The Il-Khanid dynasty of the Mongol Empire captured Iran and took the power after a nearly 40 years of war, and ruled it for 80 years (1258-1335 C / 656-736 A.H). Considering the military power and the vastness of the realm, it was one of the greatest governments in the history of Iran. However, it was also one of the most unstable of them, a battleground of domestic political crises. Therefore, because of these domestic crises, it faced its downfall while still in its apex of sovereignty. A statistical study of the Il-Khanid’s sway over Iran reveals the three influential elements in its instability and unexpected downfall: age of assuming the crown, age of dying, and the duration of kingship. This article rests only on the function of statistics in cliometrics.