A lot of people talk about certain QBs being good game managers. I hear that a lot about Brees and some Gusketeers also like to claim that he was a good game manager. I think that, in most cases, that is just someone's way of pumping up a guy they like on the basis of some intangible that cannot be verified or disproven. Let's face it, with the exception of occasional audibles, the coaches call the plays. Most of what people refer to as game management is really a reflection of the plays called by the coaches, not anything the QB has done.
That said, I think there is some QB "game management" in the way the guy plays on 3rd and 4th down. "Managing the game" basically boils down to how well the QB keeps the chains moving, which basically boils down to converting 3rd and 4th downs. Avoiding turnovers is another aspect of game management.
I was only able to find stats for this for the past 2 seasons. Gus supporters claim he was a good game manager last year, but he converted only 50/160 third and 4th downs last year, which comes out to 31.25%.
Over the last 2 seasons, Brees has converted 121 of 264 3rd and 4th downs, which is 45.8%. Culpepper has converted 98/196 (50%). Tom Brady, the poster child for "game managment," converted 45.1% (122/270). Payton Manning converted 119 of 238 (50%). These numbers do not include plays in which the QB ran for a 1st down on 3rd or 4th down.