Ningen

Following the thread discussing how bonus spell damage, and bonus spell healing work. I thought i would clarify how weapon damage interact with abilities and attack power.
First of, each 14 point of attack power increases the damage per second by +1. Meaning that a weapon with a speed of 1 increases damage by 1, and a weapon with a speed of 3 increases damage by 3.
Attack power / 14 * weapon speed = Auto Attack damage
Second, following patch 1.8. Blizzard implemented normalization to how abilities scale with attack power, the same was done in patch 1.10 to hunters as well. The change made it so that abilities would scale with weapon damage and attack power, as if the weapon was a set speed, as opposed to the actual speed.
1.7 for daggers
2.4 for other one-handed weapons
3.3 for two-handed weapons
2.8 for ranged weapons
Meaning that a rogue using a weapon with the exceptionally slow attack speed of 2.9. Would have Sinister strike calculate as if the weapon was a 2.4 speed weapon.
1000 Attack power / 14 * 2.9 = 207 bonus damage to sinister strike
became
1000 attack power / 14 * 2.4 = 171 bonus damage to sinister strike
So how do you figure out how much your instant abilities deal by looking at your stat card? lets take a hunter as an example. While the change on a general level only affects instant attacks, there are a few exceptions and multi-shot and aimed shot are two of them.
calculating aimed shot dmg. 385-451 damage, with a 3.3 speed crossbow dealing 72-134 damage.
1. Find out the difference between your equipped weapon and the normalized weapon speed.
2.8 / 3.3 = 0.848 = 84.8%
2. Look at the damage on your stat cards.
385-451
3. Subtract the damage displayed on your weapons stat cards
385-72 = 313
451 - 134 = 317
4. Subtract the % from your damage granted do you by your attack power
313 * 0.848 = 265
317 * 0.848 = 267
5. Add the damage on your weapon back to the values
265 + 72 = 337
267 + 134 = 401
Add aimed shot damage of 600 to both values
Aimed shot damage = 937 - 1001 damage
Prior to normalization = 985 - 1051 damage
It is important to note that the normalization only affects attack power. Slow weapons are still very much desirable by Rogues, Warriors and Hunters as the weapon damage as displayed on their weapons stat card is not normalized. However, the change made it so that rare drops from dungeons were not more desirable than some epic weapons.
Notable abilities not affected by normalization DESPITE being instant cast abilities
Stormstrike - Shaman
Cleave - Warrior
Heroic strike - warrior
Ghostly strike - Rogue
Riposte - Rogue
Edit: math error