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Actually, even the smaller, Balkan states were able to put together relatively large armies even in the 15th century. In the Battle of Vaslui, Stefan of Moldavia fielded an army of 40,000 Moldavians and 7,000 others against an army of 120,000 Ottomans and 20,000 Bulgarians. Who here has EVER seen Moldavia put 47,000 soldiers together? :p

I don't know that much about the Moldavian army, but I suspect that a big portion of that was either mercenaries or militia levies.

The difference in quality between professional troops and militia isn't really represented in EU3. Especially as time went on, the real limit on your ability to raise an army was your capacity to pay for either a professional standing force or a mercenary force. Manpower had little to do with it as you would often be recruiting from outside your territory anyway (rather, people would come from outside for the chance to earn the paycheck you promised). Militia could be raised to pad out your numbers, but it was often of greatly inferior quality to either professional troops or mercenaries.

Essentially, if you couldn't pay for a big, high quality army you could still raise a big, low quality army but it wouldn't stay in being for very long (peasant militias need to go back to their fields eventually).
 
When the Portuguese invaded Kongo they were faced by a vast army of (allegedly) 70,000 warriors. Even allowing for exagerration this is an order of magnitude above what can happen in the game. Same with the Aztecs who reputedly had 100,000 warriors against Cortez.

I would like to see units clearly better at different tasks though so you can tailor them to your enemy.