How do you calculate the total damage output?

According to my character sheet, my level 35 destroyer deals 514-1,028 strength damage, 0 ranged damage and 9-17 magic damage. Summing these values gives me:

514 + 0 + 9 = 523
1,028 + 0 + 17 = 1,045

Gnomeslice's level 24 alchemist, according to his character sheet, deals 2-3 strength damage, 306-612 ranged damage and 287-573 ranged damage. Summing these values gives me:

2 + 306 + 287 = 595
3 + 612 + 573 = 1,188

Does that mean that my level 35 destroyer deals 523-1,045 damage per second, while Gnome's level 24 alchemist does 595-1,188? or do these damage figures overlap, bringing a total damage per second that's less than the sum of its parts?

The Torchlight Wikia page breaks the damage formulas down as follows:

[ ( min dmg + max dmg ) / 2 ] / speed = DPS

So if you have a sword that does 25 - 35 damage every .56 seconds, this should apply:

[ ( 25 min dmg + 35 max dmg ) / 2 ] / .56 speed = 53.57

Elemental damage socket gems (not sure about other types) are tacked on to max damage and go into the calculation as such:

{ ( min dmg + max dmg) / 2 + gem dmg } / speed = DPS

So adding a +23 fire damage gem to a sword that does 25 - 35 damage every .56 seconds should look like this:

{ ( ( 25 min dmg + 35 max dmg) / 2 + 23 gem dmg ) } / .56 speed =
 94.64 rounded to 95 DPS

Armis on the Runic Games forum, created a formula that accounts for other factors that mitigate damage and give more than a raw output of the character under an ideal:

DPS = (1+bonus_damage) * (1+speed_bonus) * [(1- u * fumble%) * [(1-crit%) * base_dps + crit% * crit_dmg * crit_dps] + u * fumble% * fumble_dmg * base_dps]

The idea is basically that:

• if you fumble, you deal your fumble damage (if it’s an auto-attack, obviously)
• if you don’t, you have a chance to crit and deal crit damage (plus your crit damage bonus)
• otherwise you deal normal damage
• whatever happens, it’s all augmented by bonus damage and the appropriate speed bonuses

But it gets worse, because sometimes base_dps is actually made of different things: physical and elemental damage. In this case, I won’t type out the whole equation but basically you need to split the physical and elemental damage, calculate DPS separately, then add them up again, all because elemental damage is increased by Focus (and some specific bonus sources, like +15% ice damage) while physical isn’t.

The above is accompanied with an exhaustive explanation defining mitigating factors and how they tested to work in the study. Briefly:

GEAR

There are many affixes on gear that can impact the equation above (poetically named “(2)”).

• increases to attack or cast speed add to the speed_bonus variable
• damage increases, when relevant (and including Strength and Focus, or Melee/Ranged bonuses), add to the damage_bonus variable
• affixes modifying crit chance, crit damage, fumble chance and fumble recovery add to their respective variables

...what happens with stuff that adds fixed damage?

...It depends on whether it’s a weapon socketable (or a weapon enchantment) or not. If it is, the added damage value gets added to the base weapon damage per hit. ...if you add a Skull of Vellinque (+199 physical damage) to a weapon that deals 100 damage per hit, you’re essentially tripling the total DPS (give or take). Bear in mind that if you add elemental damage such as from Embers, it gets bonus damage from Strength AND Focus (and all other applicable bonus sources). The flip side is that ... flat-damage skill, your weapon is irrelevant and so is this socketable.

If it’s not a weapon socketable/enchantment...it gets no bonus damage whatsoever. That +173 ice damage necklace basically adds 173 ice damage to your final damage number before fumbles and crits, but that’s it. You could have 2000 Focus and you’d still only get +173 ice damage, even with skills. Note that the bonus damage from Sword and Board works like this too...

Adding to the confusion is how the game calculates it: all elemental damages are actually calculated and applied separately, which means that enemy armor will apply separately to each of them. In addition, when socketing a physical damage gem (or enchant, etc.) in a weapon dealing physical damage, the game will count it separately. In other words, any addition of physical damage applies separately from the weapon's base physical damage.

WEAPONS

1. Skills that are NOT based on weapon DPS do not transmit any active effect (i.e. DoTs, % chance to cast spells, armor debuffs, etc.).
2. Skills based on weapon DPS may transmit some, but it depends on the effect and on the skill.

ATTRIBUTES

Attributes define a lot of the damage variables. What often happens is you take an attribute, derive the base value of, say, crit chance, and then add to that all the fixed bonuses you have (usually from gear).

• Crit% = Dex * (0.2002 – 0.0002 * Dex), capped at 50.1% at 500 Dex (Dodge also follows this relationship)
• Crit_dmg = 50 + Str * 0.4, capped at 450% (technically 449.6%; basically Str above 999 doesn’t give you anything. Total crit damage
  from all sources caps at 500% in the Arcane Statistics screen though)
• Fumble% = 21%, and no amount of stats will change that number, only gear will improve it.
• Fumble_dmg = 25 + Dex * (0.3003 – 0.0003 * Dex), capped at 100% at 476 Dex
• Execute% = 9.8 + Foc * (0.2002 – 0.0002 * Foc), capped at 60% at 500 Focus (technically 498)
• Block% = Vit * (0.2002 - 0.0002 * Vit), capped at 50.1% at 500 Vit

Through that, beastmodeengaged on the Runic Games forum was inspired to create this spreadsheet with the notice it is designed around the Engineer/Emberquake class and can be modified to apply to others as well.