DeflateGate: The Wells Report Crumbles

As time goes on, the more the Wells Report crumbles.  Despite some significant scientific work***, it is clear now that the statistics are suspect, there are unexplained variations in ball pressures which just don’t make sense with a systematic attempt by an individual to lower the pressure for the benefit of a quarterback,  there are large variations in wet/dry ball pressures that are improperly accounted for and might be attributed to evaporative cooling,  and the Wells Report investigators failed to account for pressure drops in some of the Patriots ball pressures due to the long final drive up the field by the Patriots played on a cold turf field.

Their original conclusion is negated.  It can no longer be said that it is “probable” that the Patriots cheated.  The combination of these problems in the scientific analysis make it highly unlikely that cheating of any sort went on.

This result is easy to check.  Next year, or some year in the future when the weather conditions and field conditions match those of the Patriots-Colts game, just measure the halftime pressures.  This would be a “real game time simulation”, not the simulation cooked in an LA lab, which missed important game time factors. This would be the ultimate vindication, and unless the NFL changes its tune immediately, they will have to explain how they could have been so wrong.

The Statistics

Using p-values like the Wells Report does, only makes sense if you can control for all the variations in the history of two populations, in this case the Colts’ footballs, and the Patriots’ footballs.  There are three large questions that suggest that the control did not exist:

1. We don’t know which pressure gauge was used to measure the two populations. (This they worked to account for.)

2. Whether a ball is wet or dry is shown to significantly impact the rate of warming, and the starting temperature.  We simply don’t know if the small sample of measured Colts’ balls were dry or wet, and we don’t know how long each population was allowed to warm inside the locker room before measurement.  Even the Wells Report experiments show wide unexplained variations in the pressures of wet and dry balls depending on which of their experimental charts you look at.  And we have also found out independent of the Wells Report, that the Colts’ balls were kept in trash bags to keep them dry, the Patriots were not.  The Colts’ balls simply cannot be used as a control in this situation.

3.  Some of the Patriots balls spent more time on the playing field just prior to the half time measurement because of a lengthy Patriots drive up the field.  There is strong reason to believe that the field was significantly colder than the air temperature, and would have caused cooling on those balls.

And even with this uncertainty, another uncertainty involves the way the Wells Report scientists computed their statistics.  While they knew the ball pressures were rising in the locker room, they chose to use the stats from the starting pressures.

As many people have now pointed out, just points 1 and 2, coupled with the way the scientists computed their statistics is enough to render any conclusion other than “inconclusive” impossible.  With all three, the conclusion is completely negated.

In their “Game Day Simulation”, the Wells Report forgot to include the Game.

The 2015 AFC Championship Game was played on a cold artificial turf field, which caused wide variations in the Patriots football pressures measured at half time.

The Artificial Turf was colder than the air temperature, and during the game balls sitting on the cold turf at the line of scrimmage during the would have cooled off more than other balls.  In particular a number of Patriots balls were rolled around and sat on that wet cold turf during that long final drive leading up to halftime that included 4 timeouts after the two minute warning.  That drive, and the colder temperature explains the scatter in pressures seen in the Patriots footballs, as well as the lower average pressure.  This effect was not considered by the Wells Report Investigators.  (see  for details)

That the Artificial Turf was cold must not have been obvious to Wells Report Investigators in LA.  However, to us who live in New England, we can remember that during most of January, the temperatures hovered at or below 20 degrees, but on that one day of the AFC Championship, the temperature jumped from well below freezing in the morning to a balmy but wet 50 degrees at game time.  The sub-freezing ground and sand under the field would not have had time to warm up, and would have still been at a 20 degree to 25 degree temperature.  Turf fields are designed to bring their cooling power to the surface, so the ground would have been significantly colder than the air.  Moisture collecting on those artificial grass blades would have been cooled, and that cold moisture would have been transferred to the balls by contact.

This is not an effect that can be ignored.  It is not an effect that can be simulated by spraying air temperature water onto the ball every 15 minutes and then wiping it off. (This was the Wells Report attempt at simulating the game). This is an effect that could easily have lowered the Patriots measured average ball temperature by .2psi to .6psi, which by everyone’s determination is more than enough to vindicate the Patriots.

Evaporative Cooling — The Difference Maker between Wet and Dry Balls

Another effect is evaporative cooling, which should have been more obvious to the LA investigators.  Indeed, you can see it in the results of several of their charts in the report itself, one where it appears as a .1psi shift in pressure, another where it is closer to a .2psi shift,  and another where it appears as a .5psi decrease in pressure of a wet ball.   Which is it?  Or, on the actual day in question, was it even more, and did it depend upon how the balls were handled? And why isn’t this mentioned as a uncertainty in the actual results?  The scientists obviously noticed it, but did not explain it or try to control for it. Some of the Wells Report scientists would do well to consult a psychrometric chart, and see how dramatic those effects really are, and actually use them to predict the warming and cooling patterns for the wet and dry footballs.  In actual fact, the wet balls should have barely changed in pressure when brought back into the locker room.  At a temperature of 72F, and humidity measuring 20%, the wet-bulb temperature is 50F.  If the balls were at 48F (which they were not, because of other factors), then only a 2 degree shift (about .1psi) would have occurred.

Patriots Exonerated

The Physics done by the Wells Report investigators, combined with the missed fact of a cold field on which the Patriots balls sat during the game, uncertainty about wet and dry balls, and questionable statistics removes most any doubt of the innocence of the Patriots.  We no longer have to accept the bizarre and unlikely scenario of a locker room attendant casually entering the bathroom, deflating random amounts of air from some but not all of the balls, and emerging 90 seconds later as if he had just been to the bathroom for the usual reasons.  If in fact he did remove some air, it was already small without the consideration of the cold field, and with that consideration it must have been negligible, or perhaps he even added some air.

As Physicists we have done our jobs and explained the facts of the situation.  The weather can be held responsible for the ball pressures.  We can no longer accept the label that it is “probable” the Patriots cheated “unless some other unforeseen conditions are found” as given by the Wells Report.  A least a couple of unforeseen conditions for the Wells Report has been found, and there is nothing more to be said.

Beyond the Physics

From here it should be simple.  However, it is not.  People have moved beyond the consideration of physics. It has long become a struggle between public opinion, an atmosphere of suspicion promoted by the NFL leadership,  people and press who have staked their reputations on the guilt or innocence of Tom Brady, and just a bone weary public who doesn’t want to hear any more.  Despite the truth of the science, what matters now is the perception of truth held by the football commissioner who has placed himself in the uncomfortable position of being judge, jury, and executioner despite his own lack of knowledge of science.  And he has his own personal stake in the outcome.  He has accepted the Wells report as gospel truth and has already acted on it, without protecting himself or the NFL with an independent process for verifying the report, or even appealing its validity.  Even though an apology is called for, he himself would look foolish coming forward with it now.

The Future

There is one other fact about Physics which may ultimately carry the day.  It doesn’t change.  It can and will repeat itself.

It is a problem for the NFL that this scenario (the set of weather conditions — frigid temperatures leading up to a relatively warm 50 degree rainy afternoon) may repeat itself next year at some other field, and for a different set of football teams.  If someone on one of the teams complains about football pressures, and they are measured more carefully at halftime,  will the same punishments be imposed as were done this time — maybe to both teams?

The legacy of this NFL leadership is at stake.  Will they be remembered as the leaders who seriously handicapped the top team in the NFL for the next season?   Will this put an * beside any team that wins the AFC, or perhaps even the Superbowl, to say they won, but they were mistakenly given a leg up by the NFL commissioner to get there?

Or will the NFL admit their mistake, publicly apologize, and quickly right the situation?  And then they have some work to do at the NFL to make sure processes are in place to insure fairness to individuals both on and off the field.  Yes– guilty parties should be dealt with swiftly and severely, but there should be a way to appeal for a TV replay to make sure the correct call was made.


*** The Wells Report Scientists did try to do a complete and thorough job.  That is evident from their report.  However, as is often the case in scientific endeavors, other scientists review the work, and find problems that should be explained or taken into account.  That did not happen here, or at least is only now happening haphazardly through the press.  It was the process that was flawed, not the scientists, and the best that can be said for the Wells Report is that it is based on an inconclusive and incomplete scientific analysis.

If a similar problem occurs in the future, it will be important for the the NFL to develop different processes to avoid jumping to incorrect conclusions.  In this case, this led to the NFL to try to shoehorn this data onto a bizarre theory of deflated footballs, a nefarious locker room attendant, cryptic text messages, and a 243 page confusing explanatory report, rather than letting the facts themselves lead to a more natural theory that fit the facts — i.e. the weather did it.


Some more references:

Three Key Areas Where the DeflateGate Report is Blinding us with Science



#DeflateGate – Physics in Review – The Wells Report


The Wells Report, the NFL’s official report on the DeflateGate scandal, was written to try to end the scientific discussion on the football pressures as measured at halftime of the AFC Championship game between the Colts and the Patriots.

It still causes a lot of confusion.

If one were to give a peer review** of the scientific side of the report (the report was done by the consulting company Exponent), and to suggest areas that might clear up some concerns with further investigations or result in an entirely different conclusion, these are the problem areas:

  1. Artificial Turf Field Temperature — Surprisingly, this was not considered in the Wells Report at all. Under the artificial grass would have been cold sand and cold ground, frozen by the cold January weather leading up to the extraordinarily warm (for January) 50oF temperature at game time.  The turf fields are designed to bring cooling from underneath to the surface.  This would have cooled balls sitting on the grass — in particular the Patriots balls as they had a long sustained drive occurring within 20 minutes of the halftime measurements.  This may explain a wide distribution in pressures of the Patriots balls, and the overall lower average pressure.  Consideration of this may totally exonerate the Patriots.  The investigators must look into this.
  2. Uncertainty — A great deal of the report deals with the uncertainty in the pressure measurements themselves, which gauges were used, the temperature of the locker room, and the timing of those measurements.  In the midst of all this uncertainty, the conclusion reached was based on the Patriots average pressure having an uncertainty that was just outside the range of their model, and timing of measurement that was just outside their model as well.  The closeness with which these measurements were to the uncertainty range, not only requires accurate accounting of the averages, but accurate accounting of the uncertainty as well.  This is true of the measurements by the gauges, and the  uncertainty of how well the model and apparatus the investigators put together actually matched the game time conditions.   Regarding the model, there is not enough discussion about this, nor any experimental error bars that show on their charts.  The control on this was the measurement of the Colt’s balls.  Unfortunately, only 4 of the Colt’s balls were measured, and we don’t know if those balls were used in the game and were wet, or if they were not used in the game and were dry.  We don’t know if the ball boys held them in their hands and warmed them, or what happened to them.  These are difficult to consider as a proper control.  The investigators should present their results as an investigation of how their game time simulation with its proper experimental uncertainty, and the Ideal gas law match the results of both sets of balls, rather than try to adjust by making the Colt’s balls a control group.
  3. Evaporative Cooling and Uncertainty — A systemic difference between the pressure on a wet ball, and the pressure on a dry ball can be noted in the Investigators results.  Although it is not explained in the report, this might be expected to reflect the “dry-bulb”, and the “wet-bulb” temperatures found in meteorology.  The root of this is really evaporative cooling.  This is a “systemic” result, and not an experimental uncertainty error as is suggested in the charts shown by the investigators.  The charts should have reflected an uncertainty in starting temperature, and any other uncertainty that might occur in their model which might be observed when repeating the experiment, or trying out various other conditions as they describe.  Since the uncertainty is critical in coming to the final conclusion of this report, this should be dealt with correctly.  Even this change in uncertainty modeling — because the Patriots average pressure was just outside the range shown — might lead to a different conclusion.



There appear to be three competing theories to describe the football pressures as measured at halftime of the AFC Championship game between the Colts and the Patriots:

  1. Someone let air out of some of the Patriots footballs.
  2. There is so much uncertainty surrounding the measurements that no definite conclusion can be reached.
  3. There are physical processes not accounted for in the Wells Report which caused the temperatures of some of the balls to be lowered to the point to which measured pressures were achievable.

The Wells Report concluded that theory #1 is the most “probable” explanation of what occurred.  They came to that conclusion by accounting for all known sources of uncertainty, and by doing a comprehensive review of any and all physical processes which might have accounted for changes in the ball pressures.  They created an apparatus to model the “game day scenario” to demonstrate what might have happened at Foxboro that day especially taking into account transient effects due to changes in temperatures when the ball pressures were measured.  Based on the experimental results of running that model they reached their conclusion.  The data of the Patriots football measurements do not fit their model and the Colts football measurements do, so therefore the Patriots explanation is “not credible”.  Someone deflated the balls.

The Patriots contend that theory #2 is the best explanation.  The uncertain conditions under which the pressure measurements were taken, the inaccuracy of the equipment, the uncertainty in the timing and the continued claim by everyone interviewed in the case who might be culpable of or colluding with others to let air out of the balls that no such act happened, lead them to believe that this is the best explanation.  Their rebuttal of the Wells Report, including many of the non-scientific aspects of the report is published on-line here.  (Wells Report Context — From the Patriots)

Theory #3 is something that is mentioned a number of times in the Wells Report in the form of the statement:

“Therefore, subject to the discovery of an as yet unidentified and unexamined factor, the measurements recorded for the Patriots footballs on Game Day do not appear to be completely explainable based on natural causes alone. ( pg.61, Exponent Report)

This is the suggestion that some new unknown factor might cause their theory to be wrong. That unexamined factor may be the cold sand and ground under the turf field.  We start with a discussion of that factor.

Artificial Turf Temperature

The Wells report claims that the air temperature alone is insufficient to have caused the low pressures measured in the balls.  But what about the playing surface?  This concern about the temperature in and under the artificial turf falls in line with theory #3 — other physical processes not considered.

On January 18, 2015 the ground in New England was frozen from a cold January, averaging well below freezing. Despite warm temperatures that day, the turf field is expected to have been cold. A ball sitting on the wet artificial grass will cool down due to the contact. (

The cooling due to the ball sitting at the line of scrimmage in between each play, and the fact that the Patriots had a sustained drive just before half-time can explain the wide variety of pressures in the Patriots balls, and the difference between the Colts balls and the Patriots as measured at halftime.

At that time in January there would have been a block of frozen ground underneath Gillette Stadium’s field, and turf fields are designed to allow cooling from below.  In fact the turf is designed to have a layer of “high heat capacity” sand which would keep cooler on high temperature days and the grass fibers bring that coolness through a layer of insulating rubber pellets.  While in play, the balls would sit on the ball field for extended periods of time, especially the Patriots balls during a sustained drive leading up to halftime.  These balls would have experienced some of this cooling, and would have still been feeling those effects during the halftime measurements.  Was this just overlooked by the investigators, or did they know about it, and had a good reason for ignoring it?

The report should consider the playing field, and investigate the effects if any.

A separate report found here goes into more detail how this might account for all the low pressures of the balls at halftime, and even the wide variance in distribution of pressure in the Patriots balls that was found.


The Gauge:  Which one was Used?

Walt Anderson, the Referee who measured the pressure in the footballs before the game had two pressure gauges.  Subsequent tests by Exponent showed that the gauges measure about .3psi to .45psi apart.  The controversy is over which gauge was used in that first pressure measurement.   The choice is crucial.  As is pointed out by the Patriots, if we just use measurements using the gauge Walt Anderson recalled he used during the initial measurement, then the average pressure measured in the 11 footballs measured at halftime is consistent with the pressure expected by the Ideal Gas Law.

The Wells report shows this in Fig 27 of their report.  This illustrates a model which the Wells Report claims shows the time dependence of where the Ideal Gas Law for a football sitting out in the open air of the locker room warming up while being measured.  At the left side of the chart, within the experimental uncertainty of the football measurements, the Patriots balls convincingly overlap with the value expected by the model!


The Wells report contends that time dependence is the problem.  The balls took 3-8 minutes to be measured, and during that time they should have been warming up.   As shown on the chart (look at the brown curves), the flat brown line with uncertainty bars around it  shown in light brown, after 4 minutes starts to lie outside the wet-ball curve (the dashed brown line), and by the time we reach 8 minutes is almost 1.5 times the size of the uncertainty bars outside the curve.

If we use the other gauge, then the average pressure was significantly lower, and must be explained some other way.  Since the investigators fail to convincingly remove the uncertainty surrounding the gauges their conclusions should only be based on ruling out measurements made by both gauges.


Experimental Uncertainty

Key to the conclusion of the report is understanding the uncertainty surrounding the pressure measurements of the balls, and in particular determining if that uncertainty can be reduced to a level that any conclusion at all can be reached.  The investigators reached the conclusion that it was “probable” that someone had removed air from the balls.

Unfortunately a game day scenario for football manufactured in a lab would seem to have a lot of uncertainty about it no matter how carefully scientists try to reproduce, or account for the weather and other game conditions.  To show the only uncertainty in the experimental game day model as being due to dry/wet ball measurements, and then base conclusions as far reaching as they do is questionable.

Why aren’t there shaded uncertainty areas around the pressure lines depicted in graphs in Fig’s 26 and 27, on which so much of the conclusion of this report rests?   At a minimum we know there is an uncertainty in the initial measurement temperature that should be represented directly on these charts.  If that uncertainty is .1psi – .2 psi, it  can change how people view this chart considerably.  And certainly that uncertainty in the temperature measurement should not be used or manipulated  as suggested in the statement “the various temperatures were adjusted such that the measurements obtained via these simulations correspond to the Colts measurements” (pg. 57 of Exponent report).  Please, just put the correct uncertainty estimates in, and let the chips fall where they may with the data.  It is important to see that the Colts data does not align perfectly with the models prediction if that is the case.

It is also important to note that the difference between the wet-ball curve, and the dry-ball curve could be a systemic difference (see Evaporative Cooling below), and thus do not and should not represent experimental error limits for these curves!  The investigators should be able to control for these systemic effects, or suggest that some uncertainty exists because we do not know the humidity and/or air circulation that existed within the officials locker room, and representing some bound on that type of uncertainty. On some of the diagrams in the report, the wet-dry difference is about .1 – .2psi.  On other charts, like the one above, it appears to be about .5psi.

Directly related to those pressure lines is the Fig 21 graph (not shown), where the rising pressure for the dry balls does not seem to follow an exponential curve.  This suggests some other systemic problem, or at least should be explained by the investigators as to why it may be that way.

Although the investigators do a great job reducing and explaining much of the uncertainty surrounding pressure gauges, squashing footballs, stretching football leather, etc, they need to provide more accounting for uncertainty in their own model on which they base their conclusions.

Finally, it is not unusual for results to lie outside their uncertainty estimate.  With a “normal” distribution approximately one third of the time this will occur.  It is just more “probable” that by repeating the experiment it will lie within the estimated uncertainty.  Given how close this range is as shown in Fig. 27 above, the only conclusion that could be reached is that it is only “probable”, but not impossible that that the pressures in the Patriots balls could not be explained within the model.  Further experimentation including the cold turf, and showing some uncertainty due to our not knowing the humidity/evaporative cooling effects

Using the Colts Balls as Controls

A “control group” in an experiment is a set of items (in this case the Colts footballs) which are statistically similar to the the other group (the Patriot footballs) but not subjected to the changes which are being tested for.   Unfortunately, this was only a subset sample of the Colts balls.  These 4 balls may have all been dry.  We needed to add in all the balls to be sure we included balls that had been on the field getting cold and wet. Without that, we may be comparing apples with oranges.   We know there may be at least some known systemic differences in balls which were wet and dry (see Evaporative Cooling below, and not to mention issues due to their use or non-use in a game as asked in the Artificial Turf question above)?  Why not just compare everything to the measurements predicted by the Ideal Gas Law, and the Transient model.

The Distribution in the Pressure of the Patriots Footballs

The distribution of the pressure measurement in the Patriots balls is an inconvenient truth for both sides.  They are spread too broadly.  This is a glaringly obvious problem if we assume it is just the Ideal Gas Law that took the balls from their narrow distribution before the game (12.5psi +/- .1psi) to the measurements which at half time which are spread over 1.3psi.  The Exponent investigators have shown that in the lab the temperature/pressure changes are very repeatable, and follow the Ideal Gas Law.  We should not see such a wide distribution.

Even theory #1 — A person letting air out would have been greatly inconsistent in how they let air out — ignoring some balls, and letting much more out of others.  Would a random set of pressures be good for a quarterback?  Does that make sense?

And theory #2 — While averaging over the halftime pressures in these balls, and obtaining an estimated uncertainty seems reasonable, the nagging question is why did the pressures show such a large variance.  It does not seem physically reasonable.

However, theory #3 — this theory makes sense.  Very simply, the cold artificial turf theory would explain  it as due to some balls being more recently on the field than others.

Systemic Effects: Evaporative Cooling

At least one blog post showed concern about evaporative cooling causing some significant effects on the ball pressure.  In one of the figures (Fig. 27 shown above), some experimental results show two curves, one for a dry-ball curve, and one for a wet-ball curve.  They differ along this curve by about .5psi.  Although the reason for this difference is unexplained in the report, some atmospheric scientists might guess that this is the kind of difference that is accounted for by “dry-bulb” and “wet-bulb” types of measurements.  These differences arise because of evaporative cooling lowering the temperature on the wet-bulb (or wet-ball), and thereby lowering the pressure.  These effects can be larger depending upon the humidity in the air, and air circulation.

An explanation of these clearly measurable effects, whether they are due to the evaporative cooling or not, is warranted. Particularly since this difference is represented in the graphs Fig 27 and Fig 28, on which the conclusions of the report were founded.


The comments in this paper are meant as a “peer review” of the scientific evidence and experimental procedure presented in the Wells Report, in particular where that may influence the conclusion of the report.

These are some important questions that were raised in a careful reading of the scientific evidence of the report.

The expectation and hope is that the Investigators would look seriously at the effects mentioned here, and answer the questions raised.

Suggestion for the Future

Unfortunately, this experience with the Patriots-Colts game is the first in which the pressure inside the football has been called into question.  Undoubtedly, in the future there are some things that could be done better.  There could be better recording of pressure.  There could be more careful monitoring of the game balls.

In the future, to verify that the balls have not been tampered with, the pressures could be measured ahead of the game as they are now, and then measured again about an hour after the game to see if they come back to their original pressure.


**Peer Review

The scientific norm of peer review before publishing a scientific article is a time honored process which leads to fewer mistakes, a focus on critical aspects of the investigation, and wider acceptance of the results.  In this process, prior to publication, the article is sent to a handful of independent reviewers who may or may not be known to the lead investigator.  These reviewers who have general knowledge of the subject, study the report, and their comments are sent back to the investigator giving that person a chance to improve their publication, or even go back to the drawing board.

In the Wells Report, it appears there was not an outside review process.  Dr. Daniel Marlow was the lead investigator, and is clearly an esteemed physicist, but as any scientist knows, the scientific method can be fraught with making bad assumptions, failing to discover or notice key facts, and a lot of trial and error.  Discovery quite often comes through recognizing these mistakes, pressing forward, and finding the correct answers.

This, in and of itself, does not mean that mistakes were made in the investigation.  And in fact, for the topics that were considered, most scientists agree that the report by Exponent was capably done.  However by failing to have this peer review, the group did not avail itself of either a chance that others might identify problems with the report ahead of time, nor avail themselves of the wider acceptance of the results.

***Improving the Game Day Scenario Experiment

A way to further the realism of the “Game Day Scenario” is to include the football game itself.  Create a simulated field by laying some damp towels on a layer of ice and let it sit outside at 48F for an hour.  Then repeat the above experiment, but instead of dampening the balls with 48F water, periodically bring them out and push and roll them on the damp towels, and let them sit on the towels for 2-3 minutes.  Then put them back in the bag.   In the last 25 minutes — up to 3 minutes before bringing them inside for measurement, repeat the push and roll on the towels, always having at least one ball out sitting on the towels.



Official Wells Report

Wells Report Context ( From the Patriots)

MacKinnon’s Scientific Conclusion

Evaporative Cooling a Glaring Omission from Wells Report

A New Form of Peer Review