Stamina vs. Hit vs. Exp – Will it Blend?

In a forum post earlier this week, I  made the assertion about stamina:

I completely disagree about Stamina being “situational.” It is hands-down your best survivability stat, period.

A commenter offered the following question in response:

I wonder how you come to this opinion and whether the assessment can be quantified? There was a similar debate about stamina vs mastery at the start of Cata but it was never subject to numerical analysis. ….

But would it be interesting to include variations in stamina in the kind of simulations you’ve made to compare mastery, haste, etc? In your analytic work for Cata weighting stats you excluded stamina and I can see how there is an apples and oranges problem comparing it with TDR type stats. But in the simulations, it might be possible to usefully appraise it. Afterall, there’s only a limited variation in stamina we can achieve via gems and trinkets at current gear levels. For the kind of incoming damage you’ve been simulating, how often would trading that stamina for more haste or mastery or whatever, save you or kill you?

As I was writing the response, I realized it’s an interesting enough topic that it would be worth expanding into a full blog post.  A slightly edited and cleaned-up version of my response follows:

Stamina and Secondary Stats: Will it Blend?

gemblend

Can you directly compare Stamina and other Secondary Stats?

There are a few key differences between now and Cataclysm. First, let’s make it clear that Effective Health has generally been the driving force behind tanking since the end of Burning Crusade. Stamina stacking in Ulduar/ToC/ICC was the default gear path, apart from gimmick fights where you wanted a block-capped set (ex: heroic Anub’arak). The name of the game was “survive as much spike as possible” because you were usually in danger of getting two-shot by a boss.

Cataclysm was supposed to change that, and it did to a point. We worried a lot less about dying from back-to-back melees. But spirit scaling failed to make healer mana a real constraint, so we ended up not caring much at all about total damage taken. Which meant that our deaths were generally due to spikes, rather than trickle-down “deaths by a thousand cuts.” It shifted our view from “need to survive two boss attacks in a row” to “need to survive 5-6 seconds with minimal healing,” but not to “need to reduce damage taken to preserve healer mana.”  And the solution to a 5-6 second spike window is still EH.

We stacked mastery instead of stamina for a few reasons in Cataclysm, but the primary one was EH-related. Shaving 30% off of every attack is almost like having ~43% extra health (1/0.7=1.429). So we stacked a lot of mastery because it was, in effect, an EH stat – it made all of our stamina much, much more powerful, and made our damage intake smoother.  In statistical terms, we reduced the variance in our damage intake with respect to our health pools.

The fact that mastery was very good for TDR didn’t hurt, but it wasn’t the reason we stacked it – otherwise we’d have continued with doge and parry once we reached block-cap.  After reaching cap, what did most hard-mode tanks actually do? Stack more stamina!  There are a variety of reasons why, including more spike survivability, better interaction with magic damage, and the fact that stamina is often a better mana-saving stat than TDR stats are anyway.

MoP has changed things, but not very much. Healer mana is certainly being stressed in these early raids, but not because of tank throughput. In fact, I’d argue that tank throughput has not seriously stressed healer mana in any encounter released after Icecrown Citadel. A healer who’s sole job is “heal the main tank” isn’t going to run out of mana unless they’re severely undergeared or not playing very well (i.e. not used to the damage patterns on the fight). Or, in the healers’ defense, they could be healing a very bad tank that isn’t using their mitigation tools effectively.

So we’re in pretty much the same state that we were in Cataclysm. We care about spike deaths that occur over 3-5 boss attacks, or 4-10 second windows. There are a few edge cases, of course.  Heroic Feng on 25-man, for example, can hit you twice simultaneously for 200k each, or 400k burst damage in a tenth of a second.  And he can do this every ~2 seconds, making 3-second windows very dangerous.  But in general, we still care about spikes, not TDR. Hit and expertise reduce the frequency of spikes. Stamina reduces the magnitude of those spikes with respect to player health. Both are important, but point-for-point Stamina does a better job of combating spikes.

It’s value obviously varies based on your situation: when you’re undergeared, it’s very valuable; when you’re slightly over-geared, it becomes less valuable. People frequently talk about gearing strategies like “stack stam till you have ‘enough’ health for the boss,” but I think that they’re misleading themselves. ‘Enough’ is nebulous – should it be 2 attacks? 3 attacks? 4? 5? – and I think stamina retains its value fairly well even above ‘enough,’ both because of the added survivability and because of its under-appreciated benefits to healer mana.

Unfortunately, it’s very hard to quantify any of that without building a simulation that literally re-creates WoW. My damage-smoothing simulations don’t include stamina at all, because they don’t include health at all. They just calculate the distribution of damage output the boss produces over time so we can see how large the spikes get and how much each stat reduces the frequency of those spikes.  If we want to include stamina in those situations, we run into some significant issues:

  1. How much health do we choose as a baseline? This basically depends on how over/under-geared we are for the encounter at hand, which varies from player to player and from week to week.
  2. What do we do if the boss kills us during a spike? Do we keep running as usual, or terminate the sim and track this information (i.e. +100 stamina reduced deaths by X, +100 haste reduced deaths by Y, etc.)?
  3. How do we model healing? In the steady-state, your healers are producing more HPS than the DPS the boss is subjecting you to, otherwise you’d die very quickly on every pull. But that healing isn’t constant – it comes in discrete chunks (heals/ticks) at a variety of intervals (HoTs, heals with varying cast lengths) and at different magnitudes (having an excess of HoTs on the pull vs. a healer forgetting to heal you vs. a healer dying).This is probably the biggest problem, because there’s no one solution. Every tank has a different healing team, manned by different players, who heal differently. No one model can properly encompass how an “average” raid team heals, and it’s dubious at best to even define an “average” in that sense.

There are more issues, but even on this short list we’ve hit one that’s been plaguing theorycrafting for years. I remember having discussions about how to model healing as far back as early WotLK, Mel’s blogged about it before, and even to this day it’s a question that hasn’t been settled. If you model a “perfect” healer, the tank almost never dies. So you want to model an “imperfect” healer, because tanks tend to die when someone makes a mistake (healer or tank). But how do you model “bad” play when that sort of play is inherently inconsistent and varies from player to player and encounter to encounter?

As such, we’re stuck with some “hand-waving” (meaning “not rigorous”) arguments for how to relate Stamina to other anti-spike stats. I certainly don’t feel confident enough to say that I can “prove” Stamina is more valuable than hit or expertise, at least not numerically. I can at best make some good logical arguments why I think it’s better, and support that with a limited amount of evidence from logs, experiences, discussions with healers, discussions with other tanks, and so on.

I think it’s fairly telling that most tanks in the top 100 have traditionally gemmed for all-out Stamina, because they’re going into the fights fairly under-geared and prefer EH over everything else. But even that data point is limited in scope – not all top-tier tanks are theorycrafters, and in general they trust their gut and go with what seems to work. In practice, I think that they could be almost as successful gemming Spirit, because their success hinges far more on their sheer skill than it does on what 5 gems they choose.  These players are so damn good at this game that the minor differences between gemming stamina, avoidance, or control stats isn’t going to make or break their progression.

So in short, we really can’t come up with a clear numerical relationship between stamina and control stats like hit, expertise, and haste.  At least, not without writing a simulation with AI advanced enough to impersonate 25 flawed raiders making mistakes in a non-uniform, slightly randomized, slightly deterministic manner.  That’s the sort of task that’s well beyond the limit of “easily modeled.”  You could spend years doing a Ph.D. thesis on artificial intelligence and WoW raiding and still not have a suitable model for that behavior.  The best we can do is make some educated guesses about how much we should value the two stats based on what we know, what we can deduce logically, and what we can surmise from browsing logs.

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15 Responses to Stamina vs. Hit vs. Exp – Will it Blend?

  1. Helistar says:

    I remember having discussions about how to model healing as far back as early WotLK,

    For what is worth, in my tanking days (and tanking simulation days), I did model healing by taking the correlation function between taken damage and incoming healing as it appears from the combat logs and “reproducing” it in the simulation. This automatically means that it depends on healer (meaning the player, the class and the assign), so it’s not really a general approach, since on changing the raid group you’ll have to rerun the simulation….
    But it beats “perfect healing” by far if you compare the reality and the simulation results.

    • Theck says:

      That’s a good start, but even that approach has its limits. For example, the correlation between damage taken and incoming healing isn’t strictly constant. A healer reacts to a 200k damage swing differently if the attack brings the tank to 75% health than if it brings the tank to 25% health. Furthermore, it’s hard to accurately account for what other healers will do – in some raids heavy cross-healing is the norm, so a healer might jump in with an emergency heal on the tank. But they might only do that if their current assignments are fine (ex: they might not bother if they’re assigned to cast Tranquility at that point due to a period of high raid damage). So it will vary not only from healer to healer, but also from encounter to encounter. And in some cases even from attempt to attempt on the same encounter.

      And as you said, there’s the problem with the generality of the solution. If I calculate a healing correlation function based on my raid group, how applicable is it to your raid group? Now in addition to all the variables above, you add the fact that we may have different healer compositions (a raid with no holy paladins surely has a different modeling function than one with 2+).

      It’s a tricky situation, especially if your goal is to try and find generalizations that have broad applicability. I don’t want to be giving advice that turns out to be *bad* advice for the majority of raid groups, even if it’s good advice for the small subset I’ve modeled.

      • Helistar says:

        All good points.
        At the same time, just because it’s not exact, it does not mean that a simulation is worthless. I mean, look at the DPS simulations: they are performed on idealized fights and still people follow the results almost religiously :) Even if the real combats are different, you can get insight from an ideal case. In tanking this is probably less useful, but information like the one you give (= e.g. “this stat helps in flattening the damage intake”) can still help a lot in understanding what plays a role when.
        Modeling the heal with the correlation is limited, but it allows you to see which stats help if you change the healing parameters: for example you can get an idea of the impact of slower healers and see which stats help in that case: the information will be useful if you see that you’re getting gibbed in phases where healers are forced to slow down by some encounter mechanics.

  2. anafielle says:

    Dat image… total win.

  3. Benebarba says:

    So, what you’re saying is… you *don’t* want to do another thesis project?

    I can’t imagine why :P

  4. Awyndel says:

    What is sotr uptime like in MoP? Does it even come close to stamina’s uptime? And the magnutide per gem can’t be that far apart.

    • Zaephod says:

      Theck does a wonderful job of simulating different gear sets in http://sacredduty.net/2012/10/05/damage-smoothing-follow-up/ and shows the up time for each set.

      I’m almost certain you weren’t being serious with your question, but just in case…

      • Jamie Turner says:

        i think his question was a sort of tongue in cheek serious question about how stamina is there 100% of the time while SotR (the main reason we go for haste/mastery) is there only what ~50% or so of the time

        • Awyndel says:

          Well i suppose it’s a bit tongue in cheek. However I haven’t played MoP so I really don’t know the exact uptime, and I forgot where exactly to find those sims. 50% seems a bit low to me. That’s still 50% of killer spikes that those stats won’t cover. Even if the stats on the relevant gems/enchants would have a 2x value ( wich i doubt ) , that’s still not very smooth or reliable. I would say compared to stamina, sotr looks just as unreliable, as avoidance does compared to sotr, long as healers can keep up. But I could be missing something.

  5. Carina says:

    Not very much on topic, but I just wanted to say thanks for your constant work on pally-theorycrafting. It has made me a much better tank, even if my guild still struggles on normals.

    So, thanks.

  6. Jamie Turner says:

    the way i work out how much stamina to got for is simple i ask my healers ive ran through my gearing stuff with them because i got some funny looks when i rocked up to MSV a few weeks ago with a lot of haste gear looking to tank some dogs! so they understand to a degree the choices i can make and how it affects them and the easiest way i switch my stam is when im reforging have 2 stam trinkets on but then i usually swap them for vial of dragons blood and lei shins final orders (or which ever non stam trinkets i have handy) and put 1 or both in for fights where my healers want me to have more stam
    note though im not in a hardmode guild we raid 6 hours tops each week so apart from a few attempts at stone dogs my experience at hardmodes so far this teir is pretty limited

  7. Weebey says:

    This is “philosophically” a very interesting problem: the way mathematical modelling generally works is by abstracting away complexities until one reaches a situation sufficiently simple that it is tractable, either analytically or computationally. Doing so is very effective, as it turns out that in many, many cases the factors that are actually driving the process in question are not so complicated.

    Here, though, the question one wants to answer–how useful is stamina–is more or less entirely contained in the complexities one would want to abstract way. It’s value is almost entirely determined by failures of human judgment, reaction times, and so forth.

    I used to think that the right way to value stamina was by looking at a censored (i.e., constrained to live between an upper and lower limit) Brownian motion with drift (the drift corresponding to the fact that average HPS > average DTPS), and looking at the probability that such a process crosses the lower limit in a certain amount of time. I don’t know how to solve that problem, but then I’m hardly an expert on probability.

    I still think that this is a much better model than the frequently repeated “stack enough EH to not be X-shot, then ignore stamina”. However, Theck’s arguments have convinced me that it is still quite inadequate. Health pools are sufficiently small that one really does want to take into account the discreteness of healing and damage; more seriously, you want your process to ADAPT to your level of health, the state of fight, etc, which is where it’s hard to see how AI considerations don’t start to be become relevant.

    This is perhaps an overly long-winded way of agreeing, but there you have it.

  8. Ratayu says:

    So right now im at 15% exp, 8% hit, and have 582K HP, now I used 2 480 exp gems to get that, is using 2 480 stam gems increase my HP to 600K~ HP worth dropping to rougly 12% expertise???

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