6 BCS league champions and 31 at large bids to schools from those leagues. 37 teams total
6 at large bids to the remaining 25 leagues. How many of the 'mid-major leagues' have a truly competitive top one or two teams??? I don't know but for arguement's sake, assume 10 of the 25 have a minimal chance of winning a game (don't tell that to Princeton!!) That leaves us with 21 mid-majors versus 37 BCS teams. Then, the NCAA matches premier mids in the 8-9 game in the first round (Butler vs ODU for example) which puts them up against a #1 seed.
The tourney is seriously flawed in the current format but fortunately the lower scholarship limits are having some effect.