How is ranged damage calculated?

Solution 1:

Yes, by using your weapon you make the arrow stronger so you simply add the arrow's damage to the weapon's damage. IF it is the case that the weapon is enchanted then the weapon is even stronger, so

total damage = weapon damage + enchantment damage + arrow damage

is the right formula. They don't limit it by the average, because that would make those slow bows rather weak. The highest damage doesn't really make sense as then getting better arrows does in most cases not result in getting better damage...

Solution 2:

There are so many factors that go into damage calculation for physical weapons. I'll list the one's that I have found:

(A) Weapon base (for bows: bow damage base + arrow damage base) (B) Damage from weapon enchantments (C) % increase from skill level (D) % increase from perks, enchantments, potions, blessings, ect. (E) % increase from sneak postion (by default: 2x the damage + perk increase, 6x for one-handed = 12x, 3x for bows = 6x, 15x for daggers = 30x) (G) % increase from Mystic Binding perk from Conjuration school (Bound weapons do more damage)

The math involved, while not impossible, can get somewhat complicated, and there is a bit of algebra involved. So please correct me if needed.

A and B are integers and are easily calculated. It's the rest that I'm not sure about how they factor in because they are multipliers. Do they stack and if so in what order? I've noticed that from the sneak position, I can get the message in the corner of the screen that says sneak attack for 30x times damage. Where does that fit into the formula? Imagine it as:

Damage = (A (G*)) (C + D) (E) + B *With bound weapon damage increase

So keeping it simple with small and rounded numbers, if you have:

(A) Sword for 20 damage (B) Sword has enchantment that adds 10 points of fire damage (C) One-handed skill level at 50 (D) Perk adds 40% more damage, enchantment adds 20% more damage, potion adds 10% more damage = 70% more damage total

Then:

20 (1.5 + 1.7) + 10 = 74