Cursed Platypus
Unwanted
They got pretty much humiliated as soon as they met an actual western power (austria), and Autria was busy fighting other stronger powers such as France. Ottoman were mostly seen as a nuisance poking from the east.
Also, even while outnumbering their oponent 3 to 1, they would get defeated or only obtain pyrrhic victories (against minor power like albania, serbia and such), which tells a lot about the quality of their soldiers and tactics.
And it's pretty easy to muster massive, badly equipped armies of levies, except they will suck and won't stand a chance against professional European armies.
My point still stands about the reliance on number over quality.
Battle of Nicopolis 1396, Ottoman force of around 15k beats crusader armies of around 16k with about 10k French knights and other troops. France not western enough for you?
That's about it. The failed nicopolis crusade at the end of the 14th century, which was more a completely unbalanced force (by western standards) of young overenthusiastic knights blindly charging into the enemy lines, in a similar fashion to the battles of Agincour, Crecy or other Battles in the 100 year war.