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Rechecking Formula for Critical Damage
My testing at 521~763 Damage Range with a bonus critical damage modifier of 1.67 and a bonus damage modifier of 1.4 yielded bare handed attack critical hit values ranging from 1820 to 2065, which is exactly consistent with the formula as it exists. If your proposed formula were accurate, I would expect to see values in the 1400~1800 range, but I did not at any point.
I recommend double-checking that the target you're using for your tests has 0 protection, and also checking to ensure that you've properly adjusted your formula to add together any multiple sources of crit damage you may have.
My testing was with damage range 593 - 793 with 1.57 crit modifier. Expected values per wiki are in range 1838 - 2038. But I obtained few crit hits, 1757, 1816, 1734 lower than expected value.
From your calculations, I notice I didn't include bonus damage, but that's irrelavent as it wouldn't explain the lower values. I tested on brown foxes.
The chances you didn't see values lower are perhaps cause your sample was small? These four contradictory values I got from testing was from around 70-100 hits.... Appreciate your help!