# Know that you were doing wrong

When the deflate-gate story hit back in January, I didn’t write anything about it because I didn’t want to add to the confusion. It wasn’t that I didn’t know how to use the ideal gas law, it was that I understood it well enough to know that there wasn’t enough publicly available information to use it correctly (except by accident). With the release of the Wells report—and more important, the Exponent report that’s included as Appendix I of the Wells report—we now have the information that was missing back in January.

Let me start by saying that I know Exponent pretty well. I’ve been reviewing their work for about a quarter of a century, including a few reports by one of the authors of the Wells appendix. I am not in awe of them or their reputation as “one of the leading scientific and engineering consulting firms in the country.” In fact, I’ve often found crippling errors in their work, and it’s possible that if I went through this recent report on football inflation in detail—as I do when I’m being paid to review their work—I’d also find errors. But I don’t need that kind of detailed review to know that Exponent addressed the right issues and went about its testing and analysis the right way.

I should also say that I am intensely jealous of them. This must have been an extremely fun project to work on. Not only are the engineering issues relatively simple, the stakes are low. This is not a product design in which people could be injured if the analysis is wrong, nor is it an investigation in a lawsuit in which millions of dollars hinge on the results (although today’s suspension of Tom Brady could change that). And fun is only part of it. At Exponent’s usual rates—and I don’t see any reason they’d give the NFL a discount—this investigation would bring them hundreds of thousands of dollars.

But let’s get back to the engineering. In January, when everyone was dusting off their high school chemistry books and running ideal gas law calculations, three fundamental pieces of information necessary to make those calculations valid were missing from every report I read:

1. Does the volume of a football remain essentially constant over the range of pressures of interest and when the ball gets used during a game and changes from dry to wet?
2. How accurate and how consistent were the pressure gauges used by the officials?
3. What was the temperature of the air in the footballs when their pressure was checked at halftime?

It’s certainly reasonable to make an initial calculation assuming that the volume of a football remains constant. But the pressure changes of interest in this matter were in the neighborhood of 1 psi, which is only about 4% of the absolute pressure in the ball. If the volume of the ball changes by, say, a couple of percent when it gets wet, the error in a constant-volume ideal gas law calculation will be significant and will invalidate the result. Exponent reviewed this issue by using 3D scans of a ball in various conditions and concluded that any volume changes were low enough to have no significant effect—constant-volume calculations were valid.

Figure from Exponent report.

As for the accuracy and consistency of the gauges used by the officials, Exponent got the actual gauges used on the day in question (and a bunch of other gauges from the same manufacturer) and tested them. They used these test results to account for gauges’ variability and bias.

Figure from Exponent report.

By the way, did anyone back in January report that the officials used two gauges? I don’t remember seeing that.

Most important, perhaps, was the temperature of the footballs when they were tested at halftime. Everyone defending the Patriots back in January did their calculations assuming that the temperature of the footballs at the time they were tested was the temperature on the field. This leads to the largest possible calculated pressure drop—which is in New England’s favor—but made no sense to me. Is it realistic to assume that the officials did their halftime measurements out on a cold, wet field? No.

But if they took the measurements in the locker room, how long were the balls in there before the testing and how rapidly does the air in them rise back up to room temperature? There is no definitive answer to the first question, although apparently the time before testing can be bracketed through witness accounts. Exponent did answer the second question by instrumenting a ball with a pressure gauge and a thermocouple to track the rate of temperature and pressure rise as the ball was moved from a cold environment to a warm one (like I said, this is fun stuff). They used that data along with the bracketed time estimates to get more realistic values for the temperature-related pressure drop.

Figure from Exponent report.

There was more, including a “vigorous rubbing” test inspired by Bill Belichick’s bizarre press conference (Exponent must love him for adding to their scope of work). But Exponent’s investigation of these three issues show me that they were asking the right questions and using the right methods to answer them. Engineering is not about plugging numbers into formulas. It’s knowing where the numbers and the formulas come from, what their limitations are, and using judgement in their application.

Of course, it’s still possible Exponent made mistakes, but did you read those text messages between McNally and Jastremski?

And finally, we have the obvious source for this post’s title: