Tanking Teaser: Introduction to advanced healer/tank evaluation

Most everyone who's responded to this thread has the right idea. No one tanks in a vacuum. There's a lot more to do when tanking raid bosses besides soak up or avoid damage. For fights like Lady Deathwhisper, Putricide, the Blood Princes, Valthiria, Sindragosa, and the Lich King, there's a ton of movement involved. But there's no equation that'll evaluate how well a player moves or reacts.

I think we all understand the desire to be able to evaluate someone before we invite them to a pug, but there's really no way to quantify everything a player is, and certainly not something like skill and situational awareness. This borders on trying to remove the human element from the game, and that would be a horrible thing.

The initial equation seems wrong. Otherwise, I like the idea. It has room for improvement, but the fundamental equation needs to be fixed.

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Hp(t) describe how much behind the healers are on healing the tank

The common interpretation of the definition defines: Hp(t) = D(t) - H(t).
NOT
D(t)-H(t)=I*DeltaHp(t)
This is unnecessarily complicated and doesn't tell us anything. If we want to normalize for the tank's current health:

Let Hp(t) = healing deficit = D(t) - H(t)
h = Tank's maximum health
Hpn(t) = normalized healing deficit = Hp(t)/h

If Hpn(t)=1, the tank is dead. If Hpn(t) = 0, the tank is at full health.

If there's a delta involved, it's that Hp(t) = delta(D(t), H(t))

There seemed to have been a lot of responses suddenly (didnt expect them, since they cama a month after posting.

I see that you all (or most of you) have serveral things that you dont agree with in my post, and that is all good since it was by no mean supposed to be the end of it.
There have been a lot of wonderfull critisism pointing out several weaknesses in the usage ingame, the somewhat nonedirrect way of explaining and also a bit about the exact statistics, both in general and the weaknesses of using averages. Therefore I am going to mention a few things before I go back to answering the specific questions (or atleast some of them).

1. This was supposed to be a teaser to the introduction of how to evaluate some important aspects of the tank and healer dirrect teamwork (as in form of healer healing the tank). This means that it in no way was supposed to give you the ultimate way to describe a tank, and that the conclusions in it were final. Instead the introduced functions and values serve as either the core (the Hp(t), D(t) and H(t) functions) of the further analysis or as basic type of analysis over these functions, which can serve as a preliminary scan to check for large derivations from the expected - just like large derivations from the espected values of addon recorded dps often are noted when evaluating.

2. This is supposed to be a tool for the specific evaluation of healing on tanks, not how they move around, throw taunts, dispells, interups and so on. It is one aspect of the game, and should be looked upon it as that. Do by no means espect it to tell you which tank or healer knows how to best position a group of mobs, but do expect it to tell you something about what the resulting movement of their healthpool are.

3. Conserning all the problems with length of post and unessesary complications, then I can only say, that I tried to explain it through the way I thought of the situation, though that is often needlessly long and complicated. On top of that, I have the habbit of making written text longer than average for a given amount of information.

Now to look at the specific questions.

1) Lag is initially not accounted for, for one simple reason: The formulars are not builded for telling you "now the healer should be doing this/that" they are build to calculate certain values (who have their own weaknesses and limitations), which in turn can be compared to what you expect or with another parse, to check differenses. For instance, you could in theory describe some of the differenses between healing reactively, skilled proactively (start casting before the hit comes, but for when/where you expect it to come) and spamming. There are probably a valid point in the timing of events in the parse due to lag, which will have to be countered somehow, perhaps by making sure that your source of data is the point where death and timing is determined (if that is desided in one specific place, which I dont know if it is).

2) Many people seems to have ended with evaluating by the simple mantra: Did it work?
Sure, if you live and the boss die all is good. This is certainly true for first kill progression, where just being able to kill the boss is enough for you to be happy about the encounter, but what about the rest of the time? Is it okay that 60% of the raid disappeared on an easy boss which you have had on farm for months? Bu the mantra, sure it worked, you are alive and the boss bites the grass, but what about those 60% of the raid that died, when you were supposed to get quickly through that part of the raid to get to the progression area. Another way to look at it, which fits better the scope of this article, is to look at 2 different tank health during bossfight senarios. In the first the tank never really drops below 50-60% health, so the healers have plenty of marging of error and there are very little chance of something going wrong due to healing not being sufficient on the tank. In the second senario the tanks health jumps up and down between 15% and 65%, and the healers are on there toes very often. In such an encounter you run a relatively large risk that at some point the rng hates your, the healers face a minor lagspike, gets a little late or is unable to heal for a second too long, which very easily could result in a tank death. In other words, it is not just "did it work this time?" but "will it work next time", because in linear progression setups, a stroke of luck kill will not allow you to pass the boss the next time, if you have to wipe on him 10 times for the sun, moon and stars to be in the right position. Another thing challeging this is: how much of your skill did you have to pour out to make this work. Sure a good tank could carry a really lausy healer through a heroic nowadays, and everything would be "yes it worked" since the tank knew how to stay alive and kill the boss with such a bad healer, but would he enjoy it? Unless he or she was out looking for a challenge then most likely the player would feel quite anoyed by it, and would consider the other player bad, even though he would be "evaluated as fine enough" through the "did it work?" mantra. You could exchange the healer and tank there, since a good healer (assuming current standards) could probably keep the party going even if the mobs was wondering all over the place and eating triggerhappy dpsers for dinner.

3) In continuation of the simplification of "did it work", we have the: tanks (and healers too) dont operate in a vakuum, together with it is imposibly to describe the experiance and situational skills of the tanks and healers.
This is definitly a very valid point, but it is misinterpritated in the context. These tools are not meant to touch those aspects of tanking and healing, and those using these tools should know that just as you should know that gearscore does not tell you anything about a players skill, only what level his or her gear is. What they are ment for is describing what I consider the main responsibility of the tank/healer team: Dealing with the incoming damage. These tools are designed to look on how the incoming damage on the tanks are dealth with, since this is a major issue for gear theorycrafting for tanks and general tankhealing for healers. Sure, both healers and tanks do other things than these and need to be able to perform these too, but this aspect is still one of the prime functions for healers and tanks, and currently this aspect have been left to subjektive statements based on what seemed to work on first sight. Compare this to the difference between a medival carpenters experiance, that tells him that certain structures are more stable than others, to a mordern engineers/physicists calculations telling that how and why certain structures work better than others, even to the point of being able to mathematically optimizing certain values.
In a shorter way: Even though the tank dont operate in a vakuum, there are still things that correspond mainly to him or her, where some of these are related to number manipulations and thereby makes matematical analysis posibly.
For the experiance of tanks and healers and situation skills it pretty much also follows that it isnt inside the scope of these tools to describe that quantity, since the application of matematics on this is far far more complex, and will be derived in some very special ways which are either going to be outside the standard scope of theorycrafting or in need of large assumtions. Again, the tools was meant to something else, and not a complete mesaurement of "how good a tank/healoer is" but rather a "how good is the tank/healer team at managing incoming damage on the tank(s)".

4) There have been mentioned the weakness of using averages for tank health in situations where the extremes are the important points and the problems of using the Gauss-destribution variance for non-Gaussian senarios.
Both of these weaknesses are completely relavent and are the reason that these 2 attributes for the 3 fuctions are enough to fully analyse the healthbar movement of tanks. They are however relatively easy to understand in consept and are still able to tell us something. Still, there are ways to use these 2 attributes for something, and the 2 best I can think of are to preliminary get an idea if something is amiss (low average or large variance - sigma in the math) and for their simple ability that they must be cause by something. Here I mean, that a special value of mu and sigma will generally be caused by something, no matter if it is because they fit the Gauss.-derstribution or not. As you know something must have caused it, you can compile a list of posibly causes (while not all may be there though), which you could check to see if it were one of these, thereby giving you somewhere to start looking for what might have been a problem in the encounter, which otherwise might have been overlooked and just thought of has "how hard the encounter is" or something like that. It should be pointed out, that the posibly conclusions mentioned in the original post are actually things that could cause certain changes in mu and sigma and therefor could be posibly causes for the values of mu and sigma - in other words posibly problems.
To this it should be added, that there are many more attributes which are meant to much more accurately describe certain aspects, and can thereby narrow down the posibly problems to something more precise. Many of these build upon mathematics dirrectly derived for the porpuse of describing these quantities, and therefor required that they were proporly checked for being valid and useable for their porpose, and therefor were left until the real full article were done. In these, there were originally plans for describing attributes such as spike and burst damage, predicablyness, intensity of the fight (the speed of movement of the healthbar), the healthlevel per time/per insidents destributions and so on. Many of these would give a better picture of the problems with tank health in an encounter, but they would still suffer under the basic statistic problem: when compiling data into attributes you will lose some knowledge of the original data - meaning you can not go the other way, only talk about what it would have looked like if you tried to. As a last thing concerning the problem of whether the destribution is proporly Gaussian, then you baiscly need to run an analysis of how good of a fit the Guassian destribution is to the health destribution, which could be used for telling how to use sigma, but that should already be covered in the analysis of the health destribution fuctions, which was included in that part. Though I should have mentioned that the use of sigma was assuming that the health destribution function was Guassian.

5) There were a mentioning of the problem with having sufficient data to be able to use the statistic models with a usuably estimation. I will admid that I hadnt thought about checking for that, and therefor didnt compile the nessesary mathematics for this part. I will however here assume that you have a large enough data set to make these mathematics atleast somewhat usefull, which would happen around 10-20 cicles of fluctuations, which is inside on the level of a standard bossfight, but outside many/most trash fights, though these are often repeated which would then give a useably size of data. It could be done with less fluctuations, but less than 4-5 would have the models walk toward the extremes and central probability spike would have a relative large size, meaning that conclusions would end up being too unpricise.

6) There have also been some talk about the basic formula: D(t)-H(t)=I*DeltaHp(t)
Lets start with what the values in this funtion actually are. All the values are event specific numbers. This means that if at time 10.23s the tank takes 20343 damage after migration, then D(t)=20343, if he at the same time has an "when hit next you are healed for 3723" then H(t)=3723. In other words, these functions are 0 (zero) all the time exect at the exact point where an event happens and they become the exact value of change in health the tank would have. However the Hp(t) function is a bit different, it is more like the steps on stairway, just going up and down all the time. Therefor it was nessesary to introduce the DeltaHp(t) function which describes the change in the Hp(t) function, by the basic, when DeltaHp(t) has a value other than 0, then that value is added to the Hp(t) function at the point it time t. The I stands for Intertia of the Hp(t) function, and in pratice is described by the current maximum health of the tank. For units, DeltaHp(t) is unitless, while I, D(t), and H(t) is all in units of health. For the way the formula is set up, it doesnt follow the definition standard with the defined quantity on the left, but instead follow the standard for Newtons 2. Law with the cause (the forces) on the left and the result (the movement- resulting acceleration) on the right, where the inertia of the object is noted as part of the right side. The reason for normalising Hp(t) was to make the statistic on its movement and the usuability of the values derived thereof much more simple when comparing several tanks who did not have the same amount of maxiumum health. This is what made the most sense for me in understanding the formula, but mathematically it is equally possibly to syntacs the formula differently. It was however needed to introduce these concepts when looking into the later attributes, but there was not room for that in the teaser article.

I have now once again went ahead and wrote some huge wall of text, but I hope this answered the majority of the questions that have been posted.
I can see that there are people out there considering this project interesting, but not something they deem incredibly usefull in pratice. Personally I kind of expected that it would take some time to develop the aspects and consensus among these for the parts which would be most usefull in dirrect everyday analysis. For now it will most likely stay something for advanced users until it have been integrated for easy use into addons, so that it wouldnt require knowledge of the exact ways to compute the numbers to be able to even have a look at the results. This means that it will take some time before the real full article will come, but feel free to come with suggestions of attributes to work on and critic of all this (constructive, please) or just decuss the different aspects.

Putting aside the art/strategy part (which i totally believe in), the aim of the math looks very similar to the Time-to-live discussion & math that was cooking up at EJ some time ago. Kojiyama was keeping a close eye on that iirc?

But again, i really hate seeing healing & tanking reduced to math. It will push something that is 75% intangible and turn it into some number like GearScore.

I've had a 5600 gearscore druid tank try to tank in humanoid form with typhoon & moonfire. That's one example where a number meant absolutely nothing.
I've also had myself tank a full 3 minutes with my health fluctuating between 200 hp & 35%. And that's an example of where you cannot decide if it's imba healers not letting me die or imba me perfectly using cooldowns to allow healers time or a combination of both.

I'd love to see the math go forward but i'd rather it serve some more usable purpose than "evaluation".

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Originally Posted by Fledern

Putting aside the art/strategy part (which i totally believe in), the aim of the math looks very similar to the Time-to-live discussion & math that was cooking up at EJ some time ago. Kojiyama was keeping a close eye on that iirc?

But again, i really hate seeing healing & tanking reduced to math. It will push something that is 75% intangible and turn it into some number like GearScore.

I've had a 5600 gearscore druid tank try to tank in humanoid form with typhoon & moonfire. That's one example where a number meant absolutely nothing.
I've also had myself tank a full 3 minutes with my health fluctuating between 200 hp & 35%. And that's an example of where you cannot decide if it's imba healers not letting me die or imba me perfectly using cooldowns to allow healers time or a combination of both.

I'd love to see the math go forward but i'd rather it serve some more usable purpose than "evaluation".

^This

Especially the last part. I guess what I don't understand is what these numbers are going to be useful for. Like... if a healer optimizes their HPS and a tank is optimized for survivability (armor and stam) then as long as they are using their cooldowns and playing properly (the art/strategy part) then I'm not sure if it matters that the healer healed 50% more than necessary or something. Like... in the end you say "the tools was meant to something else, and not a complete mesaurement of "how good a tank/healoer is" but rather a "how good is the tank/healer team at managing incoming damage on the tank(s)." I honestly don't see the difference between the two statements, or what you're getting at or what your final math predictions are supposed to MEAN.

Also, I highly recommend downloading the Firefox web browser and using its spell check feature.

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Originally Posted by Deathshay

3. Conserning all the problems with length of post and unessesary complications, then I can only say, that I tried to explain it through the way I thought of the situation, though that is often needlessly long and complicated. On top of that, I have the habbit of making written text longer than average for a given amount of information.

And this is probably why you're meeting such strong opposition, those "unnecessary complications" are often the dominant aspects of tanking (and possibly healing as well). Now compared to DPS where the dominant aspect is the final rate of damage out, it can make sense why people want to do it. Tanking just refuses to work that way, you'll spend a lot more time dealing with those complications than you will worry about figuring out your time to live. Gear yourself correctly, don't bite off more than you can chew (meaning don't hop into ICC25 if you've only tanked heroics, work your way up), and you'll do just fine in that department.

You just get more mileage out of playing smart and reacting appropriately those complications rather than worrying about the math behind it, or at least that's what my experience has told me thus far.