If National Football League Commissioner Roger Goodell really cares about the integrity of his game, and not the protection of his own image, he will rescind the penalties assessed against the New England Patriots and its star quarterback and concede the NFL bollixed the investigation of alleged football deflation from the start.

Leaked information about the Patriots being investigated for deflating the footballs to gain an advantage during a cold, rainy evening emerged shortly after New England thrashed the Indianapolis Colts, 45-7, in the American Football Conference Championship game. A check at halftime showed under inflation of the footballs used by the Patriots.

With fully re-inflated footballs, the Patriots outscored the Colts 28-0 in the second half and quarterback Tom Brady completed 11 of his 13 passes. Football inflation had nothing to do with the lopsided victory.

Yet with scant evidence of any misconduct, the NFL allowed the silly debate over football inflation and selective prejudicial leaks to the media to dominate the two weeks leading up to its premiere event, the Super Bowl.

Subsequently, a ludicrously long and involved investigation by attorney Ted Wells — the Wells Report — used circumstantial evidence and questionable science to conclude it was “more probable than not” that Patriots personnel clandestinely deflated the game balls and that Mr. Brady was generally aware of it.

However, a new report by the independent American Enterprise Institute deflates those findings.

Its evidence, concludes AEI, “points to a simple — and innocent — explanation” as to why the Patriots footballs measured more air loss during the first half than the Colts footballs. The Patriots footballs were measured immediately, while the Colts footballs sat for most of the halftime in the warm confines of the referees’ locker room, the pressure inside them growing in accordance with physics.

“It is therefore unlikely that the Patriots deflated the footballs,” the AEI report concludes.

The report also points to confusion about which of two gauges officials used to test the footballs before the game and at halftime, gauges that produced different results; and to a lack of information about the timing of the testing.

“When the NFL hears Mr. Brady’s appeal of his suspension … it should proceed with the knowledge that the Wells report is unreliable,” wrote AEI director of economic studies Kevin Hassett and Stan A. Veuger, a resident scholar at AEI, in a guest commentary published by the New York Times.

The NFL’s case has crumbled.