike instead. If there was an encounter where Invocation could be guaranteed often (lets assume we always get an interrupt off, every CS cooldown) - what would theorycrafters value the talent at? How much DPS would Invocation be for a selection of +SP levels, and how does it compare to Tier 4 Hot Streak for a selection of low crit % ranges? (Bearing in mind it would be a build that skipped T4 Hot Streak to pickup Invocation.)

Also, I edited the (excellent) information provided by Maje and Shaewyn into the OP. In addition, a poster PM'd me recently and they will create a "Cataclysm Mage Resources" thread soon, which will be our mage forums consolidated reference for things such as: Gems, Enchants, Librams, Cataclysm reputations etc.

Maje · 10/11/10, 3:52 PM

I'm assuming T3 scales with your crit, ie. gear + buffs but not target debuffs eg. scorch. I'll make another run to see if it does.

To be honest I don't really like like how T3 is implemented, granted we may never reach the levels of crit we have now at level 85, but if we do come even somewhat close than we have a talent point we can't even utilise and it's a prerequisite for a talent we want (somewhat reminds me of Dragon's Breath and LB).

Anyway I'll run another test, with a gear amount of crit around 19% + Molten Armor (just because I want to make sure it's crit is taken into account by T3) and having Critical Mass to make sure debuffs don't get taken into account.

Maje · 10/11/10, 6:48 PM

Hopefully the last post in the series; I ran a test with the same character, using 7.49% crit chance from gear and Molten Armor + Glyph adding 5% more, I also had Critical Mass in my spec.

Crit Chance	Scorches	Crits	HS procs	Crit %	HS per Crit	HS %
0.1249	2666	483	271	0.181170292	0.561076604	0.10165041

As you can see character crit was 12.49% Critical Mass was adding 5% more so expected crit chance was 17.49% the crit rate during the test was 18.11% so pretty close to expected. Also the hs proc was 56.10% a number which according to the previous data set belongs to a 12.49% crit so it's safe to assume that any crit buff affects T3 proc chance while any target debuffs do not.

EDIT: It would be interesting to know if glyphed Fireball/Pyroblast affects T3 Hot Streak, but given that neither is free or sustainable it would be extremely annoying to check.

Elimbras · 10/11/10, 8:13 PM

Originally Posted by Shaewyn

When you graph the per cast chance of the two models (i.e. taking the integral of the per-crit function), the linear model gives you a nice parabola with a (relatively) simple formula, and a vertex at 23% crit, 9.1% per cast hot streak chance.

Thank you ! It's nice to see that the formula posted here are actually used by others.

This are minor details, but I assume the fact that I'm a mathematician.
1/ What you compute is absolutely not the integral of the per-crit function (and that would not make sense): it's just the multiplication of that function by the crit rate. In particular, the difference is that the integral of a*x is not a*x^2, but a/2 * x^2.
2/ It's even more minor, but the curve you state for the "integral" of the polynomial interpolation can't be the real one. It must be a polynomial of degree three, as the "integral" (or multiplication by x, it does not matter on that aspect) of a polynomial of degree 2.