Elitist Jerks Fire Cataclysm Discussion: OP Updated for Release

 09/15/10, 2:01 PM #76 Zaldinar Don Flamenco     Zaldinar Human Mage   Arygos Not at all. All you need is one occurrence of the following: Scorch Non-Crit Scorch Crit + HS Proc Scorch Crit + no HS proc As soon as you see that series of events you've shown that the proc on an individual cast prevents a follow up proc on a consecutive crit from the improved talent. Proving that it works this way is easy, proving that it *doesnt* is hard, thus the long test to see if it shows up. 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.
 09/15/10, 3:23 PM #77 • ash2ash Operation Asian     Lapsed Undead Mage   Mal'Ganis I think I have the formula figured out to model the new hot streak, based on tier3 hotstreak resetting the tier4 counter: Let m = crit chance Let n = chance to proc tier3 hotstreak on a crit ith spell that could generate a hotstreak (fireball / ffb / scorch / fire blast) $1st: m * n$ < only has a chance of generating a tier 3 hotstreak $2nd: m * n + m * (m - n * m)$ or $m * n + m * (m - 1st)$ $3rd: m * n + m * (m - (n * m + m * (m - n * m)))$ or $m * n + m * (m - 2nd)$ $4th: m * n + m * (m - (n * m + m * (m - (n * m + m * (m - n * m)))))$ or $m * n + m * (m - 3rd)$ ... the (m - ith) factors are the probability that the previous spell was a crit but did not generate a hot streak. Simplify: $m * n + m * (m - (m * n + m * (m - (m * n + m^2 - m^2 * n))))$ $m * n + m * (m - (m * n + m * (m - m * n - m^2 + m^2 * n)))$ $m * n + m * (m - (m * n + m^2 - m^2 * n - m^3 + m^3 * n))$ $m * n + m * (m - m * n - m^2 + m^2 * n + m^3 - m^3 * n)$ $m * n+ m^2 - m^2 * n - m^3 + m^3 * n + m^4 - m^4 * n$ Here's what I get: $\lim_{t \to \infty}\sum_{x=1}^{t}(-1)^{x+1}*(m^{x}*n + m^{x+1})$ I don't think you can fully evaluate the series, but you can determine the chance as n -> infinity with a very low error by taking three or four expansions. Unfortunately, this won't be very meaningful until we have the proc chance (or proc chance formula) for tier3 hotstreak pinned down. Last edited by ash2ash : 09/15/10 at 7:08 PM. I point my camera at stuff and I press buttons: picasaweb.google.com/pariah99
 09/15/10, 3:59 PM #78 Zaldinar Don Flamenco     Zaldinar Human Mage   Arygos Good work. See what you can make of this: Non-Crits Crits Procs 548 441 114 415 209 61 481 134 51 554 107 57 501 47 28 Tests were a level 80 vs a level 1 target dummy in Theramore with varying degrees of worgen nudity to drive the crit rate down. I plan on repeating this on a level 85 dummy with a level 85 premade once it finishes copying. Graphing it makes it look a little odd, I think more data points and isolating out level difference will help even out the noise a little bit. If someone else wants to run a tandem test doing the same thing I'll gladly parse all the combat logs and add them into my data. 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.
09/15/10, 4:23 PM   #79
Sphendule1001
Glass Joe

Orc Shaman

Jaedenar
 Originally Posted by ash2ash I think I have the formula figured out to model the new hot streak, based on tier3 hotstreak resetting the tier4 counter: Let m = crit chance Let n = chance to proc tier3 hotstreak on a crit ith spell that could generate a hotstreak (fireball / ffb / scorch / fire blast) $1st: m * n$ < only has a chance of generating a tier 3 hotstreak $2nd: m * n + m * (m - n * m)$ or $m * n + m * (m - 1st)$ $3rd: m * n + m * (m - (n * m + m * (m - n * m)))$ or $m * n + m * (m - 2nd)$ $4th: m * n + m * (m - (n * m + m * (m - (n * m + m * (m - n * m)))))$ or $m * n + m * (m - 3rd)$ ... the (m - ith) factors are the probability that the previous spell was a crit but did not generate a hot streak. Simplify: $m * n + m * (m - (m * n + m * (m - (m * n + m^2 - m^2 * n))))$ $m * n + m * (m - (m * n + m * (m - m * n - m^2 + m^2 * n)))$ $m * n + m * (m - (m * n + m^2 - m^2 * n - m^3 + m^3 * n))$ $m * n + m * (m - m * n - m^2 + m^2 * n + m^3 - m^3 * n)$ $m * n+ m^2 - m^2 * n - m^3 + m^3 * n + m^4 - m^4 * n$ Here's what I get: $\lim_{n \to \infty}\sum_{x=1}^{n}(-1)^{x+1}*(m^{x}*n + m^{x+1})$ I don't think you can fully evaluate the series, but you can determine the chance as n -> infinity with a very low error by taking three or four expansions. Unfortunately, this won't be very meaningful until we have the proc chance (or proc chance formula) for tier3 hotstreak pinned down.
Nitpick: Wouldn't the end evaluation be the following, instead?
$m*n+\lim_{n \to \infty}\sum_{x=2}^{n}(-1)^{x}*(m^{x} - m^{x}*n)$
There's always an odd number of terms if you expand the other examples, but your summation would produce an even number of terms. Since it's important to have an accurate equation, I felt I should point this out.

 09/15/10, 7:08 PM #80 Leguaran Piston Honda     Altarboy Human Paladin   Uldaman Quick question to not derail the HS discussion: Was the 10% spellpower buff on the fire spec raid utility scrapped? I'm not finding it.
 09/15/10, 7:19 PM #81 Maje Don Flamenco   Maje Gnome Mage   Naxxramas (EU) 10% buff isn't there for mages, there weren't any comments from blues about it. Also from some limited testing I've done, T3 HS proc doesn't reset T4 procs. Which does makes sense since obviously there is already an inverse relationship between crit rating and T3 procs.
09/15/10, 7:32 PM   #82
ash2ash
Operation Asian

Mal'Ganis
 Originally Posted by Sphendule1001 Nitpick: Wouldn't the end evaluation be the following, instead? $m*n+\lim_{n \to \infty}\sum_{x=2}^{n}(-1)^{x}*(m^{x} - m^{x}*n)$ There's always an odd number of terms if you expand the other examples, but your summation would produce an even number of terms. Since it's important to have an accurate equation, I felt I should point this out.
I kind of did it by just inspecting the final simplification and extracting a pattern. I think the problem is that my summation takes the contribution of not just the current iteration, but part of the next iteration as well (like plugging in t = 1 would give you m * n + m^2). I had to do it like this because the $m^s * n$ term starts at s = 1 while the $m^s$ term starts at s = 2. It should all work out in the end if you take it to infinity.

Back to some other stuff I noticed on the ptr:
• Pyroblast consumes the hot streak buff even if it doesn't have the cast time reduction. This isn't too much of an issue on live, but with the reduction in cast time of pyroblast, there's a good chance that the damage per execute time would beat out fireball even without the hot streak buff if there is no dot on the target. (ticket submitted)

• Combustion is wierd. It looks like it's only hitting for ~74.5% of what it should be off all dots except ignite.
Pyroblast = 691 per tic * 4 tic = 2764
Combustion = 206 per tic * 10 tics = 2060
2060/2764 = 74.5%
Living bomb = 1622 per tic * 4 ticks = 6488
Combustion = 485 per tic * 10 tics = 4850
4850/6488 = 74.7%
• Ignite and combustion produces some really interesting results:
7094 scorch crit * 0.4 * 1.2 = 3405 damage
Combustion = 1023 damage per tic * 10 tics = 10230
10230 / 3405 = 300%
12198 fireball crit * 0.4 * 1.2 = 5855 damage
Combustion = 1759 damager per tic * 10 tics = 17590
17590 / 5855 = 300%

I really can't find an explanation for what's going on, but if I had to guess, there's probably some double dipping going on with ignite. The non-ignite dots are probably low due to combustion not factoring in flashburn or fire mastery - there's something else going on since dividing the damages by 1.25 and 1.2 still don't produce numbers like I'm seeing.

I point my camera at stuff and I press buttons:

 09/15/10, 8:02 PM #83 Maje Don Flamenco   Maje Gnome Mage   Naxxramas (EU) Current living bomb implementation is extremely annoying, espesially trying to Impact spread the dots causes it to be removed from the main target if there are more than 3? targets around. Why not just limit the amount of exploding LBs to 3 while the rest just do the dot damage and fade.
 09/15/10, 11:32 PM #84 Shiyo Von Kaiser     Shiyo Tauren Shaman   Gurubashi Why not use a Markov chain to model hot streak? Assuming that the tier 3 hotstreak resets the tier 4 counter (intuitively I'd say it does, but it's easy to model either way): $P$ is a transition matrix, where row 1 represents state 1 (hotstreak counter=0). Row 2 is state 2 which follows state 1 after 1 crit has occurred, and row 3 is state 3 for a hotstreak proc, which always leads back to state 1. Each column is the probability to go to the respective state. $k$ is the chance of tier 3 hotstreak to proc, which is unknown at this time $c$ c is crit chance $P=\left( \begin{array}{ccc} 1-c &(1-k)c=&kc \\ 1-c=&c \\ 1=&0 \end{array} \right)=$ We can use $P$ to see which state $x(n)$ is in by using a recursive formula $x(0)=\left( \begin{array}{ccc} 1 &0 \end{array} \right)=$ since the first spell of any fight will be in state 1 $x(1)=x(0)*P=\left( \begin{array}{ccc} 1 &0 \end{array} \right)*\left( \begin{array}{ccc} 1-c=&(1-k)c=&kc \\ 1-c=&c \\ 1=&0 \end{array} \right)=\left( \begin{array}{ccc} 1-c &(1-k)c=&kc \end{array} \right)=$ Similarly expanding this we would get $x(2)=\left( \begin{array}{ccc} 1-c+2kc+kc^2 &c-c^2-kc+kc^2=&c^2-2kc^2+kc \end{array} \right)=$ Each further step, we can see it gets increasingly complex $x(n)=x(n-1)*P=x(0)*P^n$ To evaluate this model, we'll need to find a steady state vector. This vector is independent of initial conditions. $h=\lim_{n \rightarrow \infty} x(n)$ Since $h$ is independent of initial conditions, it'll be unchanged by being transformed by $P$. $hP=h$ $hP=hI$ $I$ is an identity matrix. $hP-hI=0$ $h(P-I)=0$ $h(\left( \begin{array}{ccc} 1-c=&(1-k)c=&kc \\ 1-c=&c \\ 1=&0 \end{array} \right)-\left( \begin{array}{ccc} 1=&0 \\ 0=&1=&0 \\ 0=&1 \end{array} \right))=0$ $h(\left( \begin{array}{ccc} -c=&(1-k)c=&kc \\ 1-c=&-1=&c \\ 1=&-1 \end{array} \right))=0$ $\left( \begin{array}{ccc} h_1=&h_2=&h_3 \\ \end{array} \right)*\left( \begin{array}{ccc} -c=&(1-k)c=&kc \\ 1-c=&-1=&c \\ 1=&-1 \end{array} \right)=\left( \begin{array}{ccc} 0 &0 \end{array} \right)=$ This gives us three different equations: $-h_1c+h_2-h_2c+h_3=0$ $h_1c-h_1kc-h_2=0$ $h_1kc+h_2c-h_3=0$ And since we're talking about probabilities, we know that $h_1+h_2+h_3=1$ Now, using algebra we get these terms: $h_1=( \frac{1}{1+2c+kc^2} )$ <-Fireballs/Scorches/Frostfire Bolts from state 1 $h_2=( \frac{c-kc}{1+2c+kc^2} )$ <-Fireballs/Scorches/Frostfire Bolts from state 2 $h_3=( \frac{c+kc+kc^2}{1+2c+kc^2} )$ <- Pyroblasts from state 3 Ultimately we get a ratio of Pyroblasts to non Pyroblasts of $( \frac{c+kc+kc^2}{1+2c+kc^2} )$ I don't mean to step on any toes, use whatever model you want. I plan on using this in my spreadsheet once numbers get finalized. I read most caster forums on this page frequently and don't often post, and have been working on mage theorycrafting once the Cata classes were announced. I'm pretty good at parroting others and doing simple algebra.
09/16/10, 1:57 AM   #85
jontaxe
Glass Joe

Troll Shaman

Llane
 Originally Posted by ash2ash I really can't find an explanation for what's going on, but if I had to guess, there's probably some double dipping going on with ignite.
There is almost certainly rampant double dipping of all sorts. As an anecdotal data point, my elemental shaman has a 1.07 sec cast time lightning bolt (base time 2.5s, reduced to 2 with shamanism) with 39.68% haste. Premade shaman I talked to are seeing more reasonable numbers, so I speculate that shamanism is being applied twice. (2.5 base time -> 1.5s base time with double shamanism / 1.3968 = my cast time of 1.07). My mage, OTOH, was arcane when it was copied over and I am seeing reasonable numbers for fire crit % and ignite damage.

 09/16/10, 4:44 AM #86 arch Don Flamenco     Eriond Undead Mage   Al'Akir (EU) I guess I should stop whining about FFB not having a role for fire cause it does have one. I didn't think of it before, but it actually benefits from fire specilization, thus it will be our highest damage slowing nuke. Guardian of Fire PvP since 2005!
09/16/10, 1:10 PM   #87
Bashram
Von Kaiser

Human Mage

Bleeding Hollow
Just out of idle curiosity, is there any reason that someone hasn't just looked into the game files to determine the chance to proc non-improved Hot Streak?

However it procs, Hot Streak's scaling is much improved--it looks like a mage with 20% crit would have a proc rate similar to that of a mage on Live with 45% crit. And a mage with 45% crit would have a proc rate similar to that of a mage on Live with 63% crit. That's a very, very nice change. Given that, with base crit, talents, and raid buffs, we would have 23% crit before factoring in Intellect and Crit Rating, we'll probably be able to get to 45% crit by the end of the expansion--giving us a proc rate similar to what we get in 251/264 gear.

Edit: Working with Shiyo's final ratio and my egregious assumption of a 33% proc rate on unimproved Hot Streak, a mage with 30% crit would cast .25 Pyroblasts for every other spell. This is actually higher than I had expected. A 25% proc rate on Hot Streak? Yes, please. And, yes, I know that we have no confirmation on what the proc rate is or whether it scales inversely with crit, but I like thinking.

 Originally Posted by arch I guess I should stop whining about FFB not having a role for fire cause it does have one. I didn't think of it before, but it actually benefits from fire specilization, thus it will be our highest damage slowing nuke.
While it will be useful in PvP and leveling scenarios, the current coefficients are such that Frostfire Bolt will not have a role for raiding Fire mages. As I realized on the last page, it would require a ridiculous level of Mastery to bring the Frostfire glyph DoT to a point at which Frostfire Bolt would be worth casting to maintain said DoT.

In light of that, and given that Hot Streak looks to have a proc rate similar to what it has been for the later part of this expansion, Fire's rotation will more or less be exactly the same, barring the occasional Flame Orb and more proactive use of Combustion. Are we okay with this? (Edit: Note that, if unimproved Hot Streak does have a 33% proc rate, then we'll actually be getting more Hot Streaks than we do currently.)

Further editing!

I may have to reconsider my earlier dismissal of Improved Scorch. Since the Character Copy queue is longer than the Premade queue, I got impatient and copied over a premade mage to the Test Realm. I specced him Fire, juggled between the PvE and PvP gear until I had levels of haste and crit that I feel would be appropriate for the early raiding tiers in Cataclysm, and was off to hit the target dummies.

It quickly became apparent to me that Fire runs out of mana very easily. Using gems and Evocation on cooldown, I still had periods where I was casting Scorch because I couldn't afford to cast anything else. These periods ranged from a few seconds to a minute--however long was left until Evocation or Mana Gem was off cooldown.

Is it possible that we are meant to throttle our DPS somewhat by weaving in Scorch casts, switching to pure Fireball spam only during burn phases? I assume that Replenishment and Arcane Concentration would not make enough of a difference to overcome this issue, but I could be wrong.

Last edited by Bashram : 09/16/10 at 7:50 PM.

09/16/10, 8:27 PM   #88
Allecto
Glass Joe

Human Mage

Arathor
 Originally Posted by Bashram Further editing! I may have to reconsider my earlier dismissal of Improved Scorch. Since the Character Copy queue is longer than the Premade queue, I got impatient and copied over a premade mage to the Test Realm. I specced him Fire, juggled between the PvE and PvP gear until I had levels of haste and crit that I feel would be appropriate for the early raiding tiers in Cataclysm, and was off to hit the target dummies. It quickly became apparent to me that Fire runs out of mana very easily. Using gems and Evocation on cooldown, I still had periods where I was casting Scorch because I couldn't afford to cast anything else. These periods ranged from a few seconds to a minute--however long was left until Evocation or Mana Gem was off cooldown. Is it possible that we are meant to throttle our DPS somewhat by weaving in Scorch casts, switching to pure Fireball spam only during burn phases? I assume that Replenishment and Arcane Concentration would not make enough of a difference to overcome this issue, but I could be wrong.
I had a completely different experience on the PTR with my mostly 277 geared character copy. Mana wasn't an issue, and I didn't see a reason to Scorch since Hot Streak proc'd more than frequently enough to keep Critical Mass up. And that was only self buffed. So IMHO, the only question remaining for single target Fire is whether to weave in FFB or simply spam FB while keeping LB up.

09/16/10, 8:48 PM   #89
Bashram
Von Kaiser

Human Mage

Bleeding Hollow
 Originally Posted by Allecto I had a completely different experience on the PTR with my mostly 277 geared character copy. Mana wasn't an issue, and I didn't see a reason to Scorch since Hot Streak proc'd more than frequently enough to keep Critical Mass up. And that was only self buffed. So IMHO, the only question remaining for single target Fire is whether to weave in FFB or simply spam FB while keeping LB up.
Part of my test, as I pointed out, involved mixing the premade's PvP and PvE gear in order to drive my combat ratings down. Blizzard has officially stated that they are unhappy with how high combat ratings got in end-game Wrath. Using 277 gear is more or less entirely unhelpful in attempting to model spec performance in Cataclysm, especially for entry-level raiding. Effectively, you modeled a situation that we have been told is not supposed to occur. With your crit rate, you were probably getting a large amount of mana back from Master of Elements and saving a hell of a lot from all the Hot Streaks you must have been proccing. Moreover, several beta testers have mentioned Fire's mana inefficiency--some even theorizing that Fire mages might have to raid in Mage Armor.

However, even in my premade's gear, Scorching was rarely necessary to maintain Critical Mass. Hot Streak is usually up enough to maintain the debuff by itself.

As far as Frostfire Bolt, current coefficients discourage it. The math is on the previous page.

 09/17/10, 4:06 AM #90 Zaldinar Don Flamenco     Zaldinar Human Mage   Arygos Test request for someone on the PTR or Beta that has trained Mastery (I'm going to finish up a non-mastery round of this tonight, but I figured I'd ask if someone else can gather this with mastery and save some time): 1) Spec fire, have at least LB, combustion, and ignite specced, link the spec you're using, and the tooltip added amount of damage from Flashburn. 2) Find a target dummy equal to your level if available, otherwise note the level disparity. Remove any proccy trinkets, rings, etc that add spell power. 3) Cast a Living Bomb on the target, allow it to explode, record both tick values and kaboom value (a /combatlog will suffice if you don't want to type the numbers out) and note whether or not the values were crits 4) Cast another living bomb on the target, allow one tick to happen and cast combustion. Note the DoT tick, combustion initial damage and whether or not the initial combustion hit crit, then the combustion tick damage. 5) Cast a Pyroblast on the target, allow one tick to happen and cast combustion. Same damage recording as above. 6) Cast scorch until you get a crit, allow one tick of ignite damage to happen then cast combustion. Same deal. 7) Cast a Pyroblast->LB combo, allow one tick from each and cast combustion. Same deal recording both LB and Pyro ticks. 8) Keeping LB up, cast scorch until you get a crit, allow one tick of ignite damage to happen then cast combustion. Same deal recording both LB and Ignite ticks. 9) If you're feeling adventurous, try to get a LB + Pyro + Ignite DoT to align, let ignite tick once, and combustion. Same deal recording all ticks going into it. 9 is really just icing on the cake. I think that Mastery is doing wonky things to combustion, I'll post up my findings sans-mastery when I can finish up gathering the last few data points. Edit: Thanks to Rugz and Calindra for sending over test data. I'll post conclusions in a bit. Edit2: Conclusion is that this still makes no damned sense. I'll format up what they sent in a pretty way and give some explanation later today. Last edited by Zaldinar : 09/17/10 at 10:07 AM. 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