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1) The length of the actual animation, usually the .brg file
2) Any overridden length specified in the anim files
Anim files are by far the easiest way to do this - by simply adding "length x.x" after the line that describes the anim file to use (visual or visualgranny). If memory serves, most villagers have anims with overrided lengths - though their files are pretty complicated compared to plenty of other units.
In theory, changing the animation length in the anim file (or in a 3D program) will not change the DPS done by the unit. However, there is some evidence to suggest this is not true for certain units. Certainly for special attacks that do a flat damage rate, increasing the frequency of the animation will increase DPS.
1) Use the editor's anim browser, one of the fields displays the current anim length (arguably the easiest)
2) Mod your UI to include the text field {currentUnitCurrentAnimLength()} somewhere that supports them, then just select the unit doing the anim in question and have a read
3) For BRGs, the anim length is encoded in the 4 bytes at offset 40 (if you want to script something that works on these, this is useful)
For one-offs, 1) is definitely the nicest solution, though!
As for DPS, the game adjusts damage done to be equal to DPS*animtime, except in the following cases:
1) The unit attacks more than once per anim. In this case, each attack does the expected damage
2) The unit has an area component to its attack, in which case the anim length is treated as 1, regardless of what it really is
3) The unit has a lightning attack, in which case the anim length is treated as 1
4) Some special attacks like to be special and don't act quite as you'd expect
Edit: Ah, nevermind, figured it out myself
Edit: Ah, nevermind, I'm stupid