The naming of a new executive director of the U.S. Olympic Committee is apparently imminent, and it will be a test of sincerity. Either the USOC board of directors will select a real reformer, or it will award yet another crony a seven-figure contract festooned with gilded privileges that allows them to fly premium to champagny events in five-star hotels decorated with many carats of gold leaf. In order to do ... what? What do USOC executives do, when they aren’t looking the other way on sexual abuse, and burying their faces in wine menus?

Let’s play Olympic math. It’s a fun game, because it always ends in explosions of incredulous laughter. Why does the USOC have 500-odd employees when we send just 554 athletes to the Summer Games? How come a supposed “non-profit” with revenues of $336 million gives $28 million to athletes in direct cash and assistance, and where does the rest of it go?

It would be nice if someone in Congress made the USOC’s term-limitless chairman Larry Probst answer such questions publicly, before he goes back to studying whether to order the cocotte des moules or lobster frittata. But so far, the USOC’s account of itself has been bracingly free of information and long on platitude and propaganda.

Athletes believe there is a direct relationship between the USOC’s lack of fiscal accountability and the sexual abuse scandals besetting it: at every turn previous leaders appeared to choose money over morals and seemed more preoccupied with protecting the status quo than with protecting youngsters from predators.

“The executive compensation and lavish spending without proper accountability is the root of what enables abuses,” one molested swimmer wrote to me.

These athletes want a wholesale audit and reform, because they believe that without it, without a total accounting that turns the USOC into the legitimate athlete-centered nonprofit it’s supposed to be, as opposed to the waste basket it has become, their suffering will have been for nothing.

Understand this about the USOC: It doesn’t train a single athlete. Colleges and clubs do that. It is essentially just a pass-through, a receptacle for cash that should then be funneled toward feeding, caring for and sustaining athletes in their efforts to make it to the Games. More than $293 million of its revenue comes from broadcast rights and royalties that fall in its lap because it has the word “Olympic” in its name. The USOC simply accepts its cut of the IOC’s $7.75 billion broadcast deal with NBC, as part of the “Olympic movement.”

The funny thing is, the money doesn’t really move. It gets stuck somewhere in the fat middle gut of the system. The USOC’s last tax filings show that $45 million went to USOC administrative staff wages and salaries. Another $21 million went to executive travel.

Let’s play some more Olympic math. At an Olympic Training Center cafeteria, you know what they charge an athlete to eat? Ten bucks. You know what USOC staffers pay? Five.

That sums up the entire operation: USOC staff are prioritized over the athletes they are supposed to support. This is a systemic problem. It’s not just sloppy bureaucracy. It’s indicative of an entire sinister attitude: The athletes are valued less than the functionaries.

Look more closely at the USOC’s books, and you see a pattern of misleading accounting. Much of this has been ably exposed by The Post’s Will Hobson, Howard Gleckman of the Tax Policy Center, and other analysts.

The USOC likes to counter its embarrassing numbers by claiming that “in excess of 80 percent” of revenue is devoted to its athletes through various forms of “support,” such as grants to the national governing bodies that it oversees and certifies. Let’s see. In 2016 those grants totaled $55 million. But funding an NGB is not the same as funding athletes. Much of the money just goes to more outsized executive salaries and bloated overhead. US Ski & Snowboard got $5.2 million in grant money but more than $742,000 went to former CEO Bill Marolt and $512,683 to current CEO Tiger Shaw, and that’s just two people. Track and Field’s CEO Max Siegel made $1.7 million in salary and bonuses. USA Gymnastics got about $3 million in grants, only to pay Steve Penny $628,445 in salary and another $1 million in severance, apparently as thanks for taking the Fifth Amendment before Congress over his failure to promptly report rampant sexual abuse to the police.

How is this athlete support? It’s disingenuous at best if not outright deceptive.

Let’s do some more fun Olympic math with fundraising. That’s what a nonprofit does, right, raise funds? But only about $14 million of the USOC’s money came from gifts. You know what the USOC expensed to “fundraise” that money? Ten million. Ten million to raise $14 million. In any other charity such numbers would be a scandal, if not a target of the IRS.

The USOC’s numbers simply don’t add up. It claims something close to $190 million of revenue goes to athlete “support.” Take out your calculator. Let’s say the USOC has to sustain three aspiring (Olympic and Paralympic) athletes for each one who actually makes it to the Games. That should work out to $55,000 per athlete. So why are so many of them on food stamps or working two jobs or begging money from local police stations?

The USOC is chartered by Congress and supported with hundreds of millions of windfall dollars and goodwill, and it should be one of the most excellent non-profits in the country. Instead it isn’t meeting even basic standards for operating not-for-profit. The fault for this lies with an inanimate board of directors led by Probst, that apparently has failed to exercise even cursory oversight.

Even longtime supporters of the USOC admit that something has gone badly wrong structurally and financially.

“The normal return for a not-for-profit is you spend no more than 10 percent ⅛on overhead⅜, and organizations get graded for that,” says Harvey Schiller, a former secretary general of the USOC in the 1980s and a longtime Olympic activist, who also served as a commissioner of the Southeastern Conference and on the NCAA executive committee.

The USOC needs a leader willing to undertake a wholesale audit and reassessment. Waste must be reined in; staff dramatically reduced; operations examined and streamlined; and executive pay set at sensible levels in line with not-for-profit norms. And a strong hand must be applied to make individual sport federations do the same, at peril of being decertified. Above all, it needs a leader who understands that the USOC, in and of itself, has no value, and provides no value, without athletes.

“I think you start with something which says, ‘If you only had a dollar, how would you spend it?’ “ Schiller said. “The answer is, I have to put that athlete on the starting block or in the gym at the Games.”