Readers in the U.S. are doubtless aware of the “Deflategate scandal”, in which the NFL alleged that Tom Brady, the greatest quarterback of his generation, had conspired with an equipment manager and locker room attendant, to deflate a microscopic amount of pressure from footballs in the AFC championship game. The NFL seemed to be completely taken by surprise by the Ideal Gas Law and the fact that outside temperatures below calibration temperatures would result in much larger deflation without tampering.

The findings depend on the interpretation of statistical data by decision-makers – a topic that interests me. I found the technical report by Exponent, Wells’ technical consultants, to be very unsatisfactory on numerous counts:

although they were reported by Wells to have considered “all permutations”, they hadn’t. On important occasions, they omitted highly plausible possibilities that indicated no tampering and, on other occasions, they only considered assumptions that were most adverse to the Patriots;

on key occasions, it seemed to me that Exponent failed to properly characterize exculpatory results.

At the end of my analysis, I concluded that their key technical findings were simply incorrect and wrote up my analysis, now online here.

I watched both the AFC championship and the final. I have no fan commitment to the Patriots. As someone who’s played sports all his life and whose play has always been rushed, I am amazed at how time seems to stand still for great athletes such as Brady.

The summary is as follows.



Summary of Analysis of Wells Report

The conclusions of the Wells Report ultimately depend on statistical and technical analysis carried out by Exponent, their technical consultants. The original problem, as framed by Exponent, was whether the observed pressure drop of Patriot balls could be explained by physical or environmental factors, including temperature changes and selection of pregame gauges:

We then sought to determine whether any combination of the factors listed in 7a through 7d [temperatures at pre-game, on the field and at half-time; timing of half-time measurements; wetness; pre-game gauge use] above (within ranges defined as realistic by Paul, Weiss) suggested pressure levels that matched those recorded on Game Day. If those factors could be set in such a way that the pressures suggested by the transient experiments matched the Game Day measurements, then we could conclude that the Game Day measurements could be explained by physical or environmental factors.

Exponent studied a number of permutations of factors, claiming that none of these combinations accounted for the additional loss of air pressure in Patriot balls or the difference in pressure loss in respect to Colt balls:

Exponent concluded that, within the range of likely game conditions and circumstances studied, they could identify no set of credible environmental or physical factors that completely accounts for the Patriots halftime measurements or for the additional loss in air pressure exhibited by the Patriots game balls, as compared to the loss in air pressure exhibited by the Colts game balls. Dr. Marlow agreed with this and all of Exponent’s conclusions. This absence of a credible scientific explanation for the Patriots halftime measurements tends to support a finding that human intervention may account for the additional loss of pressure exhibited by the Patriots balls.

In this article, I show that these factors can, in fact, be set “in such a way that the pressures suggested by the transient experiments matched the Game Day measurements” as follows:

Pre-game temperature around 71 deg F

Logo measurement of Patriot balls and Non-Logo measurement of Colt balls

It is therefore possible to unequivocally say that the “Game Day measurements could be explained by physical or environmental factors”, contradicting the key technical finding of the Wells Report. The corollary is that the Wells Report provides no technical basis for concluding that the Patriot balls had even been out of compliance with NFL regulations during the AFC Championship.

In previous discussions of the Wells Report, Prof MacKinnon and Hassett et al previously identified the important possibility that referee Anderson had not used the same gauge for pre-game measurements of both teams – an inconsistency that also occurred in the half-time measurements under the supervision of NFL Executive Vice President Vincent. The present article extends their work to include analysis of Exponent’s simulations and transients, showing that all relevant issues raised in the Wells Report can be fully explained by “physical and environmental factors”.

The Wells Report also revealed remarkable chaos and inefficiency in NFL protocols and procedures, even in connection with half-time measurements under the additional scrutiny of NFL Executive Vice President Vincent and other senior NFL officials. Had their protocols met reasonable standards, much, if not most, of the present, seemingly false, controversy could have been avoided.



