[anamiac]

Source: Satorri Druid = Druids wear leather gear and get a big armor buff from being a bear (370%, talented it is 492% or 403% *fact check please*). Druids cannot parry or block, only dodge. In addition to the armor buff, bear form increases the druid's stamina by 25%. Talents give the bear +10% armor from gear, +10 Expertise, +10% dodge, +16% stamina, +6% Strength, +6% Agility, and 6% reduced chance to be crit.

Since Improved Mark of the Wild now gives +2% to stats, druids who take this talent will see +18% stamina, +8% strength, and +8% agility.

[bashef]

This is an interesting thread, and well researched, full of lots of useful info for the uninitiated as well as talking points for people more comfortable with these ideas, and (remarkably) devoid of silly/biased/emotive class comparisons... so thanks!

The one thing I would say is that where numerical comparison is concerned, you have focused on expected damage taken per second. This is perfectly legitimate to explore, but as you and others will I'm sure agree, what kills tanks is spike damage, not sustained damage over time. Very rarely is it the case that damage taken over time exceeds heals received over time leading to the slow death of the tank; assuming nobody did anything stupid (a la not dispelling fusion punch dot) the most likely cause of tank death will be the case where the tank takes massive damage very quickly, and for whatever reason healers are unable to respond during the burst. A simple generic example would be a parry leading to two melee swings in quick succession; specific encounters will also have environmental factors or special attacks leading to similar scenarios.

In that vein I think there are a lot more interesting questions that crop up (although I'm not suggesting you should attempt to answer them since it would be extremely time-consuming at best and intractable at worst! It's just worth noting that this is where really meaningful comparisons apply). These issues are crystallised in the answers to questions like: what is the probability that two (three/four) melee swings taken without heals received will result in tank death? (Or equivalently what is the probability that special attack + melee swing immediately after kills the tank?)

The answers to questions like these depend on a lot of things... also it would be more interesting to consider the case where attacks are not avoided/blocked (as well as the probability of this happening) since this will be the situation that kills the tank.

Of course all of these sound like worst-case expected-time-to-live issues... which they are. This is of course the principle that underlies effective health gearing: not because it's the most efficient way to reduce expected damage taken (avoidance is better for that) but because it reduces the chance of death when your avoidance fails. This is why so many people prefer (blood) death knights and druids for progression encounters, all other things being equal.

Anyway, again thanks for the post, it was an entertaining read - I just wanted to mention this stuff since I didn't notice it anywhere in the original post and I thought it an important point to mention in a thread like this.

[Satorri]

You are right of course, the healing capacity of healers against steady damage in is not a competition at all with tank mitigation and potential healing power. Spike damage is what kills because it catches healers off guard, but that is a skill in an of itself, to know when to expect spike damage (since the RNG has all but been taken out of it with Crushing Blows).

I think one of the major reasons people favor effective health when they're nitpicking over details (I know plenty of people who just want to run behind a "good" tank, a strong player, they're less concerned with their gearing method) is that they don't understand that value of Avoidance in what you're talking about, sequential hits. At least, many have the idea that it is good but don't understand how to read the numbers.

I think it is worth touching on, though I won't get into the deeper implications right now.

First off, something worth being able to see plainly, is from basic probability. If you have an X% chance of something (refreshing the possibilities on every roll, i.e. draw card, replace card, shuffle, draw card, instead of draw card, set card aside, draw again), there is a simple formula to find out your chances of succeeding that chance multiple times in a row. That is X^(number of times in a row)%.

So, for example, if you have 60% avoidance, the mob has a 40% chance to hit you once, 0.40^2 = 16% chance to hit you twice in a row, and a 0.40^3 = 6.4% chance to hit you 3 times in a row.

To make it easy to read as a field:

 
  Total Avoidance            Chance to be hit in a row:
(miss+dodge+parry)    1 time    2 times    3 times    4 times
         30%          70.0%       49.0%     34.3%     24.0%
         35%          65.0%       42.3%     27.5%     17.9%           
         40%          60.0%       36.0%     21.6%     13.0%
         45%          55.0%       30.3%     16.6%      9.2%
         50%          50.0%       25.0%     12.5%      6.3%
         55%          45.0%       20.3%      9.1%      4.1%
         60%          40.0%       16.0%      6.4%      2.3%
         65%          35.0%       12.3%      4.3%      1.5%
         70%          30.0%        9.0%      2.7%      0.8%

So, if a well geared tank is somewhere between 50% and 60% total avoidance (which is attainable without avoidance trinkets or gems in 226 gear), you have a nearly non-existant chance to get hit 4 times in a row, and a pretty reasonable chance not to take 3 in a row. It's the word chance, of course that people get skittish about.

Find a healer who actually wants your incoming damage not to be interrupted (even unpredictably). =)

To relate that to my easy napkin math of incoming dps, and let's see what we get. Resurrecting Bosses A-C, and we'll give our tank 60% damage reduction from armor, and the full de-haste value:
Boss A hits for 10k every 1.2 seconds
Boss B hits for 20k every 2.4 seconds
Boss C hits for 30k every 3.6 seconds

If our tank has 55% avoidance (45% chance of first hit, 20% second, 9% third, 4% fourth), looking at our 8 minute window worth of attacks (400 swings from A, 200 from B, and 133 from C).

First off, over the full 8 minutes:
Boss A will only actually land 180 hits
Boss B will only actually land 90 hits
Boss C will only actually land 60 hits

Of the successful hits, 1 out of every 5 will be followed with another in sequence (invoking perfect statistical performance):
Boss A will have 36 hit pairs (72 of 180 hits)
Boss B will have 18 hit pairs (36 of 90 hits)
Boss C will have 12 hit pairs (24 of 60 hits)

Of those hit pairs, roughly 1 in 11 will be followed by a third (note: not exclusive to the hit pairs above):
Boss A will have 3 hit strings (9 of 180 hits)
Boss B will have 2 hit strings (6 of 90 hits)
Boss C will have 1 hit string (3 of 60 hits)

Suffice to say most of the times you will not see 4 hits in a row from any of the above bosses (though it can certainly happen it'll be a rare exception without mitigating circumstances like bad positioning or debuffs reducing avoidance).

We'll pull numbers back out to say that (rough approximation):
Boss A will get 3 strings (9/180), 33 pairs (66/180), which leaves 105 single hits, and 220 misses.

Boss B will get 2 strings (6/90), 16 pairs (32/90), which leaves 52 single hits, and 110 misses.

Boss C will get 1 string (3/60), 11 pairs (22/60), which leaves 35 single hits, and 73 misses.

We'll keep chaining that down to more digestible values:
Boss A = 3 times per fight he will do 30k damage in 4.8 seconds (6250 dps), 33 times per fight he'll do 20k damage in 3.6 seconds (5556 dps), and for the other 105 hits it will be only 10k damage over 2.4 seconds (4167 dps).

Boss B = 2 times per fight he will do 60k damage in 9.6 seconds (6250 dps), 16 times per fight he'll do 40k damage in 7.2 seconds (5556 dps), and for the other 52 hits it will be only 20k damage over 4.8 seconds (4167 dps).

Boss C = 1 times per fight he will do 90k damage in 14.4 seconds (6250 dps), 33 times per fight he'll do 60k damage in 10.8 seconds (5556 dps), and for the other 105 hits it will be only 30k damage over 7.2 seconds (4167 dps).

Notice that the dps levels for them are all the same, and that for my model static model of boss dps (varied with swing speed) the range will either come in short bursts or large hits spread over a slightly longer timeline. In grand average thinking, this is what you can expect for incoming damage, it's just not rhythmic which would allow your healers to fully predict it.

The more of these levels of complexity we add, the closer we get to the real thing. I think a lot of this may be helpful to know, or more, the ideas are useful to have. Ignorance still reigns in many discussions I see about WoW mechanics and their effects on gear choice. You can't fault people, of course, for not understanding the trickier mechanics, and practical application of avoidance is a tough one with the scary word, "chance."

I like to try and make more acceptable explanations and real numbers available to people who have trouble following the more complicated modelling and giant tables of values. Hopefully this thread continues to inform people so they can base decisions on somewhat more effective values and less on unsupported editorial of equally unknowledgeable people (played Telephone lately, very informative about how communication can work, or go bad).

[headknocker]

Nice summary. One minor point and one suggestion. Minor point, glyph of seal vengence will produce 10 expertise and is probably worth a mention. Realize that you're not trying to provide a definitive list of glyphed functions, but is relevant to both threat and (slight) damage reduction from reduced parry haste and is commonly used.

Suggestion, has anyone seen a time to live view of the multiple tanking classes post 3.1? I've seen a good one at 3.0.8, but nothing since.

[bashef]

Satorri - another great example of trying to bring unfamiliar and uncomfortable concepts (people who don't work with statistics don't usually have a great grasp of it!) to a more general audience.

Your examples in this case are a bit out though, so I think make the situation seem less dangerous than it is; I should also preface this by saying that I like avoidance as a tank, but do understand why effective health minimums must first be met in order to face an encounter, and in fact you probably want a comfortable cushion before looking to gear for avoidance.

What I wanted to take issue with is the damage that hit pairs and hit strings represent, or more specifically the period in which the damage occurs:

Boss A = 3 times per fight he will do 30k damage in 4.8 seconds (6250 dps), 33 times per fight he'll do 20k damage in 3.6 seconds (5556 dps), and for the other 105 hits it will be only 10k damage over 2.4 seconds (4167 dps). Boss B = 2 times per fight he will do 60k damage in 9.6 seconds (6250 dps), 16 times per fight he'll do 40k damage in 7.2 seconds (5556 dps), and for the other 52 hits it will be only 20k damage over 4.8 seconds (4167 dps). Boss C = 1 times per fight he will do 90k damage in 14.4 seconds (6250 dps), 33 times per fight he'll do 60k damage in 10.8 seconds (5556 dps), and for the other 105 hits it will be only 30k damage over 7.2 seconds (4167 dps).

If Boss A hits for 10k every 1.2 seconds, then a set of two hits in a row represents 20k damage taken in 1.2 seconds: you've multiplied the swing speed by three for your examples, but in fact the period over which you take the damage is just a single swing. To clarify: boss hits you at the end of his swing, so at time t=0 you take 10k damage. The swing takes 1.2 seconds, so then at time t=1.2 you take another 10k damage. The total damage taken between t=0 and t=1.2 is 20k (a much more worrying 16.7k dps). Similarly, three unavoided hits in a row represents 30k damage taken over 2.4 seconds (12.5k dps).

Carrying on for bosses B and C, if you take two hits in a row from boss B, that's 40k damage in 2.4 seconds. Boss C is 60k damage in 3.6 seconds. These indeed do result in the same dtps as Boss A.

This is a seriously scary scenario. A 25 man Ulduar warrior/paladin will have ~45k health raid buffed. Boss B just took him from 100% to almost dead in 2.4 seconds (assuming heals didn't land in that period). He better get a couple of holy lights between t=2.4 and t=4.8 or another unavoided hit will kill him (and three unavoided hits in a row will happen, as you say, twice in a highly idealised "average" fight). Boss C will flat out kill any tank who doesn't recieve heals in the 3.6 seconds between hits 1 and 2.

The final point, as if this weren't scary enough, is the effect parry hasting has on these numbers. Let's assume a parry occurs in the range where the swing speed gets the full 40% hasting (we're talking worst case scenario after all). For boss A, this results in taking 20k damage in 0.72 seconds (27.8k dtps). For boss B, it's 40k damage in 1.44 seconds (giving healers a whopping 2.84 seconds to respond to 60k damage if the next hit lands as well - if they can't get off 16-17ks worth of heals in that period the tank dies). For boss C two unavoided swings with the second subject to full parryhasting is 60k damage in 2.16 seconds - this is less than the cast time of a realistically hasted holy light, so healers better have been pre-casting or even a two-hit string kills the tank. Three hits in a row is 90k damage in less than 6 seconds: pretty much guaranteed tank death unless cooldowns are used.

I realise these numbers are made up, and that the models are pretty simple - and furthermore, I'm absolutely not trying to make a point about gearing for effective health or anything like that. Rather, the point I was trying to make is that periods of extreme spike damage do occur even in run-of-the-mill situations (we haven't even touched upon encounter-specific examples such as fusion punch lining up with Steelbreaker's melee swing) and that any comparison of tanks in the average case must also acknowledge that they have differing capacities to deal with the extreme damage that occurs in almost all boss fights in the current endgame.

[Satorri]

All good and true points. Though, the reason I used the full damage window instead of clipping to when the initial damage is taken is two-fold:

1.) These are general swings meant to be captured from the middle of a fight, the window starting from when the previous swing was avoided, potentially.

2.) That time before damage is taken should not be discarded unless your healers are reactionary healers (i.e. they wait for you to take damage before they *start* casting heals). The strongest healers will have a heal in queue before you take the first hit, if they require a long cast time.

In general, the state of the game is not that we can reasonably survive 3 hits in a row from most of the highest end, hard hitting bosses without heals, regardless of how much health we stack. The required effective health is a very jagged graph with teeth the size of hits we take (starting at 10k usually, which is a massive jump in health for a tank).

I appreciate your desire to make thigs scary (you must be from the US =D), but I do think the term "spike damage" is abused nowadays. Technically all damage comes in single large hits, but none of it is truly 'spikes' compared to the expected incoming damage profile (the amplitude of the damage if you look at damage on a chart).


For tanks it's all a big balance, and generally the discussions on the boards make it seem far more significant whether you gear to EH or avoidance, than it actually is. I just want to present players with the information without adding all the adjectives and encounter specifics to scare them. People will get there and develop their strategies, and they will involve a lot of work from both healers and tanks. That's the fun part. =)

[Tazncazper]

(370%, talented it is 492% or 403% *fact check please*)

Its 413% with talents and 415% with the meta

[Satorri]

How did you get that amount? That's neither additive nor multiplicative.

Did you read it somewhere or just do math from your own gear?

[Warwench]

this is a great post, it's extremely hard to follow however, but i think thats partly because of the immense scope of what you are trying to do.

blizzard needs to realise, all these numbers at the end of all this math, need to be the same. It;s not ok to have 3300vs 2900 incoming DPS, it's not ok to have 7000 health vs 8000 health.

Things, after all is said and done, have to be very similar. the mechanics have to be about the same complexity to use, the end results have to be about the same, damage taken, damage done, threat done, all gotta be about the same.

[jere]

Source: Satorri How did you get that amount? That's neither additive nor multiplicative. Did you read it somewhere or just do math from your own gear?

If he is correct, it is additive:

DBF: 370%
TH: 10%
SotF: 33%
----------------
413%

Then 2% for meta

[trezios]

In my opinion its extremely silly to place all 4 tanking classes in identical gear with different tier sets and base your calculations on that.

Each class should have multiple sets of tanking gear and choose the right combination of gear depending on the fight. Thus changing every single encounter based on the player's specific gear for that fight.

You've sort-of stated this, yet continue to post these calculations like they're fact, when they're based on unrealistic gearing.

Throwing math at stats doesn't mean its the correct math. This practice corrupts theorycrafting.

To "Staticise" (or to assume every raid encounter is static) is ignorant. You've basically done that.

In regard to "Warwench" Blizzard has stated they want to keep each tanking class unique. Not homogenize them into the ground. If they were extremely similar, that would really defeat the point of having 4 tanking classes.

[jere]

So I popped up my druid in healing gear (to get rid of enchants/etc.), but still in feral spec

Before bear form I have 2644 armor (184 of which is from agility). This value already has the Thick Hide modifier of 1.1 in it, so I haven't gone back to figure out, but I am fairly sure there is a 1.1 multiplier there.

In Dire Bear form, I have 15559 armor (again, 184 of which is from agility).

I have no items with bonus armor or armor enchants and no meta.

So (15559-184)/(2644-184) = 6.25 multiplier

That seemed high to me, so I started trying to play with the skills/talents: DBF = increases by 370% and SotF increases by 33%. But then I remembered that the wording of the dire bear tooltip said "increased by 370%. If it had said increased by 100%, we would have multiplied by 2, so 370% increase = 4.7

4.7*1.33 = 6.251

Maybe darksend can comment, but that seems to make the armor multiplier be:
4.7*1.33*1.1 = 6.8761.

I am assuming the meta is also a 1.02 multiplier, but wasn't able to test that.

From my character sheet stuff, they seem multiplicative.

[Tazncazper]

Source: Satorri How did you get that amount? That's neither additive nor multiplicative. Did you read it somewhere or just do math from your own gear?

i just added

Bear Form 370%

Thick Hide 10%

SoTF 33%

is 413%

plus meta is 2%

[Tazncazper]

Source: Satorri I thought it may be possible, but I kept talking myself out of it because it seemed too good. Can anyone confirm?

I can post a WWS from a 25 naxx i did if u wanna check the numbers



I Just looked at the WWS and in the last 25 naxx I did Savage Defense was up 16% of the time with it being applied a total of 2,501



Also looked at a 10 ulduar I did last week and it was up 17% of the time for 1,677 times applied

[Satorri]

Mmm, nice checking Jere. And sorry Taz, somehow I was leaving out a factor. /facepalm

So, multiplicative based on Jere's testing, factors:

Dire Bear Form (370% in tooltip) = 4.70

SotF increases the value in Bear form by 33%, so:

Talented Dire Bear Form = 6.251

Thick Hide will apply before the change (needs to be multiplicative), but since we only care about in Bear form, the full armor modifier (only applying to core gear, and not bonus armor, necks, rings, and trinkets, or weapons):

Fully talented Bear tank armor modifier = 6.876 (7.014 with Meta)

That's a multiplier of 588% (601% with meta)

Laborious, but if a couple other bear tanks could record their caster form armor, agility, bonus armor (rings/trinkets/necks/weapon), and their dire bear form armor, and provide that here, I'd appreciate that, just a couple should do fine for quick checks.

[Satorri]

Warwrench, truthfully that's neither realistic nor necessary. There are two angles on why.

1.) Not every situation requires the same of a tank, that's why in the past different tank classes were much more specialized. Every was good at their niche and weaker than the others at theirs. Blizzards changes appreciate the fact that when you combine REALLY hard encounters with the requirement that you carry 4 different tank classes, you're shutting down more than 80% of the raiding community who likely cannot get all four tanking classes to the same level. Instead they wanted all the tanks to be able to tackle any encounter, not necessarily perfectly equally, but close enough that it won't be win or lose just based on what sort of tank you have in your group.

2.) The player factor heavily out-weighs the stats and the numbers game when it comes to fine differences. I'm a big fan of napkin math and approximation, you'll notice that's about 90% of what I do on the boards. I do not use simulators or complicated algorithms because in the 'reality' of gameplay the nuances of positioning, skill of the tank in using their abilities and their cooldowns, the distinctions of gear level (since we don't all have the same set of gear, smart tanks play to their strengths and the same class can be played more than one way), and the almighty power of latency combined with the somewhat random factors of scripts (not just the RNG) and pathing, all combine to make the 5% variabilities we math out in ideal circumstances with dumbed down numbers and simplifying equations, a small factor.

The funny thing is that the tanking classes, on paper, have all had roughly the same survivability through most of Wrath, the problem comes not from baseline, but from special situations and flaws in the assumptions Blizz made of players. Take DK's for example. Originally they wanted DKs to be CD driven, they were substantially squishier than other tanks at the base, but if you (took and) used your defensive CDs frequently, pretty much on CD, you would end up at the same level as other tanks. The problem, of course, is that only the more experienced tanks really understood how to do that, and even then, if you missed your window to apply your next CD, you'd be in danger of taking a much higher beating, whereas chaining CDs smartly could leave you with as little as 5-10 sec per minute with that added invulnerability. They wanted to fix this to make DK tanking a little less open to danger and inconsistency if players didn't master this little nuance. Thus our armor was bumped, and our CDs weakened.

Then came the almight Ulduar PTR Patchwerk test. The discovery was surprising. DKs were designed to be the 'avoidance' tank. Other tanks have heavier health/armor or the zippy block mechanism, but we were supposed to just plain avoid if we played well (i.e using both blood runes every 10 sec, Blizz assumed 100% uptime, rightly). The problem was that you could take a boss that scaled to infinity. As the hits became bigger and bigger, Block becomes insignificant, and armor/health become meaningless. It comes down to no tank being able to take 2 hits in a row. Suddenly the DK had a very noticeable advantage. Scroll to the previous page and look at the difference in taking 2 hits in a row for a tank with 50% avoidance next to one with 65% avoidance, and there was why our avoidance got pulled down.

Now we look at the current Live and PTR setups. Plainly put Blizz has tried to preserve our CDs somewhat without giving us TOO much uptime, IBF alone stands at a 1 min CD, others at 2 min, but they are arguably still stronger than any other class's single CDs. Next to that, even after pulling our armor back down to what it used to be on Frost Pres, we can still have more armor, more health, and our CDs next to the other classes (Bears can beat us on the first two pretty handily but their CD's are not nearly the same). So, we're getting a big baseline nerf stick.

Does it hurt? Yes, honestly I don't care about the armor, I'm only saddened by it because I've been working very hard as a meatshield tank which involves picking up gear piece after piece that adds 200 health here and 100 health there, and I've clawed my way up to over 37k before buffs. It feels good to see that payoff. This patch, even after I fix all my gems to epics, will still lose me 2k health. It makes things more even, sure, but I feel like all my work just became insignificant, all that I picked up just lost value and put me way back to months before.

I think Blizz is probably doing a fine thing to avoid DK dominance among the hardcore min/maxers who look at numbers like this thread's and say, "oop, sorry [warrior/druid] you're out, the DK's in" but I still shed a tear for my personal tank strategy getting hammered down. =)

Take all these theorycraftings with a grain of salt. The point of this thread is not to demonstrate dominance, even advantage (I don't believe there is one), the point is to demonstrate the basic class mechanics and what they are best suited to, maybe provide the information that will allow people to gear or play to their strengths, or allow them to be clever and find inventive ways to do things, now that they don't have to slog through the fundamentals with a calculator.

[Tazncazper]

Caster Form armor= 9033
AGI= 980
stam= 1733
health= 24,567
Dodge= 30.20%
Defense= 418
that is in caster form

Armor
Rings= 490, 448
Trinket= 850
Back= 490
Neck= 336
Weapon= 714

Dire Bear form

29506

stam 2384
health 31,077

Dodge 40.20%


Let me kno if i forgot a factor

[jere]

Source: Tazncazper ***stats***

That fits my results then.

The 490 cloak has 154 base armor (affected by DBF and SotF) and 336 bonus armor (not affected):

Bonus Armor : 2*980+490+448+850+336+336+714 = 5134 bonus armor.

9033-5134 = 3899 AC

DBF & SotF:
3899*6.251 = 24372.649

Final Bear Form:
24372.649 + 5134 = 29506.649

[Satorri]

Sweet. Ilike having things figured out when that's possible, I'll ammend my original post.

[Mawini]

Excellent thread, as usual.

I would like to note that although you would definitely be correct in stating that a warrior's shield slam does typically cause more damage than a paladin's Shield of Righteousness (especially when shield block is up), I do believe that the conversion of the damage to holy and the threat multiplication of holy damage through RF would put the threat value well ahead of the warrior's ability.