Late Monday evening, a few hours after the NFL announced punishments for the New England Patriots and quarterback Tom Brady stemming from allegations of improperly deflated footballs, team owner Robert Kraft issued a statement criticizing commissioner Roger Goodell’s decision to suspend Brady, fine the club, and take away draft picks.

The punishment, Kraft complained, “was based completely on circumstantial rather than hard or conclusive evidence.”

Kraft’s legalistic defense echoed previous attacks of Ted Wells’s report for its lack of direct evidence, and the criticism apparently stung the author. In a Tuesday afternoon conference call, Wells, the lawyer the league hired to investigate DeflateGate, disagreed with Kraft, and said incriminating text messages between two Pats employees constitute direct evidence of a conspiracy to let the air out of balls so they’d be more to Brady’s liking.

The underlying premise of this argument between Kraft and Wells is that circumstantial evidence is too weak to support penalties like suspensions, fines and docked draft picks. Legally, this premise is kind of ridiculous. Much harsher punishments than what Brady and the Patriots face — like prison sentences — are often decided solely on circumstantial evidence. Kraft needn’t look far for an example; he testified recently in a murder trial that ended with a conviction, and all of the evidence against former Patriots tight end Aaron Hernandez was circumstantial.

“People are punished all the time based on circumstantial evidence,” said Brad Snyder, a visiting professor at Georgetown Law School. “It just depends on how reliable that evidence is.”

Direct evidence — something which, if true, supports a claim without requiring inference or reasoning — is the rarest kind. Confessions and eyewitness accounts are considered direct evidence. Mostly all other kinds of evidence — even forensic evidence like DNA and fingerprints — is considered circumstantial, because it requires interpretation to reach a conclusion.

Unless Wells obtained a confession from Brady, got an employee to testify against the best and most beloved player in franchise history, or stumbled upon a recording of Brady ordering balls deflated, his investigation was always destined to hinge on circumstantial evidence. This doesn’t mean the investigation was destined to fail. Direct evidence is not, by definition, irrefutable.

Kraft is far from alone in doubting the value of circumstantial evidence. A 2006 paper in the Michigan Law Review noted “jurors simply do not understand circumstantial evidence and thus routinely underestimate its effect on the objective probability of the defendant’s guilt.”

Kraft’s real gripe is with the conclusions Goodell made from the circumstantial evidence Wells uncovered. Luckily for Kraft and Brady, recent history shows they could get at least one, and possibly multiple opportunities to appeal to someone else to review the evidence and decide if Goodell made a mistake. The league’s punishments have repeatedly been overturned by outside arbitrators.

“This is far from over,” said Snyder. “This is probably just round one in what could be a two or three-round fight.”