Sure thing! Note, I do not know the details of how damage is calculated, so there will be a couple places in this proof where details are elided.
Axiom: The hit rate (miss vs damage dealt) is independent of weapon using the same skill.
Axiom: If a weapon hits, the damage done is drawn from 20 possible values, equally possible. I don't know the details of the maximum and minimum values, but they are a function of the "damage" attribute of the weapon.
Axiom: The expected value of a weapon swing equals the average value.
Axiom: The average value of a weapon swing equals (2 * Weapon_Base) + Bonus_Modifier + STR Modifier, which we can simplify (in notation) to 2 * X + Y
Axiom: The number of swings per minute of a weapon is inversely proportional to the "delay" attribute of the weapon.
Axiom: A weapon with a delay of 60 will swing once per minute. Note: I don't know the exact calculation here, but this will not affect the proof.
Definition: The expected damage per minute for a weapon equals the expected damage per swing multiplied by the swings per minute.
Proposition to prove: a 15/20 weapon is expected to do more damage than a 5/35 weapon. In formula: EV(15/20) > EV(5/35) where EV is the Expected Value. Note: I don't know what ratio a NTOV weapon should be, so here I'm plugging in some arbitrary numbers.
Other axioms:
- There's no procs
- hate generation (due to procs) is irrelevant
- the target is not immune to non-magical weapons
This proof is of the form
direct proof
Step 1: The expected damage per minute of the rusty weapon is average damage times number of swings per minute, or (2 * 5 + Y) * 60/35
Step 2: The expected damage of the NTOV weapon is (2 * 15 + Y) * 60/20
Proof:
(2 * 15 + Y) * 60/20 > (2 * 5 + Y) * 60/35
(30 + Y) *35 > (10 + Y) * 20
1050 * Y > 200 * Y
1050 > 200
QED