The other day I was reading a news story about deflategate that had the football pressure data in it from the AFC Championship game. Being a scientist, I gave into the temptation to plot it up, which then led to the desire for a little more data. So off my sons and I went to the sporting good store over the weekend where we purchased a football and a gauge. We took the football out of the box, and … put it in the fridge. Here’s what we found.
In all five experiments putting the football from room temperature (75-78 degrees F) to the refrigerator (34-37 degress F) resulted in a pressure drop of more than 2 pounds per square inch (PSI; Figure 1 for graph of data, simple version). Upon being removed from the fridge, the PSI increased rapidly within the first 10-15 minutes. In two cases the pressure did not return to the original pressure (by 1.1 and 0.5 PSI), while in three cases it roughly did. We did not try to replicate the conditions of the AFC game because, frankly, it was the weekend and the fridge is what I had access to at home.
Three major conclusions are clear from these experiments. First, If these experiments are generalizable to winter football with comparable temperatures, in other words all games in near freezing conditions with outdoor stadiums, all footballs will be in violation of the current NFL rules and their current enforcement approach at some point during the game. Specifically, footballs filled and tested indoors that are brought outdoors will drop in excess of 2 PSI, which is two-fold larger than the 1 PSI allowed range (12.5-13.5 PSI). If they are tested while still cold, or immediately after being brought in, they will be in violation. This is regardless of if the footballs are filled to 13.5 or 12.5, each pressure subtracting 2 PSI will be in violation. These experiments did use a Wilson Official Composite football instead of the Wilson Professional Leather one, so the results may vary (as they would also with other varying environmental parameters) but similar effects would be expected.
If ball pressure is inspected and enforced as it was during the AFC Championship games, as would be expected given the high profile nature of the disciplinary actions and the need to protect the “integrity” of the game, NFL teams are going to need a lot of backup quarterbacks to replace the quarterbacks lost each game. Visiting teams from warmer climates would be wise to play their backups quarterbacks as a sacrifice to maintain them for future games, rather than lose them for four games. Teams from colder climates will need to dedicate more of their roster space for backup quarterbacks or risk running out of them by the end of the season.
Second, the Wells report argued that the large variability in football pressure in Patriots balls was indicative of tampering while the close spread of pressure values in the Colts balls could be used as a control group (see Figure 2, simple version) Our data demonstrates this same observations can also be explained by when the timing of sampling occurs. For example, when footballs are brought from a cold outdoor temperature to a warm indoor one, as occurred in the AFC championship game, there is a period of rapid re-equilibration where measured pressure correspondingly increases rapidly, followed by a plateauing where pressure converge. The time scales and our simple experimental data are consistent with this, where pressures measured in the first 15 minutes had a PSI range of 1.5, while those measured between 16-30 minutes had a PSI range of 0.5. During halftime the Patriots balls were measured first, then 5 Colts balls were measured and halftime came to an end. Interestingly, none of the Colts balls reached their initial estimated (and not recorded value) of about 13 PSI, suggesting a loss or incomplete re-equilibration, consistent with loss of pressure observed in two of our five experiments.
Third, there’s a systematic error between the two referees’ pressure gauges of 0.39 +/- 0.06. This has been much discussed in the media and Wells report. What has not been discussed is the notion of accuracy (and in contrast to precision). In analytical chemistry accuracy is a term used to describe the confidence associated with a measurement based on how close that measurement is to the true value. To acquire accuracy, chemists typically measure certified or consensus standards that are widely shared among laboratories. The process is simple, you measure the shared standard, if your number is far from the certified number, you’ve got a problem with your accuracy. The referees chose to use two different gauges during the halftime of the AFC game given the scrutiny they expected. This was a good idea as it gives us some real life information about the performance of gauges in use by referees. Turns out that a 0.39 PSI variability is ~40% of the allowed 1 PSI range – a football that is within the allowed range by 0.3 PSI could be found in violation by an inaccurate gauge. The NFL decided to use the data from only one gauges, assuming the other was inaccurate. But this is not valid, we don’t know which gauge (if any) was more accurate because there were no standards used to verify their calibration at the time of their use. If footballs need to be above 12.5 by both gauges, which seems reasonable since we do not know one to be more correct than the other, all of the Colts footballs except one are also in violation (Figure 2, the grey area indicates allowed pressures). The gauges are calibrated in the factory, and the referees are optimistically assuming those calibrations will be maintained and not drift with wear and tear. In light of this large uncertainty in referee gauge accuracy and to avoid any possibility of being in violation, teams should fill their balls to exactly within the middle of the 1 PSI range (13.0 PSI), since 13.2 or 12.7 could be found in violation by an inaccurate gauge.
I know an immediate comment will be why didn’t we try to recreate the conditions of the AFC championship game with the smaller temperature change (reported to be ~50 degrees F outside). The short answer, as mentioned above, is that this isn’t my day job, just some simple experiments done at home on the weekend, not in my chemistry lab at work. Others have done experiments under conditions mimicking the game in question, and found similar results (~0.9 PSI decreases). But that said the scientist in me couldn’t take reading any more vague news articles about this, and I was wondering what was really happening in those footballs. Since we did not recreate the specific game conditions, I have made the conclusions generalizable to the challenges facing teams trying to comply with the pressure rules next season. But obviously I’m being somewhat flip: without taking into account changes in temperature on ball pressure (e.g. when and at what temperature the game balls will be re-examined) and having at least some policy for verifying accuracy of pressure gauges, the existing rules are basically impossible to lawfully adhere to.
There have been numerous physicists getting quoted on whether the Ideal Gas Law could explain the pressure changes. It seems fair to conclude that having lawyers asking physicists to make calculations about vessels made of pig, which are repeatedly crushed by very large human masses, used in highly variable physical environments, and measured with uncalibrated gauges is quite far from “ideal”. Here, a few actual measurements with inexpensive supplies goes a long way to understanding football pressure in real world conditions.