Ideal Gas Flaw

deflategateThe absurdity of the New England Patriots football deflation scandal—Deflategate—is reaching ridiculous proportions as new details and analysis emerge. In the court of public opinion, at least from this view, the NFL is looking worse with each passing day.

But what about the science? What about actual evidence? This is what interests tech-52, which is, after all, a technology blog.

We took a hard look for ourselves. Our bottom-line based on what we found: It is looking more and more like the NFL has a particular agenda, and the truth be damned.


If you have been living in a cave, and haven’t heard about Deflategate, the sidebar provides a summary courtesy of Wikipedia.deflategate-descrip

The NFL and New England Patriots quarterback Tom Brady have been urged by the district court judge, Richard Berman, to reach a settlement. The first round of settlement talks is scheduled for this Wednesday, August 12.

Pundits have declared that if Brady accepts anything more than a fine for non-cooperation, it will be an admission of guilt. If things continue to unfold as they have been, however, Brady may have a case for full exoneration.

If that happens, it will be interesting to see if Robert Kraft and the Patriots organization ask for the team penalty (draft choices and a $1 million fine) to also be rescinded.

Lies, damn lies, and statistics

If the science that the NFL had based its judgment on were rock solid, we wouldn’t be having this conversation. Tom Brady and the Patriots organization would be proven guilty, and that would be that.

wells-reportProblem is the science, as described in the Wells Report, is coming under serious scrutiny from third parties, and questions are being raised regarding the methodologies used, and conclusions reached, by the NFL.

As part of the investigation, Ted Wells and the NFL’s “independent” investigators hired Exponent, a California-based engineering and scientific consulting firm, to look into all available scientific evidence.

Not to color the reader’s opinion or anything, but this is the same firm that the tobacco industry hired to “disprove” that second-hand cigarette smoke causes cancer.

In our attempt to drill down on the scientific evidence, what we found was disturbing to say the least. Despite what the Wells Report says, the evidence seems to confirm that the combination of conditions—weather, temperatures, measurement tools and criteria—do more to exonerate than incriminate the Patriots.

Yup, you heard that right. And it goes against what the NFL is portraying, and what the rest of the country has assumed must be true: the Patriots are serial cheaters and got caught again. Remember Spygate? Case closed.

The amount of misinformation that has emerged—and has later been refuted—is staggering. There have been numerous reports, for example, that 10 out of the 11 Patriots footballs were found to have been deflated by two pounds or more.

That factoid has been refuted by the Wells Report. On page 68 of the report, the PSI of the 11 Patriots footballs measured at halftime of the AFC Championship Game by two officials were as follows:


The officials reportedly used two different gauges, referred to as the “Logo Gauge” and the “Non-Logo Gauge”. Only one of the 11 balls was a full two pounds under-inflated, as measured by the lower of the two gauges, and three were less than a pound below the required minimum of 12.5 PSI.

At tech-52, we were kind of surprised, because these numbers look a lot less damning than we were led to believe by various media reports. After a full 30 minutes of play in wet and increasingly chilly temperatures, wouldn’t we expect the balls to be somewhat deflated?

But what does the science tell us?

Ideal Gas Law

A lot of rather sketchy reporting and analysis has been done on a law of physics known as the Ideal Gas Law, which describes properties that apply to a hypothetical ideal gas, and therefore can be largely applied to real gases—like the air in footballs. The Ideal Gas Law was the foundation on which the scientific conclusions in the Wells Report were made. ideal-gas-law-formula

Without getting too technical, if the Patriots’ footballs were inflated to the league minimum of 12.5 PSI, and there were absolutely no environmental changes, the balls would have remained at 12.5 PSI, according to the Ideal Gas Law.

Of course, there were numerous environmental changes throughout the first half of the AFC Championship game. The temperature and air pressure fluctuated, it rained off and on, and the Patriots played offense, and thus used their footballs, 17 minutes more than did the Colts, running up a halftime score of 17-7.

Using the recorded environmental data at the time, scientists could in theory use the Ideal Gas Law to extrapolate what the PSI levels should have been and compare them to the actual measured PSI levels.

The NFL investigation claims to have done this and ruled that the environmental factors were not enough to cause the deflation measured at halftime, particularly when compared with the Colts footballs, so therefore the Patriots’ footballs had to be tampered with.

Questionable science

Turns out, however, that independent third-party scientists carefully reviewed the data in the Wells Report and found flaws in the conclusions reached by NFL investigators.

bad-scienceAlthough there were other concerns, the biggest flaw in the NFL report appears to have been not properly taking into account the temperature changes to the balls while they were being measured at halftime.

Imagine this timeline. At halftime, the NFL instructed the refs to measure and record the PSI levels of the footballs. They have 15 minutes to do this before the second half would start. So:

  • Minutes 0-3, the refs get set up in the officials’ locker room to do their tests.
  • Minutes 4-10, the refs measure and record the PSI levels of the Patriots’ balls.
  • Minutes 11-13, they re-inflate the Pats’ footballs to 13 PSI.
  • Minutes 14-15, they begin testing and recording the Colts’ footballs, but only measure 4 of the 12 balls because they ran out of time.

What’s interesting about this is that, as the balls were being measured, in a room thought to be somewhere between 67-74 degrees, they were heating up and therefore their PSI levels were increasing with each passing minute. Remember the Ideal Gas Law? The refs measured the Colts’ balls last, and only four of them to boot.

Now, that timeline is only an educated guess, because nowhere in the Wells Report was the actual timeline described.

Third-party conclusions

Nonetheless, it turns out that the Ideal Gas Law could be used to explain all the data found in the NFL investigation and conclude the opposite: that the discrepancies were caused by temperature changes while the balls were being measured at halftime, a factor which the Wells Report does not take into account.

The Wells Report’s key flaw was using the Colts balls as the control group. However, their conclusion that the amounts of under-inflation measured in the Patriots footballs when compared with the Colts footballs proved tampering was the fatal flaw. Because the Colts’ footballs were measured last, they simply had more time to increase their PSI levels.

There was one other piece of evidence crucial to the third-party conclusion that the Wells Report was wrong. During the first half, the Colts intercepted a football and brought it to their sideline. That ball was measured separately at approximately 11.5 PSI.

AEI-logoThe American Enterprise Institute study linked to earlier in this post was conducted by Kevin A. Hassett, Joseph W. Sullivan, and Stan A. Veuger. At AEI, Hassett is director of economic studies and the State Farm James Q. Wilson Chair in American Politics and Culture; Sullivan is a research assistant; and Veuger is a resident scholar.

Their conclusion based on what appears to be extremely thorough research is:

The evidence we present points to a simple—and innocent—explanation for the change in pressure in the Patriots footballs. The Patriots balls were measured at the start of halftime, whereas the Colts balls were measured at the end of halftime, after sufficient time had passed for the balls to warm up and return to their pregame pressure. There is no need to consider the alternative hypothesis—that the Colts illegally inflated their footballs—because a simple physical explanation is available.

The fact that the average pressure of the Colts balls was significantly above the prediction of the Ideal Gas Law, while that of the Patriots balls was not, is inconsistent with the findings of the Wells report. Our conclusion that the warming of the balls during halftime is the key factor overlooked in the Wells report is supported by the observation that the readings of the intercepted Patriots football, measured separately from the other Patriots balls, came in almost precisely at the prediction of the law. Under the hypothesis asserted by the Well report, the odds of this Patriots ball matching the Ideal Gas Law prediction were between 1 out of 3 and 1 out of 300. It is therefore unlikely that the Patriots deflated the footballs.

Since this is a technology blog, I’ll leave it to someone else to speculate why the NFL is so intent on demonizing Tom Brady. Given the evidence, they could just as easily find reason to fully exonerate the man who has been one of their best players for the last 15 years.

2 thoughts on “Ideal Gas Flaw

  1. Fred Dunfey

    Thanks, Jim
    I just started to read the appeals transcript. Milly asked me to read your analysis. It is consistent with what people say who have been informed by reviewing all evidence. Peace, Fred

  2. Cole

    Out of morbid curiosity I did a back of the envelop calculation myself, using a starting p.s.i. of 12.5, starting and final temps of 72 and 48 degrees F. Assuming no change in moles (because obviously we need to assume this to see if the deflation is enough), and assuming no change in volume (okay this assumption may not be as valid, but I’m pretty sure these small changes in pressure don’t affect it as much because of the rigidity of the football), I got a drop to 11.9 p.s.i, which is in line with Prioleau’s measurements.

    Obviously this would not nearly be extensive enough to see, but the fact that a simple back of the envelop calculation yields results that suggests the balls would have dropped more than a half of a p.s.i. suggests it’s at least REASONABLE that nature is the culprit.


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