Well, I've seen horse archers lose units chasing down routing units so I sometimes just let them fire at routers until they die. The problem is that, sometimes, when the routers are near them, they would move towards the routers before firing and get hit by arrows from their buddies.

There's also incidents where I would tell them to fire at somebody else because I'm using a melee unit to chase down some routers and they would still fire at those routers.