Dual-Spec 1/2: Threat Tank Build

So, I'm a bit of a mathematics nut. I go to an engineering college, and have taken all sorts of mathematics and computer-mathematics hybrid courses. Lately, my tanking routine is more or less on cruise control, so my posts here have been somewhat lacking in actual tanking-relevant content. To change that up some, I'll employ that mathyness to ensure that my two new, upcoming specs will be the best that they can be.

With the advent of 3.1.X, there's a lot of Dual-Spec speculation hopping around the forums. Many players feel that Tanks and Healers must have an alternate DPS spec to handle certain encounters (Moving from Maexxna, a single-tank boss, to Patchwerk, a three-tank boss, for example). More moderate raiders do not view this as a requirement, and I have to agree with them. After all, it's hard enough for all but the most hardcore raiding guilds to gear up everyone in a run in full i213/i226. If trying to add in a second spec for 10 of your 25 raiders, you're calling for another 10 sets of gear. This seems like a ludicrous requirement for entering new progression; Perhaps after all of the content is on farm status, this would be possible, but at that point there's no challenge left anyways - it simply becomes a means for speed optimizations, rather than a source of necessary fight-winning advantages.

There's more arguments for Dual-Spec being a matter of convenience, rather than necessity, and thus I feel justified in playing my tank as just a tank. What, then, do I do with my second spec slot? After a lot of thought and research, I've decided that the time has come for me to put aside the full-mitigation spec that I've been running for the entirety of WotLK. Enter Deep Wounds.

Tentative Threat Spec (15 / 5 / 51)
Glyphed With:
Glyph of Cleaving - Wonderful for any AoE tank job
Glyph of Heroic Strike - in 3.1.X, +5% crit chance on HS
Glyph of Blocking - More BV = More SS damage

To make a DW spec, 15 points need to go into the Arms tree. Shockwave is too powerful a tool to be left out of any Prot DPS rotation, so I feel that it must be included as well; thus, 51 points are needed in the Protection tree. This leaves 5 "flex points" that can be placed wherever necessary. How does one optimize their placement for a TPS spec? This is where that comment about mathyness comes in - I wanted to know exactly which talents would return the most net benefit. Namely, which returns more TPS per point, Armored to the Teeth or Cruelty?

There's a lot to take into account here:

• Armored to the Teeth scales with Armor. I've assumed that the tank in question has 24,000 armor for my calculations here, which is about what a set of i213 gear will return. Armor trinkets and higher-armor gear will net a large return from this talent, if they can be fit in.
• Deep Wounds "rolls," which is a new mechanic of 3.0.2. In essence, this means that multiple crits within the 6-second bleed timer will all be taken into account, so the damage of an old crit is not overwritten or clipped by the new crit - the remaining old bleed damage is instead added into the new bleed with an even distribution.
• Deep Wounds necessitates Impale, which increases crit damage by 20%.
• Weapon Speed and Weapon ilvl both influence the damage caused by Deep Wounds, as it is based off of normalized weapon damage.
• Deep Wounds can occur because of any crit that the Warrior causes. This includes: Damage Shields, Thunderclap, Shockwave, Cleave, and all of our single-target abilities. Everything counts for it, and they all apply an equal amount of damage.
• More things that I'm not remembering at the moment, for sure...

To start, let's look at the equations for basic Deep Wounds damage:

DWrank3 = (Normalized_Weapon_Damage * 0.48)
Normalized_Weapon_Damage = (Minimum_Weapon_Damage + Maximum_Weapon_Damage)/2 + (K * Attack_Power)/14

Where K is: 1.7 for Daggers; 2.4 for any other One-Handed Weapon.

Let's assume that we're using an i200 Epic Tanking weapon, because Last Laugh just hasn't dropped for us yet, and Broken Promise is just a little too slow for our liking. We can also assume that we're sitting at roughly 2,800 Attack_Power, for simplicity. Let's plug in:

Normalized_Weapon_Damage = (160 + 299)/2 + (2.4 * 2800)/14 = 229.5 + 480 = 709.5
DWrank3 = (709.5 * 0.48) = 340.56 damage over 6 seconds.

That's a fair baseline to use as the damage that our Deep Wounds will cause with each crit. Next, we need to figure out what the relative increases to that baseline are, both from AttT and Cruelty.

Starting with AttT, we gain 400/3 AP for each talent point we spend there. This accounts for:

NWD_bonus = (2.4 * 400/3)/14 = 22.8
DWrank3_bonus = (22.8 * 0.48) = 10.97 damage over 6 seconds.

That doesn't seem too substantial, but it is a non-trivial percentage increase. That is:

DWrank3_bonus / DWrank3 = 10.97/340.56 = 0.032

This is roughly a 3% increase in Deep Wounds damage per point of AttT, with the assumptions above. A stronger weapon, a stronger base attack power, and a lower armor value will DECREASE the percent benefit, while more armor value will INCREASE the benefit.

Meanwhile, Cruelty increases our chance to critically hit by 1%. This effectively increases our chance to DW a target by 1%. Since there is no chance for loss of damage for repeatedly applying DW, we get the whole benefit here.

But that's all: the benefit is a 1% increase in Deep Wounds damage per point of Cruelty. This does not scale with weapon, base attack power, or armor value. The 1% static critical hit benefit will always hold.

Now, that's the effects of AttT and Cruelty on DW, with a net ~2% leaning towards AttT over Cruelty. All that remains is the other half of the computation: how do these talents affect an Impale, no-DW spec?

Normalized Weapon Damage is used in every damage calculation that Warriors cause, with the exceptions of Shield Slam and Damage Shields. Critical Strikes influence every type of physical damage Warriors can deal, and Impale brings that critical strike damage up by 20%.

A direct comparison here is hard to make, because the damage generated by any one ability relative to your overall damage output changes based on the encounter. In general, somewhere between 20% and 30% of a Prot warrior's damage output comes in the form of Shield Slam, so the benefits of Attack Power apply to only about 75% of the attacks. Since one point of AttT augments the Normalized_Weapon_Damage by about 3% in the above calculations, it will increase the damage output of all these remaining abilities by roughly the same percentage. Thus, The overall damage output increases by

Bonus_Damage% = Normal_Damage + (NWD_Bonus/Normalized_Weapon_Damage) * %Attacks_Using_NWD
Bonus_Damage% = 1 + 22.8/709.5 * .75 = 1.0240

So, something slightly greater than a 2% average damage increase is gained from adding one point of AttT. Note: The benefits are damped in the presence of static damage coefficients (top-rank Thunderclap has a static damage coefficient of 300, for instance), so using a flat 2% average damage increase is probably a better estimate.

For Cruelty, we add a 1% chance for any ability to deal 220% damage. This equates to:

Bonus_Damage% = Normal_Damage * (1 - Crit_Chance) + Crit_Chance * Crit_Damage
Bonus_Damage% = 1 * 0.99 + 0.01 * 2.20 = 1.012

Which is a linear system, meaning that each 1% of critical hit chance increases overall damage output by 1.2%, independent of other stats.

Thus, we observe that, point for point, AttT returns More Average Damage than Cruelty on paper, independent of Deep Wounds. The difference is only about .8% in T7 equivalents, and will diminish as more attack power in the form of strength appears on tanking gear. However, more damage is more damage. .8% of 2000 DPS is still 16 DPS, which is nearly 33 TPS.

Conclusion: Until I can accrue something on the order of 6,000 Attack Power, the benefits of Armored to the Teeth will outstrip Cruelty on a 1 to 1 basis in terms of Both Deep Wounds and non-bleed damage dealt. Thus, I know that spending 3/3 in AttT and the last 2/5 into Cruelty, rather than spending 5/5 in Cruelty, will return more for my overall TPS. Of course, I'd like to take 3/3 and 5/5, but that would cost either DW or Shockwave & Damage Shields - not things I'll give up lightly for a maximal-TPS spec.

With this spec, I'll be maximizing the damage I can output while still being reasonably protected. I'll line up glyphs to augment the damage of the spec as best I can. Any Expertise, Hit, or BV-heavy gear can be saved for this spec, but the beauty is that I don't need to build an entirely new set of gear! I just need to make sure that any option slots I acquire for this threat-oriented spec provide the extra accuracy I want without jeopardizing my crit immunity. I can therefore guarantee a viable OT spec that will also help to speed up Heroics, trash, and farm-status runs; maximal mitigation really isn't necessary in any of these situations. Why, then, should I not push out that extra DPS?

Next: The tuning of my maximal mitigation spec for Progression Tanking...