GhoXen's excellent thread hasn't been updated in a while. A lot of the information is still correct, but some of it is outdated, either due to patching, more complete testing, or better data available.
The fine folks at DAITools have produced an LUA script explorer that allows us to look at script source code. One of the major scripts is apparently responsible for computing combat damage. The info below is taken from that script (and related ones). There are still some unknowns, but there's a lot of helpful stuff here.
The formulas below are incomplete, but I've tried to capture the most important elements.
PLAYER DAMAGE CALCULATION
CREATURE vs. PLAYER DAMAGE CALCULATION
Please post corrections/questions/additions below. (If you're posting a correction or addition, please make sure you have independently verifiable evidence, such as a code snippet or screenshots/video!)
[Edit: Formatting, clarity]





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