However, the coach's salary is typically paid out of the athletic revenue stream, not directly from state funds, which makes it a bit of a moot point.
(Note: To the best of my knowledge (which isn't much) this holds for Univ. of TN, Univ. of AL, and Univ. of WI. It's probably different at many other schools.)
Of course, all that having been said, the popular sports entirely fund all of the less popular, but still very meaningful athletic programs. There's also a _lot_ to be said for the secondary effects of having a popular sports team on the overall prestige and income of a university.
However, I know some very smart people who did actually choose their undergraduate program based partly on the football team.
Expensive marketing.
when you buy a pop out of the machine, what fraction of what your paying for is raw material + production cost and what percentage is so the can pay for superbowl ads so the next time you're thirsty their brand is the first the pops into your head?
In my case I said no to a top 10 engineering undergraduate school offering some scholarship and yes to the University of Alabama which was my grandad/dad's alma mater and thus our football team, an in-state school with cheaper tuition offering a lot of scholarship, and not Auburn University which had a slightly better engineering program rank but were UofA rivals. Had a _great_ uni experience and would make the same choice every time.
Had no trouble getting a job in a large company as a kernel developer straight from uni. Sure maybe doing MIT or Stanford I could have been a HVT for ~Google or I would have been in an impromptu startup by junior year.. but those student ticket prices!!!
Roll Tide. Still fly back a few times per season to go to games.
A quick look for historical data failed, but if you can find the data, the big shift should have occurred with the class matriculating in 1994±1.
Correlation is not causation, but it's not implausible that notability in athletics can have sympathetic effects for funding and student quality.
If only there were a daily 'Science' section in the newspaper to go alongside 'Sports'....
scholarships are counted at the full tuition rate
its obvious that the marginal cost of educating 80 some football players isn't 0, but its not obvious that its the full tuition rate
a sizeable chunk of students are offered some sort of financial package to attend a university,
some non zero percentage of football players come from low income situations such that it is unlikely they would be paying full tuition sans the scholarship
also a dispropotionate number of scholarship athletes are from out of state, if they disappear its unlikely that the replacement 80 some students would be paying as much out of state tuition
However, alumni donations are often strongly correlated to the performance of the sports teams (at universities with traditions of popular sports teams, anyway). Donations are a non-trivial part of a university's income stream.
Also, a prestigious sports team can definitely boost undergraduate enrollment. It's effective advertising, as several people have pointed out.
From an academic standpoint, I've seen the bad side of popular sports teams (_Heavy_ pressure on professors and TA's to give star players high grades despite a complete lack of attendance.). I personally feel like most (particularly in the southeast US) of the large schools with popular sports teams have absolutely awful undergraduate programs. That's partly just a function of being a large university, though.
There are certainly negatives along with the positives.