Why We Do What We Do (An in depth explanation of EHP and ICC 3.3.3 tanking mechanics)

[Aggathon]

When/if I get time I will be updating this and addressing people's concerns. Especially on the gaussian stuff. Looking back on it I think i was a little over-zealous in my approach and plan on re-wording it. Regardless of the actual distribution the point that EH still pushes the stochastic nature still stands.

I still need to revise the spreadsheet, and I may talk more about the relative merits of armor. I think that a blanket discussion isn't quite warranted because as with previous debates in this thread what it really comes down to is gear selection where a lot of times both parties will end up agreeing on.

However, last week was finals, this week has been post-finals/grad parties, I'm visiting my parent's now and then going to Vegas and then moving to Texas, so... I don't really have time to be as complete as I'd like. But first I do have a question for bashef....

The observation about the frequency, as well as occurrence, of n-hit-strings is interesting, too. While the suggestion is that provided n-hit strings occur with sufficient infrequency that a cooldown is always available for them (assuming that said string is life-threatening and that using a cooldown negates the danger), there are two issues with this. Firstly, the suggestion is that one is able to reactively time cooldowns to co-incide with periods of danger, there's no way to know until the n-th hit lands that you were in a lethal situation, assuming that n-1 hits aren't going to be fatal and so you couldn't pre-empt the n-th. Secondly, just because the expected frequency were low wouldn't guarantee you wouldn't see back-to-back n-hit strings and thus not be able to time cooldowns---it's the same argument as with avoidance, expected damage taken or frequency is irrelevant since you can't survive the (potentially limited) number of times where these events do occur.

I don't understand this line of logic. The bigger the "n" value is the more time you have to react. You see your health get low and you go, "oh hey, I should use a cooldown here because if I take 1 or two more hits I'll die" At least, that's what goes through my head, I often am constantly noticing both my hit points and how many more hits I can take, if I drop too low I'll use a cooldown, if I feel like the healer is going to catch up I'll risk it and not use one (or go "oh crap I'm out of cooldowns I hope the healer can save me")

Like... yes obviously you don't know if you'll take that nth killing hit, but isn't that the point? The bigger that number is, the longer the time you have to catch up to make sure that taking the nth hit doesn't matter or to use a cooldown. I often use cooldowns very proactively instead of reactively to make sure that that doesn't happen. I think that's the staple of a good tank.

Or am I missing something? What you were getting at was kind of hard to follow for me (my brain has melted and subsequently shut off due to finals and now class being over).

[bashef]

Yes I think I was probably being a bit abstract and obscure - I'll try to rephrase.

One of the posters made an argument along the following lines: what is of interest is not the probability that an n string hit will occur (where n is sufficiently large as for this to be fatal) in a fight, but the number of times it will or the relative frequency of its occurrence. Then, provided this relative frequency is less than the availability of major cooldowns (which we assume will negate the lethality of the string) there is no danger.

My argument is that this isn't really true, and here's why. If the true danger comes from n consecutive melee swings (possibly combined with some other random, i.e. non-predictable damage) then its occurrence is unpredictable. In order to use a cooldown, you'd have to do so at the latest on the connection of the n-1th swing, which means the quantity of interest is not the relative frequency of n-strings but (n-1)-swings (if the n-th connects you're dead, but you won't know that it did til you die!). Since the incidence of (n-1) strings will be far higher, I'd suggest that hoping for a major cooldown to be available would be unreasonable. To me, also, this is the essence of reactive cooldown use, since there's simply no way to account for when these situations will occur. Pro-active cooldown use to me is either using a cooldown to cover a predictable special attack/burst period, or to cover forced movement of a major tank healer.

[Aggathon]

Ahhhh I see what you're saying now. Ya that makes sense and I can agree with it.

[drae]

Amazing work Agg.

[Aggathon]

In my revision of this I'm going to add another section talking about armor vs. stamina as per a discussion that felhoof brought up that sort of discusses which values are better and how EHP is affected by the ICC raid buff more specifically.

[Acidbaron]

Nice write up, once i have a day to spare i'll read it all

[FullofHeal]

WoW. I came to this section to look up details on Warrior Tank gear selections and how to finally live through HoR mobs (start...it's all downhill after the ghosts). THANK YOU. You, in very complicated math terms (my head spins on math, though I can more or less follow the discussion) nailed on the head that which I felt all along. And explains why I keep biting. Sure it's 1-part action choices and 1-part gear, but I always felt there was something about gear that was being ignored. As a Holy Priest alt char (DPS alt-spec on both), I see both sides of the coin, and can see the difference gear choices make. Thank you.

Now to get that spreadsheet downloaded and figure my direction!

[Aggathon]

Ya, the spreadsheet has a few errors in it. I need to get those fixed, will probably do it sometime this weekend (that's why the spreadsheet isn't up at the moment)

[Agarwaen3]

I'm back and I finally have time to finish off my first reply (this post follows http://www.tankspot.com/showthread.p...850#post415850 this one)


The concern I'd like to raise is that, no matter if you can or can't mitigate dangerous bursts with your cooldowns, you want to minimize the probability of them happening, and that can be done through 2 options :
-Health
-Avoidance

As you explained, both are stochastic, one less than the other.
But the result is that the only metric you can rely on is the probability of wiping.

The debate here is mostly academic, as with ICC's health, avoidance levels, and mobs' hit sizes, this instance does favor EH in all realistic gear choices.

Anyway, here's my work :

Setup :
During a standard (melee-only) fight, we're looking for the number of streaks we're likely to take.

First step : Average number of streaks with different avoidance levels

First, an example :
Here's a simulation of a 5min fight, with a 1.5sec swinging boss (that's 150 hits). Each point of data is 100k iterations of the fight (precise enough)
We're looking for streaks of at least 3, 4 or 5 hits (that means that the curve for 4 accounts for all streaks as long as or longer than 4 hits)
I used avoidance levels from 35% to 65%, raid-level avoidance (although not 65% is irrelevant for ICC of course, it was for hyjal).

Less talk, more images :

graph1..jpg

This first graph shows a first result :
You should expect to take long streaks during a typical boss fight

Second graph is how many of those streaks you should expect within 2 minutes (it's just normalized to 2 minutes)

Graph2..jpg

Why 2 minutes you ask? To help us interpret those numbers.
For a warrior glyphed with shield wall and last stand, you'll have 2 life-savers with 2-minute cooldowns each. So any configuration (avoidance, streak length) yielding over 2 streaks every 2 minutes is dangerous (that's a landmark, since you could add in external cooldowns)

But these graphs do not answer the concern you raised that these streaks can happen back-to-back while you're out of cooldowns.
In the next series, we will simulate a fight. Every time a streak happens, a cooldown is used. If a streak happens and you have no cooldowns left, you die.
Thus, we simply simulate the probability of dying in this setup.

Graph3..jpg

You should notice that this graph shows very different curves from the others :
The addition of cooldowns to the simulation gives "S" shaped curves.
This shows that there is a synergy between avoidance and cooldowns, and that it is not a small-scale effect.

However, looking at the figures, I've come up with a few other comments :
-Streaks happen : 3 to 5 hit streaks will happen in a typical fight pretty much regardless of how much avoidance you have. But experience shows that you do survive to these, which leads to :
-Mean HPS lets you survive to said streaks : since those streaks happen regularly in fights, a "normal" amount of incoming heals will let you survive those without noticing they ever happen.
-Tanks don't die to streaks : (/taunt) They die to streaks AND low HPS

I'd like to conclude in saying that avoidance vs. EH should not be based on one streak happening, since it most likely will, but on reducing the number of dangerous streaks that happen in a typical fight.


On Heals :
I did not include heals in my simulation, as I would have needed to make huge hypothesis on those, and I think they would have messed with the results a lot.
A positive point is that those simulations showed the importance of consistency in healing


I will try to make a simulation on both the probability and the number of dangerous streaks (those that leave you without cooldowns) that happen in a regular fight, but I'd like to get some feedback on this first.


Please criticize.

Simulation code is available on demand (I wrote it in Java)

[Aggathon]

I REALLY like this data, it is very well thought out and I think explains it better than mine, and the graphs are definitely better, in addition to adding another level into the discussion (i.e. cooldown usage).

PM me and I'll give you my e-mail. If you put some labels on the axis of those graphs (what's the plural of axis anyways? Is it axis?) and send me the java code I'll add it to my posts above.

Excellent work imo.

[Satorri]

-Tanks don't die to streaks : (/taunt) They die to streaks AND low HPS

On Heals[/U] :
I did not include heals in my simulation, as I would have needed to make huge hypothesis on those, and I think they would have messed with the results a lot.
A positive point is that those simulations showed the importance of consistency in healing


I will try to make a simulation on both the probability and the number of dangerous streaks (those that leave you without cooldowns) that happen in a regular fight, but I'd like to get some feedback on this first.

I think healing is where a lot of this gets complicated. We rely on healing to stay alive. If we don't, it's not a test of our tanking either.

There is a dynamic interplay between healer and tank that is crucial, and near impossible to model in a simple mathematical way. The reason is that it is heavily based on reflex, reaction, anticipation, and all the mitigating factor for those that arise from the UI and the interweb nature of the communication.

It is never an issue of "low hps" but rather of mis-timed or too delayed heals. In other words, a bad streak combined with a healer who is distracted healing something else, getting out of fire, or not seeing the dip soon enough (or better from a good healer, being ready for the dip before it happens).



I agree, that part of the under-estimated, or harder to perceive natures of avoidance is the interplay it has with this reactionary nature of tanking and healing, something that becomes more important as healer efficiency does (*fingers crossed for Clysm). Many tanks work under the assumption (not unfounded, mind you) that all tank healers just lock sights on their tank and spam heals non-stop, the best hps heal they can manage. This does happen, though this is not what I consider good healing, it is not actually, always the case as healers do still often have to step out of fire, and when overhealing/efficiency becomes and issue, the healers who try to keep doing this will suffer.

So, realistic interplay of a smart/tactical healer and a tank involves 3 sources of random fluctuations:
1.) The pace of combat. This is only pseudo-random, as hit timers are predictable in rhythm, even when you have those with out-of-phase special mechanics, you can still keep the rhythm if you are savvy with that (musicians can do well here). That said, most people are too distracted to follow the rhythms so the product is the appearance of randomness.

2.) The scale of damage. The size of hits is generally a very small component of this (the random range on hits is actually proportionally very small), but CDs and procs tend to make that more of a variable. Triggering your important CDs and the point where they wear off, party members using their damage reductions contributions, the stutters caused if you are moving, the instances where multiple damage elements stack simultaneously, etc all make the damage taken vary in small or large degree.

3.) The availability of your healer(s). Depending on how rigorous you assign healers to set assignments, and how often they stay blindly on them (some of the best healers know when to break their assignment to cover a hole and save the group, and some of the worst healers just try to do it all at once, sometimes for a good outcome, sometimes for horrible inefficiency), you will find that you do not often have a healer focused on you and nothing else unless there is the constant risk of you dying without a steady stream of heals (read: Festergut 3rd Inhale). Good healers are prepared for the healing you need, but are also sharp to respond when there is a surprise need. The result is that reflexes are not what *should* be relied on, but they often are still important. Reflex response is what leaves room for another random element in the fluctuations in your health.


Avoidance contributes to the pace of the damage you take. It interrupts the constant flow. Many people have accurately recognized that this makes the damage less predictable, but have mistakenly extended this to be a bad thing. The issue is that you will *not* take damage when you are sometimes expected to. This is *not* the same as taking damage when you are expected not to, which *would* be a problem. It is a slippery distinction, but an important one. This stigma has haunted avoidance for a long time, and is part of what gave birth to the church of "EH is the only smart thing to do for progression." The gospel is not without merit, but its tenants are often not understood by its devotees.

Modelling is fun, and handy for a lot of things, but I think the only way to *truly* grasp the nature of the beast would require you to make what is essentially a WoW game without the graphics. You need the random elements in place, the healing needs to be filtered through the angle of player response, reflexes, and attention. In short, I think the only accurate model would be a nightmare, and really all you would end up producing is WoW without the pretty scenery.


I don't want to discourage you though, because it sounds like great fun to me. =)

[Satorri]

Random addendum thought.

If we assume healing is a constant flow with a regular period, you'll be hard-pressed to find a situation in which you meet both:
A.) the tank *can* die

and

B.) anything the tank did, other than hitting their big tank CD, would have saved them. Gear or otherwise.

[Aggathon]

Satorri, do you mind if I link that first post at the end of my "ending conclusions" ?

[Satorri]

Fine by me.

Which post? The first of the two right above your response?

[Aggathon]

Fine by me.

Which post? The first of the two right above your response?

yes

[FullofHeal]

I agree completely with all the above...as I'm both a Tank and a Healer. From the Heals side, it's exactly as described, reflexes and knowing when the nastiness will hit, and planning for such. Even so, there are random, "OH S###"" moments when a tank's heals suddenly drops, unanticipated. This could be one of those streak moments, not a special attack/situation that DBM warns of, but the coming together of Tank 'weakness' (CD, etc), Boss hit and other things going on. I can't speak for all healers, but we dread this moment, as we have a sudden gap to fill, throws off the 'rhythm' of healing, whcih leads to Tank death. This is not the single cause of Tank death, but can lead to it. I'm not a great healer by any means, but I'm sure Aliena can provide better insight into the healer side than I, but just a thought from someone who is on both sides of any instance/raid.

I can say for sure being a Tank and Heals makes me mindful of both roles. It wouldn't hurt for every tank to roll up a Healer and vice-versa to see the mechanics of each.

[Nehama]

Really good work! Puts all those lil' pieces of info I gathered from diffrent posts into one big whole.

The only 'why' left for me atm is the tradeoff of stamina vs. armor. I know it sits at roughly 14 armor per 1 stamina, but I can't seem to find the WHY for it... so I'm not entirly sure it's right, ofc.

Anyhow, great work!

[Satorri]

The only 'why' left for me atm is the tradeoff of stamina vs. armor. I know it sits at roughly 14 armor per 1 stamina, but I can't seem to find the WHY for it... so I'm not entirly sure it's right,

It is only right at certain places. The relationship is not fixed. This info is in the posts above. =)

[GravityDK]

Great essay, well done.

[Karilyn]

Welp.

That was a delight to read. I used to be in the "balanced" category too. Then sometime a year or two ago I went full EHP and agreed that my survivability seemed to go through the roof. And I've been going full EHP for a while now, using a lot of the arguments presented in that article to argue against people who said I was stacking my stats wrong.

But this is so well worded. Helps remove any doubt from my mind. Especially the part with the chart showing the effect of Icewell Radiance in reducing dodge. I didn't quite realize until I saw that, just how incredibly overwhelming it is. And how it completely destroys any viability of stacking avoidance.

I wish every tank would read this.