The Science of "Deflategate"

September 21, 2016

The science of "Deflategate" has been fuel for the court of public opinion over the past 16 months. In this same period, Exponent — the engineering and scientific consulting firm that was hired by counsel for the league to conduct an independent and objective investigation into the science of the matter — has been professionally silent. We have held the position that the findings presented in our 98-page report, included unmodified as Appendix 1 to what is now known as the "Wells Report," were comprehensive, accurate, and needed no further elaboration. We do not feel the same about the criticisms leveled against our work, and with the science portion of the litigation now complete, we would like to respond.

In presenting their opinions, our critics have ignored pertinent facts, violated basic physical principles, misunderstood or misinterpreted our analysis, and, in some cases, caused us to question whether they actually read our report in full. We have found that across the range of criticisms, two main challenges are repeatedly made. First, our conclusion about which gauge the referee used prior to the game is incorrect. Second, a simple application of the Ideal Gas Law could explain the Patriots' halftime pressure measurements. Let's now set the record straight. 

The facts regarding the gauges are clear. Before the game, the Patriots used a gauge to set the pressure of their footballs; the Colts used a different gauge to do the same with their footballs; and the referee measured both sets of footballs with one of the two gauges in his possession. All of this is undisputed, including the fact that while the referee was unsure which pressure gauge he used, he was certain he used the same one to measure both teams' footballs prior to the game. Furthermore, his pre-game measurements matched those reported by both the Patriots and the Colts. When Exponent tested both of the referee's gauges, we found that one read accurately, and one read consistently and unusually high. Since the referee's measurements matched the independent measurements made by both the Patriots and the Colts, we can conclude, with confidence, that the referee used the accurate gauge prior to the game.  Any other explanation offered to reconcile these facts is implausible.

Next, we address our critics' misuse of the Ideal Gas Law. We have been repeatedly challenged that somehow, we overlooked the basics of PV=nRT to explain the recorded pressures.  As we acknowledge in our report, the Ideal Gas Law does indeed describe the pressure-temperature relationship of the air inside the football. However, as we also detail in our report, we don't have knowledge of all the variables required to use this formula. Recall that the footballs were first measured in the warm locker room prior to the game, played with on the cold field during the first half, and then measured again in the warm locker room during halftime. It is tempting to use the Ideal Gas Law to calculate the pressure of the gas inside the football, using in the equation the known temperature of the surrounding air outside the football. This is what many of our critics have done, and it is incorrect.

Lacking a direct measurement of the temperature of the air inside the football and knowing that this temperature is constantly changing as the footballs warm up in the locker room, we don't have enough data to properly apply the Ideal Gas Law during the halftime period. Instead, we must rely on an experiment that suitably re-creates the conditions present on Game Day. Only by conducting such an experiment is one able to let the footballs warm up naturally as they would have at halftime, thus correctly reproducing the pressures of interest. This approach and the raw, unfiltered results that followed are exactly what is described in detail within our report. Our critics have misapplied the Ideal Gas Law by substituting the temperature outside on the field for the temperature inside the football, and "freezing" it for the entire halftime period while the footballs are warming up in the locker room. Doing so produces an erroneous and artificially low calculated pressure.

The above examples are not exhaustive. We have been subject to further criticism that errs in other subtle, but important, ways. Briefly, some critics have: improperly compared Ideal Gas Law calculations directly to the recorded data instead of accounting for the known miscalibrations in the Game Day Gauges; put forth statistical models that directly violate the real world physics; inexplicably misused scale bars in comparing photographs from our report; drawn specious conclusions about bent needles when test data supporting precisely the opposite effect are presented; conflated average and individual measurements instead of analyzing them separately; and inappropriately digitized and mistakenly compared data from disparate testing conditions.

Finally, we address some accusations made against Exponent, the services we provide, and our work as a whole. A common thread among comments made by journalists and casual pundits alike is reference to a 2010 LA Times article about our firm. It is unfortunate that those who resurrect this story do not take the time to independently verify the facts. 

For the nearly 50-year history of our firm, Exponent has worked on highly complex and visible projects. These projects attract attention — this attention is often accompanied by unfounded or inaccurate commentary. While mischaracterizations exist in all the examples cited by the LA Times, we address two of them here. First, the article implied that Exponent's work on behalf of Toyota in the "unintended acceleration" investigation was biased; however, reports from two government agencies, NHTSA and NASA, confirmed Exponent's findings. Second, the LA Times raised concerns about Exponent's scientific work on behalf of Chevron in Ecuador; however, a U.S. district court ruled in 2014 that the work done by others in the Ecuadorian verdict against Chevron was the product of multiple acts of scientific and other fraud. This ruling was reaffirmed on August 8 by the 2nd Circuit of the U.S. Court of Appeals.

With an aim to ensuring correctness and thoroughness, we have endeavored to review the criticisms of our work. None has given us any cause to retract or qualify our findings.

We stand by our integrity. We stand by our independent science and engineering. We stand by our conclusions.


Robert D. Caligiuri, Ph.D., P.E., FASM

Gabriel S. Ganot, Ph.D., P.E.

John D. Pye, Ph.D., P.E.

Duane L. Steffey, Ph.D., FASA

(The above four individuals are the authors of the Exponent Appendices to the Wells Report.)


To read the September 21, 2016 NY Times Article, click here.