Practical Survival

[Jameak]

Well written. Illustrates survival quite well.

[Leeroi]

It would be awesome if you could include the notion of Burst Time (Hypatia's post from Power of Avoidance) into your visual. I *think* I get it, but it would be great to see that clarified. My understanding is that Burst Time would be the number of melee hits from full health until a killing burst of hits gets you. In your graph above, (the lower Right one) if the second "blocked" hit killed you (the fifth melee swing), the Burst Time would have been around 5 or so. Is that right?

[Satorri]

It's tricky to generalize about burst time, within the concepts presented here it would depend on the amount of mitigation, health, and when your lucky roll came. It is easy to say that with X EH (factoring health with armor), you could die in Y seconds if you avoid nothing and aren't healed, but I try to focus on avoidance's general behavior of breaking up your stream of damage so your healers have moments to catch up, if they need it.

Let me mull it over and see if there's a convenient way to add that concept (need to go back and read Hypatia's pretty graphs again as well).

[Thaak]

First off, wonderful post. Hopefully it will clear up many misconceptions.

1.) Health has a linear value for your survival, meaning you simply add or subtract directly. Bigger damage means you die faster, simple as that. Armor and Avoidance deal with a percentage reduction. As that percentage approaches 100% (complete reduction to 0) each percentage increase will become more powerful in terms of direct survival. I'll use a big jump for simple illustration.

My only suggestion would be to expand this section a small amount.

1) On the table below that paragraph, maybe add a note to say that the 20% change is from 50% to 60%, not from the original value of 40% to 60%.

2)If you feel it warrants the attention, perhaps you could break this down a bit more and show how much small amount of armor(relatively small increases in physical damage reduction from armor) increases "EH" by a much larger margin. Most people don't consider that moving from 65% to 67% reduction from armor, what you really need to consider is that your moving from taking 35% damage to taking 33% damage, netting a 5.7% reduction in actual incoming damage. Orcstar touched on it here http://www.tankspot.com/forums/f97/5...mor-guide.html but i feel its one of those things that most people never consider, so they undervalue items that have bonus armor on them.

Once again, thank you for your work. Also if you don't mind I'd like to link to it from my guild Website.

[Eetabeetay]

In the above example, if you added 2,000 more health, you would survive that second hit, just barely. But if you added 2,000 more health after that, it would make no difference.

I think this needs a lot of clarification. The two factors you left out are that the boss's melee swings are the only source of incoming damage, and that you are receiving no heals whatsoever.

In many cases while tanking, there will be outside sources of damage, be it from an aura the boss has (ie Saph or Hodir), random cast spells (Mim P1), or from adds (Algalon). In all of these cases, especially when paired with heals, that 2k extra hp can come in extremely handy if the extra damage and the boss happen to hit at nearly the same time. Even if there isn't an outside source of damage, that 2k extra hp means that it takes that much less in heals for you to be able to survive another hit.

[Satorri]

Aye, Eeta, but this is rife with disclaimers making the point that this is intended to be simple. If you want to know what the meaningful health increments are for a given boss, it gets rather more complicated.

If you were to take XT for example, you'd want to know the damage input from him meleeing, plus potential collateral damage if light/grav bombs or adds are poorly handled, or the dmg rate of the Tantrums. Then factor in the reductions of CDs, different survival CDs having different affects on your EH for when you use them.

It gets very complicated and you can't generalize over every fight, or even between different portions of the same fight. Is it safe to say more health is better? Yes. Is it fair to say every bit of health you can get is the most important thing you can do? No. How do you know how much is meaningful? You really can't. The point remains that that is the nature of health stacking. If you are overkilled by 8k, that you could've had 400 more health is mostly meaningless.

This is also meant to be simple and fairly introductory.

[Hypatia]

Burst Time would be a kind of sucky thing to visualize. It's kind of a sucky metric overall, really. I can say that because I came up with it.

If you want to visualize the behavior of avoidance, mitigation, health all together, the coolest thing to do would be to make a probability curve showing "probability that you will take a fatal amount of damage in less than this amount of time." I will see if I can put together an example and it's actually interesting to look at (based on some tank numbers I saw lying around recently. If I can find them.)

[bashef]

Another nice post

Slight correction:

Your dodge and parry chances will be approximately what they appear as on your character sheet (-0.02% per level the target is above you, bosses count as level 83, so -0.06% off each). The easiest way to find your miss chance is to use an addon such as TankPoints, however for a tank at the defense cap it will be approximately 9% after diminishing returns.

It's actually 0.2% per level not 0.02% - hence the 102.4% avoid + block for unhittable.

[Satorri]

If you want to visualize the behavior of avoidance, mitigation, health all together, the coolest thing to do would be to make a probability curve showing "probability that you will take a fatal amount of damage in less than this amount of time." I will see if I can put together an example and it's actually interesting to look at (based on some tank numbers I saw lying around recently. If I can find them.)

If you can do this in a fairly easily read graphic you will truly be my hero. You are also a far better math nerd than me. =)

And good catch, Bash!! I added a 0. >.<

[Hypatia]

Satorri: Sadly, I don't think easy to read is in the cards. The essential problem is that there are too many dimensions to try to represent, so the best you can really do is say "here are some different scenarios, try to get a feel for how things are different between them." As an added bonus, people generally don't have good intuitions about probability.

Here are some sample visualizations with nice round numbers. A pretty good illustration of why people are unimpressed with block stats, too. I just used some nice round numbers, nothing reflecting real real numbers. Also note that this doesn't account for the effects of any cooldowns at all.

CAVEAT: I do not recommend making gearing choices based on these pictures. This is just to give a feel for how "fragile" various stat changes leave a tank—specifically in terms of "how quickly does the tank die if nobody can save her with healing or cooldowns?"

The parameters are: tank HP, unmitigated incoming hit, damage reduction due to armor, damage reduction due to stance, aggregate avoidance (miss + dodge + parry), chance to block (amount blocked).

Unmitigated hits of 50k on armor DR of 60% result in 20k mitigated hits. (15k mitigated for 50k vs 70%, and 24k mitigated for 60k vs 60%.)

The first graph is a "baseline", and then each graph after that modifies one of the parameters.

The height of the bars on the graph is the cumulative chance that the tank would have died after being attacked that many times. Alternatively, the remaining white area is the chance that the tank is still alive after being attacked that many times.

Note that, yes, the first, third, and fourth probability distributions are *identical*.

Baseline:



60% avoidance instead of 50% avoidance:


25% block chance instead of 15% block chance (note that the resulting survival probabilities are identical to the baseline):


2500 damage blocked per block, instead of 1250 damage blocked (note that the resulting survival probabilities are identical to the baseline):


70% damage reduction due to armor, instead of 60% (note that it's back to 1250 damage per block, I just forgot to edit the label):


Unmitigated hits for 60000 damage instead of 50000 damage:

[Satorri]

I had a moment of insight on my drive home from work. We've tried and failed to really find a way to compare EH and Avoidance. The problem being, of course, that they help your survival in very different ways.

I think I found a step to bring them closer together, not a way to draw direct comparisons, but a step in the right direction.

The idea is this:
EH is a measure of capacity and is purely a simple arithmetic matter for how much damage you can take.

Avoidance does account for a lot of damage reduced (roughly 83% x total avoidance), but the most meaningful way it presents itself is in limiting how many times the tank gets hit in an uninterrupted chain.

To account for this we need to meet them where they intersect.

Over the course of a fight, given just a single swinging boss, without additional damage effects (to keep it simple at first), a given avoidance and length of the fight you can calculate what you can expect in terms of hit chains throughout the fight. The math gets a little complicated as it requires an iterative loop to resolve the actual count. I built this into a spreadsheet. So, as an example, a boss that swings on a boss with a 2.0 swing timer, a tank with 55% avoidance, and a 20 min fight of continuous swings, you'd have the following counts (here miss = dodge, parry, or miss):

0 x 4-hit chains         2 x 4-miss chains
4 x 3-hit chains        11 x 3-miss chains
41 x 2-hit chains       62 x 2-miss chains
174 x 1-hit chains     168 x 1-miss chains
================================================
270 hits total         330 misses total

Based on these numbers, each string would have an unmitigated damage total to compare to the EH of the same tank. These unmitigated damage strings, if the boss hit for, say, 50k, would be 150k, 100k, and 50k respectively. In order for the tank to be able to survive the string, they would need EH greater than the sum of the chain to survive without heals.

Like I said, this is one step closer to closing the gap, not the solution. Every tank *should* be able to survive one hit, most bosses/modes seem to fall between 2-4 hits to kill a tank at Ulduar's damage level, the particulars depending on the fight, and most fights have additional hazards that need to be mitigated for short bursts (Hodir Frozen Blows), or additional potential damage sources that need to be avoided (Vezax enrages, though this might fall into the former categories for some people until 3.2 >.>).

I'll keep on it until I find a way to bridge the gap in a meaningful way.

[Hypatia]

Yeah. There are a lot of useful ways to look at it, honestly. But after doing that work on the Burst Time metric, I've basically come to the conclusion that there's definitely no "one number" that can really cover it.

I like your hit-chains-to-EH thing above. Note, though, that I'd suggest you express it in terms of frequency or probability instead of doing a simulation (your iterative loop? Otherwise your math is way off). It definitely does not take a simulation to calculate the likelihood or frequency of these things.

 1.84% 5+hit chains   5.03% 5+miss chains
 2.26% 4-hit chains   4.12% 4-miss chains
 5.01% 3-hit chains   7.49% 3-miss chains
11.14% 2-hit chains  13.61% 2-miss chains
24.75% 1-hit chains  24.75% 1-miss chains

 1m49s 5+hit chains  39.76s 5+miss chains
88.50s 4-hit chains  48.54s 4-miss chains
39.92s 3-hit chains  26.70s 3-miss chains
17.95s 2-hit chains  14.70s 2-miss chains
 8.08s 1-hit chains   8.08s 1-miss chains

The probability of a n-hit chain with avoidance a is (a)(1-a)^n. The probability of an n-miss chain is (1-a)(a)^n. The probability of an n+hit chain is (1-a)^n. The probability of an n+miss chain is a^n. The frequency of an event with probability p on a stream with interval t is t/p. (i.e. 2.0s/0.0501 for 3-hit.) The 5+miss chains are more frequent than the 4-miss chains because the probability of getting 5 or more misses in a row is greater than the probability of getting exactly 4 misses in a row.

So--the math is not hard at all, but the probabilities involved are such that for a simulation, you'd have to do a lot more samples to get the probabilities correct. Let's compare your hit numbers to the probable hit numbers from the probabilities I've given:

Your numbers     Probability
---------------- ------------------
  0 4-hit chains  13.6 4-hit chains
  4 3-hit chains  30.0 3-hit chains
 41 2-hit chains  66.9 2-hit chains
174 1-hit chains 148.5 1-hit chains
================ ==================
270 hits total   270.0 hits total

That's far enough off that I'm really not sure what you were doing to get your numbers.

Anyway: What it comes down to is, I think that some sort of "distribution"-based information (like showing the frequency of various numbers of hits in a row) combined with EH is best. Trying to distill things to one number was too much. Good luck.

[KnThrak]

Calculations like this make me wonder whether Blizzard shouldn't just deflate the numbers in WoW to take "time pressure" out of combat. Both PvE and PvP are "too fast paced", in a way. Sure the Lightning Bolt spamming Elemental Shaman may disagree, but from a perspective of the tank dying on the second blow if not timered/healed, and the blows coming 3s-4s apart, that's quite the small window once you factor in other abilities used in the fight.

But anyways, rambling over. :P

[phaze]

Anyway: What it comes down to is, I think that some sort of "distribution"-based information (like showing the frequency of various numbers of hits in a row) combined with EH is best. Trying to distill things to one number was too much. Good luck.

I concur with Hypatia. When you start delving into low-probability occurrances (such as long strings of hits), a short simulation becomes fairly innacurate. Mathing out the probabilities for EDF gets you the same information as the sim, without the variance.

[Satorri]

Phaze, not that I appreciate your frequent stops in to nay-say non-specifically, but would you mind actually contributing something next time? Constructive not distracting.

Knthrak, that's the fun part of playing a live action game, twitch gaming, of a sort. If you make it turn based, which many do by a variety of methods, it loses it's appeal sooner or later for the lack of really feeling like you're in control. Part of becoming the sharpest player is learning that micro-time management. Elemental Shamans feel this very closely as the current state of the class/spec requires that they fit things as efficiently as they can into the CD of their Lava Burst. The closer you can fit things into that to not waste time (i.e. delay the start of the cast off the CD or have a dead fraction of a second before starting it) the more damage they can pump out. It's an interesting game of balancing haste, sort of like the way BM hunters in BC used to try to fit Steady Shot perfectly between the auto-shot timer, but with LB, CL, and shocks now (can you tell I play an elemental shaman too? =D).

And, Hypatia, thanks for those other concepts, my probability is terribly rusty (especially since I despise the stuff when you're not dealing with an ordered system like a computer program, which of course is also probably equally silly to count on it). Here's the math-type simulation I used, as a mental exercise, to generate the numbers:

The concept is this, if, mathematically, you started stepping through the fight, you reach the first hit. Based on the probability you have a set chance of taking a hit right after. If you hit that chance, you now have the chance for the third. First, avoidance gives you the very simple count hits, (100% - Avoid%) x Total Swings. Using the probability of taking the second hit, you can figure out how many of those could come two in a row. Note that any that don't are 1-hit chains, and any longer chain would also be a subset of the number of chains with 2-hits in a row (can't get hit 3 times in a row without being hit twice). So, the linked circle of formulas works out the right real number of swings that would satisfy those chances for hits and misses in a row, over a set number of total swings (in this case 600 swings). The count is not the only way it could work out, but it is one, large number expression of what could happen. Maybe I missed a mental step in there, maybe you can help point it out since I don't see it. =)

I don't expect you can distill the relation down to a single number, but rather a field of implications. A weighted range of meaningful EH related to avoidance.

The thinking still needs much resolving, the idea came to me in traffic and I needed to put down my landmark before I kept resolving the thought.

[Trondhjem]

very good one!

[bashef]

Hypatia: the minor point first - something is nagging me about those probabilities, and it has to do with how the two, three, four chains and so on all interact with one another. A chain of exactly four hits, for example, surely must include a miss before and after the four hits to exclude the possibility that the 4-chain is part of a larger chain? I notice you have multiplied the probability of a four chain (1-a)^n by the probability of a single miss, but as I say in all but the first and last hits of a fight there would have to be an avoided hit at the beginning and the end of the chain in order to ensure you weren't only seeing part of a chain. Also the tabulated probabilities don't sum to one even though the set of possibilities is exhaustive, which makes me think we're not looking at a single random variable here but joint distribution over a set them (a Bernoulli one for each swing) and the issue with comparing two-chains with three-chains with four-chains is that the dimensionality of the variable is different in each case so I'm not sure the comparison is meaningful. I will have to think more carefully about this though, and if I'm being stupid I'd appreciate being corrected

On to the fundamental point then. My issue with trying to compare avoidance with effective health is that the simplest method (and therefore default in most cases) is to reason about expected damage/swings received/etc with a given level of avoidance (I mean expected in the statistical sense, which you might call "average"). My feeling is that by considering expected behaviour, instead of other properties of the distribution over damage taken, avoidance comes off looking better than it is simply because, on average, avoidance looks very good (I'm not sure about expected damage reduction for avoidance versus mitigation stats at equivalent itempoints - my guess would be avoidance looks better).

Hypatia's examples do exactly this (not that I'm criticising in the slightest, simply trying to be clear about what I mean):

The frequency of an event with probability p on a stream with interval t is t/p.

what you mean of course is that the expected frequency of the event is as you show. What is extremely important to point out is that the probability of getting exactly the expected value (or the closest integer to the expected value) in the case where you're looking at a discrete variable, number of hits received say, will be far smaller than the probability of getting something other than the expected value. In the case where the variable is continuous the probability is obviously zero, but this would be the case for a reasonable interval around the expected value. Put more simply, most fights will have something other than the expected thing happen - this is just the way random variables like this work!

What this means of course is that the damage a high-avoidance tank receives is unpredictable. Going back to practicality for a second, this means things like healing assignments are hard because it's difficult to estimate how much damage the tank is going to take... you can figure out how much he should take on average, but you also know that it's extremely unlikely he will take that average (although of course taking amounts of damage close to the average is more probable than taking amounts of damage significantly different from it). Given access to this information I suspect most of us would over-compensate in case damage is higher than expected, leaving a healer either twiddling their thumbs or cross-healing if it turns out to be lower than expected.

Stepping back into theoretical discussion, I believe considering exclusively expected damage received when figuring in avoidance is not the correct way to analyse its benefits relative to effective health. In fact I would suggest that variance in damage received is arguably more useful, and this paints effective health as literally infinitely more attractive than avoidance - given fixed hit sizes, the variance in damage received for a hypothetical zero-avoidance pure mitigation tank is zero. You know exactly how much he will be hit for each time, and if it's too much for current healing capacity you switch an extra healer onto him. There was an example floating around forums a month or two back about two tanks (I don't remember the specifics, so forgive me if the numbers are off), one of whom gets hit for 15-22k on each swing and the other who gets hit for 20k each and every swing. While superficially seeming better, there is a way of thinking and analysing which makes the first tank a worse choice for the encounter. Not that I'm for a second suggesting we all drop all avoidance from gear and talents to stack effective health through the roof... just that the implications of avoidance need to be made clear and understood if the goal is to compare.

This has been a long and rambling post, and the first time I've actually written out these ideas so apologies if they're not all that coherent (and also perhaps a bit pedantic and technical!). I guess what I'm thinking is that comparing avoidance with effective health is tricky because in the one case you have something which is perfectly predictable, and another which is anything but, and in condensing avoidance to its expected performance you ignore vital information about its unpredictability which makes it look a lot better than it really is given the goal of providing reliable, repeatable and (reasonably) predictable damage on a tank so that healers can learn fights and develop strategies instead of literally winging it all the time!

[phaze]

Hypatia: the minor point first - something is nagging me about those probabilities, and it has to do with how the two, three, four chains and so on all interact with one another. A chain of exactly four hits, for example, surely must include a miss before and after the four hits to exclude the possibility that the 4-chain is part of a larger chain? I notice you have multiplied the probability of a four chain (1-a)^n by the probability of a single miss, but as I say in all but the first and last hits of a fight there would have to be an avoided hit at the beginning and the end of the chain in order to ensure you weren't only seeing part of a chain.

No, probability of a given string of occurrances is completely independent of previous / following occurrances.

It doesn't matter if all the prior attacks were misses or hits (which would make the current string longer if looking at them); they don't affect the current analysis. If you want to extend the probability calculations for larger specific strings of attacks, feel free. You'll see however that they become so rare that it's not worth spending much time thinking about their occurrance.

Also the tabulated probabilities don't sum to one even though the set of possibilities is exhaustive, which makes me think we're not looking at a single random variable here but joint distribution over a set them (a Bernoulli one for each swing) and the issue with comparing two-chains with three-chains with four-chains is that the dimensionality of the variable is different in each case so I'm not sure the comparison is meaningful. I will have to think more carefully about this though, and if I'm being stupid I'd appreciate being corrected

Take each probability individually. For a two-hit chain in the above example: p =.1114. The probability of NOT having two hits in two attacks (1 hit then 1 miss, 1 miss then 1 hit, 2 misses) is .8886. Simple as that.

There's no need to try to pool all the probabilities together. Take them for what they are: examples of individual strings occurring.

On to the fundamental point then. My issue with trying to compare avoidance with effective health is that the simplest method (and therefore default in most cases) is to reason about expected damage/swings received/etc with a given level of avoidance (I mean expected in the statistical sense, which you might call "average"). My feeling is that by considering expected behaviour, instead of other properties of the distribution over damage taken, avoidance comes off looking better than it is simply because, on average, avoidance looks very good (I'm not sure about expected damage reduction for avoidance versus mitigation stats at equivalent itempoints - my guess would be avoidance looks better).

It's an analysis of probability; nothing more, nothing less. A more detailed workup falls under Expected Damage Frequency, which has been discussed in the past (by Hypatia and others).

Put more simply, most fights will have something other than the expected thing happen - this is just the way random variables like this work!

This doesn't affect the mathematical probability. It's understood that this math is just a statistical analysis; no one should be expecting probability numbers to match any given data set. The probability of a complete match itself is very low!

What this means of course is that the damage a high-avoidance tank receives is unpredictable.
...
Stepping back into theoretical discussion, I believe considering exclusively expected damage received when figuring in avoidance is not the correct way to analyse its benefits relative to effective health. In fact I would suggest that variance in damage received is arguably more useful, and this paints effective health as literally infinitely more attractive than avoidance - given fixed hit sizes, the variance in damage received for a hypothetical zero-avoidance pure mitigation tank is zero.

Sure; but this has nothing to do with probability analysis. Rather this is about individual in-game decisions (tank gearing, healing) that are being based on the analysis.

Also, the reliability of avoidance strings increases as you get more avoidance; that's the nature of EDF analysis. Feel free to read over Hypatia's earlier math on the subject.

EH and EDF are different parts of an individual player's survivability. They're both important, but I don't know if a side-by-side comparison really gives you any useful information unless you consider all the other variables as well (per-fight movement, special attacks, player deaths, latency, etc).

given the goal of providing reliable, repeatable and (reasonably) predictable damage on a tank so that healers can learn fights and develop strategies instead of literally winging it all the time!

Well, the simplest goal is to survive long enough for the event to be over (boss death, phase trigger, etc). Making damage predictable is one facet. Reducing overall damage intake is another. As long as the healers can keep up, then the predictability is sufficient to win the encounter.

[Satorri]

See, though, that last point is a very popular and HORRIBLE idea.

Consistency is not more important than taking less damage. At all. Ever. If that were a sound maxim, you could have zero avoidance and that would be preferable. As a healer, on behalf of healers, let me just say, it is OK to have moments in the fight where you suddenly do not take damage, in fact, it's bloody awesome!

Good healers are good at "winging" it to a point where they have to adapt to unexpected needs for healing. Great healers have a very low occurrence of unexpected healing since crushing blows have been removed. Avoidance may cause damage to be more sporadic, but not in the same problematic way as when it used to be coupled with unexpectedly GIANT damage spikes. Those giant damage spikes now happen but only on predictable game mechanics (i.e. Fusion Punch, Frozen Blows, Plasma Shock).

Since we're digressing slightly from the original intent of the thread, let me just say my goal here is simple but may get lost in too much discussion. I do NOT want to make an over simplified X Avoidance = Y Effective Health. I DO want to find an effective way to relate them more directly. They work differently, no misconceptions there, but the divide in the past has lead to people somehow ready to think that avoidance is bad for you, or undesirable, or it makes healer's lives harder. In general this is just inverted thinking that I want to remedy.

[Eetabeetay]

The point of survivability that I see is to increase the probability that you will survive, not to necessarily make it easier to survive average conditions. I understand what you are saying that it's not hard at all from a healer standpoint for the tank to take sporadic damage, but that doesn't mean they are unable to heal a tank that takes more damage or that they will go OOM doing so in any WoTLK fight released so far. I'm not looking to decrease the chances of myself taking a 3 or 4 string of hits, but increase the chance that I will survive a 3 or 4 string. You can't guarantee with avoidance that you will not take a 3-4 hit. Avoidance isn't bad by any means and granted you cannot go into a fight with 100% of either EH or avoidance. I don't know about other classes, but for warriors the BiS pieces for EH most often coincide with the BiS pieces for avoidance, and thus it comes down to a fairly small difference of whether to enchant and gem for avoidance or EH or some combination of both. I'm not sure if I'm just rewording what you're already trying to do but I think we should go about trying to somehow find a way to guesstimate the best balance of our avoidance and EH for a given fight.