The problem with the NCAA’s sanctions against Penn State isn’t that they punish student-athletes who had no role in the cover-up of Jerry Sandusky’s sexual abuse of boys.

It’s not that they are meaningless, “reversing” past victories that took place on the field, or that they are too harsh, damaging Penn State’s football program even after the death of former coach Joe Paterno.

The problem is much more basic: The punishment bears no meaningful relationship to the crime.

Punishment is generally thought to have one or more of three purposes: retribution, deterrence and prevention. The NCAA’s sanctions don’t credibly accomplish any of these goals.

Retribution might not be the right job for the NCAA, which, despite its pretensions, is neither God nor an organ of the government.

Suppose, however, that the true goal of the sanctions is to help right the moral wrong of the Sandusky cover-up by punishing the malefactors.

Because money doesn’t have that sort of profound weight, the moral piece of the sanctions must surely be the reversal of Penn State’s football victories since 1998.

The trouble is that it is almost impossible to say Penn State’s football victories were a result of the cover-up. Had Paterno’s teams lost most of their games instead of winning them, Sandusky would have acted just as he did; and it is safe to presume that Paterno and the rest of the university would have shown just as much willful blindness to Sandusky’s wrongdoing. It is difficult to see how punishment could be morally satisfying when it is so disconnected from the action being punished.

At most, one might say the cover-up was a product of a win-at-all-costs philosophy. But when one considers Paterno’s relatively strong record of ensuring that his athletes graduated and the absence of recruitment cheating in Penn State’s football history, it becomes clear that Paterno didn’t, in fact, believe in winning at all costs.

It is difficult to plumb the depths of his thinking in letting Sandusky continue his crimes. Nevertheless, it seems safe to assume that Paterno allowed his subordinate to get away with it because Paterno himself wanted to avoid embarrassment — and perhaps because he didn’t want the shame to tarnish the reputation of the program.

No doubt he felt shame himself; perhaps this contributed to his own moral error of denial and cover-up.

Deterrence is quickly dispensed with, too. The $60 million fine represents about one year of football revenue. Once the money is recouped, Penn State football can be back in business. As my former teacher Stephen L. Carter points out, if deterrence were the goal, the sanctions should have been much greater.

That leaves prevention, and here the NCAA sanctions look even more inapposite. What, really, would prevent Penn State — or any other major college sports program — from finding itself in this situation again?

The answer is obvious: Change the power structure that makes a football or basketball coach the most important and influential person in the university. At bottom, what allowed the Penn State scandal to occur wasn’t human frailty, but the de facto independence and control exercised by Paterno relative to the rest of the university. He didn’t report what was going on because, quite simply, he knew that he didn’t have to. If rumors reached the university’s administration, as it seems they did, Paterno knew the university could not and would not act against him.

Could the NCAA change this power structure? You bet it could. It could require that coaches be paid no more than, say, the highest paid professor at the university. (Suppress your gasps, please. I know it sounds un- American.) Wouldn’t that lead the best college coaches to go pro? Yes, it probably would — and that would be a good thing.

In the corporate world of the NFL and the NBA, the coach is just one important employee in the organization — and not the most important or the highest paid.

The consequence is that few professional coaches are surrounded by the cult of personality that we know so well from college sports. (Quick, how many current NFL coaches can you name other than your home team’s?)

Those professional coaches who do have a cult either profess a philosophy of Zen minimalism, a la Phil Jackson, late of the Los Angeles Lakers, or are so fanatically competitive that they are hated and loved in equal parts, like Bill Belichick, of the New England Patriots.

Make no mistake about it: The cult of the coach is the problem. It is heart-warming that, in the United States, the title coach has some of the same honorific qualities as pastor, doctor or president. But the most famous and prominent college coaches cannot be expected to behave responsibly when their institutional power is essentially absolute.

When the university president is an unknown compared with his or her coach, is paid far less and doesn’t enjoy the same charismatic authority in the eyes of the alumni, there is no realistic way for the president to supervise that coach or his (and it is almost always his) program. The corruption of the incorruptible Paterno is a story of the absence of any structural check on his authority.

So why doesn’t the NCAA change this? Because the coach’s cult is good for business. College athletes play for a maximum of four years, and the best football and basketball players generally don’t stay that long.

This is barely enough time to get them nationally known.

Rivalries between colleges can be branded, of course — but as any marketer knows, personalities sell better than abstract brands. The coaches are a crucial part of the product.

That is a part of why the coaches make the big bucks.

And in America, a high salary is a part of celebrity.

This vicious cycle should end. There are, of course, some cult coaches with sterling reputations. But

remember: Until a year ago, Paterno was one of them.

Noah Feldman, a law professor at Harvard University and the author of “Scorpions: The Battles and Triumphs of FDR’s Great Supreme Court Justices,” is a Bloomberg View columnist.