How Many Do We Need?

Has anyone done an actual analysis of how many troops are needed in Afghanistan?  My impression is that the majority of Afghanistan's population is not provided security by the coalition.  

I know for that for counterinsurgencies, a historically successful ratio of troops to population is around 1:20.  For Afghanistan, that would imply 500,000 troops.  We have a tiny fraction of that.  But that's just an extrapolation of history, it doesn't take into account the actual situation in Afghanistan.  Perhaps only part of the country needs a 1:20 ratio.  Maybe some parts will be fine with 1:100, or 1:1000.  I don't know.  

It should be possible for a military planner to map out the number of troops required to provide security for all of Afghanistan.  Someone should get on that.