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According to my character sheet, my level 35 destroyer deals 514-1,028 strength damage, 0 ranged damage and 9-17 magic damage. 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. 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?

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Those numbers in the character sheet seem to indicate raw damage per hit, not DPS. You can verify this by switching between weapons of similar type and observing the relation between weapon damage and your character sheet damage. –  jw013 Nov 8 '12 at 19:34
    
Unrelated, I'm curious what the alchemist has equipped? It seems unusual to me to have both strength and ranged damage unless dual wielding. However, a number as low as 2-3 strength typically means the character is using his bare hands/fists, which is odd because those numbers suggest he has a magical ranged weapon equipped. –  jw013 Nov 8 '12 at 19:36
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