Mongol forces were often dramatically outnumbered by their opponents. It was rarely the size of the Mongol army, but rather their unparalleled maneuverability and innovative approach, both to tactics and to psychological warfare, that allowed them to conquer with such apparent ease.

Most armies moved on foot, with cumbersome supply trains, and with various non-combat personnel in tow. Mongol armies were entirely mounted, carried nothing that would slow them down. Furthermore, they would bring with them multiple extra mounts which could be exchanged during battle, allowing them to maintain their nearly peak maneuverability. Beyond this, Mongol soldiers quite literally grew up in the saddle and were thus capable of a degree of mounted endurance simply beyond the reach of persons from sedentary societies. Furthermore, they engaged primarily from range. Their capability for highly maneuverable, ranged combat allowed them to effective engage numerically superior enemy forces while largely denying them the ability to effectively retaliate. Mongol armies would often wear down opposing armies to the point of physical exhaustion before moving in for the 'kill'.

All in all, their nomadic way of life, the harsh conditions of their habitat, and a combination of specific social features allowed them to effectively crush armies far larger than themselves. Mongolia, even in the time of Genghis Khan, was sparsely populated.

He started out with 25000 "ethnic mongolians," up to maybe 75000-80000 altogether once he dominated all the other steppe nomad peoples and assimilated their troops. Mongolia at the time was maybe 3/4 of a million people, so it was significant, but not impossible to get that many troops.

Mostly they had very skilled tactics and military leadership, good spies, and clever diplomacy to bribe the military intellects whose skills they needed for certain campaigns. Subutai and other generals could do amazing things with 25000-30000 men, along with some siege engineers recruited from China, etc. When your "state apparatus" is highly mobile, and capable of living off the land, like Genghis Khan, and your enemy is sedentary with cities and fields that need defending, you can dominate them with a far smaller number of men

An article was just published that found that according to tree rings, there was a stretch of extremely good weather for about 15 years not seen before or since, that coincided with Genghis Khans reign, contributed to a boom of war horses and other livestock giving them that extra boost. http://www.belfasttelegraph.co.uk/breakingnews/offbeat/weather-boosted-mongol-empire-30079703.html

I apologize this doesnt directly answer but I figured youd find it interesting.