If you are a "math guy" and you also understand the concept of statistical significance, standard deviation, and the law of large numbers, here is a thesis research study that recorded every team in the FBS and their complete recruiting class for
12 years. Specifically, they recorded the number of 5, 4, 3, and 2 star recruits for each year for every FBS school. They also recorded wins, losses, conference championships, bowl appearances, conference standings at the end of the season, and conference wins and losses for each team. The data was obtained from The ESPN Encyclopedia of College Football and online resources such as athletic department websites. Even when controlling for between school heterogeneity within the same conference (too complex to explain here, but they controlled for some of the variables you mentioned), the results were still statistically and economically significant.
http://www.econ.ohio-state.edu/trevon/pdf/Bergmen_Logan.pdf