Ballghazi is a perfect, perfectly hilarious scandal, and it just keeps getting better. To wit: The NFL, having ducked and dodged the many, varied complaints about the criminal behavior of its players, its own far-reaching municipal extortion schemes, and the long-term health effects of the game it promotes, has now released an independently gathered 243-page report on the matter of Tom Bradyâ€™s balls and their consistency during last yearâ€™s AFC championship game. Further, and somewhat surprisingly, the report comes stocked with nine pages of what seems at least meant to be taken as in-depth statistical modeling. Apparently, someone wants to leave us with the impression that the NFLâ€™s investigative arm brought techniques generally reserved for Serious Scientific Issues like global carbon emissions or a batterâ€™s expected BABIP as it correlates to True FB% to bear here.

As you might already knowâ€”regrettably, because no one should ever commit these things to memory, but NFL fandom often requires very specific, very stupid triviaâ€”the NFL requires balls to be between 12.5 and 13.5 pounds per square inch gauge (psig) during use in a game. Before the AFC championship game, the report explains, the Patriotsâ€™ balls were right around 12.5 psig, and the Coltsâ€™ were 13 psig (or possibly, since it wasnâ€™t written down, 13.1). By halftime the differences in the two teamsâ€™ ball inflation was statistically significant. Hard, or at least strongly circumstantial, evidence of real misbehavior has been sniffed out by the NFL, you are meant to conclude. Here is the model used, expressed in its additive terms:

Impressive! Here it is expressed mathematically:

Its terms are defined in the full document, embedded below, but probably this is plenty good enough to shock and awe the typical slack-jawed NFL dingus, an investigator would have to assume. Anyway, the model, which is a multiple linear regression and seems well done enough, says, basically, that some shit happened.

After accounting for the differences between two measurement instruments, and discovering that two officials apparently switched instruments at halftimeâ€”this takes up eight tablesâ€”here is a final table, with a summation of numerical results from the analysis: