No matter how you rate basketball players at big-time sports schools as “students” — critics say their full-time athletic endeavors often leave little time for anything but watered-down degrees at best — there is no doubting their excellence as sneaker salesmen. We are not talking about a crummy part-time summer job. Many millions of dollars are riding on their talents.

Among the scandals reported last week was one based on an FBI investigation into corrupt recruiting practices at major basketball programs. In this case, an Adidas executive and college staffers at several schools allegedly conspired to funnel money to recruits and their families, $100,000 in one instance, to entice them to enroll at schools where Adidas had an exclusive deal to provide shoes. Many schools are said to have such arrangements with companies. The manufacturers gain exposure that influences fans who buy their wares.

The University of Louisville, which has a stunning 10-year, $160 million sponsorship deal with Adidas, was rocked by what the FBI has disclosed thus far. Its athletic director was put on paid leave, and basketball coach Rick Pitino, who made an eye-popping $7.7 million annually for producing winning teams, and reportedly received the vast majority of the Adidas money on top of that, was “effectively fired.” There’s so much money floating through Louisville that an assistant coach — an ace recruiter — reportedly makes $550,000, more than three times what Kentucky’s governor earned in 2016. Not to overly focus on Louisville, but the school was also rocked when basketball program staffers were accused in the past of paying for prostitutes for players and recruits. Pitino has said he knew nothing about any of this. Close watchers of a basketball scene dominated by control-freak coaches scoff at the assertion.

The reaction from the sports world, among reporters, columnists and their sources, is that similar payments to recruits are widespread and well-known. The assertion that “everyone” knows about them is especially disheartening, along with the view that the NCAA turns a blind eye to serious matters while investigating small infractions with the doggedness of Les Miserable’s Inspector Javert.

But who would really want to blow the whistle on a rotten system? There’s money for all. March Madness TV rights earn over $1 billion a year from the networks. The NCAA says 90 percent of that revenue goes into programs for college athletes, but one sports columnist mocked that claim, saying they get leftovers after the money pays for grandiose buildings, coaches’ inflated salaries, etc.

These numbers represent a grotesque distortion of priorities. Decades ago, college presidents who were national leaders instead of top fundraisers might have stepped in, but that sort of fortitude seems lost. It’s unfortunate that they would never do something unconventional, such as end the unseemly partnerships with shoe companies, or share the bounty with the likes of English and philosophy departments. Or, more to the point of education, share a good portion of the wealth for scholarships for minority students recruited for their grades, rather than shooting percentage.

No, that will not happen, and schools will continue to insist that players are amateurs and cannot be paid. Unless, as revealed by the FBI, they are.