are stacked one-handed damage perks additive or multiplicative?

Question

The One-Handed perk tree contains Armsman:

• Armsman (One-Handed weapons do 20/40/60/80/100% more damage)

And the Stealth perk tree contains two perks which can modify one-handed damage:

• Backstab (Sneak attacks with one-handed weapons now do 6x damage)
• Assassin's Blade (Sneak attacks with daggers now do a total of 15x normal damage)

Are the effects of Armsman and Backstab/Assassin's Blade additive or multiplicative?

For example, let's say I have the rank 5 Armsman perk and a dagger which inflicts X base damage. My dagger should now inflict 2X damage: (X + X*100%).

Now I acquire the Backstab perk. When backstabbing, will my dagger inflict:

• 7X damage (6X + X*100%; perks stack additively)

or

• 12X damage ( (X + X*100%)*6; perks stack multiplicatively)

?

Answer

Multiplicatively. (Otherwise, it would take 5 ranks to increase dagger sneak attack damage from 15x to 16x.)

First off, this is the damage formula:

displayed damage = (base damage + item quality) * (1 + 0.4 * skill/100) *
                   (1 + perk effects) * (1 + item effects)

and for sneak attacks, most damage except that from poison or enchantments should be multiplied.

So assuming the no-ranks-in-Armsman, non-sneaking attack is x, then it breaks down like so for one-handed weapons:

+---------+-----------+-----------+
|         | armsman 0 | armsman 5 |
+---------+-----------+-----------+
| regular |     x     |    2x     |
| sword   |    6x     |   12x     |
| dagger  |   15x     |   30x     |
+---------+-----------+-----------+

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