How does bastard feudalism allow bannermen to have more troops then the obligation to supply troops? I mean that money is what was being used to train and equip the troops being supplied so how does that translate to more troops? is it just that they have more troops under their direct command but not really more overall? Also if the money is instead of obligation to supply troops, shouldnt the king also have more troops because the money goes to him?

1. To quote an earlier post:

Under the normal rules of feudalism, military capabilities were limited by the terms of the feudal agreement – you get so much land, you agree to raise so many men, the number of men per unit of land is fairly standardized – and it was hard to alter that, because the vassals’ vassals know their rights in law and get pretty litigious about it.

It’s really more when you get to what’s known as “bastard feudalism” that things start to go off the rails. Under bastard feudalism, instead of relying on those feudal agreements to raise soldiers, you convert military service obligations into taxes paid in cash and then use the cash to put fighting men on the payroll, who wear your livery and are counted as members of your “affinity.”  So now you have a system where noblemen can raise and maintain private military forces above and beyond their feudal rights – and the only limit to how many of these guys you have on the payroll is your ability to make payroll on the first of the month.

By way of an analogy, traditional feudalism conceives the relationship of lord and soldier as an ongoing contractor-client relationship with terms that are fixed by written agreement and tradition. Bastard feudalism reconceived the relationship as one between an employer and a salaried, uniformed employee, which allowed the terms to be dictated by the means of the employer and the current conditions of the military labor market. 

2. Members of an affinity were paid in cash, not in land, so while a noble only had a certain amount of land to give away to make up knight’s fees, if they could improve the productivity of their estate, then they could employ more men per acre of land then they had in the past.

3. The money doesn’t all go to the king. What makes you a noble is the right to extract rent and taxes from a given area of land, a portion of which you’re supposed to kick up to the king and the rest you get to keep. And if you were a powerful nobleman with a big private army, you might be able to get away with not paying your taxes, especially if the king you were dealing with was weak.