Post NFL editor Keith McMillan recruits a few coworkers to see if they can tell which football has been under-inflated by 2 PSI, the amount the NFL claims the New England Patriots' game balls were deflated. (Davin Coburn and Jason Aldag/The Washington Post)

Tom Brady is said to be seeking total exoneration, and it appears he’s entitled to it. The idea that Brady and the New England Patriots intentionally deflated footballs for a competitive advantage has been discredited by everyone from sidewalk chemists to Web physicists to unlicensed ceramicists, not to mention your own common sense. But most importantly, it is utterly shredded in a new scientific analysis by the American Enterprise Institute, which shows the only inflation problem is in NFL Commissioner Roger Goodell’s head.

The NFL paid millions for a fundamentally flawed report by lawyer Ted Wells that made Brady and the Patriots out to be slam-dunk guilty, based on more than 100 pages of mathematical analysis of ball pressurization . . . that turns out to be erroneous. The AEI’s report totally rejects the finding that the footballs used by the Patriots in the AFC championship game had a significant drop in air pressure compared with those used by the Colts. But the truly damning sentence is this one, buried in its erudite phrasings and equations: “The Wells report’s statistical analysis cannot be replicated by performing the analysis as described in the report,” the AEI concludes.

Basically, the math didn’t add up. It’s a standard principle in science: If you can’t replicate a set of results, then there is a problem with it. A flaw or a fraud is at work. Either you made a mistake, or you made it up.

The Post Sports Live panel weighs in on how the NFL's investigation into whether the Patriots deflated footballs before their AFC championship game against the Colts affects the team's legacy. (Post Sports Live/The Washington Post)

When the AEI analysts looked more closely at how such a mistake could have been made, what they found “astonished” them, says the report’s co-author Stan Veuger. The Wells report “relies on an unorthodox statistical procedure at odds with the methodology the report describes.” Translation: The Wells report said it would use one equation but then used a different (and weird) equation to arrive at its numbers.

“It was really clumsy,” Veuger says. “It’s the kind of mistake you’d see in freshman statistics class.”

Another phrase possibly applies to all of this:

Falsifying results.

Normally, these “special counsel” reports are airtight documents. They’re meant to give sports leagues an unshakable legal basis for discipline and protect league integrity. The report by Major League Baseball on Pete Rose’s gambling was an unassailable document of 215 pages that included 313 witnesses and seven volumes of exhibits, including bank and phone records and transcripts of interviews that made it impossible for Rose to fight his banishment. But lately the NFL has begun turning these special counsel investigations into manipulated campaigns calculated to enhance the commissioner’s profile and powers.

And they seem to be written to fit predetermined conclusions.

Twice now Goodell has ginned up false scandals that seriously and unfairly targeted individual players and damaged franchises on what turned out to be bogus or flawed evidence. Forget his bungled handling of Adrian Peterson and Ray Rice — at least those guys actually did something wrong. In the DeflateGate and BountyGate affairs, Goodell hammered people who appear to have done nothing.

After winning his fourth Super Bowl, New England Patriots quarterback Tom Brady has cemented his legacy as one of the best NFL players of all time. The Post Sports Live crew debates where he ranks among the elite. (Post Sport Live/The Washington Post)

The AEI’s entry into DeflateGate is important because the institute was a major factor in righting the Goodell-driven injustice in BountyGate back in 2012. The commissioner went all hanging judge on the New Orleans Saints, suspending several officials and players for a supposed bonuses system to injure opponents between 2009 and 2011. But then AEI analyzed injury data — something that surely the commissioner should have done. The AEI found that the Saints injured fewer opposing players than all but two teams in 2009 and all but one from 2009 to 2011. After AEI’s report was presented at an NFL hearing, the suspensions were vacated.

AEI is a conservative think tank that normally doesn’t get into sports issues. But given its experience with BountyGate, the DeflateGate case was too inviting. The discussion of ball pressurization in the Wells Report was so contested that Veuger and Kevin Hassett, AEI’s director of economic studies, decided to examine it.

“There was a lot of talk about the report not being good,” Veuger said, “and a fairly big chunk of it was stats analysis and data, and we thought, ‘We might as well look at this one and see if it holds up.’ It’s really a hobby.”

Goodell is now in a truly interesting and awkward position. In one week he will hear Brady’s appeal. He has said, “I very much look forward to hearing from Mr. Brady and to considering any new information he may bring to my attention.”

Well, here is a boatload of very inconvenient new information.

Does Goodell stand by the conclusions of the Wells report, dig in and refuse to budge — thus establishing that he’s incapable of fairly considering evidence and is a serial abuser of his powers? Does he try to parse and sidestep the AEI analysis by claiming the scientific evidence is just a small part of the case against Brady? Trouble with that is, more than half of the Wells report’s 243 pages is taken up by pressure gauges and pounds-per-square-inch analysis — all of which must be thrown out according to AEI. If the balls weren’t deflated, then what’s left? One e-mail exchange, in which Brady complained that some game balls against the New York Jets were ludicrously overinflated. Is this evidence of ill intent? Hardly. Brady’s solution to the over-inflation was to suggest the refs check the rulebook. Not the act of a cheater.

Or does Goodell do the right thing and rescind Brady’s suspension on the basis of the new info in the AEI report — thus admitting the league spent millions on a railroading farce? There is trouble for Goodell in this option, too, because it suggests the league office under Goodell’s leadership is either incapable of executing a proper investigation or unwilling to.

The AEI analysis suggests that NFL Players Association Executive Director DeMaurice Smith was right when he said the Wells report “delivered exactly what the client wanted.” It suggests that this wasn’t an investigation; it was a frame job by the commissioner’s office desperate to re-establish its authority.

Brady may or may not win his appeal. But there is one sure loser here, trapped in a box of his own making: the commissioner.