Damage Smoothing: Expertise, Mastery, and Haste

Brokenone of Mannoroth contacted me over at Elitist Jerks to ask a question about the damage smoothing simulation results. In short, he wondered if I could run two more sets to more clearly differentiate between mastery and haste, as sets #2 and #3 weren’t all that far apart. In addition, Wrathblood wanted to see a trade-off between haste and expertise. To accommodate those requests, I’ve run the simulations with four new gear sets.

Set #5 is a “mastery-heavy” gear set that takes all of the haste rating from set #3 and dumps it into mastery. Set #6 is the complement, a “haste-heavy” gear set that moves some of the mastery from set #3 into haste. Sets #7 and #8 are our “expertise” gear sets. For #7 I’ve taken set #6 and moved about 2300 haste into expertise. For #8, I’ve moved the remaining 3700 haste back into mastery to give us “expertise/haste” (#7) and “expertise/mastery” (#8) gear sets. Since that was a lot of # signs to wrangle, the table below summarizes the net stats of every gear set so far:

Set:   set#1  set#2  set#3  set#4  set#5  set#6  set#7  set#8
Str    9208   9208   9208   9208   9208   9208   9208   9208
Parry  4834   2834   2834   7834   2834   2834   2834   2834
Dodge  4892   2892   2892   6892   2892   2892   2892   2892
Mast   6758   6758   5758   5758   8758   2758   2758   6458
Hit    1521   2521   2521     21   2521   2521   2521   2521
Exp    1777   2777   2777    277   2777   2777   5077   5077
Haste     0   2000   3000      0      0   6000   3700      0

Mastery and Haste: Round 1

Here are the histograms for sets #5-6. For the earlier sets, refer back to the first post on this topic.

Set #5 (mastery):

Spike damage intake histogram for set #5

Spike damage intake histogram for set #5

Set #6 (haste):

Spike damage intake histogram for set #6

Spike damage intake histogram for set #6

And below, the associated means and standard deviations of the spike damage histograms, as well as the percentage of events that fall above 80% and 90% of maximum DTPS. Note that the data for sets #1-4 are the same as the last post.

     set #1  set #2  set #3  set #4  set #5  set #6  
mean 0.5261  0.5365  0.5444  0.5138  0.5246  0.5676 
std  0.1479  0.1341  0.1346  0.1628  0.1343  0.1353

80%  3.1340  2.2265  2.3817  3.6678  1.2462  2.4508 
90%  0.7907  0.3500  0.3770  1.2093  0.2002  0.3505

It’s interesting that set #5 (mastery) does a much better job than set #6 (haste). It gives us lower overall damage intake and roughly the same standard deviation, but significantly fewer of the “dangerous” spikes in the 80%+ and 90%+ ranges. It’s about twice as effective at getting rid of those dangerous events than the haste set.

At first this seems a little counter-intuitive. After all, haste gives us much higher SotR uptime (45.3% for set #6, as opposed to 39.7% for set #5), and one would expect that the extra coverage should do a better job of covering a 5-hit scenario. So why does mastery do so much better?

To answer that question, let’s look at the hit size breakdown for these gear sets. Unlike the DTPS histogram, this hit size plot just shows us the size and frequency every individual type of combat result (i.e. hit, block, mitigated block, etc.).

Set #5 (mastery):

Hit size breakdown for set #5

Hit size breakdown for set #5

Set #6 (haste):

Hit size breakdown for set #6

Hit size breakdown for set #6

Both the haste and mastery sets have roughly equal amounts of unmitigated hits. And as expected, the haste set has a lot more mitigated hits. But the mastery set does two things much better: it makes all of the mitigated hits much smaller, and it generates a lot more blocks. The extra blocks more than make up for the loss of mitigated hits, and the extra mitigation on the ones that are still mitigated help push the spike sizes down even further.

So, we can comfortably say that mastery wins this round, where we’ve capped hit and soft-capped expertise. Now let’s see what happens when we hard-cap expertise.

Expertise, and Mastery vs. Haste: Round 2

Here are the histograms for the two expertise gear sets:

Set #7 (exp/haste):

Spike damage intake histogram for set #7

Spike damage intake histogram for set #7

and Set #8 (exp/mastery):

Spike damage intake histogram for set #8

Spike damage intake histogram for set #8

And one last time, here are the stats for all 8 gear sets:

     set #1  set #2  set #3  set #4  set #5  set #6  set #7  set #8
mean 0.5261  0.5365  0.5444  0.5138  0.5246  0.5676  0.5656  0.5365
std  0.1479  0.1341  0.1346  0.1628  0.1343  0.1353  0.1311  0.1295

80%  3.1340  2.2265  2.3817  3.6678  1.2462  2.4508  1.4540  1.3010
90%  0.7907  0.3500  0.3770  1.2093  0.2002  0.3505  0.0095  0.0202

The real eye-opener here is what expertise does to the large spikes. You can see in the plots for #7 and #8 that events above 80% are heavily suppressed, almost as if the histogram were flattened off in that region. The statistics tell the same story: while the expertise sets aren’t quite as good as the mastery-heavy set (#5) when you consider the 80% cutoff, they’re incredibly good at eliminating the top 10%. So good, in fact, that they’re an order of magnitude better than set #5. Stacking expertise up to hard cap dropped the frequency of spike events by a factor of 10 or more, down to 0.02% or less.

Curiously, the exp/haste set (#7) did better than the exp/mastery set (#8) at eliminating the very highest spikes. And not by a small margin either – it reduced them by a factor of 2 compared to the exp/mastery set (0.0095% to 0.0202%). Oddly enough though, once you back off to the 80% threshold, exp/mastery takes the lead again. It’s hard to say for sure why we see that effect. My best guess at this point is that reaching expertise hard-cap dramatically increases haste’s ability to cover an extra swing within the 5-swing window we’re considering.

To clarify that thought: thanks to all that expertise, our HP flow is very steady, so we know we’ll reliably get a SotR off at fairly regular intervals. For example, let’s say we cast SotR to cover the first swing in our 5-swing period. With enough haste we’re guaranteed to cover the last one as well. Note that $T_{\rm SotR}$ for the exp/haste set is around 6.7 seconds, fast enough that it will definitely cover both the first and last swings in a 7.5-second period. On the other hand, the exp/mastery set only gets SotR off every 7.3 seconds. There will be some variance on that due to CS/J clashes, so there will still be some events where we can only cover one swing of the five-swing period. I think that’s the difference we’re seeing between the last two sets.

Just to make sure that we’re not seeing a statistical anomaly, I ran the entire sim again to get some idea how reliable the results are. Here’s what I got the second time:

     set #1  set #2  set #3  set #4  set #5  set #6  set #7  set #8
mean 0.5256  0.5378  0.5445  0.5132  0.5238  0.5675  0.5665  0.5367
std  0.1487  0.1344  0.1350  0.1634  0.1347  0.1349  0.1313  0.1294

80%  3.1825  2.3373  2.3692  3.6757  1.2110  2.3780  1.5237  1.2833
90%  0.7905  0.3838  0.3953  1.1890  0.1875  0.3280  0.0107  0.0217

So the results seem fairly repeatable. Sets #7 (exp/haste) and #8 (exp/mastery) seem to do the best job of covering our top-end spikes and smoothing our damage intake. I’d argue that set #8 is better than set #5 (the raw mastery-stacking set) despite the fact that set #8 takes slightly higher damage and slightly more 80%+ events, simply because of how it utterly destroys the 90%+ bracket. A similar argument could be made for #7, but it’s not as efficient a trade. Going from #5 (mastery) to #8 (exp/mastery) is choosing to take 0.07% more 80% events in order to reduce your 90% events by a factor of 10, or 0.18%. I think that trade is almost a no-brainer, to be honest.

But going from #7 (exp/mastery) to #8 (exp/haste) sacrifices 0.3% more 80% events for a meager 0.01% reduction in 90% spikes. Yes, that’s a factor of two decrease in the most dangerous spikes, but 80% spikes can be fairly dangerous too. And it’s a factor of two decrease on an already very small chance. Note also that our sets aren’t exactly hit and expertise capped – I’m curious whether hitting the caps more precisely will have any effect on the balance between mastery and haste sets.

There is one notable benefit to the exp/haste build though: DPS. Remember that with Vengeance, haste is one of our best DPS stats (often right behind hit and expertise, which you’d be capping anyway in this build!). So another way to look at the #7 vs. #8 trade-off is that you’re shifting your spike distribution around (more above 80% but fewer above 90%) in order to boost your DPS considerably. Especially in heroic content, that may be a benefit that tanks find hard to pass up.

I think that both of the expertise sets are going to be survivable enough that you could justify using either one, so choose according to your play style and preference.

Conclusions

This round of simulations has been pretty surprising. Up until now, many of us (myself included) have been more or less ignoring expertise hard-cap based on our TDR simulation results. I certainly wouldn’t have guessed it would have as strong an impact on spike damage prevention as it did. Though now that we’ve seen it, the mechanism behind it seems pretty obvious – eliminating the dangerous spike windows caused by inconsistent holy power generation. If you get unlucky with one or two parries in a row, you’re likely to be stuck with a longer period of SotR downtime and subsequently you’ll be more susceptible to taking large damage spikes.

Still, I have to wonder whether these surprising results for expertise hold up in more general circumstances. If my intuition regarding the mechanic is correct, it’s tied to being able to cover both the first and last swing in a 5-swing sequence. But what if we’re interested in a 4-swing sequence? Or a 3-swing sequence? This is an issue I want to look at in more detail, and I spent the morning modifying the code accordingly, so expect another follow-up in the next week or two.

In any event, I think it’s probably safe to revise our gearing advice for the “control” build based on these results. In the past, we’ve suggested hit to cap, expertise to soft-cap, and then mastery and haste. But I think that you could make a strong argument that our first two priorities should be to hard-cap both hit and expertise. After that, any combination of mastery and haste is good – each have their pros and cons, and it’s really hard to definitively say that one is better than the other. And of course, we may decide to revise these suggestions once we have the 3- and 4-swing simulation findings, so if you feel more comfortable with stopping at the expertise soft-cap and stacking mastery, that’s certainly viable too.

These simulations also highlight the huge weakness of an “avoidance/TDR” gearing strategy. Even though the “heavy avoidance” gear set (#4) takes the lowest overall damage and has the lowest spike distribution mean, it’s also the most susceptible to spikes. Almost 4% of all events were over 80% of max possible DTPS, and a little over 1% of them were over 90%. In a 5-minute encounter, you’ll take about 200 attacks, which is about 40 sequences of 5 swings (and to be fair, we should really be thinking about something in-betwen 40 and 199 sequences, since any set of 5 swings within that 200 could be a spike event). Out of those 40 sequences, an average of 1-2 will be an 80% spike. Out of 100 sequences, you’ll see an average of one 90% spike.

Shifting that dodge and parry into hit, expertise, and mastery or haste can reduce the likelihood of 80% spikes by a factor of 3 and that 90% spike by a factor of 100. While we can’t say that this makes you 3x or 100x more survivable, it’s pretty clear that abandoning avoidance is a large survivability increase. You’re choosing to preferentially eliminate the most dangerous events at the cost of a little more throughput damage, and I think any healer will tell you that’s a good trade.

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37 Responses to Damage Smoothing: Expertise, Mastery, and Haste

  1. Dan Paladin says:

    Hi Theck,

    Any chance whatsoever we can get some theorycrafting on stat weights for Monks, similar to what you have done for warriors? I’ve more or less decided on the switch to Monk and would love some quality information.

  2. Great post, as usual. If ignoring avoidance stats is a viable gearing method for tanks, does that mean using DPS gear and gemming for stamina becomes a viable alternative as well? My instincts say no, but I wouldn’t begin to claim I can back it up with math.

    • anafielle says:

      I think that considering some pieces DPS plate and some pieces tank plate is becoming a thing of the past. With the same amount of stamina on both, the devs have been trying to eliminate the distinction entirely since Cataclysm, and they now may have “succeeded” now that tanks care (a great deal, according to this post) about those precision stats for mitigation.

      I suppose that strength plate is now a lot more like cloth. I know myself, I’m looking at all the strength plate for both my specs. I’m looking at pieces with crit and thinking DPS, and pieces with avoidance and thinking “tank”, but as for the rest of the strength plate? Anything goes. We’re all in the same pool now.

      I’m not a huge fan of the idea. This should be really fun once plate gear starts dropping in raids.

    • Wrathblood says:

      Ryan, yes, absolutely it is. Essentially, anything but Crit is now a paladin tank stat (Prot Warriors hate Haste but are otherwise in the same boat) and of the other traditional DPS stats I think you’d be hard pressed to come up with even one that’s clearly worse than Dodge or Parry. That having been said, Dodge/Parry are still quite good for Prot Warriors so they’re not entirely gone yet.

  3. Newsom says:

    This is all very interesting, but I’m still slightly confused about where stamina comes into the picture. Do we want to gem for stamina above expertise hard cap for example?

  4. Newsom says:

    gem stamina > expertise hard cap*

    • Jackinthegreen says:

      The metric I’ve always seen go around is enough stamina to survive the hardest-hitting stuff, then go to town with whatever else floats your boat. Which brings up an odd situation for these simulations because we can actively get rid of the spikes now. With the way secondary stats have been buffed from gemming, if good gearing and reforging aren’t enough to cover expertise and hit to taste then gemming will probably play a significant role.

      • Theck says:

        I’ve always been skeptical of the “reach an EH threshold, then gem avoidance” strategy. I’m of the opinion that stamina stacking even above some mythical EH threshold is helpful. So my bias is towards Stamina being a very attractive stat for gemming and enchanting.

        The doubling of secondary stat itemization on gems brings up an interesting question though, as Newsom points out. Do I still gem stamina, or do I take advantage of the double itemization on expertise, hit and mastery?

        Since you can’t reforge for Stamina, gemming is the only way to get it. So my take on it is that you want to reforge as much of the dodge and parry on your gear as possible into hit and expertise to try and hit those caps. If you can successfully do that, then you’re home-free to gem Stamina. If not, then picking up expertise and hit gems is probably worthwhile.

        The strategy here is to try and maximize Stamina while constraining yourself to capping hit and expertise. I’d cap hit with reforging first, since it shares the “blue” color with Stamina. That way you can gem Stamina in blue and exp or exp/stam in reds.

        But what do you do if you can’t reach the exp hard-cap? Do you gem expertise or stamina? I don’t think there’s an easy answer to that. Expertise reduces spikes, but having more stamina makes all of those spikes less dangerous, because they’re smaller relative to your health pool. I think in the end, it will come down to personal preference. In 25′s, where EH is still king, I’d lean towards stamina. In 10′s, where tank damage is generally smaller and doesn’t stress EH as much, I’d probably lean towards the “smoothness” stats.

        • Nooska says:

          From a “best compromise” wouldn’t gemming stam/stat gems be the way to go though? that way you take advantage of both getting stamina through gemming, and the doubled secondary stats on gems.
          The tradeoff is thatr you halve the stamina possible.
          The benefit is that you gain stamina in every gemslot, and you can match all socket boni (I would presume) – and with no hard cap on our control stats apart from hit and exp, you can’t waste your secondary budget (and if you need to use exp/stam gems for some sockets and are in risk of overcpaping exp, you can just reforge it to haste/mastery)

          • Theck says:

            That all depends on how much you value mastery/haste vs. stamina. If we work under the assumption that hit/exp are the primary stats we care about for spike prevention, and capping those is your first priority, then it just becomes a question of whether we feel like haste/mastery or stamina does a better job at keeping us alive. I think you could make strong arguments for either, to be honest.

          • Kira Milne says:

            Right, however, I would argue that effectively eliminating large spikes also reduces the need for a large health pool to give the healer time to react, making avoidance more attractive in my opinion, after removing the spikes.

  5. Brokenone says:

    This is exciting stuff! I look forward to the 3 and 4 swing scenarios. I’m betting in those smaller scenarios #8 pulls ahead of #7 since you no longer get the second ShoR for the last swing in either. However, I bet if you look at a 6 swing scenario #8 also pulls ahead since you get the advantages of extra Mastery without seeing the advantage of an extra ShoR in the window. Think it’s worthwhile to check the 6 swing scenario as well?

  6. Zaephod says:

    2 Things: 1.) How does this affect tank-specific designed gear, such as our tier gear?
    2.) Typo up there talking about sets 8 and 9, instead of 7 and 8. It’s not a big deal considering you define the sets inline with the numbers, but since your words are spread around like tanking gospel, I figured you’d want to know.

    Thank you again, Theck and the Sacredduty team!

    /salute

    • anafielle says:

      The team is a myth; Theck carries all of us :D I’m just here to say “WHOA!!” and admire his super cool graphs.

      (thanks for the comment!)

    • Theck says:

      Thanks for the correction, I’ve fixed the typo.

      As far as tank-specific or tier gear, it’s an interesting quandary. Unlike Cataclysm, where we tried to replace or avoid gear that had any sort of threat stat on it, we’re now going to be seeking out those pieces. Luckily, Blizzard seems to have realized this, because 4 out of 5 of our tier pieces have hit or expertise on them. None of them are dual avoidance, luckily – the weakest piece is the legs, which are mastery/dodge.

      Curiously, the *ret* legs are perfectly itemized for us: mastery/expertise. So there’s an easy and reasonably-available solution for that off-slot. There are also several non-tier options (hit/haste boss drop, haste/mastery and dodge/expertise from Klaxxi rep).

      I think the two-piece protection bonus is definitely worth getting. The 4-piece is optional from a survivability standpoint, in my mind, but it’s also a decent DPS increase. Taking off-set pieces instead of going for 4-piece may be a better survivability decision though.
      Edit: Oops, I misread the 4-piece as “damage of your SotR” rather than “damage mitigated by your SotR.” Strike that last comment, 4-piece is very nice, and we’ll want to get it (definitely worth a little dodge/parry, which we’ll of course immediately reforge out of).

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  8. Hammer says:

    Based on your analysis, does this make the “Living Steel Weapon Chain” desirable now?

    • Theck says:

      It’s certainly nice. I’m not sure if I like it better than the Colossus absorb though. You can find hit/exp elsewhere, but the Colossus effect is fairly unique. That said, the bubble is pretty small, but I’ve heard the proc rate is rather high to compensate.

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  13. Tsyndr says:

    Does anyone know if in LFR as a plate tank, you could be awarded a “DPS” plate piece that maybe has hit/exp or hit/haste. If I recall, they said that the LFR loot system would only award you something role specific, which means we’d only get pieces with classic tank stats like dodge/parry/mastery on them. Does this mean I should do LFR as ret to gear up my prot set?

    I’m also worried that even though Blizz wants us to be using active mitigation, they won’t like us rolling on “dps” plate and may adjust things to make dodge/parry more valuable. So then the question is, what should I spend my VP on? What about the Sha of Anger epic boots quest drop? The dps plate ones are haste/mastery while the “tank” ones are dodge/parry. I’d hate to pick up the “dps” boots only to have blizz adjust stuff to make me wish I had picked up the “tank” ones.

    * I don’t have that much time to play so I need to streamline my gearing.

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  19. severon says:

    New to tanking and so far having fun doing it. I’m wondering does raiding tank setup advice hold for 5 man heroics as well? If not, is there a guide for how to configure my tank for 5 man heroics?
    To share I mostly run 5 mans and right now I’ve been going with Parry as my number 1, master, and then hit, expertise and haste and finally dodge. From this guide sounds like I’m way doing it wrong…

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