Elitist Jerks Fire Cataclysm Discussion: OP Updated for Release

 09/20/10, 5:34 PM #106 Skallewag Piston Honda     Skalleper Gnome Mage   Moonglade (EU) Hmm, I´m not convinced. Fireball ought to be higher dps without setbonus support. During the course of an expansion setbonuses are somewhat temporary. First you haveto aquire the gear and you have it a very powerfull bonus will restrict your choise on upgrades and when the upgrades are finally major enoughe to outweigh the bonus you´re back to square one. I guess fireball might have outscaled scorch by the time you want to replace the set but it still seems odd that those spells should be so close to eachother untill way into raiding content. A good mage should always shine but a casual one should still be able to look at a spec and grasp the basics of how it works. Plopp plopp kaboom! This is an intelligent signature.
 09/20/10, 5:45 PM #107 Bashram Von Kaiser     Bashram Human Mage   Bleeding Hollow With the recent increase to Fireball's damage, glyphed Frostfire Bolt is even less likely to work its way into Fire's rotation. While I have no proof that we wouldn't reach the level of mastery required to make it worth casting over Fireball, I find it highly unlikely that we would. If nothing else, the interaction between Flashburn and Ignite would make crit too ridiculously valuable for Fire. And removing Ignite from Flashburn's bonus would make the mastery too weak of a statistic. Scorch, meanwhile, received a ridiculous boost. Beta mages are now spamming Scorch and doing more damage than they do casting Fireball. This isn't going to last, methinks. Either numbers will be tweaked or entry-level gear will have enough Intellect to render Scorch redundant. As far as Fire being a more movement-and-adds based spec, I'm not sure I'm comfortable with that vision. Yes, we should consider the existence of such fights...but we should also be aware that single-target fights do exist. I'm worried that we're going to be balanced around movement and/or adds. Pyromaniac scares the crap out of me for just this reason--if I had to pick a talent to be replaced by something new, Pyromaniac would be the one to get the axe. On a different note, a possible solution to the mana problem might be a slightly altered version of Empowered Fire's second effect. It could be tacked on to...Molten Fury, I guess? I'm thinking something along the lines of: Molten Fury 3 Ranks Increases damage of all spells against targets with less than 35% health by 4/8/12%. In addition, whenever one of your periodic fire damage effects deals damage, you have a 33/66/100% chance to regain 2% of your base mana. Assuming that the DoTs are allowed to tick fully, Living Bomb and Pyroblast would give back 8% base mana, Ignite would give 4%, and Combustion would give 20%. It wouldn't be a ridiculous amount, but it would keep us floating a little more comfortably than we do now. Last edited by Bashram : 09/20/10 at 6:12 PM.
 09/21/10, 12:13 AM #108 Frah Von Kaiser   Frah Human Mage   Frostmane (EU) I have been a bit fed up of the queues for instances on beta so I decided to spam a target dummy with various amounts of crit to see the T3 hotstreak proc chance with various low amounts of crit. Basically with anything 20% or less the chance seems to be in the 70-75% region. I was looking to see if the chance to proc per crit was your chance to not crit. This seems to not be true though. I can't get more than 20% crit self buffed so cant test with higher values atm EDIT World of Logs - Real Time Raid Analysis thats the log. 556 crits 388 procs roughly 70% proc 20% crit from gear 5% crit debuff on mob level 60 target dummy no improved hot streak Last edited by Frah : 09/21/10 at 1:26 AM.
 09/21/10, 6:53 AM #109 Maje Don Flamenco   Maje Gnome Mage   Naxxramas (EU) Thanks for the log; There is something odd going on with Ignite, I'm guessing the mastery bonus is ~31.9%. As seen from the following. [04:21:34.733] Fragain Scorch Old Worlder's Training Dummy *1* (O: 6988) [04:21:36.855] Fragain Ignite Old Worlder's Training Dummy 1 (O: 1841) [04:21:38.779] Fragain Ignite Old Worlder's Training Dummy 1 (O: 1841) [04:21:38.779] Old Worlder's Training Dummy's Ignite fades Now check the following: [04:28:20.514] Old Worlder's Training Dummy's Ignite fades [04:28:21.517] Fragain Scorch Old Worlder's Training Dummy *1* (O: 7180) [04:28:22.705] Fragain Scorch Old Worlder's Training Dummy *1* (O: 6939) [04:28:23.878] Fragain Ignite Old Worlder's Training Dummy 1 (O: 2481) [04:28:26.002] Fragain Ignite Old Worlder's Training Dummy 1 (O: 2481) [04:28:28.007] Fragain Ignite Old Worlder's Training Dummy 1 (O: 2481) [04:28:28.007] Old Worlder's Training Dummy's Ignite fades Why 3 Ignite ticks... there should be 2 the damage does seem to add up (somewhat 14121 * 0.4 * 1.319 = 7450.2396 actual 2482 * 3 = 7446). For the full log expected Ignite damage is 3,936,673 * 0.4 * 1.319 -> 2,076,988.6748 actual 2,025,397 or about 51.5k less.
 09/21/10, 7:42 AM #110 Zaldinar Don Flamenco     Zaldinar Human Mage   Arygos They definitely changed Tier 3 HotStreak from its earlier state, I'm not seeing it scale with crit rate anymore. Here's what I've got from four tests last night: Procs Crit NonCrits 122 170 1421 22 28 1479 194 280 1046 94 119 71 Crit Rate Procs Per Crit 0.106851037 0.717647059 0.01857996 0.785714286 0.211161388 0.692857143 0.626315789 0.789915966 Which comes out to a 70-78% proc rate, the 78% ones being on low data point count tests. Test 4 used Frost Nova and Shatter to drive the crit rate up to 62%. A 70% flat proc rate may not be a bad assumption at the moment, which is a bit ridiculous. And Maje on your ticks on ignite, how much haste do you have? Haste is supposed to add an extra tick when you're fast enough to fit one into the normal debuff window. To truly model the game, we first must research it. http://zaldinar.wordpress.com/ Proven TheoryCrafting Stuff, chain casting in a PTR near you soon.
 09/21/10, 8:41 AM #111 Maje Don Flamenco   Maje Gnome Mage   Naxxramas (EU) The log isn't actually mine, it's Frah's, see the post above the one I made. Though it doesn't make much sense at all because Ignite ticks every 2 seconds, as far as I know haste will not make ignite last 6 secons on the target, which is the case in what I linked. EDIT: Actually I know what happens: [04:28:21.517] Fragain Scorch Old Worlder's Training Dummy *1* (O: 7180) [04:28:21.919] Old Worlder's Training Dummy afflicted by Ignite from Fragain [04:28:22.705] Fragain Scorch Old Worlder's Training Dummy *1* (O: 6939) [04:28:23.123] Old Worlder's Training Dummy's Ignite is refreshed by Fragain [04:28:23.878] Fragain Ignite Old Worlder's Training Dummy 1 (O: 2481) [04:28:26.002] Fragain Ignite Old Worlder's Training Dummy 1 (O: 2481) [04:28:28.007] Fragain Ignite Old Worlder's Training Dummy 1 (O: 2481) [04:28:28.007] Old Worlder's Training Dummy's Ignite fades In this case Ignite is applied [04:28:21.919] and should tick in 2 seconds, it's also refreshed just as it's about to tick so it ticks after 2 seconds and gets refreshed for another 4 which amounts to 6 seconds or 3 ticks. So there is only the odd damage differences to account for in this case about 51k damage. Last edited by Maje : 09/21/10 at 8:52 AM.
 09/21/10, 10:06 AM #112 Bashram Von Kaiser     Bashram Human Mage   Bleeding Hollow Now, I'm no brilliant mathematician, but I'm competent enough to be able to use most of the formulae I run across. In testing Hot Streak proc rates, I've noticed a discrepancy between ash2ash's series and Shiyo's Markov Chain. For those who don't want to click back to page three, here are the formulae: ash2ash worked out this series: $\lim_{t \to \infty}\sum_{x=1}^{t}(-1)^{x+1}*(m^{x}*n + m^{x+1})$ Shiyo's Markov Chain ended with this ratio of Pyroblasts to non-Pyroblasts: $( \frac{c+kc+kc^2}{1+2c+kc^2} )$ Now, working with the new observed proc rate of 70% on unimproved Hot Streak, I tested both equations at 23% crit and 56% crit.* The series yielded Hot Streak proc rates of 17.39% at 23% crit and 44.64% at 56% crit. The Markov Chain, however, yielded proc rates of 28.59% at 23% crit and 50.08% at 56% crit. Something is clearly up--especially since the Markov Chain allows you to have a Hot Streak proc rate that is higher than your crit chance. Of course, as I said, I'm no mathematician. I could just be doing things wrong. *These arbitrary crit values are slightly less than arbitrary. With base crit, raid buffs, and talents, a Fire mage with zero intellect and no critical strike rating would have a crit chance of 23%. I highly doubt that we'll reach more than 33% additional crit from gear, so I used that ceiling as the upper crit chance that I tested.
09/21/10, 11:05 AM   #113
Tyrian
Bald Bull

Human Mage

Frostmourne
 Originally Posted by Zaldinar A 70% flat proc rate may not be a bad assumption at the moment, which is a bit ridiculous..
Would make sense, I initially read these comments as Blizzard having balanced the proc rate around an expected 20-25% crit for Cataclysm. With a 70% proc rate at that crit level, it should average out to Hot Streak Pyro being the equivilant of Frosts' Brain Freeze proc rate, ~15%.

09/21/10, 11:41 AM   #114
Zaldinar
Don Flamenco

Human Mage

Arygos
 Originally Posted by Tyrian Would make sense, I initially read these comments as Blizzard having balanced the proc rate around an expected 20-25% crit for Cataclysm. With a 70% proc rate at that crit level, it should average out to Hot Streak Pyro being the equivilant of Frosts' Brain Freeze proc rate, ~15%.
Could be. 0.7 * 0.2 = 0.14 and 0.7 * 0.25 = 0.175, this is true, but that doesn't take into account improved HS increasing the proc rate slightly. Once the calculus folks generate a graph we can see how things look over an expected reasonable crit range (say, 15%->40%?)

To truly model the game, we first must research it.
http://zaldinar.wordpress.com/
Proven TheoryCrafting Stuff, chain casting in a PTR near you soon.

09/21/10, 12:15 PM   #115
andastra
Don Flamenco

Human Mage

Kilrogg
 Originally Posted by Tyrian Would make sense, I initially read these comments as Blizzard having balanced the proc rate around an expected 20-25% crit for Cataclysm. With a 70% proc rate at that crit level, it should average out to Hot Streak Pyro being the equivilant of Frosts' Brain Freeze proc rate, ~15%.

That would make improved hot streak a lackluster talent, however. At 25% crit rate, it just bumps the proc rate for the spell after a crit from 17.5% to 25% for 2 points. It would make sense at that point to make hot streak the 2-point talent and improved hot streak the 1-point talent.

09/21/10, 12:34 PM   #116
Elimbras
Don Flamenco

Dwarf Priest

Eitrigg (EU)
 Originally Posted by Bashram [...]
In short, both are not valid ;-)

In long :

1/ Shivo solution:
There is a detail error in Shiyo final solution. The equation system is valid, but its solution is
$h_1=( \frac{1}{1+2+c^2-kc^2} )$ <-Fireballs/Scorches/Frostfire Bolts from state 1
$h_2=( \frac{c-kc}{1+2+c^2-kc^2} )$ <-Fireballs/Scorches/Frostfire Bolts from state 2
$h_3=( \frac{c^2+kc-kc^2}{1+c+c^2-kc^2} )$ <- Pyroblasts from state 3

leading to a ratio of Pyroblast / Non-Pyroblast of
$Proc_{HS}=\frac{kc+ (1-k)c^2}{1+(1-k)c}$

2/ Ash2ash solution: First, I've done the explicit computation of the series, as well as (shorter) computation of the limit.
But more importantly, the modelization was not correct : you need to be really carefull when modelling such talents, and it's better to write everything in a proper probabilist setting, and verify the axioms at each simplification step.

It is possible to have closed-form formula for Ash2ash method (rewriting with more Shiyo more conventional notations)
$S\lim_{A \to \infty}\sum_{n=1}^{A}(-1)^{n+1}*(c^{n}*k + c^{n+1})$
$S= kc + \lim_{A \to \infty}\sum_{n=1}^{A}(-1)^{n+1}*(- c^{n+1}*k + c^{n+1})$
$S= kc + c^2 \lim_{A \to \infty}\sum_{n=0}^{A}(-1)^{n}*((1-k)* c^{n})$
$S= kc + c^2 * (1-k) * \lim_{A \to \infty}\sum_{n=0}^{A}(-c)^{n}$
$S= kc + c^2 * (1-k) * \lim_{A \to \infty} \frac{1 - (-c)^{n+1}}{1+c}$
$S= kc + c^2 * (1-k) * \frac{1}{1+c}$
$S= \frac{kc+c^2}{1+c}$

Note that this limiting result was easier to obtain.
Ash2ash method is based on the following recurrence on the probability to proc HS at the n Fireball :
$P_n= k*c + c * (c- P_{n-1})$
At the limit l, we have l = k*c + c^2 - l*c, and hence
l = (kc + c^2) / (1+c).

However, the base recursion is not valid. Consider a probabilistic setting.
The first term is the probability of T3 HS.
The second term is (but without proper justification) the probability of T4 HS. However, both events are not exclusive. You can crit for a second time in a row, but also have simultaneously the T3 proc chance that is triggered. This leads only to a single HS proc, but is counted here twice.

In other words, the correct recursion is :

$P(\text{Spells n procs})= P (\text{T3 HS}) + P (\text{T4 HS AND no T3 HS})$
$P(\text{Spells n procs})= P (\text{Spell n crits}) * P(\text{T3 random variable}) + P(\text{Spell n crits and does not proc T3 HS}) * P(\text{spell (n-1) critted and had not procced any HS})$

By definition, a HS can be procced only on crit spells. Hence, Hs procs events are included in crit events, and we have that
P(Spell n-1 critted and did not procced any HS) = P(spell n-1 critted) - P(spell n-1 procced any HS).

The correct recursion is then :
$P_n= k*c + (1-k)*c * (c-P_{n-1})$
Its limit p verifies :
$p= k*c + (1-k)*c*(c-p) = k*c +c^2 - k*c^2 - p * (c-k*c)$
$p= \frac{k*c + c^2 (1-k)}{1 + c (1- k)}$

You can verify that it is the same as the (corrected) Shiyo result.

Final comment:
I've corrected both formulas. But please note that HS was changed in a recent patch, and can now procs from Pyroblast also. Hence, both models are currently not valid.
The new models, and their solution, are left as exercise to the reader (but they are a lot simpler).

Last edited by Elimbras : 09/21/10 at 12:45 PM. Reason: Weird page editing + final comment

 09/21/10, 1:06 PM #117 Frah Von Kaiser   Frah Human Mage   Frostmane (EU) The log I did earlier was with 12.72 mastery rating (Increases the dmg done by all periodic fire effects by 31%) haste was 6.53%. In case this does anything for ignite. That log might not be the best to check for ignite I think I started the log without mastery and finished with since I wanted to get 3% haste in arcane. I will spam scorch with no haste and what little haste I can get and see what it's doing with ignite. :P I will also find something else to watch on TV or a movie and spam fireball and see if the 70% is the same for it. Lastly I am going do the same again with the improved hot streak and see if it really is improved or broken :P
09/21/10, 1:06 PM   #118
Bashram
Von Kaiser

Human Mage

Bleeding Hollow
 Originally Posted by Elimbras Mathmathmath $p= \frac{k*c + c^2 (1-k)}{1 + c (1- k)}$
Ahhh, okay. With this equation and a 70% proc chance of unimproved Hot Streak, 23% crit gets you a proc rate of about 16.55% and 56% crit gets you a proc rate of about 41.62%. Obviously, those are slightly off due to Pyroblast proccing Hot Streak, but they're close enough for a rough estimate.

That means that, in entry-level gear, Hot Streak will proc about as much as Brain Freeze. If combat ratings get inflated to the point at which we have 33% crit from gear--which I believe Blizzard wanted to avoid--it will proc about as much as Arcane Missiles.

That continuum seems really clean to me, personally--puts us as a sort of middle-ground between Frost and Arcane in terms of proc chance. We'll never be gods of Pyroblast-spam, but we still get a nice increase to proc frequency.

Edit: If the proc rate of unimproved Hot Streak were changed to 1-c, 23% crit would give you a 17.98% proc rate and 56% crit would give you a 32.13% proc rate. So, our entry-level proc rate would be a little higher, while we wouldn’t scale to ridiculous levels. Even at 90% crit, Hot Streak would only have a 45% proc rate. While I had been previously hoping for a static modifier, I must admit that 1-c would be a rather good model.

Last edited by Bashram : 09/21/10 at 2:49 PM.

 09/21/10, 1:14 PM #119 Maje Don Flamenco   Maje Gnome Mage   Naxxramas (EU) Those equations are also not valid simply because at the moment T3 Hot Streak doesn't reset T4 procs (and they assume it does), so if you get a T3 HS from one crit the next crit will proc the T4 one.
09/21/10, 1:41 PM   #120
Zaldinar
Don Flamenco

Human Mage

Arygos
Build 12984 numbers on Level 85 Combustion with *no* mastery (not even trained).

Pyro: 522 Tick
Combust: 5650 Crit, 173 tick

LB: 1355 Tick, 1355 Kaboom
Combust: 5688 Crit, 451 tick

Scorch: 5542 Crit, 1109 Ignite
Combust: 5636 Crit, 554 tick

LB: 1355 Tick, 1355 Kaboom
Pyro: 522 Tick
Combust: 5570 Crit, 755 tick

Pyro: 11115 Crit, 2223 Ignite, 522 Tick
LB: 1355 Tick
Combust: 5530 Crit, 1764 Tick

It lines up exactly as expected on the LB + Pyro grouping if we ignore the LB explosion (Not a bad assumption), at ~83% of expected for only LB (no kaboom, 66% with) or only Pyro. And 147% of expected for LB + Pyro + Ignite (no kaboom, 132% with).

In short, it still looks wonky even without mastery. It seems to get extra damage out of ignite, and gets different damage out of summing DoTs than the DoTs themselves.

edit:

 Originally Posted by Maje Those equations are also not valid simply because at the moment T3 Hot Streak doesn't reset T4 procs (and they assume it does), so if you get a T3 HS from one crit the next crit will proc the T4 one.
I assume you have some sort of documented test to back this up? Last push there was a combat log with a case of:

Scorch non-crit
Scorch Crit, HS proc (Through Tier 3)
Scorch Crit, No HS proc

Indicating the inverse.

Last edited by Zaldinar : 09/21/10 at 1:53 PM.

To truly model the game, we first must research it.
http://zaldinar.wordpress.com/
Proven TheoryCrafting Stuff, chain casting in a PTR near you soon.

 Elitist Jerks Fire Cataclysm Discussion: OP Updated for Release