Other than overwhelming numbers, what other reasons were there for their temporary success? They had no military training whatsoever, and (initially) very little in the way of arms and armor.
Not the 1381 one, but in general:
1.) element of surprise: a revolt can happen anytime, no prep time like for an inter-country war
2.) numbers, you mentioned
3.) knowledge of terrain, guerilla tactics
4.) internal struggles in the upper classes: barons do not help a fellow baron in case of such a revolt, and when the fire spreads on his own turf, it is already a f big fire
5.) they, in fact, do have some military experience, at least the leaders. The biggest peasant revolt of Hungary, the one in 1514 led by György Dózsa, broke out in the camp of a crusade under organization against the Ottomans. Not everyone who took part had a military training, but they had a solid central part made of trained men and lower-ranking, yet very experienced noblemen- like Dózsa himself. Not every noble is pleased with the current status quo, a revolt is an opportunity to change it.
6.) fanatism. The aforementioned 1514 revolt broke out when the crusade was cancelled- priests told the people that the nobles revoked the absolution the pope promised them for the crusade. But Wat Tyler himself was also religious, great fan of the priest John Ball who also took a leading role in the 1381 rebellion.
Out of this, the main outlines
-give the peasants one pretty solid HQ unit
-let them appear and disappear, whatever that in your ruleset is called
-their morale shall be a bit random: fanatics at first, but, as the better-equipped enemy massacres them, getting easy to break. Better yet, some special characters to give them morale.