I'll add a few cents here. When the mongols rolled into Poland and Hungary in 1241 they had one of the better tactical generals of his day in Subutai. I cant argue with the military composition of the mongol army as represented in MTW because of game balance, however the mongols should have better generals.

Subutai was a brilliant commander, on the same level (if not higher given his conquests) then any western or muslim counterpart. The only way to represent this advantage to the mongols is to have more quality commanders, or one uber commander. The mongol military system wasnt based on class (like the western armies of the day) it was based on ability.

At present in MTW you have the Khan at 4 stars, which is fine, but he had plenty of expirenced capable commanders that had been trained in china and asia minor for years.

Creating more capable commanders will help with force composition as well, as mentioned earlier, the mongols didnt go into Poland with many koreans or chinese footmen (save for engineer crews)