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

[Kojiyama]

Well, one can never clarify too much!

(I do see some point to what's being said, though. I actually think your statement at the top of this page is more clear than some of the previous ones, Agg.

And, really, there is a bit of a point to be made somewhere that adding avoidance--even though the element is based on a psudo-random element--lowers randomness by making avoidance more consistant. The more avoidance you have, the less of an impact the random nature of avoidance has on the end result. So, while it is random, it isn't random at a consistant rate! 1% dodge on its own is extremely swayed by its random nature while it approaches no randomness at 100% dodge. That may be a better definition of your avoidance curve to clarify the way avoidance is affected by random numbers.)

[Delmonte]

Or use, you know, perfectly serviceable words like "random" and "randomness" instead of jargon that a small proportion of your readership will actually understand.

Sorry, I tried to use words that would be accessible to everyone, the thing is though I feel that maybe this is a slightly more subtle concept than I first perceived and I want to explain it as clearly and precisely as I can from a purely logical point of view.

Why don't you just tell us what your point is, in one sentence?

From the logic put forward by Agg, it does not follow that Stamina is not random and dodge is.

Then see my posts for the reasoning behind why I say this.

[Satrina]

That comment was aimed at Bovinity, not you, for his "I think pretty much everyone here knows what we as gamers mean when we bring up RNG..." comment. The great majority of readers here don't actually have a clue what RNG means. With great popularity comes a greatly varied audience.

[Aggathon]

I sent you a PM Delmonte.

[Delmonte]

That comment was aimed at Bovinity, not you, for his "I think pretty much everyone here knows what we as gamers mean when we bring up RNG..." comment. The great majority of readers here don't actually have a clue what RNG means. With great popularity comes a greatly varied audience.

Oh sorry, my bad. But yeah, I'm not convinced everyone does understand what is meant when people say one thing is random and another isn't, that's not at all a criticism or poor reflection on them, or to say they are not as intelligent as those who do, it's simply that rigorous logic and maths are not something that they use frequently or study. Maths is one of these things that you can get more and more rigorous about too, I'm sure there are many levels on which I do not yet (and maybe never will) fully understand 'simple' concepts in maths.

[felhoof]

What I think would be a more interesting question to be answered is this: Why is it more valuable to stack EH over avoidance when both are essentially governed by randomness? EH becomes better when the stochastic nature of damage and healing appear to be emphasized (IE, when you cannot survive more than a couple hits without heals and healing events are large), and avoidance becomes superior when this is de-emphasized (when there are a lot of small damage events in a row, as per Algalon). Now I mentioned briefly about how good armor and resistance are when partial heals are factored into the mix - and that's one reason that armor is so strong for fights like Algalon, where there is a very good chance that at any moment you will not be fully healed.

But why does avoidance work well there but not on (say) Festergut or LK?

We've also seen cases where the incoming damage is so great that an unavoided set of attacks is going to kill you regardless of your EH unless you are fully healed; this was the case for things like berserkers on M'uru and Brutallus. Again, why (mathematically) is EH stacking inferior in this situation? (and it assuredly was).

The answer, clearly, is that the kind of randomness matters when figuring out what is more important. In WotLK (at least on fights like LK), healing is completely unreactionary, cooldowns are scheduled far ahead of time to events known well in advance, and damage comes in high enough increments to two or three-shot people. In this situation, the randomness is whether or not the heal being cast will coincide with the damage, whether or not the damage received will be great enough to kill and what the latency is. Incoming damage is very spiky in terms of raw DPS, but large events are still known.Healer disruption is common. This is the randomness of discrete events.

In situations where avoidance seems to shine, damage is consistent and spikes of damage are rare but dangerous. Both proactive healing (Brutallus, M'uru) and reactive healing can be important, but ultimately are meaningless to a certain point. The randomness is in the string of hits more than anything - and as we've seen from the math above, avoidance is very, very good per % at causing X strings of hits to fail, especially once avoidance goes above 50% and X is greater than 4. Deaths were caused by bad strings of damage combined with heal disruption more than anything; incoming damage tended to remain fairly consistent. In that respect, the randomness that was trying to be solved was the randomness of non-tank related events.

Hmm. I'll have to think about that more.

[MellvarTank]

From the logic put forward by Agg, it does not follow that Stamina is random and dodge is not.

Then see my posts for the reasoning behind why I say this.

I believe you meant dodge is random, and stamina is not.

Even this does not make sense in context of the whole document that Aggathon has written. You are looking at one misuse of a term and extrapolating to an entire document, which is why we were arguing. Here is how you can sum up this whole argument in a clearer fashion to avoid an argument such as this in the future, as arguing hasn't done any good:

So I took a long shower and was fairly flustered by the idea that stamina could be RNG, and I had an epiphany. Stam isn’t RNG, it diminishes RNG. Stacking stam is a way to decrease variability in a boss fight! If stam were RNG, in my opinion, that would mean that stam could give you 8 hit points, or it could give you 12 hit points. It doesn’t, it gives you a base of 10 hit points every time (times modifiers, obviously). To demonstrate what I mean by decreasing variability by stacking stam, some graphs are the best way to demonstrate this.

I do not believe that RNG is the appropriate term to use here because:

If stam were RNG, in my opinion, that would mean that stam could give you 8 hit points, or it could give you 12 hit points.

The same could be said for dodge. The difference is the mechanic that uses the stat, not the value of the stat itsself.

Saying this would make it incredibly clear (and concise) as to what you had an issue with, and it would open up the author to ask you to elaborate on whichever point he required clarification on.

[Kojiyama]

After thinking about this a bit this morning, one thing that I definitely see the point being raised in the last page or so is that the 'proof' that Stamina is not random does not really indicate such a thing.

In fact, the normal distribution graph on the first page proves clearly that Stamina and Stamina's value is highly affected by the random nature of incoming damage. While adding Stamina will reduce the risk associated with the variance of incoming damage, it does not remove it. Therefore, the impact of Stamina is always affected and influenced by said random factors.

Additionally, it could be implied by the distribution on the front-end that Stamina has a fully consistent impact in terms of moving one along the normal distribution probability of survival--however, that is not strictly true in a real-world scenario. Obviously, the graph in the OP uses a fully normal distribution with uniform variance. In smaller sample space, a boss could hit for the maximum value 2-3 times in a row and dramatically shift the impact of Stamina in that short period of time.

This is not to say Stamina is bad, but it is to point out that the implications of random numbers on the value of Stamina seems to be brushed aside with nice normal distributions and uniform variance, while Avoidance is given flashing red disclaimers highlighting the chance of irregular variance patterns happening. Surely, if one is going to apply normal distribution and uniformity to analyzing the impact of random numbers on Stamina, the same uniformity should be assumed for Avoidance as well. To another extreme, if one is going to talk about the worst-case of Avoidance having irregular distribution, should not the same thing be applied to the random elements affecting Stamina?

To move on from this, after some thought it seems as if talking about 'random vs. non-random' is a bit of a misnomer, and it would perhaps make sense to put all the stats on the scale of how they affect the distribution of damage.

Health: Changes the point you are at on the distribution curve, but has no impact on the mean or variance
Avoidance: Changes the nature of the distribution curve, reducing the mean and altering variance
Armor: Changes the nature of the distribution curve, reducing the mean and reducing variance

Moving further on this, to address felhoof's points, I believe that if one were to plot distributions of various scenarios, one could easily find distributions where the point on a curve modified by avoidance with current health offers a higher probability of survival than moving your point forward on the unmodified curve by adding only health. Additionally, adding various quantities of armor, avoidance, and health to alter the properties of the distribution at the same time as increasing health could have a dramatically more (or less) probabilistic impact than adding any one factor alone.

I may post some graphs illustrating what I mean if I have some time later--keeping in mind that this was mostly occurring to me while on the way to work this morning and may or may not make any sense.

[Satorri]

Mmmmmm, there were a couple nuggets in there that sparked something as far as metrics for avoidance and health. It will take some time to ferment though, I'm quite sure; particularly about expressing the survival range. Adjusting view points is great! nomnom


And on the subject at hand, odd though it may be...

Your health state is pseudo-random because of the combination of elements effecting it: damage range on attacks, bubbles/blocks adjusting that value, avoidance (is always there on avoidable attacks), the availability and scale of heals (which also has a range built in, plus crits which can amplify the range), and the tank's ability to stand in, or avoid fire, and use CDs. Health state will have a lot of randomness.

Stamina does not have a random component. X Stamina will always give you Y health, and max health is significant only in respect to everything else. By the same measure you could say Dodge rating is not random, but the value it brings will not apply on every hit. Common comprehension paints health as a static and avoidance as a question mark.

If you want to look at it this way, health is random because of avoidance et al. No stat exists in total isolation of effects.

[Kojiyama]

Yeah, you are certainly correct on some of those points.

I guess the subtle differences are simply that the values themselves--e.g. Stamina and Dodge Rating--have a consistant effect but an inconsistant statistical value. The value of either contribution will be swayed by the various random elements surrounding them.

For instance, 10 Stamina will always give you 100 Health, but the statistical benefit of 100 Health is not always constant. The same applies for Avoidance to a greater or lesser degree. (Avoidance gets a bit more abstract due to DR, however as the DR contributes a normalizing effect the same general principle can apply.)

I think, either way, that it is fair to say that the probabilistic effect of adding a set unit of either Stamina or Avoidance is stochastic in both cases. As much as we would like for it to be deterministic, it really isn't as there are far too many random factors for it to be as such--after all, the biggest random factor is probably the humans on either side of the keyboard.

At the end of the day, all these methods are simply forms of statistical risk reduction. While Health is probably the most straightforward and easy to grasp, it is not always a superior form of risk reduction in every case nor can it ever fully remove risk in normal conditions. (While Avoidance and Health both have the capability to remove risk completely at extreme levels, but such levels are not possible to reach. Armor is naturally capped as well.)

As Agg pointed out in the OP, adding Stamina reduces the risk of dying due to random elements, but does not remove it completely. Additionally, as shown on the distribution curve, this is not a linear or constant increase in survival probability per unit Stamina either.

[Satorri]

My project I set myself some time ago was to come up with a way to roll all of these elements into an expression that will be easier for people to comprehend side by side (without falling into the pitfall of trying an equivalence system). It has been percolating for a while, and I've made steps forward, but still no silver bullets.

You can be sure that if/when I do, I'll be sharing it liberally.

[Aggathon]

@Satorri: and you will become an icon of legend because of it if you do figure it out =P

@Jayde: I think you hit the nail on the head when you said the graphs are affected differently for armor, health, and avoidance. I've been talking to Delmonte in PMs and in the last one I kinda talked about this.

My contention that stamina is "less random" than avoidance (which I realize is an extremely vague term) from the avoidance point of view can be illustrated this way:

Say you have a completely unbaised coin (50% chance to be heads, 50% chance to be tails, the WoW Mechanic equivalent would be 50% chance to be a hit and 50% chance to avoid an attack on the tooltip).

Now say you flip that coin 9 times and you get 5 heads and 4 tails. When you flip it the 10th time it does not mean that it will be tails and thus match the unbaised coin's nature of being 50/50 because 50/50 is simply the average. Sometimes you'll get more, sometimes you'll get less but on any given toss it's still 50/50, it doesn't always sync up so that it IS 50/50 over time though.

Which is my point that on a boss fight 100stam=100stam but 50% avoidance does not mean that on a certain bossfight you WILL avoid 50% of the attacks.

So Stam moves the "Z" value of the curve towards survivability, but avoidance moves the mean of the curve up the "Survivability axis" so to speak.

[Kojiyama]

Yeah, definitely see what you're saying.

Avoidance generally introduces higher variance to the curve in addition to adjusting the mean while Stamina has no impact on variance or the mean and simply moves you along the axis of the same curve.

So, the key factor is really the introduction of higher variance rather than it being more or less random. (Which may sound silly, but it probably pays off to be precise in these terms considering this type of math already hurts my brain!)

However, the tricky bit happens in situations where both factors are being altered at the same time. For instance, say you lower the mean and increase the variance through avoidance then add the same health offset as you did without the avoidance modification. In that case, it is highly possible that the axis shift after the mean and variance alterations to the distribution provides a larger statistical increase in survival than it would have without.

The tricky and potentially unintuitive bit is that by increasing your chance of survival in some situations (even in the same fight) you are potentially decreasing your chance of survival in others. If you absolutely know you will never encounter the situation you are decreasing your survivability for, then such can be a no-brainer, but this not always the case.

[BruisedOoze]

Stamina does not have a random component. X Stamina will always give you Y health, and max health is significant only in respect to everything else. By the same measure you could say Dodge rating is not random, but the value it brings will not apply on every hit. Common comprehension paints health as a static and avoidance as a question mark.

It's tricky because I could make the statement 'by the same measure I could say while Stamina is not random, but the value it brings will not apply on every miss.' Logically stamina then necessarily has a questionable property associated with it due to avoiding an attack being random. And this is part of the 'stamina is random' argument.

Of course, while Stamina may not have value on every miss, there are misses where it does have a lot of value. This gets into the whole discussion of having that buffer for extra healing. And is one of the reasons why stamina appears to have a more static value in addition to adding an another hit you can take. The hits are not the only spot you're benefiting from it, a number of your misses are as well. Which is in the article there as well.

This is why treating as one as being random related and not the other is tricky. And this follows into what Kojiyama later says. At the end of the day the statistical arguments are still likely there to support Aggathon's claims.

[Aggathon]

Would the area under the curve + distance up on the curve = survivability where the distance of the total curve is a function of EHP, HPS, and DTPS?

Ouch... my brain... it hurts...

[MellvarTank]

/head asplode

[Delmonte]

Would the area under the curve + distance up on the curve = survivability where the distance of the total curve is a function of EHP, HPS, and DTPS?

Ouch... my brain... it hurts...

I think with the different way all these things can affect survivability, as some people have mentioned, it would be hard enough to combine them into one curve or value in a meaningful way in just one particular instant in a fight and then you still want to know how things play out over a period of time even if it's a small one. You could look at survivability in a few different ways, for example, given one set of conditions:

What's the probability I will die in one particular instant in a fight?
What's the probability that my Hp will go up or down by X amount in one particular instant in a fight/how much HP will I have after this one instant?

I think these 2 could prove incredibly hard if you consider all factors and then you can ask:
What's the probability that I will die in a 5 second period of a given fight? '/head explode' as someone put it. I think simplifying things and trying to cover some sort of 'napkin maths' probability could be a good guideline for people though, it's just a question of bearing in mind the limitations of the tool.

I think people are having more joy trying to just assess what the main situations are that tanks can die in in a given tier of a given expansion and at the moment, the feeling is that EHP is more beneficial in these situations for a lot of good reasons that you and others have stated. Trying to assign a mathematical number to describe it all in one seems extremely hard and may just give an incredibly confusing answer.

[Aggathon]

Ya, that was more of an semi-inside joke between those of us that have attempted to model this before... and wasted days of our lives trying to do so... and failed...

[tlitp]

This thread, much like its brethren, is full of contrasts - be it gems in the dirt, be it tail chasing.

Stamina/hit_points/armor_class/avoidance_stats are not random; health_pool/damage_mitigation (through armor&resistance)/avoidance are. Correspondingly, the interesting metrics are all RNG-driven... and you need to look no further than WoW's combat table to understand why.

[Delmonte]

Ya, that was more of an semi-inside joke between those of us that have attempted to model this before... and wasted days of our lives trying to do so... and failed...

Ah ok, I get jokes (in the voice of Homer Simpson)....