If you watch college football or basketball on television, chances are you’ve seen the ad: a men’s tennis player strokes a forehand, then morphs into a construction engineer in a hard hat. As a woman emerges from water-polo practice, her swimsuit changes into photojournalist togs.

“There are over 400,000 NCAA student-athletes,” a voice intones, “and just about all of us will be going pro in something other than sports.”

In other words: For all the expensive hoopla over football and men’s basketball — and for all their scandals — the NCAA wants you to know that most student-athletes compete in joyful obscurity and really are scholars as well as jocks.

So how come the University of Maryland is about to dump eight intercollegiate athletic teams, including, yes, men’s tennis and women’s water polo?

Despite the televised exploits of Terrapin football and men’s basketball, the athletic department at College Park has run millions of dollars in deficits for five years. Something had to give, so university President Wallace D. Loh accepted a commission’s recommendation to cut the teams. Together with administrative savings, this should reduce the athletic budget by about $5 million next year.

What we have here is a case study in the true priorities of big NCAA member institutions. Some teams on the chopping block are bastions of the student-athlete ideal at College Park. Except for men’s tennis, they have some of the Maryland athletic program’s highest graduation rates — 90 percent for men’s cross-country and track, according to an October NCAA report.

Fewer than half of the Maryland men’s basketball players and fewer than 60 percent of football players graduate, embarrassing a university that prides itself on high academic standards.

But these are “revenue sports”; their income, much of it from TV, subsidizes all the other sports. Alumni love them, too.

So they were spared, even though they also account for the vast bulk of the athletic department’s costs, in the form of the football team’s 85 scholarships, head football Coach Randy Edsall’s $2 million salary and men’s basketball Coach Mark Turgeon’s $1.9 million annual pay.

The justification for these salaries and scholarships is that you can’t make money unless you win, and you can’t win unless you pay for the best coaching and playing talent. Yet revenue from men’s basketball and football has been declining for years, mirroring the teams’ declining win-loss records — which is the main reason for the cutbacks to the likes of track and water polo.

An alternative strategy might be to reduce the “revenue” programs to a more human scale — say, the lower-budget approach of the academically excellent schools, such as the Naval Academy and Bucknell, that participate in the Patriot League. There’s no law that says Maryland, or any other school, has to play in the Atlantic Coast Conference.

In accepting the cuts, Loh acknowledged that “the current business model of intercollegiate athletics nationwide is inequitable and unsustainable.” He promised to “work with the ACC, the NCAA . . . to reset the balance between academics and big-time athletics in higher education.”

Meanwhile, however, Loh has been urging expansion of the ACC because of the potential “positive financial impact on every member school due to anticipated increases in television revenue.” See you at the Final Four!

In short, Maryland is doubling down on the big-time athletic paradigm — and all the tensions between that model and the academic mission of the university — in the hopes that better days are coming for its prestige sports.

The closest that anyone at College Park came to thinking outside this box was the university Senate executive committee’s mild observation that “the criteria used in selecting the teams for discontinuation did not specifically consider the academic achievements of the students.” Now that’s speaking truth to power.

The ideal of the scholar-athlete is an ancient and beautiful cultural norm, inherited from the Greeks and epitomized in our time by such people as Byron R. White and Alan Page, football heroes who went on to become justices of the U.S. and Minnesota Supreme Courts, respectively. Alas, your tickets to college football and basketball no longer underwrite that ideal.

There are alternatives. Maryland offered track, water polo and the other imperiled teams one shot at survival: If they raise eight years’ worth of operating expenses — about $30 million — between now and June, they can stay.

It’s a tall order. But donating to these beleaguered student-athletes would do more than support a good cause — it would also register a protest against the warped priorities that prevail at too many institutions of higher education.