What drives me nuts about this residual force stuff, aside from how arbitrary it is, is that there's never any thought to exactly what these 50,000 should do. Basically, as the violence rages around them they're supposed to sit there to ensure that... there isn't even more violence raging around them. But it isn't really enough people to actually intervene, especially given that not even close to that many would be combat troops.
Forget what the hell the mission is besides intimidating the neighbors and the always friendly and pliable Baghdad central government. The reason why all the residual force levels are clustering around 50,000 is simple: that is what the US can support. The Congressional Budget Office looked into what a sustainable occupation looked like in 2003 and its conclusion is simple:
After the winter of 2004-2005, the United States could sustain--indefinitely, if need be--an occupation force of 38,000 to 64,000 military personnel using only combat units from the Army's active component (and some support units from the reserves), the option that constitutes the base case in this analysis. With a force of that size, the occupation would cost $8 billion to $12 billion per year, CBO estimates [emphasis mine]
Another stupid answer to a stupid question
'Cause we can!