Most of the time they're reasonably sane. Two forces facing each other down, they run together or shoot projectiles at each other, projectiles/sharp things hit, people die. There's generally two or three characters on each side - two for siege weapons, three for most other units - and you can get a rough sense of how powerful a side is by how many of those little miniature horses are left.
Most of the time the battle animations work great.
Every once in a while, not so much.
I've seen two archers standing in a city, while the attacking hosremen run . . . across the water, from ten miles away, only to die before even being shot at. I've seen musketmen clotheslined by knights traveling at about three times the speed of sound. I've seen a battle end, only to watch the attacking forces run right through the city and keep on going past it.
Just now, I watched a rifleman kill three pikemen in a single shot. I don't know where he's getting his ammunition, but I want some of it.
Somehow, the most amusing part of all of this is that the battle animations are just visual glitz. They mean absolutely nothing in-game, they're just a representation of what the combat calculations already did. So when any of these weird things happen, it doesn't actually matter. The game continues on perfectly reasonably.
It must be very confusing to be a soldier in this world, though.