Unlike many rules in the NFL, where sometimes a catch isn’t a catch but a tuck is (or was) always a tuck, this one is clear: Footballs are to be inflated between 12 1/2 and 13 1/2 pounds per square inch. ESPN has reported that 11 of the 12 balls used in the first half of Sunday’s AFC championship were underinflated. Cold weather can cause a lessening of air pressure, but in 11 of 12 cases? Is weather that uniform in its effect? If so, what happened to No. 12?

The host team for the AFC championship game was New England, which in 2007 saw coach Bill Belichick fined $500,000 for his role in the video recording of an opponent’s defensive signals. (There’s also a rule against that, although Belichick claimed he wasn’t clear on what was prohibited.) The Patriots beat Indianapolis 45-7 to advance to the Super Bowl.

So there’s the scenario: Maybe the greatest coach since Lombardi leads his team to the biggest game in North American sports, only to see his team, which was caught cheating once, become the subject of an NFL investigation as to whether or not it cheated again. Holy mackerel.

It will be fascinating to see how Roger Goodell, the commissioner who has lately gotten nothing right, deals with this. As maladroit as Goodell was regarding the Ray Rice case — first he was too weak, then too strong — serving as a moral exemplar on societal issues isn’t what the NFL was founded to do.

At base, the NFL is a football league. Its charter is to stage fair and competive games. There’s reason now to wonder if the playing field for a conference championship was equal. Such a thing might happen in Italian soccer, where bribes for refs are part of a club’s operating budget, but not in our football. Or so we’d like to think.

Before Ray Rice played his first NFL game, Goodell was botching the disposition of the Patriots’ I-Spy affair. He levied fines and took away a No. 1 draft pick without viewing the incriminating tapes — Goodell is the world champ at not watching pertinent recordings — and then ordered those tapes destroyed. The late Sen. Arlen Specter, then head of the Judiciary Committee, was so incredulous that he summoned the commissioner to Capitol Hill.

“You preserve the evidence,” Specter told the Associated Press after the session, which ran 100 minutes. The Senator was then asked if he believed the NFL sought to cover up its mess. “I think there was an enormous amount of haste,” Specter said, which was Hill-speak for “Ya think?”

Belichick had won three Super Bowls when his electronic eavesdropping — he admitted it had been ongoing since 2000 — came to light. He has won none since. (Intriguing, no?) If he’s allowed to coach in this Super Bowl and his Patriots win, Belichick will be handed the Lombardi Trophy for the fourth time. That would not, however, make him a Lombardi. Earlier this year, Don Shula referred to him as “Beli-cheat.” In 2012, Baltimore’s John Harbaugh called the Patriots’ three titles “stained.” A franchise that should be esteemed for excellence is viewed as a rogue elephant.

There’s also this: The Patriots’ Robert Kraft is, after Pittsburgh’s Dan Rooney, the NFL’s most respected owner. Kraft has been a supporter of Goodell’s, who needs all the help he can get. Photographs indicate that Goodell attended a party at Kraft’s home the night before the AFC championship. No conflict of interest there, huh?

We can’t really say the NFL is in trouble — we Americans love our football too much for the NFL ever to be in real trouble — but a line must be drawn. If, over these next 10 days, his Patriots are found to have cheated (again), Belichick should be suspended for the Super Bowl and for all of next season. No, those footballs didn’t cause his team to win by 38 points, but this would be one instance where the intent trumps the result.

If we shouldn’t expect sports to teach us how to live our lives, we should at least have some assurance that our biggest sport won’t countenance serial cheating. As Sen. Specter said back in 2008: “We have the right to have honest football games.”