Akraen's (in)Complete Frost Stat Analysis

[Akraen 230]

Update: I need to clarify a small error in just the data labels for crit/mastery, when I was making my graphs I used the same series labels for Experiment 1 in all graphs. Obviously as you increase +haste rating and keeping crit intervals constant, mastery is reduced. Don't be alarmed, the crit rating and haste is constant, but you're not expected to reach 24k mastery in an 18.9k haste scenario! Your real target is 18969 haste, 15598 mastery, 1500 crit - I'll update those data labels soon.

 

Disclaimer: The data you see before you is not based off actual gear profiles, instead it uses logic based off crit gain intervals with the purpose of spotting a trend. The following assumptions were made:

• Stat budget of an item level 581.80 mage with item level 580 Purified Bindings of Immerseus.
• Yu'lon, Stormlash, and other sources of damage excluded from the analysis would not be significant enough to skew the data.
• This assumes 100% uptimes and all raid buffs.
• AMR indicates 62.47% haste is 18960, though on Lhivera's TC-Lite, with raid buffs included, I could not get the next LB breakpoint to occur until 18969 haste (62.5%) - since it's only 9 rating, I'm erring on the side of caution until I get clarification on this.  Update: I had it checked and rechecked and it's most certainly 18960, Lhivera will be updating his stuff.

 

Stay tuned to an update to my guide with this new information.

 

Frost Mage 5.4 - Explained

Up until this point, those of us who try to take a stab at theorycrafting frost mage have fallen into the same traps. We backward engineer parses to try to explain results. Data has been obscured, often with too much information or influence from fights themselves. I could create a "solution" such as 14242 haste->mastery to explain successful parses, but I couldn't explain why I perceived that to be the best method.

 

We advanced further into the "multiple builds" theory - which suggested that there was a choice among mastery, mixture, and haste builds, each with their own advantages or disadvantages.

 

DPET numbers were used to help explain the differences-- and the data was not surprising. We know that the way our stats work together is like a system of checks and balances-- no one stat scales each spell, and some scale each other or inhibit each other. This interaction is not too difficult to map.

 

In some prior posts, I explained the value of crit to a frost mage, but I still had some lingering doubts as to whether it would exceed the amplification of stat ratings from PBoI. Turns out it does not.

 

So I wanted to find some new logic-- a new angle to analyze the problem. Simulations are a mindset that have to be put on the back burner until we first look at how our actual stats are impacted by Purified Bindings and what that means for average damage, DPET, and which stats add the most DPET to all of our spells.

 

I started by setting up a series of 6 experiments, using haste as a control for each setup. Within the 6 experiments there would be a series of up to 12 combinations of crit/mastery, starting crit rating at 1500 and increasing it in intervals thereof. PBoI's amplification was used to calculate how much rating that left over for mastery. Don't worry, it's unlikely you'll get to the ideal number of 18969 haste / 1500 crit / 15000 mastery-- that might not even be possible, but the goal is to get as close to there as possible while preserving the LB/NT breakpoint.

 

For each of the 6 experiments I began with the raw, unaffected-by-PBoI average damage (crit included) and then created a formula to reverse-engineer the crit rating, apply the amplified bonus, and add it back in to the average damage. This creates a clean, verified value that we can use to create DPET tables:

 

Then it just takes some cast times to find out DPET!

 

 

Now at this stage of the analysis we can look at how crit/mastery relate to haste by pinning each of the 6 experiments against each other. Remember, we are not adding up the DPETs here, or doing any simulations. The only logic here is that changing stats influences DPET, resulting in a very easy-to-read trend analysis. Green = Good; Red = Bad:

 

From there it is simply a matter of looking at the sum of the gains on a percentage basis. This means ET%s don't matter, simulations don't matter. The % gain from one stat combination versus another stat combination. These DPET calculations could be extrapolated into a simulation, but they don't need to. I call this experiment Differentials By Spell:

As you see above, the impact the change in build has on Frostbolt + Icicle is relatively small, but becomes significant at the highest haste breakpoint.

Brain Freeze comes out to be the biggest loser as haste values increase and is the outlier for shatter cap as well. However keep in mind this doesn't take into consideration the increased proc rate that comes with haste!

Ice Lance DPET levels out as one would expect, at 50% haste. Though this does not take into consideration additional FoF procs from having a higher amount of haste!

Water Elemental does something funny: he loves haste! His stats fluctuate with ours, and he takes a tiny advantage by being in our ideal stat ratio of 18969h>mastery

That Living Bomb breakpoint is huge and ultimately is what decides our ideal stat ratio. However, crit's benefit does not do enough to give crit a lead over mastery in the overvall view. (ps: no idea why one of those cells is white)

Frozen Orb stops gaining DPET past the GCD. Nothing to see here.

 

Now remember, I'm not simply adding DPET values here, that would be a horribly inaccurate representation of data. The goal isn't a simulation, and the conclusion is startlingly clear because the ignored factors (such as procs) would give haste an even larger advantage, but it's just not needed to prove the stat scaling. This is an aggregate of the % of gain you receive in various stat builds, resulting in higher DPET across the board, influenced by Purified Bindings of Immerseus.

 

The purpose of this analysis is a demonstration of what stats mean to your spells. It is still a true statement (and an important takeaway) to note that these results will fluctuate depending on the encounter scenario-- on spoils for example, haste at any level conquers mastery, while the reverse is true on Iron Juggernaut. Always pay mind to that fluctuation and note that it is reasonable to set up your frost mage in any way, this is simply the best explanation for how to gear, gem, and reforge from now until 6.0.

 

I'm considering frost mage solved

 

tldr; 18960 Haste > Mastery & minimize crit is the answer

Edited May 27, 2014 by Akraen

[emitecaps 0]

Wow that's an intense write-up! Great stuff Akraen, can't wait to give this a try tonight!

[Kver 65]

I suppose all of it kind of makes sense, but I wonder how big the differences really are. I mean, your experiments were done in a 581 BiS. I am 576 with seriously great itemisation and I get to 3k crit with 13k mastery(or something) with 19k haste, for me it seems to be a lot less relevant, because I don't have the leftover budget to really do anything big with.

 

Still, your research is great. It is what I tried to do with fire(But ended up being unable to do because pyro herp), and it's definitely one of the better ways of mapping interaction directly. It'll be essential to do it this way in WoD when all stats are "equally" strong(They'll never be, of course).

[Akraen 230]

Yeah it's troublesome to get down to 1500 crit, usually 3-5k is where most mages will land simply because of itemization. On the other hand, we are now in SoO for ages and can try to get our true BiS items.

 

Now that we have this, we have the code to find our actual BiS gear. Just remember everyone these differences are small. I have a 580 crit/hit ring, remember-- it's worth it to still go for item level above itemization.

[emitecaps 0]

I'm running some tests right now, would this benefit anything lower than BIS? I'm testing on 560 gear

Edit: I'm doing roughly 3-5k more dps at 560 ilvl for anyone that's curious hehe. 

Edited April 7, 2014 by emitecaps

[Akraen 230]

Shouldn't matter what gear level you're currently at - it's just without good gear it'll be tough to get enough haste.

 

I used the same core/secondary stats and spellpower across each experiment so that we could easily identify the trend. The trend is present regardless of gear. Even at 9577 haste, for example, you can see the data.

 

So regardless of your gear, the goal should be to work towards the same ratio of stats: 18969 haste then mastery.

 

My mistake up to this revelation was recommending 14242. You can see why I thought that based off individual DPET calculations. However, it's nice having a solid answer now. I still advocate people doing what's comfortable-- but there's enough of an answer now for me to just link this thread and say "do that."

[Oltier 471]

Too much free time... I guess... Great job mate! :D

[Akraen 230]

Like no free time at all, now I would like to sleep for a couple days :P

 

Don't worry I can nap under my desk at my office.

[Muphrid 2]

 

 

From there it is simply a matter of looking at the sum of the gains on a percentage basis. This means ET%s don't matter, simulations don't matter. The % gain from one stat combination versus another stat combination. These DPET calculations could be extrapolated into a simulation, but they don't need to. I call this experiment Differentials By Spell:

 

Can you clarify this?  Are you comparing stat setups by adding %DPET increases for each of the various spells without regard to ET%?  Or something else?

[Akraen 230]

Can you clarify this?  Are you comparing stat setups by adding %DPET increases for each of the various spells without regard to ET%?  Or something else?

That's the old mindset, I'm not doing that.

 

SimC needs to be fixed for simulations. This isn't my goal.

 

The differentials are created by stepping up haste levels with a consistently increasing crit rating interval of 1500, then residual mastery. The gain by changing stats on DPET is what's calculated relative to the prior haste level (experiment). Since it's percentage gains/loss, there really is no harm in adding together the differentials. This isn't representative of a rotation, only a gain from stats.

 

The theory is that PBoI's amplification effects are important in deciding how to gear, gem, and reforge in order to maximize the highest impact on your spells. We always knew how mastery/haste interacted, but it was unclear which breakpoint of haste is where we should stop-- 50% was the obvious choice in practice, but sims kept saying stack haste-- I'm very confident that the story this tells is the happy compromise, 62.5% haste is the victor.

[Avengedlol 0]

So im a little confused on what to do. I can only get 16,727 haste out of my current gear, should i keep that or wait it out with 14,242 haste until i can go with the full 18,969?

[Akraen 230]

Frost helped me point out a minor flaw in my FoF+IL calculations (it was giving additional weight to crit past shatter), so I've updated that in my workbook and will be uploading new images once I get the labels updated too.

 

This had no impact on the conclusion, so no worries.

[Akraen 230]

So im a little confused on what to do. I can only get 16,727 haste out of my current gear, should i keep that or wait it out with 14,242 haste until i can go with the full 18,969?

Whichever you want, it's such a tiny difference. You can work towards your goal or play it safe in the meantime.

[Frostedmages 3]

My personal thoughts are that this is less about how to gear, but more about better understanding frost DPS, where our damage is coming from, and how the different stats effect our spells damage contributions.

 

The applications to current gearing, especially now that we're well past the final tier in MoP, are limited. However, this puts us in a good place to move into WoD with a good understanding of Frost mechanics so that when numbers start appearing and we're in the beta we can hit the ground running with Frost DPS balance. The goal, from my perspective at least, being a well scaling, balanced Frost spec which is viable in a PvE environment.

Edited April 7, 2014 by Frostedmages

[Aoeina 0]

Great Job Akraen.

 

Fascinating that 18969 actually ends up being the preferred haste cap.

 

And yeah I am one of those people that can hit 18969 haste sadly I just cant get below 3k crit.

[Muphrid 2]

That's the old mindset, I'm not doing that.

 

SimC needs to be fixed for simulations. This isn't my goal.

 

The differentials are created by stepping up haste levels with a consistently increasing crit rating interval of 1500, then residual mastery. The gain by changing stats on DPET is what's calculated relative to the prior haste level (experiment). Since it's percentage gains/loss, there really is no harm in adding together the differentials. This isn't representative of a rotation, only a gain from stats.

 

The theory is that PBoI's amplification effects are important in deciding how to gear, gem, and reforge in order to maximize the highest impact on your spells. We always knew how mastery/haste interacted, but it was unclear which breakpoint of haste is where we should stop-- 50% was the obvious choice in practice, but sims kept saying stack haste-- I'm very confident that the story this tells is the happy compromise, 62.5% haste is the victor.

 

 

Sorry, I'm still not clear on what's being added to what.  It sounds like you're not adding individual spells together.  Are you adding a single spell's %DPET increase from, say, experiment 2 over experiment 1 with experiment 3 over experiment 2 to get the % increase between experiments 3 and 1?  Or something else?

[Akraen 230]

Would you like me to email you the spreadsheet? I'm not against your critique here, but we could end up talking past each other for a while when I'm perfectly happy just sharing the source. Then if you see any problems we can get them fixed more expediently. Just let me know your email address.

[Frostedmages 3]

You had me until you started comparing DPETs from different spells to each other and then summing their % constributions.

 

I have no idea why you are doing this. Each experiment is basically being calculated in a vacuum, and is ignoring everything except for it self. Additionally, comparing one experiment to the other seems odd. It would make more sense to declare one a baseline or control, and then compare all the others to that control. I also don't think that adding the % DPET increases and then comparing these to eachother at different haste levels is something you should be doing.

 

What you can do here is basically say in a vacuum, the DPET of each spell scales a certain way with mastery and crit at a certain haste level. You can mix/max for each of these spells individually, but adding them all together is wrong. Once you remove each spell from it's vacuum you have to take into account spell ratios.

 

You can see this in the LB contributions. It's essentially the entire reason why 18k > 14k in your DPET comparisons. Is this the case in the real game though? Even if you go to 18k haste LB won't be your highest damage contributor. Statments like ",this is simply the best explanation for how to gear, gem, and reforge from now until 6.0", are over-reaching the analysis done here.

Edited April 7, 2014 by Frostedmages

[Ashe 0]

At 18969 haste, we should be hitting 6 ticks of LB, correct?

 

http://us.battle.net/wow/en/character/whisperwind/Ashe/simple

 

http://i.imgur.com/Z6sfTYN.jpg

 

My actual haste rating is 19025.

 

Custom Weights for AMR are:

Haste (to 18969) 3.6

Master: 3.45

Crit: 1

Haste > 18969: 0

[Akraen 230]

You had me until you started comparing DPETs from different spells to each other and then summing their % constributions.

 

I have no idea why you are doing this. Each experiment is basically being calculated in a vacuum, and is ignoring everything except for it self. Additionally, comparing one experiment to the other seems odd. It would make more sense to declare one a baseline or control, and then compare all the others to that control. I also don't think that adding the % DPET increases and then comparing these to eachother at different haste levels is something you should be doing.

 

What you can do here is basically say in a vacuum, the DPET of each spell scales a certain way with mastery and crit at a certain haste level. You can mix/max for each of these spells individually, but adding them all together is wrong. Once you remove each spell from it's vacuum you have to take into account spell ratios.

 

You can see this in the LB contributions. It's essentially the entire reason why 18k > 14k in your DPET comparisons. Is this the case in the real game though? Even if you go to 18k haste LB won't be your highest damage contributor. Statments like ",this is simply the best explanation for how to gear, gem, and reforge from now until 6.0", are over-reaching the analysis done here.

That's not what the calculations are, Frost. I don't know why you try to strongly pull apart things without even thinking them through.

 

It's not % contributions, it's % differentials. The gain in damage from 14k to 18k is the extra LB tick. It's a massive jump in DPET. LB doesn't need to be your greatest source of damage done, that's the wrong mindset. I'm not doing a simulation here, I'm looking directly at how gear impacts the calculations of your spells. The % differences in jumping from one breakpoint to another reflect simply the DPET gained by changing stats.

 

You are still in the wrong mindset, re-read the entire post.

[lynx 19]

 

• AMR indicates 62.47% haste is 18960, though on Lhivera's TC-Lite, with raid buffs included, I could not get the next LB breakpoint to occur until 18969 haste (62.5%) - since it's only 9 rating, I'm erring on the side of caution until I get clarification on this.

 

Always trust AMR. TC-Lite is broken in regards to LB/NT dpet. I can go into more detail if you're interested.

TC-Lite mastery calculations are also broken btw 

Edited April 8, 2014 by lynx

[Akraen 230]

Always trust AMR. TC-Lite is broken in regards to LB/NT dpet. I can go into more detail if you're interested.

TC-Lite mastery calculations are also broken btw 

 

Negative sir, he fixed the mastery calcs.

 

And please, go into more detail. I speak with Lhivera regularly and I'm sure he'd like to know your wonderous insights.

 

I gotta take a step to the side here and air a little frustration. Not directly at you lynx, just in general. How come so many people will critique the work of a very few people, but not contribute to finding workable solutions? When I first began trying to dissect frost mage in Tier 14 and posting findings on forums, I said flat out (and have many times since) that I am by no means a math guy.

 

I'm a wordsmith, a creative mind for intense pattern recognition and conceptual analysis. Even professionally, my job is to digest an incredibly complicated software system and relate it to businessmen in sensible terms. I love to read and study everything from philosophy to quantum mechanics. But math? I just never put the time in and my degree didn't require much more than a couple calculus courses.

 

I'd absolutely kill for you sleeper experts out there to actually help me out. It just does me no good to point out flaws and not offer solutions. I'd rather you simply not exist or not post in your current form. If I ever quit theorycrafting and the mage community it'll be because of the type of burnout you experience when you spend hours and hours obsessing over solving a problem only to find one know-it-all on the forums tell you that you're wrong.

 

All I want are answers. I don't care what the answers are. And sometimes it feels like I'm the only one trying to find them.

[Muphrid 2]

All right, I reviewed the formulas that you plotted.

 

 

As far as I can tell, the plot "Sum of Projected Gains..." does the following:  for each spell, you calculate the % increase in DPET for that spell, relative to the previous haste value.  You sum these together to get a total across all spells, and then you sum this number with the % increases from previous haste values.  Is my understanding correct?

 

If so, I suggest some improvements.  First, these percentages must be weighted by some ET% to sum to a meaningful quantity: that would be the percent increase in DPS.  I know you said, several times, that your goal is not to conjure up a simulation.  However, I cannot see how this measure, which essentially gives each spell equal weight, is substantially different from a calculation with poorly-chosen (i.e. not corresponding to any real frost mage's) weights.

 

Second, you can't add percentages from one haste value to the next. Example: I have $100.  I add 50%, and then I add 50% of that total.  I do not now have 100% more dollars (which is what you're doing -- $100 + 100%x100 = $200).  I instead have $225 ($100 + 50%x$100 = $150; then, $150 + 50%x$150 = $225).  The percentages used here obey the same rule, so you should take the percentages, convert them to multipliers (e.g. +12% = 1.12) and then multiply those out.

[Akraen 230]

As far as I can tell, the plot "Sum of Projected Gains..." does the following:  for each spell, you calculate the % increase in DPET for that spell, relative to the previous haste value.  You sum these together to get a total across all spells, and then you sum this number with the % increases from previous haste values.  Is my understanding correct?

 

That sounds like my method, yes. Though I don't double dip - it's from the reference point of 9577 that I calculate the gain/loss for each spell. So the jump in 9577 to 18960, or 9577 to 14242.

 

 

 

 

If so, I suggest some improvements.  First, these percentages must be weighted by some ET% to sum to a meaningful quantity: that would be the percent increase in DPS.  I know you said, several times, that your goal is not to conjure up a simulation.  However, I cannot see how this measure, which essentially gives each spell equal weight, is substantially different from a calculation with poorly-chosen (i.e. not corresponding to any real frost mage's) weights.

 

 

Everyone busted my balls about ET%s last time. The purpose of this analysis was to avoid needing them. We can't seem to solve anything with ET%s because they fluctuate too much and much of them have nonexistent values, such as icicles and waterbolt. I can't wrap my mind around a method to model that.

 

I'm going to need more of a suggestion than to just weigh the values, because when calculating direct contribution in DPET from gear, I don't know why it needs to be related to a particular rotation. Where would you get reliable ET%s? I get the value in weighting them if you're trying to create a fight scenario. However in this thought experiment I'm trusting intuitive judgment to make the call, since I don't know of a way to compare, say, Spoils of Pandaria Heroic to Thok. I'm letting raid experience decide that with the most detailed gearing information given.

 

Intuitive experience is an assumption I wish I didn't have to make, but I don't know a way to calculate that.

 

 Second, you can't add percentages from one haste value to the next. Example: I have $100.  I add 50%, and then I add 50% of that total.  I do not now have 100% more dollars (which is what you're doing -- $100 + 100%x100 = $200).  I instead have $225 ($100 + 50%x$100 = $150; then, $150 + 50%x$150 = $225).  The percentages used here obey the same rule, so you should take the percentages, convert them to multipliers (e.g. +12% = 1.12) and then multiply those out.

 

 

Perfect example of peer review. I'll update that along with the few other minor tweaks for the next update.

[Muphrid 2]

That sounds like my method, yes. Though I don't double dip - it's from the reference point of 9577 that I calculate the gain/loss for each spell. So the jump in 9577 to 18960, or 9577 to 14242.

Sorry, I think I was being sloppy. Let me clarify: in each individual spell's chart, you seem to calculate the % increase in DPET as the difference between that level and the previous level's DPET, divided by the current level's DPET. That's sound (although I personally would use the previous level's DPET as the baseline--this is more clearly understood as, "I changed my stats, this is how my DPET changed from what it was before, percent-wise").

So that's okay. Using the 9577 baseline for percentages is just for the total cumulative gain chart, right?

Everyone busted my balls about ET%s last time. The purpose of this analysis was to avoid needing them. We can't seem to solve anything with ET%s because they fluctuate too much and much of them have nonexistent values, such as icicles and waterbolt. I can't wrap my mind around a method to model that.

I'm going to need more of a suggestion than to just weigh the values, because when calculating direct contribution in DPET from gear, I don't know why it needs to be related to a particular rotation. Where would you get reliable ET%s? I get the value in weighting them if you're trying to create a fight scenario. However in this thought experiment I'm trusting intuitive judgment to make the call, since I don't know of a way to compare, say, Spoils of Pandaria Heroic to Thok. I'm letting raid experience decide that with the most detailed gearing information given.

Intuitive experience is an assumption I wish I didn't have to make, but I don't know a way to calculate that.

Do they fluctuate a lot? I thought you had found that they change very little across large ranges of gear, but maybe they fluctuate a lot between fights. That, however, doesn't bother me too much; one of the things I ultimately wanted to do was to be able to theorycraft DPS for several different fights with different ET% profiles. I personally wouldn't have a problem choosing a simple fight (Jug is what I'd consider ideal for this, in a single-target scenario) and doing the bulk of the analysis off of that, or consider a handful of profiles (a multidot profile would be Protectors; an AoE profile might be...Spoils? Galakras?). But for this first analysis, a single-target profile ought to be plenty.

One of the tools I always wanted to have was a way to measure ET%s from a parse or from a mod. A parse doesn't do it yet without a lot of processing. I know of no such mod that can do it out of the box at this time, either. But I think that would be the ideal tool for being able to do this kind of analysis tailored to a given fight. I always expected, though, that the best way to get ET%s would be empirically, with a tool like simcraft being a passable substitute for estimating ET%s in very simple cases only.

Anyway, my point is that simply adding up these DPETs is no different from a very oddball weighting where each spell has the same share of ET%. That is, we have frostbolt, FFB, Ice Lance, Frozen Orb, and a bomb as rotational buttons, right? Adding them up without weights is equivalent to giving them all equal weights: 20% weights for each. Now, choosing ET%s may be kinda sketchy, but we know that Frozen Orb won't have a 20% weight, so right away we can see that that may throw things off-kilter.