Normalization

Normalization refers to an Attack Power adjustment made to instant attacks in patch 1.8. Hunter ranged instant attacks were also normalized in patch 1.10.

Background
Auto-attack damage consists of two components: the weapon's nominal damage, and damage from Attack Power (AP). (Wands are an exception; they aren't affected by AP.) To keep AP's effect on damage per second (DPS) constant given equal values for other stats, AP is multiplied by an amount proportional to the weapon's nominal speed (time in seconds between attacks). (This is not the same as your actual attack speed with the weapon, which means that haste and AP give a larger increase to auto-attack DPS together than separately.)

Before normalization occurred in patch 1.8, instant-cast special attacks used the same weapon-damage formula as auto-attacks, even though their rate was determined by the global cooldown and therefore independent of the weapon's speed. Because of this, slow weapons with lower weapon DPS could lead to a higher total damage per second than faster weapons with higher nominal DPS.

One notable example is the Barman Shanker, which was at this time considered by many as the best rare dagger due to its exceptional high swing time, although there were other rare daggers with higher nominal weapon DPS (or item level) available.

Formulas
The normalized weapon damage for instant attacks is:



where  is:
 * for daggers
 * for other one-handed weapons
 * for two-handed weapons
 * for ranged weapons
 * weapon speed for non-normalized attacks (see below)

Prior to patch 1.8, the weapon damage used for instant attacks was:



Note that ...

is simply the formula for weapon (white) hit damage, as. The nomalized formula treats your weapon as if its swing time was a certain normal value for its type (1.7 sec for daggers, 3.3 sec for two-handed weapons, etc).

Nearly all instant attacks based upon weapon damage are affected by normalization; only a few are not.

Examples of normalized instant attacks
...
 * Rogue
 * Shiv
 * Sinister Strike
 * Ambush
 * Backstab
 * Mutilate
 * Hemorrhage
 * Warrior
 * Overpower
 * Mortal Strike
 * Whirlwind
 * Devastate
 * Hunter
 * Multi-Shot
 * Aimed Shot
 * Death Knight
 * Blood Strike
 * Obliterate
 * Paladin
 * Crusader Strike
 * Divine Storm

Non-normalized instant attacks

 * Druid
 * All weapon damage based attacks, since druids in bear and cat forms have fixed weapon speeds.
 * Rogue
 * Ghostly Strike (old)
 * Riposte (old)
 * Shaman
 * Stormstrike
 * Warrior
 * Cleave
 * Heroic Strike
 * Retaliation
 * Rend
 * Slam (technically, this is not always instant)
 * Hunter
 * Wing Clip
 * Mongoose Bite (old)
 * Scatter Shot
 * All weapon damage based pet attacks, since each pet type has a fixed weapon speed.

Examples of instant attacks not normalized
These are examples of instant attacks that are not based on weapon damage, and thus are not normalized.
 * Rogue
 * Gouge
 * Kick
 * finishing moves
 * Warrior
 * Execute
 * Bloodthirst
 * Revenge
 * Hamstring
 * Shield Bash
 * Shield Slam
 * Mocking Blow
 * Intercept (old)
 * Pummel
 * Hunter
 * Arcane Shot
 * Concussive Shot
 * all stings
 * Counterattack

Note: Druid feral attacks were not normalized. They are unaffected by weapon speed. Mages, warlocks, and priests have no instant melee or ranged abilities.

Tips
With normalization, the weapon speed is now less influential on the total damage per second of characters, although weapon speed still has a small influence because the base weapon damage of instant attacks is higher for slow weapons of same weapon dps. Nowadays weapons with higher weapon dps are generally preferred over ones with lower weapon dps (regardless of weapon speed), although there are exceptions like Windfury Weapon.

The normalization coefficients mean that a two-handed weapon will give the most damage from attack power, except when using an attack that can explicitly use two weapons. This means, for example, that a death knight should always use a two-handed weapon, unless using the talent Threat of Thassarian and a rotation built around it. (Even as a tank, the death knight will otherwise be unable to generate enough threat, since most threat comes from instant weapon-based attacks and is proportional to damage.)