We all know that level 80 talents are not balanced in the slightest at level 70. They aren't even terribly balanced at level 80 in poor gear. The problem is mage instants really do not scale very well at all, which just leads to us being overpowered and consequently nerfed when gear is bad and then being overpowered when gear actually gets decent. The change was probably justified for most of the pvp that is currently going on right now on the ptr and on beta but it was a change that further guarantees that mages won't scale well and additionally hurt the already boring frost play style.. Basically.. The change was poorly thought out and will only hurt us in the long run. Again this has already been discussed upthread so do take the time read back a ways before posting.

Sorry, but balancing the spell for starter level 80 gear in duels is poor thinking, and Blizzard's falling into the same trap you are, and for a second expansion in a row. DF is already significantly less powerful in group PvP (which is supposedly where balance is focused) due to healing and dispels, and when season gear starts to roll out, mages will once again be left with poorly scaling instants and terrible damage compared to melee who scale far better with their weapon dps increases.

This was an ill-conceived nerf even from a PvP standpoint, but I'll let Affix do most of the arguing on that front since my focus is on PvE. I'm at least smart enough about PvP to know not to think about balance in ANY way based on duels, though.

For pvp scaling, basically, what it all comes down to is the scaling of Cone of Cold, Fireblast, and Ice Lance. A PoM Pyro spec with arcane barrage will have less issues with scaling, but I only see it being superior to frost in 2s in the long run, maybe I'm being close minded. My thoughts are you have arcane barrage which has a very good coefficient and pyroblast scales very well. With the nerf to deep frost, I think it does lower the build closer to arcane's level.

The biggest culprit with our scaling issues is Ice Lance being simply terrible. They should really ramp up the spell damage coefficent on frozen targets.

With the nerf to JoW I pulled the point out of Arcane Power simply because Mage_Arcane was right on the mana-sustainability edge and popping AP pushed it over the edge. When I rolled back the JoW change, I did not put AP back in.

Mage_Arcane_Slow is wasting time and mana to keep Slow up on the target so that the other Mage specs can take advantage of Torment.

A note on specs: I have no personal experience raiding outside of a Shadow Priest. While it is easy to identify the talents that provide consistent DPS gains vs the ones that provide little/no gain....... it is much harder for me to identify the good utility/survivability/filler talents.

Therefore, the specs in the SimulationCraft config files should not be used as recommendations for raiding. (Feel free to quote me on this anytime for any reason!) They are merely a method of analyzing a very narrow aspect of raiding: Single-target damage, no AoE, no moving around, full burn, etc.

I would love to have someone (unlike myself) with real Mage experience take over ownership of the SimulationCraft Mage model and profiles. As I've said multiple times: I know how to build the car.... and I can drive it to the grocery store..... but not on the racetrack.

The error introduced in modeling procs as a flat buff is one of under-reporting benefits under stacked cooldowns if you can synchronize them to full effect.
The error introduced by modeling dependancy on stacked cooldowns is that you need to be able to synchronize those cooldowns to the boss fight in question.
If you wind up having to move to avoid the proverbial fire when you just hit your cooldowns you lose huge dps.

Modeling will never be fully accurate and certain fights will be better for specs that show lower dps in these calculations that we run. However, if frost is 1000 dps lower than the fire under these models, it better bring something to the run that you really need. Otherwise the raid leader really ought to be talking to you about respecing since you will be showing up in the dmg meters below too many other peeps.

For the frost mage you bring survivability and ( i had hoped ) good mana regen. Let's face it - survivability means nothing on a boss fight. If the boss targets you for more than 1 attack you are toasted no matter how good a healer or ice block you have.

Arcane brings the theory of AB spam which most people agree should be insane dps but completely unsustainable mana wise and/or Torment which looks to be a neat idea if we can find a way to get the snare on the bosses we need the min/max dps for. Personally, I find the non-AB spam rotations we are trying to eke out more boring than AB spam.
Given that you can't keep AB spam up for more than a minute at any given time, it's actually kinda fun to see how many clearcasts you get or how much JoW repleneshment you get to keep it up before you have to shut down and regen.

I love your ideas and was looking at that spec ( almost ) myself as a potential because the PoM-Pyro 2 minute mage is also just plain fun as well as being a 'serious' raid spec.

With a bit more work I found a hot streak modeling I could live with. It's fairly easy in Excel to make one row showing individual crit chances, another row showing if they critted or not that you can use to find pairs and add an additional "if" formula that says if the prior row procced hot streak, this row fails no matter if there was a crit earlier or not.

I then took 65000 rows, and recalculated a few times to get the range. It's good to +/- .2% for estimating hot streak proc rate. at 50% crit rate, which looks to be the natural rate for fully talented fire+no raid buffs, you get about 1 hot streak proc in 6 casts.

I ran some quick numbers for 70, with the idea of "what do I want to do in the 3.0 patch till Wrath comes out" as frostfire bolt is off the table etc. Interestingly if you look at these rotations at 1200-1600 spell power

1. scorch, pyroblast whenever it procs
2. scorch, flame blast whenever it's up, pyroblast whenever it procs
3. scorch/fireballx8, pryoblast whenever it procs

Rotations 2 and 3 are within 1% on DPS and DPM, well under the error bars for my assumptions so statistically equivalent within the limits of my model.

Rotation 1 costs you about 13% dps for 30% DPM improvement, kinda similar to scorch spam today.
Theoretical DPS for any of these is MUCH higher than today, even without weaving in living bomb.
I really don't see why they're bothering to nerf boss health given the DPS boosts.

Fireball improves with spellpower and of course the glyph will make a big difference. Crit greatly favors
the first two rotations. Spell impact (if it remains at 6%) slightly favors the fireball rotations,
because pyroblast doesn't get it and you get nearly twice the pyroblasts with rotations 1/2 as with 3. You do need 3/3world in flames to get this level of performance from those rotations, and for #2, you need
improved flame blast (reasonable on a frostfirebolt or PVP build, that won't use fireball and needs 5 tier 1 points)

My guess is that at 80, the fireball scaling stuff will outstrip the crit-scaling stuff, or hot streak will get
some kind of internal cooldown.

I think however that when a fight dictates short, fast casting with fairly frequent movement, going
closer range and doing a scorch-fireblast-pyroblast rotation won't give up as much DPS as we're used
to giving up in that kind of fight. It's also a pretty good pvp rotation, mixing in the instant aoe's when
even scorch is too slow.

If you want a rough rule of thumb for hot streak, this is a fairly decent approximation:
crit rate is 1 proc of hot streak in N casts (ignoring the instant pyroblast casts, which can't proc it)
35 is 1 in 11
40 is 1 in 9
45 is 1 in 7
50 is 1 in 6
55 is 1 in 5
65 is 1 in 4
75 is 1 in 3
100 is 1 in 2

As long as we have not seen the last patch before release, builds can change from day to day. The build you use are showing a theoretical max dps in a raid setting, and no one would probably be able to reproduce them in-game. This is all fine, since the tool is a great way to test a lot of different scenarios fast (compared to in-game) and everyone can download an try every thinkable spec in no time. IF you can keep the great car running, then we all can practice our racedriving skills.. It's a great tool, you just have to know the numbers for what they are, and use a wee bit of time to learn how to test your own ideas. If one of us hit's a golden build, we can always let you know.

Keep up the good work, and don't worry there are plenty of wouldbe race drivers at these tracks

Well the problem isn't an error in modeling so much as it is an error in generalization. It's quite obvious that different classes and specs will perform at differing levels depending on the encounter. If a simulator is just trying to say that classes do X dps as a general case it is quite inaccurate. Cooldowns really cannot be accurately modeled for the general case.

Let's take the extreme case and say all dps tests were done on M'urmur. The fire mage would be rather uncontested. Perhaps all fights are now 40 seconds in length. A mage with coldsnap would be pretty hard to beat. Fight length is not the only mechanic that has a dramatic effect. Lets take dps time and movement into account also. I would argue that the general chart that was laid out is rather meaningless.

Edit: And to the 'have to move while cd's are up'. It doesn't happen that often as most 'fires' are a bit predictable in their timing, or rather there are optimal times where you likely won't have to move.

I see a lot of people trying to find Hot Streak's value by running sims or doing 6-digit trials, which simply aggrevates me. I'm going to hit this problem with what I suspect is an unnecessarily large hammer so we can have a publically-derived closed-form solution and forget about it.

We're going to use a Markov Chain. In short, a Markov Chain means that you have a discrete sequence of states, each state represented by a random variable, and the probability distribution of each random variable depends only on the state of the previous variable (ie the chain has no long-term memory, refered to as the Markov Property). Specifically, we're going to use a 3-state homogenous discrete markov process (homogenous means each variable has the same possible states, and the same transition probabilities; discrete means we have individual events (nukes), not continuous states). Each variable is the Hot Streak state after casting one hotstreakable nuke. The state possibilities are as follows: did not crit (x) , HS stack to one (y), HS proc (z). A homogeneous Markov Chain can be represented by a matrix which is basically a catalogue of the probabilities of going from any state to each of the other states. For crit chance c, (let d=1-c) the transition matrix is such:

If you have a vector (x,y,z) normalized such that x+y+z=1, then these represent the probability of being in those given states for a particular cast. Multiplying that vector by the transition matrix gives the probabilities for the next cast. Eg, if you're in the second column (one HS stack), you have probability c of going to the third column (crit and gain a HS proc) and a d=1-c chance of going to the first column (fail to crit, clear the HS stack). The next vector is a set of probabilities of various states. Multiplying again gives the probabilities for the next cast, etc. What we're looking for is the asymptotic behavoir of this vector, what it eventually looks like after umpteen-billion casts.

As you may or may not recall, the eigenvector of a matrix represents (among other things) what a vector will eventually look like as you repeatedly multiply it by a matrix.* The chance of any nuke sufficiently being a hot streak proc is the third entry in the eigenvector of this matrix corresponding to an eigenvalue of 1 (eigenvalue 1 is necessary so the probabilities stay normalized). Just to verify that there is such an eigenvector, the characteristic polynomial** is

Now we solve the eigenvalue equation, with the restruction that x+y+z=1:


The normalization allows the first entry to tell us that x=d (the chance of the previous cast not having crit is 1-c--big surprise!), y = c(d+z), and z=cy. Subbing the first equation into the second,

Quick sanity check: some arithmetic says that z+y = z + z/c = c, so the normalization still holds true. This result also agrees with previous simulation results, which is good.


Now I don't want to see anymore goddamn Hot Streak sims, mm-kay?


* Eigenvectors x of a matrix A are the vectors such that Ax = cx for some constant c***, called the eigenvalue. Proving this takes some grunt work so just take my word for it: Any vector y can be broken into a weighted sum of eigenvectors of A, so you can see what Ay looks like by breaking y into eigenvectors, scaling those by the respective eigenvalues, and putting them back together. Multiplying by A several times repeats this process; eventually the product is dominated by the eigenvector with the largest eigenvalue. This is why the eigenvectors of a matrix represent its asymptotic behavoir.

** Eigenvectors satisfy the matrix equation Ax = cx. Rearranging this, (A-cI)x = 0, where I is the identity matrix. The determinant of this matrix (A-cI) gives a polynomial in c, called the characteristic polynomial. The eigenvalues are the solutions to this polynomial.

*** Eigenvalues traditionally use the greek letter lambda (), not c. But, I am lazy.

As complicated as that problem is, I think very few people here, even us who have taken college calculus, understand any of it. At least without brushing up on things I have no desire to ever see again.

In terms we can understand...?

PSGarak, what you did is far more accurate... but requires knowledge of eigenvectors and a Markov Chain (which I've taken quite a lot of various college math and never heard of). What I did with a sim was something pretty damn accurate and something that a student of programming 101 could easily replicate and understand. I applaud you for your accuracy, I really do, but don't act like sims are worthless and pointless when I'd bet heavily that your precise calculations would yield roughly the same results for any well-written simulation. Also, I know with 100% certainty that my sim is perfectly accurate (at least in respect to the build that I wrote the program for), but I'm really struggling to figure out your math because, frankly, it's well over my head.

Again, thank you for the technical calculation and I take your word that it's accurate, but please don't act as though a far more simple way to find things out is worthless.


Also, dedmon... it was mentioned that you left Arcane Power out of your build for your simcraft because it wasn't sustainable... and frankly I cannot imagine that (barring a 71/0/0 build) you wouldn't be able to find some 57/0/14 variant that can take advantage of AP and use a very good frostbolt rotation. Problem is, I've looked back about 10 pages or so and I can't find the builds you were using for the simulation. Could you please link to the post showing the builds you were using?

If C is your crit chance, X the chance to proc Hot Streak on any given cast.
Then the event that you crit twice in a row (chance C^2) means that either your second cast procs Hot Streak (X) or your first cast procced it (X) and your second cast is a crit (C).

I.e. C^2 = X + X*C. Divide by 1+C to get X = C^2/(1+C).

The tricky part is realising that the events are exclusive, complete and independent where needed for multiplication.

I disagree about the conclusions about the effectiveness of modeling. It is true that you will never be able to model the exact conditions of a given fight, the point of a model is not to nit pick over the times you have to move or have an unusually high molten fury window (ala more dps dead by the time that window arrives, weighting things toward the fire mage), it is simply meant to give a rough idea of dps output under reasonably ideal conditions.


Obviously fight mechanics will vary dps results dramatically, but many of us want to know how things shape up under stand and nuke fights, with no pushback issues or high movement, we want to know the potential.


If we can see plain as day that one specs potential under reasonable conditions is dramatically lower than another, then we know what needs to be buffed/toned down.

If demons numbers are anywhere close to being accurate, currently deep arcane and deep frost are dramatically lower in dps compared to deeper fire with either ffb or fireball as the main nuke.

Frost and arcane are well over 10% dps less than the fire/ffb specs, I want to know how these things match up under reasonable conditions so we can make the case that those numbers are unacceptable if not altered in a meaningful way in upcoming builds.


If the model is off then that can be tweaked later on more accurately represent the typical dps under ideal situations, but we need to get a rough idea of the potential.

Yeah. My math broke down there. I was halfway to an equation and I could not figure out how to represent the fact that getting a proc resets the clock with algebra. I was trying to solve a three state equation too, but chose the wrong states (double crit that procs, double crit that does not proc, and "not double crit") and hurt my brain. Of course I thought this way because it's trivial to write a program that knows the prior result in the time axis. The math is a lot easier if you focus on only one roll of the dice instead of two and the relationship between them.

20 years ago I could have done the above equation, but I haven't needed to solve problems like that since I stopped doing mechanical engineering and started programming for a living and I wasn't going to bust out my old textbooks for a game. These days it's easier for me to write a program to calculate the area under a curve by geometric approximation than to do an integral.

Solution by trial leads to same results and I was able to knock out useful results in about 20 minutes effort.

I'm happy the equation turned out to reduce to something simple. And yes, it matches the results from my simulation tests, which means I don't have to trace the math myself to satisfy me, as I know my simulation accurately modeled the behavior. (it's a very straightforward if-then branching problem).

Another thing I learned from my simulation is that while the numbers may say you'll proc in 6 casts, like all truly random numbers you'll get long dry spells and clusters of procs. This dynamic is very large on the scale of 30 seconds and pretty large on the scale of 3-6 minutes. WWS results may show some variability, so you'll want to check the pyroblast count if you get either really high or really low numbers compared to what you expect.

Config file: simulationcraft - Google Code

Output: SampleOutput - simulationcraft - Google Code

I can say with confidence that it is likely that every profile in that config file could be optimized.

I welcome constructive criticism because I would like the specs to be as realistic as possible.....

Sorry for my abrasiveness. I just think it's cruel to computers to run a hundred hours of simulations to get an approximation when it seems so simple to me to get an exactly accurate closed-form solution. There's also no room for interpretation or statistical flukes like simulations have. I think there's a tendancy around here to jump to sims instead of algebra, which to me seems both sloppy and lazy, but I think that's a result of how I was brought up. Not that sims give bad results, but monte-carlo techniques were always described to me as a method of last resort when the problem was too difficult. An entire DPS rotation with cooldown synchronizations is a difficult problem that I would use monte-carlo for, and I'm well aware that enh shamans are literally impossible to model; hot streak proc chance never struck me as such.

I'm a little surprised less people got what I was saying, I was always under the impression that people who have been taught programming enough to write a sim have been taught intermediate linear algebra and some statistics. There's no calculus involved, and you don't need to know what Markov Chains actually are, they're just the formal name for that use of eigenvectors, which is pretty similar to the asymptotic population example that everyone gets when they first learn it. If you don't know more about eigenvectors, you should browse wikipedia some time. They're quite awesome. I'll edit the post clarity.
[e] Edits done. I hope that makes more sense now.

Well, FWIW I even took extra math courses during my graduation. But despise all of this and having learnt them at some point, I was thoroughly happy to forget all of it as soon as the course was done. Thing is it might be easy for you to model things using mathematics; to me its natural to use programming. As a result for me I just go with the path of least resistance to get the end result.

Ded... why do you have the mage using Molten Armor instead of Mage Armor? Imo glyphed mage armor will completely fix mana problems you'd have from popping AP. If the chart I have from the 2.4 spirit change is still accurate, 50% casting regen would yield over 250mp5 at 777 int and 411 spirit.

Also, as was pointed out, maintaining slow is a horrific dps loss... a GCD every 15 seconds will be just shy of a 10% dps loss (because of haste), so it would require having at least 2 other TotW mages and no other way to 'snare' the target to actually net a benefit. I mean, at that point has the discussion really been raised that if they're intending for us to Slow our target every 15 seconds that TotW is a worthless pve talent? My feeling is that it's specifically designed (because bosses generally can't be snared) to *not* apply to an actual boss encounter...

If that's really the case, then my argument for the best deep arcane pve build would be:

http://talent.mmo-champion.com/?mage...50323102505321

for Frost using [ ABar/FB, MBAM ] rotation or

http://talent.mmo-champion.com/?mage...50323102505321

for Fire using [ ABar/Fireball, MBAM ] rotation.



I guess with both of those it makes far better use of AP, especially since 2 minute AP will share a cooldown with the activateable trinkets and every other IV. I think that were you to use glyphed Mage Armor rather than Molten Armor, you could really bang out a lot more dps being far less careful about your mana consumption since your spirit-mp5 will be ridiculous.

Also, if your concern is that trading Molten Armor for AP is a dps loss, remember that AP popped religiously equates to a 12.5% dps gain (actually more since you'll be popping trinkets at the same time) and so if you can sustain casting while popping AP, you'll gain more from doing so than using glyphed Molten Armor.

The problem with this is the assumption that blizzard's modelling is the same as our own modelling. The sheets they use might give results under X, 2X and 3X amount of pushback, and Y, 2Y and 3Y amount of movement in an encounter. For blizzard's results you might get a much closer delta between the 3 specs. You can't right now say 'Our stand and nuke models show disparity!' and at the same time admit that stand and nuke is not the standard encounter design.

Edit: as i'm typing this we're fighting hex lord and I would love to be able to AB him during spirit bolts. To give an example.

Quick and alarming interjection:

Dampen/Amp

If someone with Beta access could not only show the worth of these spells in PvE, as well as ask for a group buff with a reagent, that would be stellar. Last thing I want is to lose or have reduced utility because only the people that don't know what they are talking about are doing all the talking.

Surely, you mislinked the builds.

Just to point out something here. As arcane, if you don't cast AB theres not much reason to go frost over fire. The main reason to go frost for frost channeling is that is cuts 10% of the final AB mana cost, whereas MOE returns the non-final AB mana cost. So for AB stacked casts you want an arcane/frost skeleton. However, as long as you do not delve into that territory the incentives really aren't there.

For all practical purposes, MOE > frost channeling. The only difference for non stacked-AB spells is that MOE doesn't works on AM. Thats it. I'm pretty sure its kinda of a wash at that point given that you only cast AM on procs anyway, so it kind of makes up for the slightly better mana 'regen' of MOE over frost channeling.

15 / 120 * 0.3 = 3.75%

--- edit: well you edited your links after I posted.

edit: new patch

pre early alpha hearsay

-Torment the Weak - Your Frostbolt, Fireball, Frostfire Bolt, Arcane Missiles, and Arcane Barrage abilities deal 4/8/12% more damage to Snared targets.