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.
Mak Saito
about how the balls could be found to have low air pressure in a football game, but it’s always interesting to read about. One thing I think could result in a loss of pressure is repeated testing of a ball. I have to think that every time the gauge needle is inserted into the ball and removed, some air must be released. I can’t begin to say how much, or how quantifiable it might be, but it seems possible.
I’ve tested that and it is true that it happens. Maybe I’ll try the experiment soon.
I should clarify too that in these five experiments we left the gauge in the ball throughout the experimental time period to avoid this exact issue.
Did you monitor a gauge-in-place ball at a constant temperature over time to establish the integrity of the needle seal and the gauge itself?
Next season, I wonder if we’ll see some dastardly QB “overinflating” footballs on a hot day.
Yes, we did, and you can see that this is true in Figure 1 in experiments 1 and 2 at the end of the experiments the pressure is constant for 30 and 35 minutes, respectively.
We did this experiment early this morning. Inserting the needle and removing it 5x then the recording PSI value, then repeating that process 6 times (for 30 insertions and removals, averaging the change after each 5 insertions and removals). Each individual needle insertion and removal caused a mean of 0.034 +/- 0.01 PSI decrease per measurement. So ten measurements dropped the PSI by 0.3-0.4 PSI.
Perhaps the same corrupt climate scientists who have been plundering taxpayers for DECADES in a vast conspiracy to terrorize the public and profit from the resulting groundless hysteria have now used their ill-gotten gains to buy access to those patriotic Americans who love sports and football.
Perhaps the evil scientists have used the legitimate concern of tens of millions of loyal Americans about the appearance of unsportsman-like conduct on the part of heroic role models like Tom Brady to insinuate actual SCIENCE into this important issue. How dare they!
A clever plot indeed. Very clever.
As a NCAA football guy who isn’t a Pats fan, this is all really silly. Silly by the Pats, silly by Brady, and silly by the League.
In 1990 or so, MLB outfielders were wearing gloves that exceeded the 12″ limit from tip of web to heel. It was obvious. They were all doing it. First basemen, too. Know what Fay Vincent did? He (quietly) discussed the problem with the equipment makers and the managers. He reminded them that the integrity of the game matters, and they had to bring the gloves back to 12″. He told them that the umpires had free range to measure, and if they caught anyone, that player would be ejected for the game. That wasn’t a particularly harsh penalty — missing less than a whole game out of a 162 game season — but the embarassment would have been substantial.
Know what happened? Nobody got ejected. The players had a few weeks to break in new legal gloves before the season started, and they did. A few groused a bit, but it fixed itself. No scandal. No tainting a championship player or team. No arbitrary enforcement.
The balls were underinflated. It was a violation. Had the team been interested in following the rule, they would have simply reinflated the balls outside. It seems to me that the Pats knew, and were happy to take the same advantage that every other team was also taking.
The team and the League handled it poorly. Going forward, it seems to me that the best answer is to make the officials be in charge of providing and handling the footballs, rather than letting the offensive team provide their own ball.
And as far as cheating goes – in the second half, when fully inflated balls were used, the Pats scored double the points.
So…was it cheating or first half SABOTAGE by those who called it to the NFL’s attention?
That the Patriots were violating the rules is inarguable. Were they doing it willfully, and did they believe that they would gain an advantage in doing so? I don’t know enough to assert with confidence, but I expect so. Personally, I don’t think it’s a big deal even if they were doing it on purpose to gain an advantage.
But yes, we agree. Goodell is no Vincent, not by a long shot. It seems to me that the NFL, as a league, has (always?!) been more short-term profit/showbiz driven than the MLB. Just my opinion though, as a fan of MLB (over NCAA) but NCAA over NFL.
Pierce is a must read for this farcical controversy. It’s safe to say Brady probably knew what was going on and deflated the balls-whose pressure the League basically allowed players to control. I don’t see how Rodgers preferring an overinflated ball makes him a saint and an underinflated ball makes Brady a villain. If ball pressure was so important, the NFL should have maintained it’s standardized pressure and kept the balls in the hands of the refs-by allowing Quarterbacks and teams to be in charge it opened itself up to this possibility-and it has done nothing to address it.
Brady at worst, should get the ball tampering fine and move on. The team shouldn’t have lost any picks or been fined since it’s on him. I suspect, had he initially admitted responsibility that may have been the case, though the media might have crucified him and tried to keep him out of the Super Bowl.
Neither Goodell nor Brady were willing to agree to a shorter suspension, so now our legal system is taking over. It’s a win win for the NFL. They made a great heel out of the Patriots, Brady in particular, and Super Bowls with our team in them always garner ratings records since most of the country wants us to lose and there is a growing Pats Nation across the country that wants us to win. You didn’t see that for the Harbaugh Bowl back in 2013.
It means those opening four games, including two usually stale AFC East affairs, will now be widely watched whether Brady plays or not. And “coincidentally” the game where he comes off the suspension is against our biggest conference rival and future league golden boy Andrew Luck. The NFLPA has a fairly good case that the Welles report was biased, that Brady wasn’t given a fair hearing, and even rival players are quietly saying off the record they hope Brady sticks it to the league.
The worst part is when the coverage starts and we are subjected to ridiculous farces like narrowly acquitted murder suspect Ray Lewis calling on Brady to be banned from the game, child beater Adrian Peterson suiting up in the Twin Cities, and Ray Rice quietly getting signed by a desperate team (Cowboys and Bears are rumored landing spots). And Seau’s daughter giving an anti-NFL speech at his Hall of Fame induction, posthumous of course since the league has done nothing to address concussions but deny it’s own scientific conclusions and intimidate opponents. But boy, did Brady single handedly wreck football….
In my view, that is precisely what makes this a farce.
When Brady initially denied responsibility, he was accused of using balls that were DRAMATICALLY underinflated, by as much as 2 PSI. That turned out to be true.
First of all, I don’t have a dog in this race. I don’t watch or care about football, nor do I watch or care about the Patriots (or the Red Sox, Celtics, or Bruins).
Your statement that the balls were “DRAMATICALLY underflated, by as much as 2 PSI”, is precisely the point of the thread-starter. In my view, the thread-starter presents a reasonably convincing case that the variations in pressure that all the hysteria is about are some mix of:
1. Problems in data gathering
2. Within the error margin of the flawed data collection
3. Likely to be universal, at least at every outdoor game
The only thing that turned out to be true was that measurements taken by uncalibrated instruments in uncontrolled settings showed the cited pressure difference.
If I stick an uncalibrated thermometer into a pot of boiling water, watch it climb to 212 deg F, then take it into the room with my new AC and, after waiting 5 minutes, “measure” the room temperature as, say, 125 deg F, am I correct to demand a refund claiming that AC is broken because it hasn’t kept the room at 72 deg?
It appears to me that whatever this continuing “issue” is about, it rather less to do with truth and rather more to do with the theater of professional sports. While theater has tragedy, joy, romance, despair, and all the other human emotions — it is still theater, and not fact.
I think it’s well worth establishing, rather than assuming or asserting, the factual basis from which all this hoopla springs. In my view, the thread-starter strongly suggests that we haven’t done that.
If there truly is not an agreed-upon reference against which the instruments were calibrated, and if there truly was not a fair, accurate and repeatable process for measuring the pressure of the balls in question, then it seems to me that it is inaccurate to assert that any balls were underinflated — never mind the rest of the scandal.
What’s next, giving the referees loaded coins to toss?
Thanks. Glad someone understood what I was saying!