NEW YORK — Every time the National Football League does something dumb, which is often, a lot of people call for Congress to revoke its tax exemption.

Pro football teams are for-profit companies that pay taxes, as the NFL likes to reiterate. But the league office itself is classified as a 501(c)(6) nonprofit organization, along the lines of the U.S. Chamber of Commerce. You can argue about whether that exemption should apply to the NFL, but it quite specifically does.

The more interesting question is why the NFL wants to remain tax exempt.

The league office loses money in a typical year. So it wouldn’t pay taxes anyway, and the exemption doesn’t save any money. The exemption also requires the NFL to make a lot of disclosures – like the comically immoderate salary of Commissioner Roger Goodell, last reported at $44 million for 2012 – that it would probably prefer to keep private. And every time an NFL player does something terrible, the league’s favorable tax treatment creates an added distraction, agitates Congress and causes journalists to write commentaries like this one, only angrier.

So why not give up the exemption voluntarily, as Major League Baseball did in 2007? Especially since MLB has said that its transition was “tax neutral”?

That’s a mystery, even to economists who have studied the league. But here are two possibilities, which I’ll try to keep un-boring.

• First, the league’s primary business these days is no longer football, it’s financing. In 1999, the NFL started a loan program to help teams pay for new stadiums or upgrade existing ones. About half the stadiums built in the past two decades have benefited from the program, which the league has used to offer loans on hugely advantageous terms. Loans, in fact, make up most of what the league office now does: Seventy percent of its assets are loans receivable, notes John Vrooman, a sports economist at Vanderbilt University, and 76 percent of its liabilities are loans payable to third parties.

“It is not altogether clear that the tax-exempt status gives the league an additional advantage in the credit market, but it sure looks that way,” Vrooman told me. “This seems to be the only real financial reason for the NFL league office to keep its tax-exempt status in the face of now-troubling PR.”

If its exemption was revoked, the league could also be on the hook for a lot of income related to the stadium-loan program without being able to take deductions for costs that were incurred while it was still a nonprofit.

• The second possibility is a little more complicated. (I’m indebted to Jeffrey Tenenbaum of Venable LLP and Roger Colinvaux of Catholic University for help in figuring it out.) All 32 NFL teams pay dues and assessments to the league office each year. In 2012, they totaled about $10.2 million per team, according to the league’s Form 990.

Those dues are tax-deductible. To the extent the NFL doesn’t spend them immediately to benefit its members, teams are able to deduct business expenses sooner than they otherwise could. And if the league office used the money from dues for capital improvements – say, for facilities upgrades – a team could then convert what might have been its own capital expenditure (which can’t be deducted immediately) into a business expense (which can be). If the league lost its exemption, both those benefits would evaporate.

In other words, it looks like the primary beneficiaries of the NFL’s tax exemption are, in fact, the teams – those wildly profitable private enterprises that the NFL insists pay their fair share to the tax man. So when the league’s lawyers say things like “None of the NFL’s profits escape tax by virtue of the league office’s tax exemption,” this is true insofar as you share their definition of words like “none,” “profits,” “escape,” “tax” and “virtue.”

Exactly how much those tax advantages are worth to teams is impossible to determine without seeing their books. But it’s fair to say they’re worth all the aggravation, misunderstandings and calamitous publicity the exemption episodically causes. Otherwise the league would drop it. That’s one kind of cost-benefit analysis the NFL is actually pretty good at.

— The Washington Post News Service with Bloomberg News