Here is something I wrote to go along with the whole avoidance/stam concept. The simple fact is avoidance alone isn't enough, you need avoidance/expertise/hit.
Currently I run around 16k unbuffed, 27 dodge, 18 parry, 450 block value (a limitation to my gear based on the fact that we are currently only 4/5 and 5/9 right now), with 127 hit rating and 20 or 25 expertise rating (depending on which gloves I wear).
On bosses like KT, where the hits have large gaps between, HP stacking seems to work best. But for bosses like Rage, Archimonde, Kaz'rogal, Azgalor, Gorefiend, or Najentus, which can hit hard and often, some levels of avoidance make life a lot easier. And considering that 1 expertise rating is worth about 11 block value in terms of threat generation, stacking some avoidance with expertise does the following.
1) Limits your parries. There is no faster way to die than to go on a string of parries.
2) Lowers the chance that you will be subject to a crushing blow after a parry because odds are you're avoiding enough that a third free swing in the 5 second period will not catch you without a shield block charge up.
The difference between 18k and 16k is absolutely nothing when the boss is hitting you for 7-9k a pop. Fully raidbuffed, you'll have 23k or so? I've got around 21k.
If a bad silence occurs, the odds of you absorbing hit, hit, hit with a parry in between the speed the hit up is far higher than someone with appropriate avoidance. Neither of us has even a prayer to survive 3 hits anyway, so the extra 2k HP mean antpiss.
But in reality, the greatest stat we have now is expertise. Taking parries off the table is the fastest way to avoid spike damage. Unless your healers suck, the only thing that is going to get you in the long run is the spike damage. You take a nice combo of hit, parry, crush, and its not likely you can survive it.
Avoidance Stacking:
By general theory, avoidance stacking past a base of 62% raidbuffed (which is about 60% avoidance on a boss 3 levels above) is detrimental to tanking, especially considering usually thunderclap and either a demo shout/CoW is on the mob.
But in terms of actually looking at stats and how they affect theoretical survivability and threat generation:
As an example in gearing I will use the following:
Base:
500 defense
20% dodge
20% parry
30% block
700 block value
6 expertise (from spec)
0 Hit Rating
In terms of SURVIVAL, there are a couple of main goals.
1 ) The first is to limit the probability that you are hit 3 times in succession. This, coupled with any parries to speed up the incoming damage, greatly increases the chance of a crushing blow landing. In other words, reducing the spike damage probability cycle.
Given the above base, the overall avoidance is just under 50%. The odds of being hit 3 times in succession are 1 in 8, or 12.5%. This is given more directly by (1 – x)^3, where x is the raidbuffed avoidance against a mob 3 levels above you.
The marginal gain at this point of 1% additional avoidance is around .8% (meaning 51% avoidance results in the chance of being hit 3 times in succession is reduced to 11.7%). We’ll save this formula for later. Because the gain/loss is NOT linear (it’s a quadratic gain curve (the dertivate of the basic cubic function), the only thing that means anything is the base formula.
2 ) The second is to understand that on average, you will be attacking the mob at an approximated rate of 1.25 times per second (one warrior ability every 1.5 seconds with 200 ms lag, and one normal swing/heroic strike every 1.6/1.7 seconds), so you need to limit the number of cycles that result in parry/parry on successive swings (which results either in 2 sped up swings from the target, or potentially one insta-swing/one 40% hasted swing). Either way, it results in the warrior taking one additional attack in the 2 attack cycle (you get swung at 3 times in the time it would normally take a mob to swing twice).
It’s been debated, but the number I see make the most sense for boss parry rate is 10.6%. Assume E is your expertise rating. The boss parry rate is best approximated by (10.6 – E/4)%. The chance for a parry/parry with the base (6) is .83%, or given the swing state of 1.2 attacks/s, you will incur a cycle approximately once every 100 seconds. We’ll use that as the base for later as well.
Over the course of 100 seconds, it is expected that with a base expertise of 6, you will incur 1 parry/parry cycle and a total expected number of parries of 10.
The formula for this is:
Expected Time per parry/parry cycle = P = ( 1/ [(.106 – INT(E/3.9425)/400) * 1.2)]
Expected Number of Parries per cycle = P * 1.2 * (.106 - INT(E/3.9425)
3) Stacking certain levels of Stamina is just important period. There is no number that isn’t enough. Same with armor. Fortunately, most of the itemization points that you get are stuck in these two stats, so generally, the upgrades themselves will stack these two stats in abundance for you anyway.
Threat Generation:
Based on known formulas:
1 Weapon Expertise rating generates approximately 1.7 TPS up until weapon expertise = 22 (all block/dodge off the table), and approximately .7 TPS afterward until weapon expertise = 42. After that there is no more benefit.
1 Block Value provides a static TPS increase of .16
1 Strength provides a roughly static increase of .2 for prot builds. Yes, strength does have a scaling element based on hit rating, crit rating, expertise, and weapon speed (for devastate calculations), but barring something stupid, its in the ballpark of .2.
1 Hit Rating provides .7 TPS until you cap at 142 hit rating. After that it provides 0.
With 6 expertise, 12% crit and 0 hit rating, the hit chart is as follows:
9% miss
4.1% dodge
9.1% parry
4.1% block (when applicable)
21% glancing
40.7% hit
12% crit
[top] 26.2% miss
With 22 expertise, 12% crit, and 142 hit rating
.1% dodge
.1% block
5.1% parry
21% glancing
61.7% hit
12% crit
5.3% miss
Just as you want to minimize the chance that you incur a hit, hit, hit, you ALSO want to minimize the chances of being missed three times in a row as well. Given a base cycle of SS, Revenge, Devastate, Devastate, 4 consecutive incoming misses leaves you rage starved, resulting in either you having no threat generation until you are hit or worse, you have no rage to hit the shield block button, risking getting 2 shot.
The odds of 3 misses in a row = x ^ 3, where x is your avoidance. Now, also with this it is important to note that this rage starvation is generally mostly mitigated by by ensuring that you are not also consistently missing attacks. (giving you a more reliable second source of rage). The estimation most relevant is that you want to limit the chance of 3 consecutive incoming misses combined with you missing 2 consecutive attacks. (that will allow for at LEAST shield block to be active)
In the base stats example, this chance would be:
(.5 ^ 3) * (.262^2) = .8%
If that % is anything over .4%, its bad, because that translates into more than 1 expected such moment per 5 minutes.
Assuming you stack just avoidance to 60%
(.6^3) * (.262^2) = 1.5%
Clearly, stacking JUST avoidance leads to bad results. 1.5% means about every minute or so, the tank will either be forced to generate 0 threat from abilities for a few seconds and/or not have shield block up until after the hit. Either way, that tank will find him/herself SOL a lot.
Rage Generation:
Quite Obviously, a Warrior needs rage to tank. Considering a typical big hitting boss whacks on plate for around 7-8k (with debuffs up), and swings approximately every 2.4 seconds (with imp thunderclap up), the base incoming damage to the warrior (assuming no crushes, because I don’t have the time or inclination to deal with a first order partial calculation), of 3k DPS.
Given the known rage formula, that is about 30 rage per second incoming absent avoidance. At 50% avoidance, that number becomes 15 rage per second incoming, and at 60%, 12 rage per second incoming. The formula to remember is approximated by:
Incoming Rage from Damage Taken = 30*x per second
Since the cycle for an average tank is 6 seconds, (SS, Rev, Devastate * 2, Shield Block * 1.2) The base rage required to sustain the cycle = 49. (assuming imp sunder armor).
Now, there is also the measure of net damage from the heroic strike/autoattack cycle.
Every successful auto-attack results in 6 rage being generated. Every heroic strike results in a loss of 9 rage (assuming imp heroic strike)
The net rage gain/loss is:
autoattacks *6 – heroic strikes *9
Subject to
Autoattacks + Heroic Strikes = (6/weapon speed)
So, every 6 seconds, we have to balance the net:
180 * x + autoattacks (1 – miss%) * 6 > 49 + H.S (1 – miss)* 9 + H.S (miss) * 2
Subject To:
Autoattacks + H.S = 6/weapon speed
Hope some of that helps.
If anyone wants to tackle the specific math (I would recommend using a program like Latex, MathCAD, or anything else that can solve partial matrixes with a supplied determinant) themselves, I’ll be happy to give you the format of the n-bound matrix to plug the numbers in.
Keep in mind, solving this via matrix leads to DIFFERENT results for every boss. (the final column needs to contain boss swing speed, average damage, average crush, 0 and relative parry rate) The primary input (since you are solving an n-bound nonlinear with a known determinant (and yes, the equation is ALWAYS a second degree exact equation), you will get a different optimal set of numbers for avoidance, expertise, hit, shield block, and stam. It will give you the relative importance levels of each stat from 1-100. (you get this by basing the matrix subject to those variables all being greater than or equal to 0 and adding up to 100.
If you want to calculate the determinant itself, it is based on the itemization base for each extreme (nothing but stam, nothing but avoidance, nothing but shield block, nothing but hit, nothing but expertise, all sitting over the base of 15000 health, 50% avoidance, 300 shield block, 0 hit, 6 expertise).
To give you the answer in layman's terms for any hard hitting boss (average of over 8k per hit, 12k per crush), it will yield ballpark 60% avoidance, 43 expertise, 300 shield block value, 91 hit rating, and 17.5k ish unbuffed health)
Since those numbers are theoretical and generally not easily acheived, many people substitute a bunch extra + hit for the expertise that cannot be gotten, get some of the natural shield block value that comes with some of those pieces (Gauntlets from Teron, Myrmidon's Treads, etc,), and stam whereever else they can get it.
But the bottom line. At base damages that are low, shield block value is more important. At a base damage of say, 3k per hit, the raw shield block value number is 3.8, meaning 3.8*350 = 1330 is the ideal number. Once base damage starts to creep up over 5-6k, there is not a single instance where weighted shield block value would be over 0. At the 9k level of base damage, the raw number yielded is in the -1.8 ballpark of shield block value, meaning ideally, you would lose 630 shield block value ( to have a -280 shield block value), just so you can use that to get more weighting elsewhere. It is all about regulating the damage that comes in as best as possible, and limiting the spike damage scenarios. The risk of spike damage being catasrophic on a boss hitting for 3k is next to nothing unless under extrreme duress (like RoS phase 1), whereas the odds of it being catastrophic on harder hitting bosses is much much more likely.