Try losing large amounts of archers and light troops but do it late in the battle after other troops have fallen. But to really prove them you must try and disprove them. The type of weapon the man fell too, may have an influence on the caualty recovering, but it may just be coincidence, or that they happened to fall first. Without the General and healing ancil, you only get the small random chance per man, which always exists. This is modified by the type of healing anciliary that the General has. My theory based on close observation, is that you get X% of the first casualties back (as Tollheit said), and then every other casualty has a small random chance of healing. If the ai has no long ranged missile troops, then your slingers/archers normally stay out of melee totally (unless you do some strange things with them )) The reason in my experience, that you get most of your Archer/Slingers back, is that generally they die first, as they are the first to be targetted by ai missile troops.
When I think about it, I'm not too sure about the "missile" casualties recovering bit either. Whoever gets "killed" first seems to have the highest chance of being healed, with those falling to missile fire also having a high probablity. Then a random percentage is applied on top of that. The chirgeon seems to heal more than the doctor, who heals more than the herbalist. You seem to get a percentage of the total casualties back (assuming a healer ancil). This is true without exception to my knowledge. If you assault a stone wall with say a unit of Pedites as Rome, and they win but lose 90% of their number, then after the battle (as long as you win and have a General with a anciliary), you'll get most, even all of them back sometimes.
It's also to do with which units die first in a battle, without a shadow of a doubt.Į.g.