I've seen quite a few warrior tank defense analysis pages floating around the web, but haven't yet really found the other side of the equation, namely, the warrior tank dps -- at least, not to the same depths. What stats should a warrior tank add to do the maximum dps, and therefore, the maximum threat per second? So, I decided to give my hand a go at making one using the formulas and numbers I was able to find from trustworthy sources (such as wowwiki) and see what I came up with. Forgive me if I made any mistakes, this is my first guide attempt.
So, without further ado:
WARRIOR TANK DAMAGE PER SECOND
Obviously, this is going to depend a lot on your choice of rotation. This is a half-decent 60-second rotation against a boss. It's not perfect, nor does it apply in every situation, but an okay average to use as a baseline.
Shield Slam x8*
Revenge x 9*
Concussion Blow x1*
Heroic Throw x1
Non-damaging abilities (including demoralizing shout, taunt, charge, commanding shout, bloodrage, or using a trinket) x5
This counts the 40 global cooldowns you have access to in 60 seconds.
Abilities that do not affect the global cooldown (such as Shield Block) are not listed.
The use of Rend in a defense-stance rotation might seem odd at first, but I feel it belongs there. Besides the fact that it's an attack that does fairly good damage for the rage, you might have that new Blood Draining enchant which can proc on a bleed effect.
Meanwhile you get some melee attacks. With a 1.6 speed weapon (very common tank weapon speed) you get 37 attacks per minute.
Abilities marked with a * can be dodged, parried or blocked. Expertise will help these. Melee attacks are in this category.
Assumptions being made:
-- your target is a single boss monster lvl 83 with 6% dodge and 14% parry chance.
-- You are using a one-handed weapon and a shield, have full 400 weapon skill, and therefore have an 8% miss chance against a boss.
-- 5 stacks of sunder are up at all times (because you'll probably do that first against a boss)
-- Your shield block value (SBV) is what your tooltip says when you mouseover the "block" section of your defenses and NOT the bonus given by gear. It already takes into account the 1.30 multiple caused by talents.
-- Shield Block buff is up for 2 of the shield slam attacks per minute.
-- Your hit is below the hit cap, and your expertise is below the "soft cap".
-- 10 of your melee attacks are Heroic Strikes.
I realize that some of these estimates are a bit on the pessimistic side. For example, Sword and Board could cause your Shield Slam cooldown to instantly refresh, allowing you to use it faster and possibly even get a third hit while Shield Block is on. Or, maybe you use the Glyph of Revenge which would allow you to use Heroic Strike a lot more frequently without rage starvation.
The damage bonus for the one-handed weapon specialization talent (5/5) and the damage penalty for defensive stance apply to everything. They can't really be turned up or down by gear, and as such, are left completely out of this calculation. (Yes, they do actually affect your dps, but because they apply proportionally to everything, it's just a single multiple that can't be changed. Adding it, or leaving it out, has no impact on what stats you want to improve)
Weapon Damage, average per swing, is noted to be weapon's DPS, plus Attack Power/14, times weapon speed. Heroic Strike adds 495 per hit, so a faster weapon would increase the damage, but there aren't a ton of tanking weapons faster than 1.6 weapon speed. The new one from the Trial of the Champion 5-man Heroic (Peacekeeper Blade) is one of those weapons.
Thunderclap: (300 + 0.12*AP) times 1.30 due to the Improved Thunder Clap talent
Shield Slam: (1025 + Shield Block Value)
Revenge: (1615 + 0.207*AP)
Concussion Blow: 0.75 * AP
Shockwave: Also 0.75 * AP
Heroic Throw: 12 + AP/2
Rend: 380 + Weapon Damage over time. At one hit per minute, the full damage will definitely accrue.
Devastate: weapon damage plus 202/stack. Since we are assuming 5 stacks at all times, that's Weapon Damage + 1010
Heroic Strike: flat bonus of 495 damage. It does extra damage if the target is dazed, but for the sake of argument, pretend it isn't.
AP = Attack Power
SBV = Shield Block Value (again, given when you look at your Defenses tab on your character sheet, not your gear's bonus to the stat)
DPS = the weapon's base DPS, what a website would say if you looked up the unmodified weapon
Based on all of these, damage per minute should be
TC: (300+0.12*AP)*1.3*2 = 780 + 0.312AP
SS: (1025+SBV)*8=8,200 + 8*SBV, plus 2*SBV for the two slams where Shield Block is up
Rvg: (1615 + 0.207*AP)*9 = 14,535 + 1.863*AP
CB and SW: 0.75*AP * a total of 4 = 3.00 AP
HT: 12 + AP/2
Rend: 380 + (DPS + AP/14)*1.6 = 380 + 1.6DPS + 0.114AP
Dev: [(DPS + AP/14)*1.6 + 1010]*10 = 10,100 + 16DPS + 1.143AP
Melee: (DPS + AP/14)*1.6*27 = 43.2DPS + 3.086AP
HS: [(DPS + AP/14)*1.6+495]*10 = 4950 + 16DPS + 1.143AP
This sums up to 38,957 + 11.161AP + 10SBV + 75.2DPS
All of this damage is affected by your miss chance. Of this damage, 792 + 3.062AP is not affected by dodge, parry or block, (the Thunder Clap, Shockwave, and Heroic Throw attacks) and the rest is.
So, your DPS should be 649 + 0.186AP + 0.133SBV + 1.253 weapon DPS, assuming you hit with every single attack.
A lvl 80 warrior should have a base expertise of 6 from talents. This lowers parry and dodge by 1.5% each. This means, without any other bonuses, the boss has a total avoid chance of 25% against most of the tank's attacks.
Each point of +hit on gear (HR) adds 0.03% chance to hit.
Each point of expertise on gear (EXP) lowers the chance to dodge or parry the same way.
There is little to no +crit tanking gear. Crtical hits affect all the above attacks with pretty much the same multiplier. While exceptions exist (such as "critical blocks" in Shield Slam, and the Tier Devastate bonus), such are minimal. Besides, a tank should count on skill, not luck, to maintain threat, and while a tank will get a few crits in 60 seconds, they should not be relied upon. As such, I will largely ignore critical hits.
Factoring this into the damage done above, this works out to be
As you can see, the stats feed on each other. Raising Attack Power OR Hit Rating will help, but raising them BOTH will help more.
SHOULD I BUFF ATTACK POWER?
If you are talking gems, food, or enchants, probably not. Gems and food that offer +AP almost always have a +STR variant that adds half as much, which turns into the same amount of +AP anyhow, PLUS the strength adds to Shield Block Value as well by 0.65*STR.
Therefore, I will now replace AP by the Attack Power formula, which for a lvl 80 tank, is 220 + 2*STR. I will leave SBV alone, since the mouseover portion of the defenses tab includes the strength bonus. Additional bonuses to either stat will be handled more carefully below.
Yes, Armed to the Teeth will further increase the damage, and yes, it's still a good talent. However, I'm not adding armor value to the already clogged calculations, and we will assume the tank in question doesn't have that talent.
WHAT ABOUT DAMAGE SHIELD?
As a general rule, I don't like to count any ability that requires me to take a hit in order to do damage as DPS. It's not under your control, and the side effects are distasteful. That aside, Damage Shield on a hit or block does 20% of your SBV, and I don't think it can miss or be dodged/parried. Assuming the boss you're fighting attacks once per 2 seconds and that your total avoidance (dodge/parry/miss) is 40%, that's 30 attacks, 18 of which cause Damage Shield to go off, and adds 18 * 0.2 * SBV to the damage per minute, or 3.6SBV. If your Defense, Dodge, and/or Parry are very high, this value actually drops, however with diminishing returns on dodge and parry, even a very good tank won't have avoidance much higher than 40% total.
Example Tank A is using mostly gear from Naxx10, Heroics and T7, and has chosen a balanced gear approach with both avoidance and attack stats.
DPS 143.4 Red Sword of Courage
He should do 31303+2420+17001+1128+9990+8088+529+646+2404+395+5 56+679 = 75,139 damage over the course of one minute, or 1,252 dps
This should seem high. After all, NONE OF THIS includes armor reduction of your enemy, which will (even with 5 stacks of sunder) be noticable.
Example Tank B is using a mix of Naxx25, Ulduar10, and Valor gear aimed mostly at dodge and parry. As such, his hit and expertise are not as high.
DPS 163 Peacekeeper Blade
He should do 31303+2346+19926+1281+11156+9193+573+712+1470+283+ 380+472 = 79,095 damage over the course of one minute, or 1,318 dps
As you can see, this damage is not much higher. The low expertise is holding Tank B back from doing more damage and, therefore, more threat.
Using Tank A's stats as a baseline,
-- adding 100 Str (including the +65 bonus to shield block this creates) adds 46 dps
-- adding 100 hit rating adds 40 dps
-- adding 100 shield block rating (which becomes +130 due to talents) adds 27 dps
-- adding 10 weapon dps (if that was even possible) adds 11 dps
-- adding 100 expertise adds 65 dps
Using Tank B's stats as a baseline,
-- adding 100 Str adds 45 dps
-- adding 100 hit rating adds 43 dps
-- adding 100 shield block rating adds 26 dps
-- adding 10 weapon dps (if that was even possible) adds 11 dps
-- adding 100 expertise adds 69 dps
Results: Strength, hit rating, and expertise all seem to be "about the same value" to the game as a whole -- the fact that +40 str, +40 hit, and +40 expertise food all exist and all take spices to make is a good indication of that, and gem bonuses to these 3 stats are all worth the same as well. Note, however, that to the typical level 80 raid tank, expertise provides the most total damage per second. Strength and hit are about the same as each other, and shield block takes a noticable gap behind them to pull in fourth place. Adding dps to a weapon solely for the purpose of adding total damage to a tank's rotation doesn't seem to be worth it. Of course, better tank weapons tend to have better base damage-per-second anyhow, but going out of your way to get the next weapon up the ladder isn't super important to threat generation.
Notice that Tank A gets more from the "damage stats" of strength and shield block, and less from "accuracy stats" of hit and expertise, than Tank B. This is because Tank A has tried to maintain a healthy balance of offensive stats. However, the differences between the balanced Tank A and the less offensively geared Tank B are small, and all five stats are in the same order for both.
Once your total expertise gets so high that the boss monster cannot dodge, the extra damage you get from stacking even more expertise drops to half. This puts it behind both strength and hit, but still ahead of shield block. Of course, once you hit the hit cap, or the expertise hard cap, adding more has 0 effect.
Shield Block Value actually has a total of four "caps" when it comes to offensive stats. The lowest is when your total shield block value hits 2,400 when you pop Shield Block. While this value changes a bit depending on your base shield's block value, it's around 1100 (and Tank B is pretty close to that value, without using much in the way of shield block gear). Adding shield block on top of that lowers the already low value SBV adds offensively. Simply put, it's not worth putting much into shield stats for offensive use. (Most sites I've seen don't like shields for defensive use, either)
WHAT THIS MEANS FOR THREAT
A very large portion of tank's threat comes from the damage they do, times their large threat modifier while in defensive stance. Therefore, adding any amount to dps automatically adds the corresponding proportion to threat per second. However, many attacks (such as Heroic Strike) do a flat threat addition when they hit. What does this mean? Expertise and hit cause a bit more threat-per-second than the remaining stats of strength, shield block value, and dps. If you're not sure whether to up strength or hit, go with hit.
WHERE TO PUT YOUR OFFENSIVE TANK STATS FOR MAX THREAT PER SECOND
#1: Everything into Expertise until the soft cap (see also: Rhinolicious Wyrmsteak)
#2: Strength and Hit Rating equally until hit rating hits the hard cap
#3: Strength and Expertise equally until expertise hits the hard cap
#4: Everything into Strength until you run out of slots.
Shield Block Value and weapon DPS are incidental stats and there is little to no benefit in upgrading them at the cost of strength, expertise or hit.