Increased retention/graduation rates. The more a school's football team wins, the more students stick around and graduate. Some call this "football chicken soup" because it gives students some comfort. Some schools' big athletic programs are matched by big academic resources, too.
Increased ranking: Academic rankings, especially in U.S. News and World Report, increase with winning football, according to studies. One reason is that the ranking is based on how peers assess your college. Football can make your school more appealing.
Increased donations/state appropriations. Multiple studies have found athletic success bumps up athletic giving and general giving to the university. Simply having a football team produced larger state appropriations for schools, on average 6 percent higher.
Increased licensing/branding. Boise State, for example, went from $210,000 in royalties before the 2007 Fiesta Bowl to more than $1 million last year.
Giving back. The profits of winning football programs help provide non-athletic scholarship funding, new buildings and other upgrades.
Degree completion programs. Former student-athletes can return to their colleges and attend tuition-free. These programs are funded through sports-related revenues.
Negative correlations. Athletics, and football, can be the most visible part of a university. Unfortunately, that's not always a good thing. The most notorious example occurred at (SMU), where the football program received the NCAA "death penalty" because of major violations. Applications fell, but later rebounded. Sometimes football is not the most efficient, cost-effective way for a university to achieve its athletic goals.