Is the Dual Savagery perk multiplied by the Assassins Blade perk

the-elder-scrolls-v-skyrim

From elderscrolls.wikia.com/wiki/Sneak_(Skyrim):

Assassin's Blade

Sneak attacks with daggers now do a total of fifteen times normal damage.

From elderscrolls.wikia.com/wiki/One-Handed:

Dual Savagery

Dual wielding power attacks do 50% bonus damage.

My question is, assuming I have both perks, am wielding two identical weapons and my weapon damage is X, will I do 2X * 15 * 1.5 = 45X damage or 2X * 15 + (2X * 1.5) = 33X damage?

If anyone is able to back up an answer with examples from in-game, that would be great.

Note: Don't consider the Armsman perk, the damage multiplier from one-handed skill and the damage multiplier for power attack vs regular attacks. I left them out deliberately for clarity, as I already know they stack.

Best Answer

I tried this out in-game and yes, it does stack as in your first example.

Using a steel dagger with 10 display damage (10.36 actual) and the Dark Brotherhood gloves, I achieved 932.4 damage; without the perk, 621.6. The exact damage formula without the sneak bonus from UESP is as follows:

Damage = 
((Right Hand displayed Damage * (1 + Power Attack Bonus) * (1 + Dual Power Attack Bonus) * (1 + Power Attack Perk) * (1 + Dual Power Attack perk)) * Dual Power Attack Mod)
+ ((Left Hand displayed Damage * (1 + Power Attack Bonus) * (1 + Dual Power Attack Bonus) * (1 + Power Attack Perk) * (1 + Dual Power Attack perk)) * Dual Power Attack Mod)

Power Attack Bonus = 1 if power attacking
Dual Power Attack Bonus = 0.125 if power attacking with dual weapons
Power Attack Perk = 0.25 if power attacking and you have Savage Strike or Devastating Blow
Dual Power Attack Perk = 0.5 if power attacking with two weapons and you have Dual Savagery
Dual Power Attack Mod is 2/3 for the right and 1/3 for the left hand

As the wiki notes, you don't actually need to attack with both weapons to get the bonus, just have 2 equipped.

Related Topic