WoW Math I - Poison vs Sharpening Stone

So I'm cruising the guild forums in the class section when I come across on of the recruits giving out tips to another member asking for help with their damage performance. Most of his stuff is good and valid - he suggests a decent combat spec, he drops the tip to use blade Flurry for an additional haste when the opportunity arises, he throws out a Nefarian trick. But then he proceeds to make claim that sharpening stones are superior to poisons for mainhand. Now, normally I wouldn't have minded, but he throws out some terrible "math" to prove his point.

Not word for word here, but the cut and dry is he instructed the member to check his Attack Power DPS addition from his character sheet, add the +8 from the dense stone, and then to multiply it by the backstab factor and lethality.

And gee, wasn't that the most misleading pile of...yeah. I had to step in, knowing for fact that it was wrong - and that he was factoring in numbers that didn't belong in the comparison.

The current instant attack formula (as of patch 1.8) is:

[(AP/14) * Weapon Speed Constant] + Weapon Damage + Sharpening Stone + Enchant

Note that attack power, while affecting the overall damage on the attack, is simply added to the base damage. Since there are no multipliers, it doesn't matter what I sharpen, enchant, or coat my blade with - the attack power contribution is the same.

So I typed up some quick and dirty comparisons that didn't factor in miss, dodge, parry, block, armor reduction, or resistances. I was hoping to get the point across to him with my basic math skill.

Quick and Dirty (Dense Sharpening Stone)
========================================
Base Damage
+8 damage per hit on a weapon that swings every 1.8 seconds.
8 / 1.8 = 4.44 base added dps

Base Crit
Assume 30% crit rate
Critical melee attacks do an extra 100% damage
4.44 * 0.3 * 2 = 2.66 dps added to crits (in addition to base dps calculated above)

Base Damage Per Backstab
+8 damage * (150% from backstab + 30% from 5/5 opportunity)
8 * 1.8 = 14.4 base added to backstab

Backstab DPS
60 energy to perform backstab / 10 energy per second = 1 backstab every 6 seconds
14.4 / 6 = 2.4 base backstab dps

Crit Backstab DPS
Assume 60% crit rate (30% base + 30% from 3/3 Improved Backstab)
Critical melee attacks do an extra 100% damage
5/5 Lethality Adds 30% to the critical damage bonus
2.4 * 0.6 * 2.3 = 3.31 dps added from crits (in addition to base backstab dps)

Total: 4.44 + 2.66 + 2.4 + 3.31 = 12.81 dps gain


Quick and Dirty (Instant Poison VI)
===================================
Base DPS
Weapon Swings once every 1.8 seconds
Average damage of 130 per application (112-148 range)
20% chance of application per swing
130 / 1.8 * 0.2 = 14.44 base proc dps

Backstab swings
60 energy to perform backstab / 10 energy per second = 1 backstab every 6 seconds
130 / 6 * 0.2 = 4.33 backstab proc dps

Total: 14.44 + 4.33 = 18.77 dps gain

Instant Poison VI shows 5.96 dps higher than sharpening stones.

Again, this is quick and dirty, and is under normal conditions. For example, with hyper energy regeneration (Essence of Red from vael), the stones will come out ahead. With 3/8 Bloodfang, the poison application bonus will raise the dps for poisons. In an in-and-out fight like Geddon or Sartura, the stones are better again.

He's still claiming sharpening to be superior to poisons, and scoffed my math above since it didn't "factor in AP or resists". As I said in my opening, AP will contribute the same for either weapon buff, and reiterated this to him. I also stressed the point again that these calculations were quick and dirty, so I didn't factor in resists just as I didn't factor in damage reduction - which would probably tilt more in favor of poison in many scenarios, since armor reduces every hit, while resists tend to be less constant.

In the end, I have no intent to make an argument out of it. As I said on the guild forums, he can continue to use his stone, and I'll stick with my poison. Doesn't bother me one bit.

Edit: Just realized that in an unlimited energy situation (like Vael as stated above), the difference isn't all that huge. For instance, using the constants from the above calculations, we find poison slightly ahead.

Average additional backstab damage from dense sharpening stone:
14.4 + (14.4 * 1.3) * 0.6 = 25.63 additional damage per hit

Average additional poison damage from instant poison vi:
130 * 0.2 = 26

As crit rate rises, sharpening stones become more effective. I can't be bothered with the math, but there will be a point of crit% where stones will prove superior. Of course, that point is moot for most endgame bosses, since critical hits against them have an artificial cap around the 30% mark for standard melee attacks.

 

Yeah, cannot deny being a

Yeah, cannot deny being a nerd. After all, I've got a spreadsheet containing all items in the game that are upgrades broken down by DPS figures, item slot, zone, and DKP value... everyone needs a hobby though, right?

 

I'm a more effective killer

I'm a more effective killer when I know how to best hurt my target.

Knowledge and understanding is power. ^^