That's ridiculous, you don't kill people with long distance archer fire. Maybe in the Total War games but certainly not in reality!!!Doesn't this happen in the archer's phase? Then, it is quite realisticaly acceptable imo, since you have the following: imagine those doomstacks having many many archer companies that would insta-hit all or almost all of the defenders, while themselves would be under the cover of a tortoise type formation made by the rest of thousand of soldiers. The thing is that those 500-1000 don't really get in melee combat, where they would indeed be able to kill opponents at a close to 1:1 ratio.
Also, a small force confronted with a much larger one would definitely not line up for a regular battle. The larger force would have to catch them first and then force them to fight. And the fight would certainly not involve the 30,000 man army maneuvering to fight a 3,000 man force. They would split off maybe 10,000 and have them battle the smaller force. So it is not unreasonable that the larger force suffers casualties. The game in no way reflects this.