Well, I have a friend who pointed out that there was no stirrup in Alexander's time, but Mongol armies had them.
Makes a big difference for cavalry, of course.
Again the problem is people are far more familiar with Alexander than Jenghis Khan or the Mongols.
To this day "Horde" is used to designate a multitude of people, when it actually was a (fairly small) Mongol military unit.
The Mongols were outnumbered in basically every battle they ever fought, often by 2 to 1 or 3 to 1. Thing is those defeated tried the PR move of exaggerating the number of Mongols to make their defeats look less bad.
One of the reasons that Genghis won was because he was so brutal to any enemy that defied him. When a city didn't open the gates, he laid siege, and when he finally got inside, he killed everyone inside, except for the women, who they raped . As a result, he didn't have to lay siege that often. He wasn't brutal because he wanted to kill people; he killed indiscriminately in certain situations because it helped him accomplish his objective.