Aradan has done as good a job here explaining what we have figured out as I could, but it may be a good idea to organize this more clearly into what is known for sure(as much as we can be sure), and what is a guess.
The to kill and to hit formulas we are very confident of.
However, what *exactly* happens when a unit is hit, but not killed (fails the lethality check) is not clear. In MTW, there was a knockback effect that temporarily reduced the enemy's defense rating by a fixed number (6 I think) until the unit recovers from the knockback. I suspect there is something similar going on in RTW, but RTW added knockdowns and also still has knockbacks.
When a unit is knocked down, it is unattackable until it gets back up. You can see this when the last man in a unit gets knocked down, his enemy's start running around randomly because they can't find a target. However, it also can't attack while on the ground. Knockbacks could still function just like in MTW, but I don't know how long the defense penalty lasts or how large it is. I would love to test it but can't fathom a reliable way of doing it.
Aradan's guess is as good as mine and definitely note what he said about the random seed. If you refight a battle by clicking the crossed swords Icon, the game uses the same random seed as in the previous battle. Different orders will create a different results, but giving the same or similar orders will produce the same or similar result.
I should also mention that there are other important factors that determine the combat effectiveness of a unit, and both of them are things that shouldn't if CA was smart.
The skeletons/animations affect combat ability.
Take two identical units and give one fs_dagger skeleton and the other fs_swordsman. The swordsman unit will win every fight. I am not entirely sure what it is about the skeletons and animations that affects the combat ability, but our best guess is that it is a combination of the number of frames per attack animation and -id parameters associated with the attacks (as in skeletons.txt).
Increasing the attack delay (second to last parameter on stat_pri line which CA set to 25 for all units) can help mitigate the effects of the differences in attack animations, but doesn't completely eliminate the problem. Aradan did a bunch of tests to figure out how much the difference is between various skeletons. What he did was take identical units with attack delay 25 and different skeletons, and adjust the unit's lethality (or compensation factor as the compiler calls it: last parameter on stat_pri line) until the two units were roughly equal. I would publish the list, but I am not yet sure if factors other than the attack delay could change the effectiveness of the skeleton. So, I can't say for sure how universal the results are.
unit radius and unit height (the extra parameters on the soldier line) also affect the combat ability of a unit, but to what extent exactly, I do not yet know. We will be testing those sometime in the next month I hope, but there are only 3 of us.
At some point in the next 2.5 months, we will try to compile a comprehensive guide that covers all our work and results, but we are too busy trying to get the new version of FATW balanced to put together a real guide. Hope that helps some.
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