Formula for single hit damage

[vor_lord]

So the other night in a SM Library run, I encouraged Alram's 36 rogue to roll on the Hypnotic Blade. He was reluctant, as the int bonus does him no good, and the fast speed makes it a poor choice in the main hand, particularly for ambush.

So discussion afterward (he did roll at my urging, luckily no one else wanted it) made me doubt whether I was correct. His current main hand dagger is Broad-Bladed Knife, which, while the DPS is poor, has a very slow 2.0 attack speed. I had to concede that I didn't run the attack power numbers to see if I was correct in assuming that the huge DPS margin between the two was actually enough to make it better in the context of a single hit. I'd always done such comparisons by simply measuring the average of min and max.

So, I thought about it and came up with this. I'd like to have people correct me if I'm wrong. There are two parts to single hit damage as I understand it, the weapon portion, and the attack power portion. The attack power portion will scale up depending on the weapon speed.

Formula for single hit damage:


(WpMin + WpMax)/2 + AtkPwr*WpSpd/14


While the original question dealt solely in terms of ambush, I believe ambush is a % multiplier and an additional flat add on top of this, so just this formula should be sufficient to answer the question.

So, our two weapons:

Hypnotic Blade: 26-49, 1.4 WpSpd
Broad-Bladed Knife: 23-44, 2.0 WpSpd

Setting these two weapons equal, I want to see how much attack power you would need before the Hypnotic Blade lost in terms of single hit damage comparatively. This comparison is easy as neither weapon has a mod that changes attack power:


(26+49)/2 + AtkPwr*1.4/14 = (23+44)/2 + AtkPwr*2.0/14


Solving for AtkPwr yields 1.33. This makes sense because the weapon only portion is very near, and the attack power portion scales up quite a bit quicker on the broad-bladed knife.

Does all this look correct?

It's a pretty good bet that a level 36 rogue has more than 1.33 AtkPwr :blink: so it appears that I was wrong to encourage him to declare need. So, I'm sorry for pushing you to take this Alram -- good news is it was greed for everyone else.

[Alram]

Thank you for posting this.
Other questions arise.

1. How much more damage does a faster dagger have to do before it becomes more desirable than Broad Blade Knife in the main hand?

2. Under what circumstances is it more desirable for a rogue to use 2 fast daggers with high DPS?

[lemekim]

Why couldn't he use it in off-hand? I think that would be the best choice in this situation, as the dagger is fast (and thus is great with poisons), and will give decent boost to his DPS.

[Alram]

Why couldn't he use it in off-hand? I think that would be the best choice in this situation, as the dagger is fast (and thus is great with poisons), and will give decent boost to his DPS.
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I am using Swinetusk Shank in the main hand.

edit: I am using Swinetusk Shank in the off hand.

[Concillian]

Thank you for posting this.
Other questions arise. 

1. How much more damage does a faster dagger have to do before it becomes more desirable than  Broad Blade Knife in the main hand?

It depends on how much AP you have. As was demonstrated, speed is a very large factor in terms of Ambush and Sinister strike damage.

This is why dagger rogues farm up Toxic Revenger

Also,
Tigerbane (farily common drop)
and Silent Hunter (obtained from Horde quest in Arathi)
Are popular, easier to get, alternatives to the blues.

Also Fiendish Skiv (Horde quest in Duskwallow) but that is higher level, I think around 45 or so.

2. Under what circumstances is it more desirable for a rogue to use 2 fast daggers with high DPS?
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Umm, none?
I guess if you went with slice and dice + poisons it might work out, but overall mainhand = slow and offhand = fast. Physical offhand damage is cut in half, but poison procs are full damage, so a substantial amount of extra damage can come from the off-hand in terms of poison damage. Posion damage percentage difference will be simply the ratio of the weapon speeds. so going to a 1.3 speed weapon from a 1.5 speed weapon, poison damage picks up by 1.5 / 1.3 (~15%)

[Zarathustra]

Am I completely off here, or is this being made far more difficult than it really should be?

Ignore the speeds. Ignore the DPS. Just look at the damage ranges. Which one is higher? That's your best bet for instant-attack skills.

Am I missing something here?

Edit/Addition: Meh. Silly Zar forgot that attack power adds DPS and not straight damage (why, I have no idea Blizzard). Move along, folks. Nothing to see here. :whistling:

[Concillian]

Am I completely off here, or is this being made far more difficult than it really should be?

Ignore the speeds.  Ignore the DPS.  Just look at the damage ranges.  Which one is higher?  That's your best bet for instant-attack skills.

Am I missing something here?
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Yes you are... attack power.

a 1.4 speed dagger gets:
AP * 1.4 / 14
added to it
and a 2.0 speed dagger gets:
AP * 2 / 14
added to it.

An example in addition to the example that vor lord layed out is when my rogue finished SM I got this sword:
Sword of Omen (Thundercats, HO!)
I replaced this sword (a reward for Blackfathom Deeps):
Outlaw Sabre

Despite the fact that Sword of Omen was higher raw damage (39 - 74, 56.5 avg vs. 35 - 67, 51 avg) The Outlaw Sabre would consistently hit for more damage with Sinister Strike because the Sword of Omen was just too fast. the difference in AP contribution was HUGE, plus Outlaw Sabre adds even more AP

Because the Sword of Omen is a full 35% extra DPS on the normal attacks, plus extra poison, it's still doing comparable or better damage. But, min-max damage is not the whole story, and I think that was the whole point of vor lord's post.

[vor_lord]

Edit/Addition:  Meh.  Silly Zar forgot that attack power adds DPS and not straight damage (why, I have no idea Blizzard).
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The reason is to not favor fast weapons. If the attack power portion added straight damage, we'd all be wielding 1.3 speed weapons.

As it is, the current setup clearly favors slow weapons in many ways due to the prescence of instant attack abilities and big one shot abilities.

You could argue not to have a second term in the equation at all. I imagine that could be made balanced -- you'd have to make attack power be some kind of multiplier effect instead:


((WpMin + WpMax)/2)*some_formula_like_attack_power


There are four classes of effects to consider with weapon speed (ok so I'm making these up on the fly for purposes of discussion, please be gentle):

1. Instant or one shot attacks.
These include Overpower, Mortal Strike, Reckoning, Sinister Strike, and Ambush. These favor slower weapons, due to the use of attack power. You don't really get more of these using a fast weapon, so making them count favors a slow one.

2. Straight chance to proc on every attack with static effect on damage
These include +dmg weapon enchants, paladin judgments, and rogue poisons. Because the effect of the proc is the same regardless of weapon speed, more procs = more damage. Because the chance to proc (things like +dmg enchant are 100%) stays the same, more attacks = more procs. So these favor fast weapons.

3. Straight chance to proc on every attack, but effect varies on weapon itself
These include all shaman weapon buffs, and chance to proc extra attack talents (such as warrior Sword Spec). Flametongue, rockbiter, and frostbrand all scale appropriately to not favor any weapon speed. A similar balanced result is obtained with Sword Spec, as you'll get more extra attacks with a faster weapon, but they are smaller, so it evens out.

Windfury is an exception in this class -- while it is a straight chance to proc, and you'll get more procs and therefore more extra hits with a fast weapon, it is skewed toward slower weapons due to the big attack power bonus that the extra attacks obtain.

4. Proc per minute effects
These generally tend to be balanced for any weapon speed, but as the effects vary this may not be true. In particular, when the effect itself changes depending on attack power (like Seal of Command) it will continue to favor slow weapons. A few PPM effects theoretically may have a higher enough procs per minute to require the use of a faster weapon to obtain the full expected number of procs -- however I'm not sure if any of these exist.

[Zarathustra]

The reason is to not favor fast weapons.  If the attack power portion added straight damage, we'd all be wielding 1.3 speed weapons.

As it is, the current setup clearly favors slow weapons in many ways due to the prescence of instant attack abilities and big one shot abilities.[right][snapback]84890[/snapback][/right]

Given the overwhelming bias in favor of slower weapons, I can't see this being a good reason. Right now, slow = good on a mainhand or 2-handed weapon. There is little incentive to use the faster ones.

[vor_lord]

Given the overwhelming bias in favor of slower weapons, I can't see this being a good reason.  Right now, slow = good on a mainhand or 2-handed weapon.  There is little incentive to use the faster ones.
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I'd agree that the strategy has failed to a certain degree, but I'm nearly certain this was the intent. With straight damage, odds would be overwhelmingly in favor of faster weapons.

I think Blizzard is trying to address this somewhat. The new Bloodthirst talent means they are at least thinking about it.

[Ruvanal]

You could argue not to have a second term in the equation at all.  I imagine that could be made balanced -- you'd have to make attack power be some kind of multiplier effect instead:


((WpMin + WpMax)/2)*some_formula_like_attack_power

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The AP * weapon_speed / 14 is a muliplier effect. The problem is that they leave as using the weapon_speed in all cases including the instant attack skills. They should have made it more like

AP * skill_speed / 14

Where you could probably treat the instant attack skills as a 1.0 second speed and then adjust for any skills that used a longer set up speed. The raw swinging of the weapon could still use the AP * weapon_speed / 14 that is already in place.

[Quark]

The AP * weapon_speed / 14 is a muliplier effect.  The problem is that they leave as using the weapon_speed in all cases including the instant attack skills.  They should have made it more like

AP * skill_speed / 14

Where you could probably treat the instant attack skills as a 1.0 second speed and then adjust for any skills that used a longer set up speed.  The raw swinging of the weapon could still use the AP * weapon_speed / 14 that is already in place.
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That would be smart, and an extra line of code to boot!

Yeah, this is something I've argued before. Instant skills shouldn't be based off weapon speed in any way. "Next Melee" skills like Heroic Strike, sure, but not Backstab.

[vor_lord]

Wanted to update this thread as of patch 1.8 for the following instant abilities:

Whirlwind
Mortal Strike
Overpower
Sinister Strike
Backstab
Ambush

For instant attacks, as of 1.8 the speeds used are:
Daggers = 1.7 SPD
Other one hand = 2.4 SPD
Two hand = 3.3 SPD

Formula for single hit damage:


(WpMin + WpMax)/2 + AtkPwr*WpSpd/14


So damage range is the most important stat as of 1.8 for these skills.