Were Teutonic Knights even there? Some while back, this was discussed on TMP and the source(s) quoted said "Not". The Teutonic presence was a much later interpolation. There is nothing from the period of 1241 showing their inclusion in the polish army.
Mongols have their "fanboys" just like the other "Killer Elite" armies of the ancmed period. I would rate these (by popularity) as follows:
Japanese Samurai
Alexander the Great's army
Mongols
Seleucid-Macedonian successor states armies
Romans, Imperial first, Republican second
Ottomans
English armies of the HYW
Swiss (pushing the limits of "ancmed" a bit)
Crusader Military Orders (pick your fav)
Vikings
Normans
I'm only listing what comes immediately to mind, and of course it is my opinion on the relative order of popularity.
Vis-a-vis Mongols, since the OP is about them:
As the article notes, much about them is not unique, but typical of Steppes "Turkish" armies. The true invincibility of the Mongol invasions was the core thinking or "world outlook". This can possibly only show up on the wargames table as better morale, even a lot better morale, than anyone else. Tactics were identical to other Steppes armies. Mongols arguably had more heavily armed troops than other typical Steppes armies. But only the "fanboys" would push for "40%"!
There wasn't anything special about the "heavy" composite bow used by the Mongols and their adherents. All such bows were the standard missile weapons of Eurasian, nomadic horsed archers. Like all bow using nations, an upper c. ten percent of archers would/could pull a stronger bow than the line troops average. I favor the theory that such troops were especially recruited into the elite "guard" or household units of the Mongol rulers.