Ok tollheit, interesting points. But to really prove them you must try and disprove them.

Try losing large amounts of archers and light troops but do it late in the battle after other troops have fallen. The light troops seems to always recover, lets see if its because of a value recovery or if its because they are normally the first to fall. I've found that many of my archers and slingers come back after battle; but I like to protect them and make them avoid all enemy contact unless I am not paying attention and they get flanked. Even so they tend to recover considerably....why?

Point 2: Lazy or not you can't really justify anything unless you do actually try a melee battle. Arrows seem to equal units that recover, so only using units killed by arrow fire is only evidence to what we already suspect; try and do the same with a large melee fight.

Like drewski said, maybe you get a certain percentage of troops back plus a random chance per man. Is this testable? Refighting the same battle a few times should sort it out.