Thursday, May 15, 2008

You, Me, Attack Power and Dupree

Attack Power is one of the more interesting stats for physical DPS classes. At the most basic level, we can all understand one simple truth – more of it is better. And yet, why it is better and the intricacies of the mechanics it impacts are often misunderstood. I have often noted this to myself when discussions about Attack Power come up in Guild Chat and the ill-informed start chirping up with bad information. A series of blog entries over at Priestly Endeavors illustrated to me that even people I generally consider pretty knowledgeable can misunderstand Attack Power.

Before I go into detail about Attack Power, I want to provide a quick caveat. I know what I am about to discuss is applicable to Rogues, Warriors and Feral Druids. I am less familiar with the mechanics of Shamans, Paladins and Hunters – so I won’t talk directly about how this impacts them. Broadly speaking, these are general principles and SHOULD apply to the other classes, but I’m not going to offer prescriptive guidance on a class that I don’t have intimate knowledge about.

Attack Power and White Damage
The term white damage is simply a way to describe our standard auto-attack (or auto-shot) damage that comes from swinging our melee weapon. If we use an ABILITY other than auto-attacks, this is considered yellow damage – which I’ll talk about in a later section.

When we think about white damage, the easiest thing to figure out is how much damage is caused by our weapon. All you need to do is hover over your weapon and look at the item tooltip to see how much damage it deals. However, the formula for the actual white damage caused by each weapon strike also includes Attack Power.

All classes convert Attack Power to DPS at a 14:1 ratio (14 AP = 1 DPS). This holds true at level 1 and level 70. For example, 140 Attack Power converts to 10 DPS. Now, different classes derive Attack Power in different ways, but that 14:1 ratio always holds true. For example, a Warrior gains 2 AP for every 1 STR and a Rogue gains 1 AP per 1 STR. However, both of them convert AP to DPS at the 14:1 ratio.

So the formula for Damage Dealt by Attack Power looks something like this:

(AP/14) * Weapon Speed = Damage Dealt Per Strike due to Attack Power
Example: (2000 AP / 14) * 2.6 Weapon Speed = 371 Damage Per Strike

One thing to consider is that the amount of DPS remains constant at 14:1 regardless of the actual Weapon Speed. You don’t get more white damage DPS from a slower or faster weapon; it will always be the same.

Attack Power and Dual Wielding
The notable exception to how Attack Power scales for white damage is Dual Wielding. The reason is because Attack Power is applied at the 14:1 ratio for BOTH weapons. However, because your OFFHAND weapon suffers from a damage penalty – you don’t get the full benefit.

For your OFFHAND, the formula looks like this:

((AP/14) * Weapon Speed) / 2 = Offhand Damage Dealt Per Strike due to Attack Power
Example: ((2000 AP / 14) * 2.6 Weapon Speed) / 2 = 186 Offhand Damage Per Strike

When you consider that this damage is IN ADDITION TO the Mainhand damage, it becomes pretty clear that the benefit for scaling Attack Power is significantly better for Dual Wielders than Two-Handed or Single-Handed weapon users. In fact, if you use talents (like Dual Wielding Specialization) to increase your Offhand damage, then you can gain even more incremental benefit for Attack Power.

However – Dual Wielding does come at a cost and it exacts a 19% miss penalty. The base miss penalty on a same level mob is 5%, so anyone who Dual Wields gets an unmodified 24% chance to miss. This is one reason why +hit stats are very important to Dual Wielders. As that stat increases, more of the benefit from their scaling Attack Power is realized.

White Damage and Haste
As pointed out in the previous two sections, Attack Power is very much a part of White Damage. Therefore, anything that acts as a multiplier on your white damage works as a multiplier on Attack Power. The primarily multiplier I am talking about is, of course, Haste and it you can get it from items (like Drums of Battle), talents or abilities.

Now, the first thing to remember is that Haste is not going to change the amount of damage dealt in each individual strike. The formulas (above) used to calculate how much damage dealt from the strike remain unmodified. What DOES change is the frequency of attacks. If we use the first example, our strike will hit for 371 every 2.6 seconds. If we enjoyed a 30% Haste, that same 371 strike would occur every 2 seconds. The effective DPS from Attack Power increases from 143 DPS to 186.

You’ll notice that this is exactly a 30% increase in DPS for 30% Haste, so we can effectively assume that each 1% of Haste is the equivalent of an extra 1% in WHITE damage. Interestingly, your crit % has a very similar effect on white damage. The basic theory is that a 1% crit rate would lead to double-damage 1 time in 100 strikes. This is the same damage amount as 101 strikes or 1% more damage than 100 strikes. Therefore, a 1% crit rate leads to a 1% increase in damage.

Now keep in mind I am strictly talking about the effect on white damage (and I am ignoring the multiplicative effects). Haste vs. Crit vs. Hit can become very convoluted, so I point this out more as an illustration for how these things impact Attack Power. The purpose is to explain why talents (like Imp Slice and Dice, Flurry) and abilities that provide Haste are so valuable.

Yellow damage and Attack Power
I described yellow damage earlier as damage caused by your non auto-attack abilities. That’s not entirely true since yellow damage can also be sourced from things like Poison procs, but as it relates to melee classes it is generally true. Yellow damage comes in all sorts of variety because there are lots of different types of abilities. Some of them have nothing to do with Attack Power at all. Others, like Bloodthirst, are 100% determined by your Attack Power.

You can usually find the “formula” for how an abilities damage is derived by looking it up on Wowhead. For simplicity, I am only going to talk about those how Attack Power impacts yellow attacks that are based on Weapon Damage.

By now, you should be able to calculate how much damage is dealt in a single strike for white damage. A slower weapon will deal more damage in a single strike than a fast one.
Let’s compare a 2.6 one-handed sword to a 2.0 one-handed sword:

Example: (2000 AP / 14) * 2.6 Weapon Speed = 371 Damage Per Strike
Example: (2000 AP / 14) * 2.0 Weapon Speed = 286 Damage Per Strike

The 2.6 sword deals 85 damage more per strike at 2000 AP than the 2.0 sword. Well Blizzard, smarty pants that they are, figured out that was a bad idea for attacks that were instant, so they decided to normalize it based on weapon type in patch 1.08. So, all weapons of a type use the same weapon speed to calculate the Attack Power portion of the instant attack.

1.7 for daggers
2.4 for other one-handed weapons
3.3 for two-handed weapons
2.8 for ranged weapons

So, in our example above – the 2.6 and 2.0 one handed swords would have both been normalized to 342 damage per strike from Attack Power. If we had used a 2.0 Dagger, then the damage per strike would only have been 243 from the Attack Power. And a two-handed sword would have see even more benefit at 471 damage per strike.

BUT—here’s the kicker—they did NOT normalize the base damage provided in the weapon tooltip. The sword with 189-285 damage and a 2.6 speed and sword with 1.5 speed and 95-178 damage both have comparable DPS. However, the 2.6 sword has an average damage of 237 for each individual strike and the 1.5 sword has an average damage of 137 per strike. The net effect is that the 2.6 sword will do roughly 100 damage more on each individual strike.

Why is this important? Because when yellow attacks are INSTANT or faster than your normal weapon speed, then you want each of those attacks to carry as much punch as possible. Many of these attacks are also use modified weapon damage, like 150% Weapon damage. That means our above 2.6 weapon speed sword would provide 237+342 = 579 Weapon Damage which is modified by 150% to 868 damage. By contrast, your 1.5 weapon would have done 137+342 = 479 * 150% = 719 in damage. That’s a 149 point difference (or 17% decrease) in the amount of damage dealt by the instant attack of the 1.5 sword. This is why melee classes are generally advised to put the slowest possible weapon in your Mainhand.

Attack Power compared to other things
One terribly difficult thing to gauge is how important Attack Power is relative to other stats as a contributor to your overall DPS. Quite frankly, it can change pretty dramatically depending on how the rest of your gear is itemized and even as you level.

I pointed out in the past section that Critical Strike and Haste both effectively provide a 1% increase white damage per % point. At level 20, what is more valuable – a 1% increase or 28 attack power? Well if my DPS is only 20, then a 1% increase is only .2 DPS while 28 attack power is a 2 DPS increase (10% damage increase). Of course, at level 70, a 2 DPS increase may be almost insignificant particularly compared to a 1% increase for 800 to 1000 DPS.

Still – Attack Power is incredibly valuable because as I have hopefully pointed out by now, it’s one of the most basic building blocks of the DPS formulas. After all, 1% of zero is still zero. Dual Wielders, in particular, get even more incremental benefit from Attack Power and talents or abilities that provide Haste.

It also means different things to different classes and specs. One thing I always find pretty comical is the envy that some Rogues get over a Feral Druids Attack Power. The reality is that they are itemized very differently and for very good reasons. Of course a Rogue is going to have less Attack Power – they Dual Wield and they have abilities (like SnD) that provide significant Haste. Blizzard would be out of their mind to provide them similar Attack Power in the itemization. Instead, they very much force Rogues to look at +hit gear to take advantage of the Attack Power they are wasting in misses.

Sometimes we are asked things like, what’s better 100 AP or 1.21% to crit? Hmm. Well, that’s not such an easy question to answer now is it?

Edit: It should be pointed out that Kirk at Priestly Endeavors understands Attack Power, he just chose to ignore it in some of the theory crafting he was performing. His latest entry (here) does a much better job of explaining his point and including Attack Power in his discussion.

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