Dumb Horde

I'm playing as the Byzantines and I have just conquered all of Asia Minor. Things are starting to look up and I'm finally starting to generate some good cashflow since I control all the way to Alexandria. Then the Mongols show up. I figure I'm screwed because all of the Middle East is all cities so I can make money. They arrive near Baghdad, and naturally I figure I'm going to loose it. Well, the horde walks right past it and attacks my only fortress in the region at Mosul.

I had wisely stocked Mosul with 10 units of Trebizond Archers, and unwisely 4 units of peasants. So they lay seige with about 4000 troops. The next turn they attack me rather than wait it out. Its 4000 versus my 1000 troops. During the battle I kill their Khan with my archers and the battle ends with my decisive victory of 935 kills to 400 somthing. So far, so good.

Two turns later, they assult it again, and a battle ensues, I kill the new Khan and have another decisive victory. The horde seems pretty stupid to me. It is the only castle I have in the region of a bunch of extremely rich cities. Whats going on here? I'm going to wipe all those dummies out with them continually assulting my archer stocked fortress.