I think I found this study several years ago, when discussing the ratio of security forces to population necessary to win a counter-insurgency. The 2% rule (20 security forces per 1,000 people) isn't carved in stone.
I rarely felt we lacked sufficient troops to win in Iraq as I did a number of back-of-the-envelope calculations over the years, using different troop density assumptions for different regions of Iraq. Many supporters and opponents of the Iraq War relied on the "rule" and claimed we had too few troops to win and even argued the surge was way too few to win. Yet we won.
I've started to apply my same reasoning to the Afghanistan campaign and we sure look like we're in spitting distance of having enough troops to win. The above study is useful again, given the current debates.
As always, rather than debate what level of troop density to achieve in Afghanistan, I'd rather start with a conviction that we deserve to win and a decision that we will do what it takes to win for as long as we need to fight.