Garrison assignments after capturing a town/castle

[jdm311]

I'm currently a marshal of the North and at war with the Iron Islands. I have about 400 troops. I assembled the Lords and their armies (roughly 2000 troops) and took Pyke and Lordsport, declining the option to ask for both of them as rewards. The garrison was then set to 12 and 15 troops, respectively. So I am waiting around for the Paramount to assign them to somebody so they can add to the garrison and prevent them from being easily taken from the lurking Ironmen. From prior experience of being summoned by the marshal and conquering a town or castle, there is usually many more troops garrisoned, like ~ 60-200. My question is: what factors are involved in calculating how many troops are garrisoned? Why is it so low for me? I believe if I ask for it as a reward, I can take the risk of supplying my own troops to the garrison, but in the chance that I do not get the fief, would lose those troops. It would be seriously costly to do that for every castle/town on my currently ambitious campaign.