On Measuring Survivability

The last few posts have garnered a lot of comments, and some of them have indicated that there’s some misunderstandings about the simulations we’re performing.  This set of simulations started back in September, and has been evolving ever since.  And the rationale behind how we perform the simulations is spread out over 6 months of posts.  It seemed like a good idea to consolidate that information in one place.

Basic Modeling Problems

First, let’s consider the point of modeling.  Obviously we want to generate data that helps us make more informed decisions about how we gear and play.  For modeling to be of any benefit, it has to generate information that’s useful.  And generally, that means that you want the model to be accurate.

Most people would assume that means you want the model to be perfect – all-inclusive, with tanks and healers that play perfectly and react with mechanical precision.  But in fact that’s not the case.  Consider what would happen if we did have perfect tanks and perfect healers.  Your perfect tanks would execute their rotation flawlessly, never miss an encounter cue, and would always apply their mitigation skills in the most optimum way.  Your perfect healers would react flawlessly to spikes in damage intake, always select the correct heal at the right time, and would be as mana-efficient as possible.  In your perfect model, you’d have at least enough healing to cover damage intake given perfect conditions, so your perfect healer would never run out of mana.  And the net result would be a tank that never dies.

Unfortunately, that perfect simulation wouldn’t be very useful.  If the tank plays perfectly and never dies, then it barely matters how they gear or what they do.  They’ll be unkillable with any reasonable gear set.  Which highlights the flaw with a perfect simulation: it’s not accurate.  It doesn’t reflect reality. Because in real encounters, players make mistakes and tanks die.  And there’s a fairly high correlation between those mistakes and tank deaths.  Which means that if we want a good, useful simulation, we need to account for that imperfection.

Imperfect Tanks

Unfortunately modeling imperfection is almost as hard as modeling perfection is.  For example, let’s consider how many ways there are to model an imperfect tank.

  • Active Mitigation Usage – You could do it by varying the precision of their active mitigation.  For example, a sloppy player might be macro-ing Shield of the Righteous to Crusader Strike – essentially the “S” rotation we’ve used in the past.  On the other extreme, you could model a near-perfect tank that pools holy power and only blows SotR early during what seems to be a spike – the “SH1″ and “SH2″ rotations we’ve used.  And there are hundreds of variations in-between that differ in effectiveness based on the logic used to control SotR usage.  But which one of those best models a real tank?
  • Rotation – Maybe your tank is perfect and follows CS>J>AS>SS to the letter.  That’s pretty easy to model.  On the other hand, maybe your tank slips up and prioritizes J over CS once in a while by accident.  But how often do they do that?  Are they just as likely to push AS ahead of CS as well, or forget to cast SS when it’s available? Again, we have an infinite number of variations based on the probability distribution you use to determine whether the player makes these errors.
  • Latency – Maybe the player lives next to the server farm, and has sub-millisecond latency.  On the other hand, maybe they’re playing from Australia, and regularly struggle with pings of 350 ms or greater.  Cast queuing helps quite a bit to mitigate these problems, but it still affects events that you need to react to in-game, because even with perfect reactions you’re behind by your latency value.  How much latency should our imperfect player have to deal with?
  • Player Reaction – And even if you live next to the server farm, nobody’s reaction time is instant.  So a player’s response to an event will always be delayed somewhat based on their reaction time and attentiveness.  They may react more slowly to an event if they were watching some other information stream, like DBM timers or their action bars.  How often does our imperfect tank stand in the fire?

It should be evident from this that there’s a huge parameter space to work in here.  And the problem is that it’s very, very difficult to determine what’s “average.”  A reaction time of a full second is certainly below average, but there are players who operate at that capacity.  A completely perfect rotation is possible, but awfully difficult – arguably difficult enough that even the best players can’t manage it.  Everyone slips up once in a while.

Meloree posted a great comment on the last article that I’d like to quote, because it seems fairly relevant here:

As far as imperfect play goes – during wrath/Cataclysm the best I managed to do over the course of a full fight was roughly a 1.53s GCD average over 10 minutes. Thats roughly 98% efficient, and it’s pretty close to an upper bound – not many people ran a tighter rotation than I did. ….

I regularly saw parses from good tanks – in well progressed heroic mode guilds – who weren’t better than ~80% efficient at their rotations. ….

Being more than 90% efficient in your rotation places you in the upper half a percent of tanks in WoW.

So if even the greats are struggling to beat 95% efficiency, what’s our estimate for an average tank?  90%?  80%? 70%?  More to the point, do we really want to be running simulations for an average tank?  The readership of this blog in particular is decidedly skewed towards above-average.  Not many tanks of average or below-average play quality actively seek out blogs to try to improve their play in the first place.  And of the ones that do, how many are willing to struggle through my verbose and technical blog posts?  Probably a small minority.

Imperfect Healers

More problematic yet is the matter of healers.  How do we model an imperfect healer? They have many of the same complications that tanks do.  Latency and reaction time are obvious factors one can tweak.  But the difficult part is really the healer “rotation,” because there really isn’t one in most cases.

For starters, their rotation varies based on the situation – they may be focusing on single-target healing if they’re assigned to a tank, or on area-of-effect healing if they’re assigned to the raid.  And in a 10-man raid, often one healer will be switching back and forth between those two play styles constantly based on the demands of the encounter.  So the type of healing you get depends not just on your play, but on what’s going on with the rest of the raid as well.

Further, a healer’s play style is far more reactive than tanking or DPS play. They may have a basic rotation they use as a default during less dangerous periods, but they switch gears and change cast priorities during a crisis.  They’ll use different spells if the tank has four or five GCDs to live than they will if death could happen in two or three.  And while healers don’t have active mitigation, they do have cooldowns they can throw at the tank if the shit really hits the fan.

So there’s a huge number of variations in how you model an imperfect healer.   Is the healer a little slow to switch modes when the tank takes a spike?  Or do they over-commit to expensive heals and run out of mana too early?  Or do they just not make effective use of their emergency buttons? We could model a “dumb healer” that just spams their mana-efficient heal on the tank regardless of what else is happening, but that’s probably not an accurate model of even the worst healers.

And just as for tanks, each healer plays a little differently.  The model of one imperfect healer may not give accurate results for a different healer.  Not to mention the inherent variations between healers of different classes with slightly different toolkits.  The results may be totally different for a healer that relies heavily on HoTs than they would be for a healer that heavily leans on absorption effects or direct heals.  How do you build a model that’s general and widely applicable when the inputs are so widely varied?

The short answer is: you don’t!

Rethinking The Approach

It’s clear that there’s way too much variation involved here to write the sort of modeling software that most people think of when they talk about wow.  We could certainly write an equivalent to Simcraft, given enough time and effort, but it isn’t clear that it would give us much in the way of useful results.  Tracking things like “how often does the tank die” would vary significantly based on the details of your imperfect healers and tanks.

Not to mention that, while we could model a healer any way we wanted, in practice we have no control over how they play.  We might even have a different healer from week to week or encounter to encounter.  Tying ourselves down to a particular healer model is doomed from the start to be too specific – it just won’t give us results that we can apply everywhere.   We need something that is both more general and simpler to implement.

So we go back to the drawing board.  All the way back to the beginning, in fact.  We reconsider what survivability means at a fundamental level.  What is the root cause of tank death?  I’ll put forth the following hypothesis:

Hypothesis: Tanks are in the most danger of dying when their instantaneous average damage taken per second (DTPS) greatly exceeds their instantaneous average healing received per second (HRPS).

Now, that certainly shouldn’t be very controversial.  I’ve basically said “you die when you don’t get enough heals,” but put it in a more technically rigorous form.  We all know what it means to not receive enough healing.  That happens when our healers are distracted or otherwise incapacitated – in other words, when they make a mistake.

And we’re also familiar with the first half of that statement.  Our time-averaged DTPS goes up when we take a lot of damage in a short period of time.  In other words, a damage spike.  To illustrate that thought, let’s consider some data.  Here’s what the DTPS profile may look like for a tank over an entire encounter (this happens to be Council of Elders):

Tank DTPS

Tank DTPS plotted against time for an entire encounter.

This is the broad overview, showing how damage fluctuates over long periods of time.  We have extended periods of high intake and periods where the tank isn’t actively tanking anything.  Rather than look at the broad view, let’s narrow our focus to the section in the middle, with the large spike followed by three smaller spikes.  That looks like this:

DTPS

Tank DTPS plotted against time for a ~two minute period.

So over a two-minute period, our tank sees massive fluctuations in damage intake.  It drops as low as 40k DTPS, and spikes as high as 150k-230k DTPS for 5- to 10-second periods. The danger periods are obviously these peaks, where damage intake abruptly increases – these are the moments when we’re most at-risk of dying.

From the same log, the tank healers’ average healing throughput is about 100k HPS.  Of course, during this period it gets ratcheted up to around 220 HPS (and other healers chime in to help).  But then again, this is from a log where the tank didn’t die.  If the healer hadn’t cranked his output up fast enough to meet this new level of damage intake, we’re very likely looking at a dead tank.

Let’s assume for the moment that we don’t have any control over our imperfect healers.  Let’s also assume that they screw up every so often during the encounter – maybe they fail to react to a spike quickly enough, or maybe they just stood in fire too long and have to move or break off of the tank to heal themselves.  If one of those screw-ups coincides with one of the damage spikes, we’re probably going to die.

If we accept the premise that we have no control over what our healers do, just what they perceive, then what can we as tanks do to minimize the chance of this happening?  This is what a scientist would call an “overlap integral” problem.  We can increase our survivability by reducing the likelihood that a spike and a healer screw-up overlap in time.  And how do we do that?  Well, consider what would happen if we had a way to perfectly smooth our damage intake, such that instead of the pink line, it looks like the blue line on this plot:

DTPS over a 2-minute period before and after a perfect smoothing algorithm.

DTPS over a 2-minute period before and after a perfect smoothing algorithm.  And by “perfect smoothing algorithm,” I mean “Photoshop’s Line Tool.”

Suddenly everything changes.  First, we don’t have any big spikes to worry about – our mean intake is a little over half of our peak intake (and higher than our average), but it’s very steady.  So it’s far less likely that the healer’s screw-up coincides with a period of extremely high intake, because there simply aren’t any periods of extremely high intake.  More subtly, and perhaps more importantly, the fact that there aren’t any big spikes that require the healer to change modes means that it doesn’t matter if they’re a little slow in doing so.  In practice, that’s a big deal because the “slow to react” healer model is far more likely to cause the sort of overlap that kills you than random healer movement is.  So our “perfect smoothing” mechanism turns a tank that dies some of the time into a tank that never dies.

Now of course, this is an unrealistic model – we have no way to perform this perfect smoothing (outside of Photoshop, at least).  But it gives us a clear goal to aim for.  As tanks, we can’t make our healers play better.  But we can give them an easier damage profile to work with: one that doesn’t require rapid fluctuations in healer throughput.

So I propose the following corollary to our hypothesis:

Corollary: If spike damage is dangerous, then minimizing the frequency and magnitude of high-damage periods is the most direct way to increase survivability.

This is a nice, tidy little statement.  It narrows our focus from an all-encompassing simulation with many variables to a much smaller subset of parameter space.  Instead of worrying about what the healer is doing, we just concern ourselves with the damage intake profile we receive.  In essence, we’ve removed healers from the equation.

Of course, without healers, we don’t have much use for health either.  If we’re only concerned with the plot of damage taken per second, it doesn’t matter how much health we have.    So if we’re ignoring healers, and we’re not tracking tank deaths, then keeping track of the tank’s current hit points is no longer necessary, and we can add “tank health” to the list of things we can cut from the simulation.

Now, that sounds awfully controversial when taken in isolation.  What use is a simulation without healers or tank health? But it follows rather naturally from the corollary.  We’ve been conditioned to think that for a simulation to be useful, it must model everything down to the last detail with near-infinite precision.  But that just isn’t always the case.  It’s great if you want details about a specific situation.  But not if you want general, portable results that apply to a great variety of situations.  By eliminating healers and health from the equation, we can focus our efforts on variables we can control and make sure our modeling of those factors is as accurate as possible.

Building the Simulation

Now that we’ve defined the problem, we can go about building the simulation.  This part is pretty boring unless you’re enthralled by mathematical detail and code, so I’ll try and summarize it as briefly as possible.  We want our sim to do the following:

  1. Simulate a tank being attacked by a boss
  2. Track the damage intake as a function of time
  3. Take the resulting series of damage events and perform calculations on that sequence

Each of these steps has a number of details to consider.  For example, we need to choose the boss’s damage so that we can appropriately assign Vengeance values.  We’ll also need to estimate the player’s gear so that we can appropriately calculate avoidance and block chances.  And of course, later on we’ll want to be able to vary both of these parameters.

Likewise, since we’re tracking damage intake, we need to properly calculate mitigation and absorption effects.  Since our mitigation depends on the tank’s rotation and active mitigation usage, we need to model all of that as well.

The simulation I’ve written does all of those things and more.  It’s a Monte-Carlo style simulation, which means that it simulates combat the same way the game calculates it – making rolls for each event as they happen.  So for example, it cycles through a loop, incrementing time until an event (like a boss attack) occurs.  It then rolls to see if that boss attack is avoided.  If so, it rolls again for a grand crusader proc.  If not, it rolls to see if it was blocked, and so on.  It works the same way for our rotation, following a priority queue (which we can modify) to cast spells and update the system according to their result.

We run it for a very long time (10k minutes of combat, generally) to smooth out random fluctuations and get stable, statistically significant results.  And the output is a string of numbers that looks something like this (but a lot longer):

[... 100 55 0 70 0 100 55 55 38 0 100 55 38 100 0 0 0 100 55 55 100 0 ...]

Where each number represents an amount of damage.  So 100 would be a full boss attack taken to the face, 70 would be a blocked attack, 55 would be an attack mitigated by a 45% mitigation Shield of the Righteous, 38 would be an attack that was blocked and mitigated by SotR, and so on.  In practice these values vary a bit more because of absorption effects (Sacred Shield), but that’s the basic gist of it.

Once we have that string of events, we perform some post-processing on it.  We perform a moving average to generate the sort of data you would see in a World of Logs plot like the one I’ve shown above.  We then take that moving average and calculate how many of its elements exceed a given threshold – say, 100% of the player’s health.  This is the data I present in the tables.  In essence, it’s telling you the two things we care about most: how many spikes are there, and how large are they?

A Word on Healing

One drawback of this style of modeling is that without player health tracking, healing becomes awkward.  That wouldn’t be a problem if it weren’t for the fact that we have a non-trivial amount of self-healing abilities.  For example, how do you model a Word of Glory or Seal of Insight heal if you can’t… well… heal?

The answer is that you treat them as short-term absorption bubbles.  If WoG heals us for 200k health, we instead give ourselves a 200k absorption bubble.  We keep the duration short because this healing is only relevant over short time windows.  In the case of WoG I’ve been using 3 seconds, which is probably too generous; for Seal of Insight I’m using 1.5 seconds.  It wouldn’t make sense to grant a 200k absorption bubble that lasts for 10 seconds, because in 10 seconds a real healer would react and top us off.  So the absorption needs to only apply to boss attacks that happen shortly after the heal occurs.  Another way to think of this is that, by not modeling healers, we’re assuming perfect healers that never let you die, and they react within a few seconds.  Thus, if the absorption bubble isn’t used up within a few seconds, it just gets wasted (i.e. turns into overheal).

Which brings up another issue with healing in this model: overhealing and efficiency.  We need to make assumptions about how much overhealing occurs. For Seal of Insight, you can think of this as trying to estimate how many procs occur when we’re already at full health since our simulation doesn’t have health.  But the issue is a little more subtle than that, even.

To illustrate why, consider the following example: lets say you take a 200k attack from a boss, and react by casting a 200k WoG on yourself.  Your healer also drops a 200k Holy Light on you in response to the attack.  Which one of you overhealed, and how efficient were you?

Logs will base the answer on whomever acted first.  But that doesn’t cut it for our analysis.  Either way, there was 200k worth of overhealing happening in that scenario, and whether it was my WoG or the healer’s Holy Light, one of them was wasted.  No matter who the combat log credits with the overhealing, I would have been better off letting the healer top me off and using that holy power on a Shield of the Righteous instead.

I tend to take a rather pessimistic view on healing efficiency for that reason.  I generally assume that the healer is going to do what they do regardless of whether I WoG or not, because they can’t assume that I will WoG at any given moment.  And likewise, I can’t assume they’ll stop healing me because I know where my WoG button is.  Since neither of us can reliable predict the others’ actions, we’re bound to cause a good chunk of overhealing.  This is less true with incoming healing notifications on unit frames, but not all frames have this capability, nor do all healers use it on frames that do.  However, since opinions vary on this, I generally present results for a variety of overheal levels when I’m discussing results involving WoG.

A Word on Patchwerk

To wind down this post, I want to have a quick discussion about one of the more common criticisms of this sort of modeling.  The simulation is a Patchwerk model, which for newer players means “a boss that blindly melees you and does nothing else.”  But real fights rarely look like Patchwerk.  Real fights have tank swaps, movement, different phases, magical damage.  The criticism I often see is that because of all of those factors we’re ignoring, these simulation results have no relevance to real play.

I think that attitude is a bit narrow-minded, and I don’t think it’s entirely valid.  Sure, there are tank swaps.  Sure, you’ll use cooldowns during a fight.  But you’re obviously not going to die when you don’t have aggro. And you’re probably not going to die while you have Holy Avenger up and are coasting along on 100% uptime of a 50+% damage mitigation buff. You’re not very likely to die when you have a big cooldown running either, for that matter. You’re not even that likely to die right after a tank swap, since you’ll have extra SotR uptime during that period if you’ve pooled holy power.

You’re most likely to die when you get a big damage spike, and that really only happens when you don’t have any of those safety nets. It happens when you just get unlucky and take a couple big unmitigated melees because you’re rebuilding Holy Power.  In other words, it happens in the in-between sections of a fight, when you’re essentially tanking Patchwerk.  By that logic the simple, Patchwerk simulation much more relevant than it would initially appear.  Thus, I think a boss mindlessly hitting you is a pretty good model for the bulk of our death scenarios.

The “big, predictable boss attack” death scenario is pretty dangerous too, and shows up a lot in current content.  But I think it’s less dangerous than many seem to think if you’re using active mitigaton properly.  Shaving 50% off of the predictable spike, and likely one of the neighboring melees as well, usually makes it quite manageable.  Often it reduces the big attack to less than a regular melee swing.  And since it’s a predictable spike, your healers know its coming – they have DBM timers telling them that you’re going to take a big spike in X seconds, so they are more likely to use proactive tools, like absorption shields, small cooldowns, or simply pre-casting a heal on you so that it lands right after the large attack does.

In any event, the “big predictable attack” is something I plan on adding to the simulation once I get time – possibly even before the next round of data posts, since the Seal of Insight code is almost finished.

Despite all of that, it’s worth remembering that specific bosses or mechanics can lead to different strategies being optimal.  We’re trying to model the most general situation possible so that it’s applicable to as many fights as possible.  But mechanics like Dread Thrash can certainly trump steady-state modeling.  A boss like Lei Shi forces us to reconsider whether the model is applicable to that particular boss.  If we had another Algalon-like encounter where you have three healers spamming the tank just to keep up with the damage, you may care a lot less about smoothness and a lot more about stamina, armor, or even avoidance.  This model abstracts all of those things out, so it’s important to keep in mind that this is a guideline for when all of those other effects are already taken care of.  A good tank needs to know when the model is appropriate and when to break from the model to handle specific problems.

Summary

This post doesn’t really have a conclusion.  I haven’t presented anything incredibly new here.  Tanks doing high-end content have been focusing on spike damage for years now.  But up until recently, we really haven’t had good tools to quantify those concerns.  We’ve been able to calculate total damage reduction fairly reliably in the past, and often that metric was used as a stand-in to approximate smoothness.  But the simulations I’ve run in the past six months have demonstrated the inadequacy of that approach.  A stat like haste can be absolutely terrible at reducing total damage taken while being fantastic at reducing spike events.

I hope that the logic behind the simulation is more apparent now, though.  It should, at least, address the common criticism that the results can’t be valid or useful without including healers.  While it’s definitely important to consider what healers think and how they react, I don’t think it’s critical to have a specific healer model in mind when answering the question, “what makes me more survivable.”  While our simulation doesn’t model healers at all, the thought process that we used to arrive at our observables certainly did.  So they are included in the simulation in an indirect manner, in that rather than participating in the simulation explicitly, they determined how we perform the simulation and assess the results.  Healers are the lens we look through when we decide what metrics accurately reflect our survivability.

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34 Responses to On Measuring Survivability

  1. Lakh says:

    A question which somewhat touches on the human-error element… how much clipping is ok?

    If CS comes off CD in 1.3 seconds, I assume I use Judgment if I have it… but how much would I be losing by using AS if that was what was up? And how about if it was CS vs J with CS coming available in 0.7s? Et cetera.

    And yeah, I always get frustrated with guildies who talk about using Simcraft etc in helter skelter mode. You model for the ideal, and you use that model to understand how you adjust to non-ideal circumstances. Non-ideal circumstances are generally just chopped up segments of Patchwerk anyway, the only real question is what you should be doing on the transitions between Patchwerk segments.

    • Theck says:

      Clipping is a pretty big deal – you really don’t want to push CS back much at all, if possible. It’s going to be a pretty significant HPG loss to push it back any more than a few hundred milliseconds. I don’t think there’s ever a situation where J should be ahead by as much as 0.7s unless you’re hitting the 1-second GCD cap, at which point rotational dynamics change drastically.

  2. Fasc says:

    Very good write-up, thanks for this Theck.

    The self-healing assumption is really where I wanted to dig in because I wasn’t sure how you modeled such things. A Guardian isn’t nearly so binary as a Paladin in that you have very fixed finite resources to use and using SotR means not using WoG right then, and vice versa. I can very easily pool Rage to have Savage Defense active and on top of that pop a 40-50 Rage FR immediately after the hit lands (if it lands at all, standard Tortos behavior). But as you say, the Healers will do as the Healers will do, so unless I’m landing a pretty big FR in enough time to get them to reign in a mega-heal, then they are just going to lay it on thick anyway. That just puts any RPS (rage per second) stats at a very weak level in terms of survivability as getting the minimums to just maintain SD when necessary are pretty trivial at this point. Dodge and Mastery scale poorly so that leaves just Stamina.

    Which leaves me still a question for you about your prior write-ups in light of this blog’s explanation: How exactly does Stamina do anything under your assumptions?

    If we minimize the magnitude of spikes via Stamina, yes the boss automatically deals a lesser chunk of damage to me relative to my health, but my instantaneous average damage taken per second doesn’t actually change, and the instantaneous average healing received per second must still be there for me to survive. Be it a good Healer or a crappy Healer, the Healer’s response needs to be the same for success. So even with this explanation, I’m not sure on how sold I am on the idea that Stamina is a solid smoothing stat if it isn’t actually impacting the DTPS or the HRPS. If we’re going to measure strikes against us relative to our health pool, then so too must healing, which decreases at an equal rate, which doesn’t really smooth anything at all. That is unless I’m misinterpreting your definitions of magnitude, it seems to me that Stamina has little value in smoothing or eliminating spike situations if we eliminate the need to account for healing and health according to the simulation parameters.

    • Theck says:

      Good question. You’re absolutely right that stamina has no effect on your DTPS. However, it does make that damage smaller compared to your maximum health. In other words, it raises the “danger” DTPS threshold.

      Imagine, if you will, drawing a straight line on the graph at 150k DTPS and calling that the “danger” threshold. Above that line, your healer needs to dig into their bag of tricks, because something bad is happening. Having extra stamina gives them more time to react and makes all of those spikes less lethal, so it has the effect of raising that line, say to 170k DPTS. Stats like haste or mastery reduce DTPS, but don’t move the line at all. Both serve the same purpose, it just depends on your frame of reference.

      The key is not to assume that the healer is only capable of steady throughput at 100k HPS. They can and will adjust their steady throughput to match average DTPS quite naturally – that doesn’t cost them attention or reaction time, because it’s throughput damage that they just deal with. It’s also t he reason TDR is a fairly weak metric – taking lots of very steady damage isn’t all that dangerous, you just assign an appropriate amount of throughput healing.

      Another way to think of it is that stamina squishes the entire DTPS curve – think of it as scaling the curve based on your health. In the extreme limit of having a few million health, the curve looks basically flat, and you’re certainly not susceptible to spikes anymore. The spikes become manageable because the healer doesn’t need to react, they just need to keep healing and their base throughput will eventually catch them up.

      This is also why stamina is not as useful in 10-man. The DTPS curves are already pretty small compared to healer throughput and tank health, so while the increase in stamina makes them easier to heal, it’s also not all that useful – they were already pretty easy to heal, so improving that doesn’t have a significant impact on how their healers play.

      • Fasc says:

        I understand the squish I think, but I guess I’m probably still thinking too much into specifics and what we actually have control over with our gear. As much as adding several million of HP would be lovely since Healers could all practically Atonement spam their way to victory, that’s not realistic. What is realistic is having a difference of 150k+ in total Health if you were to stack Stamina up tremendously, and I’m not sure how appreciable that amount is on various content (you mention 10man) when you don’t actually make that death blow or series of swings actually push you out of the ‘danger threshold’

        Paladins have more ways of differentiating the damage so it probably works much better for you guys (blocking, actual absorbs, etc) so this might just be too much of a Guardian thing with us either eating full damage or nothing at all. I can definitely accept Stamina for your Paladin model a lot more now in that light, since you can hit those times that you can “take another hit” so to speak and thus the Stamina did its job of padding you enough to actually get an appreciable response from the Healer(s).

        I wonder though how your particular model would show Guardians. Right now we pretty much stack RPS stats (foremost Critical Strike after Hit/Exp caps) provided we have “enough” EH, in which we stack Stamina (faster and more effective than Mastery) until we have “enough” and go back to RPS stats. Since it is very easy to assume that our worst-case scenarios are just flat smacks to the face only mitigated by stance/armor (since that’s pretty much what happens when we don’t Dodge), we have pretty distinct breakpoints we need to survive for a reasonable Healer team to respond to. But that all assumes that RPS stats in excess of what is needed for Savage Defense (+45% Dodge) can be appropriately dumped into Tooth and Claw (essentially an absorb but a debuff instead of a buff) or Frenzied Regeneration (Rage into Healing at 2x Vengeance at 60 Rage). TaC would work nicely in your simulation but FR heals can be so small at times (and at other times massive) that I don’t know if would fit well with a fixed small window absorb assumption.

        • Theck says:

          The “get enough stamina to survive N boss hits” logic tends to break down when thinking about a broad category of different encounters. Between HoT ticks, DoT ticks, environmental damage, and so on, even damage ranges in-between integer boss attack values can be relevant. Add in blocking, SotR mitigation, Sacred Shield absorbs, and random Seal of Insight procs and you may as well be looking at a continuum. And in that case, marginal stamina gains can be pretty strong.

          I think Guardians are probably the tank that comes closest to the integer-attack approximation though, as your damage intake is much more binary. If I re-wrote the model for druid mechanics, I suspect what you’d find is that stamina’s value was moderate to low if you were in-between integer boss values (i.e. in-between 5.0 and 6.0 health, normalized to boss swing size), but would ramp up dramatically when near one of those integer break points (i.e. approaching 6.0). It wouldn’t drop off immediately above 5.0 though, as things like DoT ticks, absorbtion effects, and what not tend to act as “blurring” agents.

        • Weebey says:

          In addition, it appears that mobs naturally have a wide variance in their swing damage, even after controlling for cooldowns, absorbs etc; it’s hard to get a precise figure just from looking at logs without doing a controlled experiment, but it appears that a max damage melee attack can be close to 50% harder than a min damage one. This should be enough to smear out any EH threshold one might want to define, even for druids.

          In any case, even if you believe that EH thresholds are relevant to tanking, this doesn’t justify the standard practice of stacking “enough” EH–where typically “enough” is some fairly low level, e.g. the EH that comes naturally on your gear–and then shifting to other stats. The maximum survivablility strategy could well be “reach the highest EH threshold attainable in your gear, then shift to other stats”, which is quite different.

      • Lakh says:

        It seems like what you’d me more interested in looking at, rather than a DTPS curve, would actually be the delta of the health % statistics that Skada/Recount keep, yeah?

        • bryjoered says:

          Yeah, even though stamina may not have *as large* an effect on the smoothness, I think that it is still very helpful in 10 man situations. In 10-man it’s more of haste is only “slightly” worse than stamina at smoothing as opposed to “noticeably” worse. In that case, where haste is only slightly worse, if you are a good tank that follows his rotation well you are going to want to go haste for the dps increase. On the other hand, if you are undergeared, progressing through heroics or are just mistake prone, stamina would probably suit you a bit better.
          Since I’m a warrior, whose offensive prowess is somewhat maxed after capping hit/exp. I’m going to want to stack stamina. Upping Mastery does increase your dps, but not nearly as much as Haste does for paladins.

  3. Argent says:

    Let me preface this by saying that I am not 100% sure what I about to say is going to be relevant. There is a very real possibility that I misunderstood parts of the post.

    I am not sure completely ignoring tank health / stamina is a good decision here. For the purposes of smoothing out damage spikes it’s irrelevant, yes, but I think it matters enough to warrant its own place in the sim. The reason for this is that an ideally smooth DTPS curve can be interpreted in two different ways – as an absolute value (e.g. 150k DTPS) or as a percentage of the tank’s health (e.g. 20% health TPS), and it’s the second model where I think tank health could make a significant difference.

    If we only look at the size of the boss’ swing and follow the absolute DTPS, it feels like we are discarding most of what you/we talked about in the last few blogs – namely what constitutes a spike. If I am sitting at 700k health and a boss hits me for 150k my healers will be much less concerned than if a) I am sitting at 500k and a boss hits me for 150k or b) if I am sitting at 700k and a boss hits me for 250k. The ratio between tank health and boss hit is important. Since we are ignoring healer behavior in this sim, this doesn’t feel like that big of a deal, but I think it is. If my damage intake is perfectly horizontal, but it’s horizontal along the 30% of my health line because I have no health, then that’s pretty bad. Or at least much worse than if the line was along the 50% of my health mark.

    • Theck says:

      You misunderstood, or more accurately, I didn’t explain it well enough. Instantaneous tank health is being ignored, but *stamina* (i.e. total health) is not. The thresholds we look at are measured in percentage of the tanks maximum health, so stacking stamina does have a smoothing effect. In fact, it’s a very strong smoothing effect, which is why stamina tends to be the most effective smoothing stat in the simulations (see the last few blog posts for examples).

      So your intuition is exactly correct – stamina is definitely a smoothing stat worth considering. To repeat my response to Fase: if you stack enough stamina to get a few million health, all of the damage curves look pretty flat, and you’re very easy to heal. But we’re not ignoring it, it’s already baked into the sim. :)

      In fact, one example Mel likes to toss around to combat the erroneous “mana sponge” idea is the tank that has ten billion health but no avoidance or mitigation. Is he hard to heal? Not really, since he doesn’t even need to be healed to survive.

      • Argent says:

        Good to know! I was mildly concerned the last 3 blogs went out through the window when I wasn’t watching…

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  5. Fasc says:

    Right, in terms of Paladins I think it works fine to move away from simplified “enough” discourse because of the high variability.

    And yes, I agree, it was one of those things that came up commonly back in Wrath when people were looking at how to edge over enough to live through Heroic LK and other nasties. Getting above a particular known threshold (usually by taking the upper end of a melee hit plus other known spikes) and then a bit more for that extra cushion “blurring” as you mention.

    I need to learn how to code better, sadly a skill I missed going through engineering course work.

  6. Paul Hallett says:

    Great post Theck. I can’t stand listening to tanks blame healers – unless your house is in order, don’t go criticising other’s!

  7. Frobes says:

    Is there anyone that does warlock theorycrafting like Theck does for pallies?

  8. Brandon says:

    Could you explain how a tank would measure the efficiency of their rotation?

    • Adam Wee says:

      I think there are two ways you could measure your efficiency: First, are you following a priority system and sticking to it? I.e., CS>J>AS>T6 talent>HW>HoW>Con, to quote the Icy Vein’s single target priority, and which they thoughtfully give credit to Theck for checking at the beginning! If you aren’t following a strict priority system, it would be to the detriment of your holy power generation.

      The second measure of efficiency, which is the one that I believe is discussed in this blog post, is measuring how many FAST you are at performing that priority system. There is a hard cap on this, due to the global cool down (also known as GCD). However, while the goal is perform as many actions as possible due to many factors (distraction, hardware issues, latency) it is impossible to fill every single GCD. Meloree’s 98% GCD efficiency is, to be frank, astounding.

      • Brandon says:

        Thank you for taking the time to write out a reply but what I really wanted to know was how you would actually assess how close you are to 100% efficiency going by the standard you described in your second paragraph.

    • Meloree says:

      Find a tank and spank boss in WoL, or a segment of a bossfight that’s tank and spank. Try to clip out any haste effects (heroism/bloodlust).

      Total up the number of CS attempts you had (hit, crit, dodge, parry, miss), multiply by your raidbuffed CS cooldown, and divide by the number of seconds in combat.

      To doublecheck, you can do roughly the same thing with Judgement, but multiply the end result by 1.125 to account for the effective base CD of judgement being 6.75s.

      • Brandon says:

        Thanks for the answer. The best I could find was an achievement attempt of Primordius for pure tank and spank. Do you have any particular favorite boss from this tier or last for calculating your own efficiency?

        • Meloree says:

          Sorry, man, no idea. I don’t play WoW anymore. But you can always highlight a segment of any fight where you know you have 100% time on target, and just check that part. Just try to make sure it’s at least 2 minutes long, to minimize variation.

      • zeften says:

        How did you arrive at 6.75s for effective CD of Judgment? Is there a formula that can take into account haste effects?

        • Ergil says:

          The idea is to look at whole cycle of our rotation (CS – J – X -CS – X – J – CS – X – X), which without haste takes 13.5 seconds ( 9GCDs). You can see that in these 13.5 seconds there are only two Judgements, so effective CD would be 13.5/2 = 6.75. To take haste into account you would shorten the duration by your haste, so for example if you have 30% haste raidbuffed, it would be 13.5/1.3 = 10.38, leading to a Judgement CD of 5.19.

  9. Llewellyn says:

    Hi, I just have a few questions. 1. am I missing something? okay for one, I have several bad habbits as a tank, 1 is that I user HoTr spam rather than CS spamm. and 2, I prioritise J over CS without focusing. But even when I do make a point in spamming CS over J, J stil ends up above CS on dps. I will post a few logs and armory. Thanks for the feedback.http://eu.battle.net/wow/en/character/twisting-nether/Esg%C3%A0roth/advanced
    http://worldoflogs.com/reports/rt-adrgotjxljwv6doi/details/5/
    http://worldoflogs.com/reports/rt-nqepq9rgt52vr66l/details/1/

    • Theck says:

      I’m not sure what your question is, exactly. J will be higher DPS than CS, because it hits a good bit harder. But CS>J gives you more holy power generation, thus more SotRs.

  10. Critastrophe says:

    Hi, I have two questions. The first being about adding haste into my gear set. Would it be optimal to add it slowly say from 4% ~8% ~12% allowing for my timing and my “imperfect” healers to adjust instead of putting it all in at once. I currently have 20% Mastery and use C/Ma for 10m N. Secondly I enjoy all of your endgame Hard Mode theory but was wondering if you ever had the time, you might be able to create a area or section with more accessible (less?) information for people behind the curve such as myself. I love coming to this site but sometimes find the information intangible compared to my current state of play. Thanks, if this already exists and I have missed it please direct me accordingly.

    • About haste increase, I think that you are the only person who needs to get adapted to the differences between C/Haste and C/Mastery, cause, in theory, your damage spike with C/Haste will be much smoother, so your healers will be thankful. In practice, your rotation will be harder to track, cause the GCD will put pressure on your fingers reactions and awareness to not waste HP generators.

      • Critastrophe says:

        So then it would make sense to socket/gear haste in increments while I adjust my timing rather than Slootbagging it all in there and trying to adjust. Correct

    • bryjoered says:

      The only problem that I see with haste gearing is that you are fighting with melee dps for gear and all that dodge/parry plate goes to waste. You can certainly reforge that dodge parry gear into haste tho and socket it etc. I don’t think gearing for mastery is a bad thing, It does a good job at smoothing, while not being quite as good as haste, but you lose the dps increase that is so attractive with haste. The benefit of this is that if you miss on GCD or too or miss time your key presses it won’t be nearly as punishing. Either way the gear that you will have the most access to will probably be tanking str plate, which can be converted into a haste set for a not quite as optimal, but far easily accomplished solution.

    • Theck says:

      There are already plenty of good places to go that are more accessible – Maintankadin, Icy Veins, Tankspot, MMO-Champion, and even Elitist Jerks. Most of the information you find on those sites is heavily influenced by my work, and do a decent job of distilling it down to be accessible.

      I regularly review the Icy Veins guide to ensure it’s accurate, so that’s a good place to start.

      I don’t think your healers need to adjust at all. It really comes down to how well you can handle the transition from 4% to 12% haste. If you can do it all at once comfortably, go for it.

  11. Azia says:

    Very interesting read. I have a question about gearing protection, specifically the tier 15. So from what I’ve read the 4set and even the 2set bonus doesn’t seem that good and since a lot of the pieces don’t have optimal stats (e.i chest, legs, hands) is it even worth going for the set bonus? Would it be better to go for non-set pieces with haste stat? What are your thoughts?

    • Theck says:

      I take a rather dim view of the T15 4-piece bonus; others seem to like it. I think it’s mostly up to personal preference, to be honest.

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