If you’re not an American football fan, think of this as a story of a $13 billion company that can’t get its head around basic science.

Fans are all too aware of the multi-year battle—with an estimated joint cost of $20 million—between the National Football League (NFL) and a marquee player, Tom Brady of New England Patriots. In 2015, an NFL investigation found it was “more probable than not” that Brady was ”generally aware” of supposed efforts to deflate footballs below league-sanctioned levels in an effort to make it easier to grip, though whether that would even help is disputed.

The league suspended Brady for four games, and Brady sued, backed by the player’s union. He won a district court ruling, then lost on appeal before three judges on the 2nd Circuit; this week he asked for a hearing where all the judges in the court would consider his case.

On May 24, a group of 21 scientists and engineers at major American universities weighed in on the legal battle uninvited, filing a friend-of-the-court brief (pdf) to back Brady’s request for a hearing. They say that the NFL’s science is deeply flawed and that “courts should not be powerless to consider the absence of scientific proof when a proceeding is so interlaced with laws of science.”

The case against Brady consists of two parts: One, the league’s contention that the footballs couldn’t reach their state of deflation naturally, and two, circumstantial evidence garnered from text messages and interviews that could be read as a competitor obsessed with the state of his equipment, or a conspiracy to cheat.

I should disclose that I’m a Brady fan, and I don’t believe the circumstantial evidence is compelling. You don’t have to agree with me! But you should listen to these scientists: The level of football deflation Brady is accused of promoting is not only natural, but common at NFL games.

We are talking about the Ideal Gas law. As temperatures fall, as they do in late-season NFL games, the pressure of the air inside the football is also reduced. This is “natural, inevitable, and not subject to debate,” the brief says. The scientists point out that even the NFL concedes that footballs deflate naturally. But they believe that Brady is responsible for some unspecified further amount of deflation.

The scientists think this also makes very little sense. The NFL is assigning Brady blame for some additional amount of deflation, but the pressure ranges the league cites are within the margin of error of the tools the NFL used to measure the pressure on the football, that is, between .14 and .53 pounds per square inch.

“We provide this analysis to explain what the ‘science’ used by the league is not,” they write in their brief. “It most assuredly is not scientific proof that the Patriots’ footballs lost pressure beyond the drop caused naturally by the Ideal Gas Law.”

Consider this further bit of analysis. The scientists gathered temperature data for more than 10,000 NFL outdoor games since 1960. They assumed a locker-room temperature of 70 degrees Fahrenheit and that footballs were inflated to 13 pounds per square inch of pressure ahead of each game, and found that 61% of games would have been played in temperatures that would lead to “deflated” footballs as judged by the NFL.

Data collected by the scientists and engineers shows a long history of NFL deflation.

So not only can the NFL not put its finger on what exactly Brady is responsible for, what he’s accused of is common.

Of course, it’s not as if the NFL has a strong record on scientific comprehension, underscored by the latest news about its clumsy efforts to skew a government panel investigating brain damage resulting from football. In the Brady case, its scientific analysis comes from a consulting firm called Exponent, which infamously found that second-hand smoke doesn’t cause cancer when working on behalf of tobacco companies. The NFL paid $2.5 million to attorney Ted Wells to investigate Brady; it’s not clear how much Wells paid Exponent.

Even if you don’t like Tom Brady or care about the NFL, hopefully you can sympathize with the scientists’ and engineers’ “professional conviction that scientific principles be explained and put to fair use”—and not be up for sale.