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)

Roger Goodell can restore a sense of loftiness to the NFL commissioner’s office with a simple expedited decision. He should lift the suspension on Tom Brady this week and turn his disciplinary eye on the vague, sloppily enforced league rules that caused DeflateGate in the first place. This is his best way out of this infernal case, which is as damaging to Goodell and the league office as it is to Brady and the New England Patriots.

Goodell is due to receive briefs in Brady’s appeal of his four-game suspension this week, but that’s not what is holding up a decision. DeflateGate has become such a highly politicized affair that it’s difficult for Goodell to reach a verdict that won’t undermine his office. If Goodell lifts the suspension, he implicitly casts aspersions on the work he assigned Ted Wells, the league’s legal-partner-investigator whose report cost $5 million and yet contained flawed scientific analysis and inconsistencies. But if he leaves the suspension in place, it will be an obvious abuse of power based on highly questionable evidence and Brady will sue, aided by the NFL Players Association, to strip the commissioner of his disciplinary powers for lacking fairness and neutrality.

Do you see a negotiated peace between those two options? I don’t. But there is a third way out of this mess, if Goodell has the insight to find it and to take it. The beauty of this third way is that it’s based in the truth. He can rule that there simply isn’t enough evidence to make a fair decision and decline to assign blame. He should instead declare that the primary lack of integrity in this situation rested not with Brady or Wells, but with the NFL’s lax protocols governing the game balls.

Goodell can legitimately say that it is impossible for him to evaluate “the preponderance of evidence” for the simple reason that there is none. The referees at the AFC championship game failed to write any of their pregame ball measurements down. This single but crucial fact tends to go unmentioned in all of the argument over pounds per square inch and the Ideal Gas Law. The intellectual skirmishing over results by the science by consultant Exponent that cannot be replicated, the armchair analysis by everyone from statisticians at the American Enterprise Institute to weathermen?

All of their numbers are guesses.

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)

Each team provided 12 game balls, and it was referee Walt Anderson’s job to check that they were pressurized according to the rulebook that circumscribes inflation levels of anywhere from 12.5 to 13.5 psi. According to his best recollection, he recalls the Patriots’ balls were somewhere around the 12.5 level, while the Indianapolis Colts’ balls were at 13.5. He thinks.

Why not double-check, you ask?

Because he didn’t write anything down.

Here is where this entire affair begins to smell so bad that you need an atomizer to clear the air. Despite this uncertainty, a “league source” the following day leaked a false and highly prejudicial report to ESPN that 11 of 12 footballs were more than two pounds under pressure. The story was wildly incorrect and irrevocably poisoned the well for the Patriots, yet the supposedly neutral commissioner never bothered to correct it. He then ratcheted the whole thing up further by hiring Wells to launch a million-dollar investigation.

The trouble is, the Wells report was never going to get past the lack of accurate or even measurable data. Referee Anderson also recalls that two gauges were available, one of which gave higher readings. Which one did he use? He thinks he used the higher one — but he didn’t write that down either. Now, it would have been really, really good if he had written those things down. Because if he had, everything that comes after in the Wells report wouldn’t be just projection and guesswork.

The NFL can’t know the meaning of measurements at halftime, and whether they showed the footballs were irregularly deflated, if there is no way to know for certain what they were at the start. Or what the temperatures were in the rooms in which they were measured. How hot or cold was it — a crucial factor in measuring the effect of the ideal gas law? Not written down either.

It’s not Wells’s fault that he was assigned the job of writing a scientific report based on no data. As physicist-blogger Drew Fustin observes, to call something scientifically certain, “I’d expect to have the pre-game measurements carefully recorded, along with the room temperature at the time of the recording,” he writes. Also the atmospheric pressure, and the relative humidity. For instance, if Exponent projected that the temp in a room was 70 degrees, that might be reasonable. Unless there were a dozen people crowded in it.

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)

The inability to say whether the balls were tampered with renders all of the other evidence, such as phone calls, open to interpretation. Wells has tried to argue that text messages between Brady and equipment managers are “direct evidence and inculpatory,” but that’s nonsense. The NFL’s own rules allow quarterbacks from each team to choose and massage balls to their liking and to tell equipment managers how much to inflate them. There are no messages in which Brady directs that footballs be set at illegal levels. In fact, according to the Wells report, at one point Brady instructed the managers to show the rulebook to refs who had overinflated some game balls.

Based on this, Goodell is expected to render certainty? He should refuse to do it. His own reputation as well as the authority depends on his ability to put fairness above office politics. His proper focus should be on improving league protocols, not reading unintelligible gas equations based on blanks.

League officials, not the teams, should be in charge preparing one set of game balls, with the pressure and game conditions carefully noted. And they should use regulation gauges that are coherently calibrated, not tire gauges from the trunks of their cars.

Goodell’s predecessors Paul Tagliabue and Pete Rozelle were certainly conflicted and engaged in infighting, but when it came to disciplinary matters, they were able to preserve the idea that they hovered a foot above the fray. All good commissioners do. Goodell has lowered himself in DeflateGate, ironically over a matter of air. The only way to put some loft back into his office is with a speedy, fair dismissal.