Deflategate and Errors in the Wells Report

Readers in the U.S. are doubtless aware of the “Deflategate scandal”, in which the NFL alleged that Tom Brady, the greatest quarterback of his generation, had conspired with an equipment manager and locker room attendant, to deflate a microscopic amount of pressure from footballs in the AFC championship game. The NFL seemed to be completely taken by surprise by the Ideal Gas Law and the fact that outside temperatures below calibration temperatures would result in much larger deflation without tampering.

The findings depend on the interpretation of statistical data by decision-makers – a topic that interests me.   I found the technical report by Exponent, Wells’ technical consultants, to be very unsatisfactory on numerous counts:

  • although they were reported by Wells to have considered “all permutations”, they hadn’t.  On important occasions, they omitted highly plausible possibilities that indicated no tampering and, on other occasions, they only considered assumptions that were most adverse to the Patriots;
  • on key occasions, it seemed to me that Exponent failed to properly characterize exculpatory results.

At the end of my analysis, I concluded that their key technical findings were simply incorrect and wrote up my analysis, now online here.

I watched both the AFC championship and the final. I have no fan commitment to the Patriots. As someone who’s played sports all his life and whose play has always been rushed, I am amazed at how time seems to stand still for great athletes such as Brady.

The summary is as follows.

Summary of Analysis of Wells Report

The conclusions of the Wells Report ultimately depend on statistical and technical analysis carried out by Exponent, their technical consultants.  The original problem, as framed by Exponent, was whether the observed pressure drop of Patriot balls could be explained by physical or environmental factors, including temperature changes and selection of pregame gauges:

We then sought to determine whether any combination of the factors listed in 7a through 7d [temperatures at pre-game, on the field and at half-time;  timing of half-time measurements; wetness; pre-game gauge use] above (within ranges defined as realistic by Paul, Weiss) suggested pressure levels that matched those recorded on Game Day. If those factors could be set in such a way that the pressures suggested by the transient experiments matched the Game Day measurements, then we could conclude that the Game Day measurements could be explained by physical or environmental factors.

Exponent studied a number of permutations of factors, claiming that none of these combinations accounted for the additional loss of air pressure in Patriot balls or the difference in pressure loss in respect to Colt balls:

Exponent concluded that, within the range of likely game conditions and circumstances studied, they could identify no set of credible environmental or physical factors that completely accounts for the Patriots halftime measurements or for the additional loss in air pressure exhibited by the Patriots game balls, as compared to the loss in air pressure exhibited by the Colts game balls. Dr. Marlow agreed with this and all of Exponent’s conclusions. This absence of a credible scientific explanation for the Patriots halftime measurements tends to support a finding that human intervention may account for the additional loss of pressure exhibited by the Patriots balls.

In this article, I show that these factors can, in fact, be set “in such a way that the pressures suggested by the transient experiments matched the Game Day measurements” as follows:

  • Pre-game temperature around 71 deg F
  • Logo measurement of Patriot balls and Non-Logo measurement of Colt balls

It is therefore possible to unequivocally say that the “Game Day measurements could be explained by physical or environmental factors”, contradicting the key technical finding of the Wells Report.   The corollary is that the Wells Report provides no technical basis for concluding that the Patriot balls had even been out of compliance with NFL regulations during the AFC Championship.

In previous discussions of the Wells Report, Prof MacKinnon and Hassett et al previously identified the important possibility that referee Anderson had not used the same gauge for pre-game measurements of both teams – an inconsistency that also occurred in the half-time measurements under the supervision of NFL Executive Vice President Vincent. The present article extends their work to include analysis of Exponent’s simulations and transients, showing that all relevant issues raised in the Wells Report can be fully explained by “physical and environmental factors”.

The Wells Report also revealed remarkable chaos and inefficiency in NFL protocols and procedures, even in connection with half-time measurements under the additional scrutiny of NFL Executive Vice President Vincent and other senior NFL officials. Had their protocols met reasonable standards, much, if not most, of the present, seemingly false, controversy could have been avoided.


  1. Posted Jun 23, 2015 at 3:47 PM | Permalink

    Link to your analysis is off. Correct link.

  2. Willis Eschenbach
    Posted Jun 23, 2015 at 3:52 PM | Permalink

    Steve, that is simply hilarious. Tragic, but hilarious.

    I sometimes think that you will run out of outrageous things to report on, but you just go and conquer new fields.

    Well done, that man!


  3. Joe
    Posted Jun 23, 2015 at 4:33 PM | Permalink

    The difference in 12psi and 13psi in a football is huge, at 14psi, the ball becomes nearly a rock. Same with a basketball. As much as the players in any sport will complain about ball pressure, football, soccer, basketball, volleyball, etc,. The higher the pressure, the less ball control the player has.

    Its a little hard to believe that nothing was said and that none of the 6 or 7 game officials who are constantly handling the balls did not notice an underinflated ball.

    I called BS when the report went out –

    • Danley Wolfe
      Posted Jun 23, 2015 at 6:01 PM | Permalink

      Joe, you are right but putting into perspective…. the pressures are gauge therefore 12 >> 13 >> 14 psig is really 26.7 >> 27.7 >> 28.7 psia (absolute) corresponding to increase from base 12 psig of 3.7% and 7.5%… which seems not so huge.

      • Steve McIntyre
        Posted Jun 23, 2015 at 10:19 PM | Permalink

        Another way to appreciate the slightness of the amount in dispute is to convert the pressures to football temperatures.

        The amount in dispute is about 1 deg F during an interval in which temperatures are going from 48 to 73.5 deg F.

      • Joe
        Posted Jun 24, 2015 at 8:28 AM | Permalink

        Dan – I presume the 12 psi plus 14.7psi = 26.7 psi is ball pressure in excess of the ambient air pressure (14.7 psi being sea level air pressure. If so, thanks for the correction.
        That being said, the difference in ball behavior, the feel, the bounce, the hardness, the touch of the ball with as little as 1 psi difference is huge. My point is that with 6-7 game officials, and the ball being touched by 2-3 game officials between every play, the probability of not getting caught during the game is pretty slim.
        I will let someone my knowledgable is probability/statistics to calculate the odds, though my educated guess is the probability of not getting caught is remote.

      • Posted Jun 24, 2015 at 10:27 AM | Permalink

        Danley Wolf brought up the difference between absolute pressure and what most gages measure.

        Good technical practice is to use psia and psig notation, for Absolute and Gage respectively. (Well, Gauge for remnants of the British Commonwealth. 😉

        Most gages people encounter are actually measuring the differential between the pressure of interest and ambient atmospheric pressure (which is pervasive and local, for most things a good reference point).

        Traditional velocity meters measure difference between the impact pressure of the medium and ambient – an aircraft pitot tube for example. (Basic weather instruments traditionally use

        Today other technologies are available, hot wire sensors in automotive fuel injection and automatic CPAP machines for example.

        • Posted Jun 25, 2015 at 1:08 PM | Permalink

          Argh, sorry, I didn’t finish the thought that wind measurements traditionally used a rotating cup device, the anemometer.
          A pedantic digression anyway.

      • Posted Jun 24, 2015 at 10:34 AM | Permalink

        Danley, “Joe”‘s point is one of structural mechanics of the ball, which I expect include how much the material stretches and variation of resistance of the ball to pressure (bounce on hitting something, indentations that aid fingers retaining grip) with internal pressure.

        He’s saying that is not linear.

        I am not knowledgeable on that, you may want to dig into it.

        • Posted Jun 25, 2015 at 1:06 PM | Permalink

          Here’s an article claiming the pressure difference would have had little effect on the quarterback’s performance:

          Beware it is simulation not real tests. Flow analysis is often used these days, but real tests are needed.

          Steve: that actual amount of deflation in dispute is 0.2- 0.38 psi (the amount of gauge bias) and this is equivalent to a temperature difference of about 4-8 degrees F or the pressures at 52 deg F vs 44 deg F. Hard to believe that Brady’s performance would be impacted by such small amounts of pressure.

    • tony2046
      Posted Jul 13, 2015 at 1:15 PM | Permalink

      Hi Joe. That is the funny little side note in all of this. Watched numerous ex and current football players demonstrate that they could notice the difference of 2 psi in footballs and then asked “why didn’t Brady notice?”. Assuming that all footballs are inflated in 70 deg rooms: Why didn’t the players during the Ice Bowl notice or complain that their footballs were close to 4 psi deflated? Why didn’t any player who played in a game at freezing temperatures notice that their footballs were close to 2 psi deflated? Why didn’t any of the players who played in a 115 degree game in Phoenix notice that their footballs were over inflated?

      It is evident by the NFL’s own SOP that they never knew or never cared about the effects of weather on a football until approxiamtely five months ago.

    • Gdn
      Posted Aug 1, 2015 at 9:06 PM | Permalink

      Just an FYI…

      A regulation basketball is 7.5 to 8.5 PSI.

  4. Steve McIntyre
    Posted Jun 23, 2015 at 4:52 PM | Permalink

    My article has been linked at the Patriots’ reply to the Wells report:

    • MikeN
      Posted Jun 25, 2015 at 12:21 PM | Permalink

      Steve, were you in contact with Tom Brady’s team. I think they could have used this a few days earlier.

      Steve: I had corresponded with the Patriots’ lawyer about 4 weeks ago, saying that they really needed to do technical analysis on the science. He sent a polite reply. I had intended to write something up about 3 weeks ago, but have been feeling really tired lately and not getting much done. I sent a slightly earlier version to the Patriots’ lawyer a day before the hearings and he said that he forwarded it to Brady’s reps, but I didn’t hear from them. I’ve also corresponded with Kevin Hassett of AEI and sent him a copy of an earlier draft. I get the impression that Brady’s team didn’t focus as much on the science of the Wells Report as they ought to have IMO. Some of the press commentary criticized Brady for more or less re-iterating that he didn’t have anything to do with any deflation, but, if there wasn’t any deflation, then I’m not sure what else he could be expected to say.

      • mpainter
        Posted Jun 25, 2015 at 2:08 PM | Permalink

        One gets the impression that legal types do not relish highly technical issues that neither they nor juries can easily assimilate. Understandably- a normal human trait.

  5. mpainter
    Posted Jun 23, 2015 at 5:38 PM | Permalink

    I don’t know the details, but if a compressor was used to inflate the balls, there is the fact that compression heats air.
    If a hand pump was used, then compression heats air.
    When the inflated balls adjusted to ambient outside temperature, there would have been a loss of pressure.
    I read the Wikipedia entry on this and there seems to be the most tenuous circumstantial evidence against the Club and Brady, and I am a fan of neither.

    • jorgekafkazar
      Posted Jun 23, 2015 at 7:45 PM | Permalink

      There’s also the question of whether the compressed air was adequately and consistently separated from any condensed water. Even a small amount of wet air in the ball can have a large effect on its subsequent pressure. It’s not unusual for a compressed air system to puke liquid water downstream of the accumulator/separator.

    • chrimony
      Posted Jun 24, 2015 at 8:05 AM | Permalink

      While the evidence is circumstantial, it’s damning, even if environmental factors can’t be ruled out from the measurements. 1) They’ve got video of the perp taking the balls with him into a bathroom. 2) The text messages show two underlings conspiring to deflate the balls.

      The excuses that came from the Patriots after the report came out were pathetic, and I say this as a Pats fan who went to college in the Boston area. The only real questions are: how much Tom knew, when, and if he had any hand in directing them beyond his complaints about some overinflated balls in a Jets game.

      • MikeN
        Posted Jun 25, 2015 at 9:07 AM | Permalink

        The extent of the conspiracy is texts ‘Help the deflator’ and ‘Deflate and enjoy the new shoes’, contradicted by the fact that these happened before the season, yet later texts show Tom Brady getting upset with highly inflated footballs. The needle not work then?

        • chrimony
          Posted Jun 25, 2015 at 5:37 PM | Permalink

          There were texts before the season and during the season. In fact, after the Jets game and before their next game, there were text messages with Jastremski saying, “Can’t wait to give you your needle this week :)”, with McNally replying, “Fuck tom…make sure the pump is attached to the needle…..fuckin watermelons coming” (McNally being the guy who was caught on video taking the balls into the bathroom, pissed off at Brady here because of the rebuke following the Jets game).

          Don’t know what happened with the Jets game that the balls were overinflated, but you would have to bend over backwards to put an innocent spin on these text messages, combined with the fact that McNally took the balls with him into a bathroom and then brought thm back in the Colts game.

        • MikeN
          Posted Jun 25, 2015 at 8:25 PM | Permalink

          The Wells Report presented things as McNally is guilty, so then everything gets interpreted by the reader in that light. For example talking about how he was unable to inflate the footballs in the locker room because of the extra personnel that week.
          This evidence seemed self explanatory at the time. He didn’t bring balls back, he continued on to the field, meaning he stopped to use the bathroom.
          The text had to do with issues of giving needles to the refs for when they do the pregame checks. The watermelon is he’s saying he won’t help Tom in making sure the refs get it right.
          If he was deflating as a conspiracy, why do they have to give him a needle every week?

      • Rob Potter
        Posted Jun 25, 2015 at 9:52 AM | Permalink

        The text messages show nothing of the sort. They show a couple of people making jokes with each other. You may consider them as “conspiring to deflate the balls”, but that is your opinion. As to contact between Brady and the “conspirators” – what would you do if you were suddenly accused of something? You would contact the people involved and ask them what is going on. To NOT contact these people would have shown a much more guilty position on the part of Brady.

        You say you are a Pats fan, but it is clear that you have already made up your mind by referring to “video of the perp”. I get tired of people always being referred to as “alleged” perpetrators, but this is exactly the point Steve is making – you have to bend over backwards to keep an open mind otherwise everything becomes confirmation bias.

        Steve has pointed out that – in his analysis of the measurement data – the report did not consider all options for environmental factors. This in itself shows that the author(s) of the report did not go into this with the required “open mind”. It seems plenty of other people have already made their minds up on this issue.

        • MikeN
          Posted Jun 25, 2015 at 11:55 AM | Permalink

          Indeed, this was the case of the dog that didn’t bark. If Brady is conspiring, why no immediate phone calls to talk about what the investigators asked? Why wait until morning?

        • chrimony
          Posted Jun 25, 2015 at 5:50 PM | Permalink

          Yes, they are joking with each other… about deflating footballs.

          I am a Pats fan, and I initially gave them the benefit of the doubt. I thought it was entirely plausible environmental factors caused the discrepancy, and initial reports wondered just how they would deflate the balls in the first place after the officials checked their pressure without anybody noticing. It was after the report came out that included the text messages and the fact that there was video of McNally taking the balls into a bathroom that led to my mind being made up. So to me he is a perp, not even alleged.

          And no, you don’t have to “bend over backwards” to keep your mind so open that your brain falls out. The analysis by McIntyre only shows that it is plausible that environmental factors could explain the measurements within uncertainty. However, it doesn’t state that environmental factors were likely the cause. Nor does it explain the text messages combined with the fact that McNally took the balls with him into a bathroom.

        • Steve McIntyre
          Posted Jun 25, 2015 at 9:31 PM | Permalink

          it doesn’t state that environmental factors were likely the cause.

          the question is whether the Wells Report established technically that it was “more likely than not” that the balls had been tampered with in the AFC Championship game. I don’t see how anyone can conclude that the technical data shows that.

          An issue that I didn’t parse in my writeup, but which deserves more analysis, is that Exponent’s deflation experiments resulted in consistent ~0.72 psi deflation which doesn’t match the observations at all with Logo initialization of Patriot balls (where no tampering matches just fine) and is about as far below with Non-Logo initialization as no tampering is above. So Exponent cannot say that this is “more likely” than no tampering.

        • mpainter
          Posted Jun 25, 2015 at 6:32 PM | Permalink

          There is no reason why “deflating footballs” cannot be a standing joke among Patriots employees. To joke about something like that seems natural and normal. There is more than one interpretation that can be put on the vague text references.
          Deflation now is no doubt a joke with many NFL personnel, and what does that mean?

        • MikeN
          Posted Jun 25, 2015 at 8:27 PM | Permalink

          Oh it wasn’t deflate and enjoy the shoes, it was deflate and give somebody that jacket. The Pats explanation that he was on a diet makes sense here.

      • Posted Jul 16, 2015 at 12:30 PM | Permalink

        The problem is that it’s nearly impossible to conjure up a rational tampering explanation based on the ball measurements.

        Look at the average differences from expected using a 71F indoor temperature in the pre-game and Exponent’s slower recalibration curve:

        3 Patriot balls clearly were unarguably not deflated. So right off the bat, you need a tampering scheme that involves only deflating a few balls — how does that make sense? In inclement weather games, they sometimes go more than 12 balls deep in a rotation.

        Assuming someone could explain that, another 3-6 balls are literally a few tenths below expected, which is *exactly* what would be expected by a ball that is moist/damp. It would border on physically impossible for none of these balls to be below what is expected based on temperature alone given that it was raining that night.

        So you’re left with an explanation in which only a few balls are deflated, and those balls are deflated by 1-2 PSI, but instead on order of a few tenths of a PSI. You’d have to believe something completely contradictory for this to make sense: That Tom Brady is so particularly about PSI that a few tenths matter to him that he has McNally deflate (despite him not being able to naturally detect natural PSI changes with temperature, but that McNally only deflates a few footballs. Keep in mind, all of the halftime measurements are quite inline with what physics predicts.

        Frankly, none of it really makes any sense based on the measurements.

  6. Posted Jun 23, 2015 at 6:02 PM | Permalink

    I think this might have a problem on pg 13:
    The range of readings was 0.65 psi (from 12.55 to 12.3psig).

  7. Posted Jun 23, 2015 at 6:08 PM | Permalink

    Nicely done!

  8. Pat Frank
    Posted Jun 23, 2015 at 6:25 PM | Permalink

    The NFL seemed to be completely taken by surprise by the Ideal Gas Law…”

    Too funny! 🙂 It’s good to see that the intervening 6 weeks haven’t eroded your talent for drollery, Steve.

  9. Posted Jun 23, 2015 at 8:52 PM | Permalink

    Reblogged this on I Didn't Ask To Be a Blog.

  10. Posted Jun 23, 2015 at 9:52 PM | Permalink

    Reblogged this on

  11. Steve McIntyre
    Posted Jun 23, 2015 at 10:22 PM | Permalink

    If anyone has thoughts on evaporative cooling, I’d be interested. This phenomenon was raised in some sports blogs shortly after the game, but not pursued because it didn’t seem relevant to outdoor pressures in saturated air.

    But returning to the officials room with relative humidity of 20%, it seems easily a strong enough effect to potentially affect a deg F or two in the transient. I included some links to interesting Youtube demonstrations of the effect, including explanations of the “Dippy Bird” toy.

    • mpainter
      Posted Jun 24, 2015 at 5:36 AM | Permalink

      Evaporative cooling-a wet ball? In the case of deliberate evaporative cooling, alcohol would be much more effective than water.

      • Steve McIntyre
        Posted Jun 24, 2015 at 12:21 PM | Permalink

        The pheomenon that interests me is what happened in the officials’ room – and was entirely unintentional. No one was “trying” to cool the balls, but wet balls returned to the dry officials’ room would be cooled to some degree by evaporation.

        • dougbadgero
          Posted Jun 25, 2015 at 6:11 PM | Permalink

          It would depend on wet bulb and dry bulb temperature in the each location. Outside in the damp the wet bulb and dry bulb temps would be identical, or nearly so. In the equipment room it would depend on humidity, but it is completely plausible that wet bulb in the room was actually greater than wet bulb outside. In which case the ball would still heat up when brought into the room just somewhat slower as energy was lost to latent heat as the ball dried. This would be no easy problem to model with a T&H code. And I suspect the initial conditions are not known in sufficient detail.

          Is this info available?

        • MikeN
          Posted Jun 25, 2015 at 8:29 PM | Permalink

          I think the Wells Report has numbers for inside and outside humidity and temperature.

          Steve: outside saturated. inside 20% RH

        • Posted Aug 20, 2015 at 4:48 PM | Permalink

          Evaporative cooling would have had a dramatic effect in the locker room. Have you heard anything more on this?

          Note: 72F, 20% humidity => 50F wet-bulb temperature! (Learn how to use a psychromatic chart to figure this out). The wet balls should have barely risen in temperature (and therefore pressure) within the locker room.

          The graph from the Wells report showing rising pressure of a wet-ball can only have occurred if either the humidity was higher than 20%, or the ball was only partially wet (for example, there was water in the seams, but not on the major surfaces.)

  12. Posted Jun 23, 2015 at 11:50 PM | Permalink

    Presumably, the calibrations used homogenized data from a basketball in LA, upside down, which teleconnected to the game ball. A bit of peer review and we’re all good.

    You, Mr. McIntyre, are a Big Balls funded deflation denier.

    I rest my case.


  13. DB
    Posted Jun 24, 2015 at 7:47 AM | Permalink

    Was there not correlative weight and pressure readings taken from opponent balls, did they display the same differences, since they were present in the same conditions? Forgive my ignorance on this subject.

    • Tom T
      Posted Jun 25, 2015 at 2:03 PM | Permalink

      As Steve points out the colts balls were measured but not in what would be considered a good control.

      Personally I believe that the complaint itself is its own variable. The officials went into the locker room with the intent of seriously checking the patriots footballs. This makes this time different from all other times.

      The amount of over site brought on by the colts complaint is in itself a new variable. It makes sense to me that the officials spent more time on the patriots footballs than a usual inspection. Which let the Colts footballs warm more than usual. This is evidenced by 11 patriots balls being checked and only 4 colts balls being checked. The referees ran out of time.

      The wells report is making assumptions working from information supplied to them by the officials about a standard check. But this wasn’t a standard check.

  14. DB
    Posted Jun 24, 2015 at 8:09 AM | Permalink

    It’s all so stupid to be so caught up in, imo. Just finished reading your report Steve. They should forget about this entirely. In the future, return all balls back to official control, use same instrument to measure pressure of all balls. I mean the ways to fix this is so simple. Although I still hate the Patriots and Bellicheat.

    The truth is, that sometime within a few years, global warming will be so severe, weather extremes will be so severe, that football will be impossible. Air matresses will deflate and inflate within moments, and basketballs will deflate mid-air, while re-inflating before hitting the ground due to extreme temperature swings. Food production has been correlative to global temperature, so we will stop food production, therefore solving global warming, and any air pressure concerns within sports.

    • Shawn Marshall
      Posted Jun 24, 2015 at 3:26 PM | Permalink

      You are right – with global warming all footballs must be equipped with pressure relief valves:>)

      • michael hart
        Posted Jun 26, 2015 at 6:25 AM | Permalink

        Yes, but there’s going to be a new Golden Age of Ballooning.

    • Michael Edwards
      Posted Jun 28, 2015 at 1:01 PM | Permalink

      Love the snark. For one or two words, I thought there was some lefty issue but you hit the goal, and goal post, and then some.

  15. CaligulaJones
    Posted Jun 24, 2015 at 9:44 AM | Permalink

    Considering some would say that Warmists follow a religion, and that many would say the same about NFL (or all sports: don’t forget that “fan” is short for “fanatic”…) this is less parody than “reality hasn’t caught up to it yet”.

    See: Monty Python skits from 45 years ago…

  16. curious
    Posted Jun 24, 2015 at 9:57 AM | Permalink

    As DB note, clearly this is another area of human activity which is victim to the unfolding tragedy that is CO2 induced climate change. Not only do wider temperature extremes impact the consistency of ball pressures but, as the CO2 content of the atmosphere heads ever upwards, the speed of diffusion of out of rubber bladders can surely only be described as “unprecedented”. I believe that a tipping point in the extinction rate of ball sports is already locked in and only immediate and dramatic action will prevent us from a future world where bouncing ball sports are just a memory and our children know nothing but badminton. When will we learn?

    • Joe
      Posted Jun 24, 2015 at 11:11 AM | Permalink

      Curious – “prevent us from a future world where bouncing ball sports are just a memory and our children know nothing but badminton.”

      the most recent climate studies show that badminton cock will travel much slower in the CO2 laden air.

      • MikeN
        Posted Jun 25, 2015 at 8:31 PM | Permalink

        Feather or plastic shuttles? In my experience the squash players become very good at badminton.

        • joe
          Posted Jun 26, 2015 at 7:12 AM | Permalink

          Feather cocks – must keep the sport pure

  17. Matt Skaggs
    Posted Jun 24, 2015 at 11:05 AM | Permalink

    This is exactly the sort of narrow data re-analysis that often confuses juries into acquitting the guilty. That happens because the public is remarkably ill-equipped to judge the relative value of different kinds of information. Let’s step back and take a bigger perspective. The NFL and its contractors constructed an exhaustive root cause tree as to what could have caused the data discrepancies. That was the right move. They then attempted to systematically decompose the cause tree using data analysis and simulations, the right move again. Lacking the full set of information, they made assumptions to allow them to construct a reasonable set of scenarios. They also made simplifying assumptions to allow simulations. Next they mapped the supporting and refuting evidence against the cause tree and came to the conclusion that the Patriots doctored the balls. In doing so they probably overstated their case WRT environmental factors, as Steve claims. Rather than ruling out environmental factors, the NFL should have described the Wells report as supporting – but not conclusive – evidence for tampering. But resolution of the cause tree was not dependent upon the Wells report. As Chrimony attests, there was other strong supporting evidence, “1) They’ve got video of the perp taking the balls with him into a bathroom. 2) The text messages show two underlings conspiring to deflate the balls.” To that I would add Brady’s refusal to allow his phone records to be searched. So while some doubt can be cast upon the strength of the argument against environmental influences, that has little effect on the resolution of the cause tree.

    • Steve McIntyre
      Posted Jun 24, 2015 at 12:27 PM | Permalink

      Matt, equally one can say that Exponent’s analysis was “the sort of narrow data analysis that often confuses juries into” convicting the innocent.

      If they claim to have examined “all permutations”, then they ought to have done so.

      There were some points in Exponent’s analysis that also really seemed unfair to me – a point that I didn’t really bring out very well in my writeup. In particular, their discussion of Figure 30 simulations. They should have pointed out that the discrepancy between simulations and observation was within their uncertainty. Instead they emphasized the difference. They should also have pointed out that simulations at 71 deg F initialization would have been as low as observations. Their failure to do so really made their report look to me like motivated reasoning rather than an independent report.

      • MikeN
        Posted Jun 25, 2015 at 12:23 PM | Permalink

        Given the detail in the rest of the report of scenarios they simulated, I conclude they were paid by the hour, and made great effort to think of as many things they could do to get more money. If there are permutations missing from the report it is more probable than not that the testing was done but deliberately left out.

        Steve: as an analyst, the absence of Logo Gauge 71 deg F scenario disturbs me. They could argue why they think it unlikely, but the technical people should have left it on the table.

        • mpainter
          Posted Jun 25, 2015 at 1:11 PM | Permalink

          It is easy to imagine that they would have taken a more careful approach, had they known that their work would be dissected on Climate Audit.

        • MikeN
          Posted Jun 25, 2015 at 2:42 PM | Permalink

          When reading the report, I was surprised when they said the Logo gauge and No Logo gauge made no difference given the small changes under discussion. I didn’t notice the omission of 71F.

          Steve: Exponent’s “trick” is easy to miss, but so was hide-the-decline. It isn’t mentioned by either MacKinnon or Hassett et al. But once you notice it, it’s hard to maintain a belief in their impartiality. Their conversion to Master Gauge scale also seems to me to hide another ~0.12 psi. Notice how the consistent 0.38 psi difference between paired measurements shrinks under the conversion. I mentioned this in my writeup but perhaps didn’t emphasize it enough.

    • Steve McIntyre
      Posted Jun 24, 2015 at 12:40 PM | Permalink

      Matt, construed fairly, I think that the data considered in the Wells Report should not “support” a finding of tampering.

      A further comment on the role of “narrow data analysis” and guilt/innocence. In Ontario and elsewhere, there have been scandals about oversold and false data analysis by forensic specialists, used to convict the innocent – sometimes when no crime was committed. I recall such things from the news but haven’t googled references other than

      Anderson’s recollection was that he used the Logo gauge and, according to that gauge, in my opinion, the data does not show tampering, with the very slight effect purported by the NFL, only due to adverse reasoning.

      • Shawn Marshall
        Posted Jun 24, 2015 at 3:33 PM | Permalink

        has anyone considered whether increased CO2 in the balls caused backradiation heating thus raising the pressure and maybe Brady was simply trying to comply with the rules?

    • Follow the Money
      Posted Jun 24, 2015 at 3:27 PM | Permalink

      This is exactly the sort of narrow data re-analysis that often confuses juries into acquitting the guilty.

      This ‘case’ would never get to a jury. Two gauges with two different readings…admitted by the quasi-prosecution here no less?? A judge would not even get to the atmospheric physics theoretics. Consider a drunk driving prosecution. Defense lawyers spend much time attacking the science and procedures, the maintenance of testing equipment and so on. There’s a not insignificant industry of technical expert witnesses involved in these cases for prosecution and defense. The testing ‘evidence” would be laughed out of court.

  18. Les Johnson
    Posted Jun 24, 2015 at 12:07 PM | Permalink

    I had done the calculations right after the incident was reported. From 72 deg F to 45 deg F, using the COMBINED GAS LAW (not ideal), the pressure would fall to 13.3 psi.

    But here is the kicker. The NFL does NOT specify the temperature at time of testing!

    The Patriots could have inflated the balls to the legal lower limit, at a temperature of say 85 deg F. By game time, they would have deflated to nearly 12 psi.

    Not specifying the test temperature makes any test meaningless. One could get any pressure you wanted, by simply varying the temperature at inflation and testing time.

    Steve: the balls are delivered to the officials’ room an hour or so before measuring. Realistically they were measured at that room temperature which was believed to be 67-71 deg F. My guess is that it was more likely 71 deg F than 67 deg F.

    • Les Johnson
      Posted Jun 24, 2015 at 12:23 PM | Permalink

      Yes, in that timeline the football should have been at ambient. But as you state, that is a wide range of possible ambient temps.

      But my point still stands. Not defining test temperature makes the pressure measurement meaningless.

      Steve: in that respect, yes. In very cold weather, the NFL has prevented teams from warming footballs, even though non-warmed footballs would be out of pressure compliance. So it’s not as though the NFL was rational on this. Also, the NFL had no protocols for gauges. The amount of supposed deflation is dispute is the same amount as the bias between gauges.

      • MikeN
        Posted Jun 25, 2015 at 10:06 AM | Permalink

        Prevented teams from warming them, but there are sideline heaters during the game. If the Colts gameballs go near those heaters, either inadvertently or ‘inadvertently,’ then even the Logo vs Non Logo explanation is not needed.

  19. Steve McIntyre
    Posted Jun 24, 2015 at 12:17 PM | Permalink

    Pielke Jr blogs on Deflategate mentioning this post:

    • Posted Jun 24, 2015 at 5:19 PM | Permalink

      Just yesterday, Steve McIntyre, known for being a thorn in the side of climate scientists via audits of some of their work, published his own critique of the Wells report. Like AEI, McIntyre finds the Wells report to be fatally flawed.

      Insert joke about Climateballs. I’m tired 🙂

      Steve: Nice. 🙂

  20. stan
    Posted Jun 24, 2015 at 12:44 PM | Permalink

    Steve, there is another stats related analysis on this topic. You might enjoy sinking your teeth into it as well. This guy looked at the fumble numbers for the Patriots since the new rule was adopted allowing the teams to supply the balls. I’m really curious how much stock to put in the fumble analysis. Here is an example —

    • MikeN
      Posted Jun 25, 2015 at 10:09 AM | Permalink

      I think that is more correlation does not imply causation. More likely is that Bill Belichick got an analysis that led him to emphasize players who don’t fumble. He took his starting running back who fumbled a lot and in one game just had him walk up and down the sideline with a football.

      Steve: the idea that the most successful team of the period would be attentive to not fumbling is unsurprising to me. In respect to the Wells Report, the issue is irrelevant since the Wells Report didn’t discuss it or rely on it. If they had, we could see how they addressed this issue, but in respect to the report itself, it’s moot.

      • stan
        Posted Jun 25, 2015 at 1:52 PM | Permalink

        Sorry. The idea that the Pats coached non-fumbling better is ridiculous. Seriously. Having played and coached major college football, I can’t believe anyone is silly enough to even try to make that argument.

        I just asked if you wanted to take a look at it. I didn’t say Wells did. It is related.

        • mpainter
          Posted Jun 25, 2015 at 2:16 PM | Permalink

          If under inflated balls were the cause of the Patriot’s outstanding fumble record, I have no doubt that every coach in the NFL will be straining his brain trying to figure out how to circumvent the pressure rules.

          Some coaches are more effective than others. That is why we have winners & losers, coaches that last & coaches that come and go.

        • MikeN
          Posted Jun 25, 2015 at 5:16 PM | Permalink

          Just as they say it is ridiculous to claim that PCA creates hockey sticks. It merely elevates them to the top. Belichick signed Ben Jarvis Green Ellis who went 4 years without fumbling.

        • Gdn
          Posted Aug 1, 2015 at 10:12 PM | Permalink

          Some of the issues:

          1) the comparison of Patriots players fumble rates when they play for the Patriots to when they play for other teams is completely reliant on the miscategorization of a single players kick-return fumbles as RB or WR fumbles. Kicking balls are fully controlled by the referees.

          2) the author uses seemingly innocuous reasons to artificially exclude teams which have offensive styles similar to that of the Patriots since 2007 (when they majorly changed offenses), and which have similarly low fumble rates.

          3) the author uses fumbles lost, rather than fumbles. For fumbling – the statistic purported to be due to a very small PSI change – the Patriots have only been best in the league once.

          4) the Patriots fumble less on the road – where the balls are under the control of the opposing team – than they do at home games. Unless you subscribe to the counter-intuitive proposition that the Patriots’ opponents have been conspiring to provide an advantage to the Patriots, this seems a pretty strong piece of evidence that the author has strung some misleading and cherry picked strings together.

          Here’s a collection of analyses:

  21. dearieme
    Posted Jun 24, 2015 at 2:10 PM | Permalink

    “The NFL does NOT specify the temperature at time of testing!” Cretins.

    “Also, the NFL had no protocols for gauges. The amount of supposed deflation is dispute is the same amount as the bias between gauges.” Morons.

    It’s just as well there’s not much money involved in this business, eh?

    • Duster
      Posted Jun 24, 2015 at 6:51 PM | Permalink

      You have to keep in mind that the NFL is composed of jocks, not geeks. The hazards and limitations are self evident. The difference is similar to that between science reporters and scientists. One may have heard of STP, the other will know what it means.

  22. Mike Singleton
    Posted Jun 24, 2015 at 2:33 PM | Permalink

    Perhaps exploding footballs due to temperature driven over pressurization could be adopted as a new measure for global temperature?

    It may even be more accurate and less subject to “adjustments” than the thermometer based temperature records. Either the football has a hole in it or it doesn’t, a binary state that lends itself to computer modeling. Record keeping in the form of punctured footballs would consume a fair amount of storage so a business opportunity for some of the green investment funds.

    One can imagine the position titles, V.P. of broken balls etc.

  23. mpainter
    Posted Jun 24, 2015 at 2:58 PM | Permalink

    Some considerations:
    Most definitely a wet ball from a wet circa 50° F ambience would be delayed in warming when placed in a dry circa 70°F ambience. Some calculations might be made if all were quantified.

    But, how wet were the balls? Were they left exposed to the weather or were they protected and if so, how well?
    In this respect, did the practice of the opposing teams differ? In other words, were the Patriot’s balls more exposed than the other’s? Did field conditions differ from one sideline to the next, in terms of wind and weather? If the Patriot’s balls came in at half time wetter and colder, this could explain a lot of the difference in pressure, imo.

    • mpainter
      Posted Jun 24, 2015 at 3:01 PM | Permalink

      Nesting messed up again

    • Gdn
      Posted Aug 1, 2015 at 10:18 PM | Permalink

      The Patriots and Colts balls were both handled differently, and were subjected to different conditions.

      The Colts balls were protected from the rain in plastic bags, while the Patriots balls were sitting in a ball bag in the rain.

      The Patriots had possession of the ball during most of the second quarter, including all but a few seconds of the last five minutes.

      Counter to this, the Patriots were apparently using a Colts ball for part of the first half.

  24. Posted Jun 24, 2015 at 6:23 PM | Permalink

    There is no doubt that a softer ball is easier to handle. The Pats are right to use lowest allowable pressure. Did they overdo it?
    NFL should remove all balls from team control and require both teams to use the same balls.

    • Duster
      Posted Jun 24, 2015 at 6:53 PM | Permalink

      But then any screw up would be the due to an official. Can’t have that.

    • Gerald Machnee
      Posted Jun 24, 2015 at 10:52 PM | Permalink

      Maybe they did not want to play HARDBALL.

    • Navy Bob
      Posted Jun 29, 2015 at 6:39 PM | Permalink

      Sly – not by everyone. Aaron Rogers has said that he prefers harder footballs. He freely admitted, I believe in a press conference, that he routinely has his footballs overinflated, beyond the legal maximum. So in one case, the NFL severely punishes one team and its quarterback with what it admits is not hard evidence, but only more probable than not, based on improper statistical analysis and ambiguous at best text messages, while in the other case, there is ironclad proof – a freely given confession – that a player violated the exact same tampering rule, and the league does absolutely nothing, not even a comment. It’s easy to understand why many Pats fans feel the entire affair was a setup.

  25. Posted Jun 24, 2015 at 6:30 PM | Permalink

    Speaking of a wide range of temperatures and effects of the weather — Here is one that everyone seems to miss —

    There was a cold ball field which the Wells Report investigators completely missed. In Boston that January, the average temp was less than 25 degrees, and warmed up to 50 degrees suddenly before the game. The ground under the artificial turf would have been very cold. Artificial turf is designed to bring up coolness from below, so we can expect the wet turf field to be significantly colder than the air temperature. Just before halftime, the Patriots had a long drive during which many of their footballs were involved in, and those wet balls would have been cold from the turf.

    In essence, he Wells Report “Game Day Simulation” failed to include the Game. As the balls sat at the line of scrimmage on the cold turf in between each play, they cooled well below the air temperature. With a 15 to 20 minute rate constant, they still would have been feeling that cooling when measured at halftime. This explains the wide dispersion in Patriots pressures, as well as the lower average temperature.

    See for a more complete analysis.

    • Steve McIntyre
      Posted Jun 24, 2015 at 11:17 PM | Permalink

      I think that different wetnesses are the most likely reason for variability but through evaporative cooling, though one would need to do some simulations to demonstrate this.

      In one online demonstration of evaporative cooling, (see gauze was wrapped around a thermometer, secured by elastic, and dipped into water at room temperature then removed. The thermometer was connected to a computer and readings taken, as air was blown over it (by a hairdryer said to be without heat). The opening temperature was ~30.7-31.2. It then dropped 10 deg C to 21.5 deg C merely by air blowing on it.


      If evaporative cooling similarly lowered the ball temperature of some individual Patriot balls (in varying degree depending on wetness properties), then that would account for pressure variations.

      A point that I didn’t discuss in my article, but should have, were Exponent’s own deflation experiments. Exponent had armwavingly hypothesized that only tampering could account for observed pressure variations, which are large – again a topic that warranted discussion in my note. Late in the day, they commissioned employees to experimentally deflate balls, to show feasibility. The experiments showed that people could deflate 12 footballs in the time allowed, but – and Exponent failed to discuss this important point – the experiments resulted in very consistent deflations of ~0.72 psi per ball with very narrow standard deviation, either across observer or between balls. So their deflation experiments did NOT explain the variability.

      The consistent 0.72 psi deflation was achieved by three different Exponent employees with negligible practice. So inconsistent deflation as an explanation of variability is made less likely by their experiments.

      • MikeN
        Posted Jun 25, 2015 at 9:45 AM | Permalink

        I find it surprising that they managed to achieve such a consistent pressure while trying to establish that balls could be deflated in a short timeframe. Presumably to get footballs deflated quickly, you would be less precise. That they achieved such results suggests to me an inaccurate simulation.

      • dougbadgero
        Posted Jun 25, 2015 at 6:35 PM | Permalink

        Result of this experiment would depend critically on the humidity in the room. If RH was 100% temperature would not change when air was blown on it.

        Steve: as I noted in my writeup, the relative humidity in the room was a dry 20%.

        • dougbadgero
          Posted Jun 26, 2015 at 7:58 PM | Permalink

          That would result in significant evaporative cooling. However, that seems like an unrealistically low relative humidity. A typical HVAC system would not result in such a low RH. Assuming temperature was 74F, dewpoint is 30F. This is below the evaporator air side outlet temperature in a typical HVAC system………..unless the system is designed for a freezer. Do they use desiccant towers to dehumidify?

          Steve: here’s what Exponent said: “They were then exposed to a temperature of 72–73°F and approximately 20% relative humidity (which represents an approximation of the temperature and relative humidity in the Officials Locker Room at halftime) for 2 hours.”

        • dougbadgero
          Posted Jun 26, 2015 at 10:22 PM | Permalink

          Yup I saw that. I am questioning the accuracy. If I were building this in a T&H model I would attempt to determine provenance of all the data and get a physically plausible reason for the RH. What was the basis of their approximation?

          I don’t think your analysis would turn on that issue though. Based on my reading of the info the physical data is inconclusive. Not surprising, there would have been no reason for data to have been taken at sufficient granularity to model this properly. Culpability should have been based on other evidence.

        • MikeN
          Posted Jun 27, 2015 at 9:09 AM | Permalink

          Because of the connections to outside, might they have a dehumidifier like people put in basements?

        • dougbadgero
          Posted Jun 27, 2015 at 4:58 PM | Permalink

          A dehumidifier is just an AC loop. The problem with any AC system resulting in such a low dew point is that ice would be forming on the evaporator coil. That is why AC systems are not normally designed that way.

  26. Beta Blocker
    Posted Jun 24, 2015 at 8:37 PM | Permalink

    What is needed to prevent these kinds of controversies in the future is something we might call the US Game Ball Pressure Reference Network (USGBPRN) which uses a standardized set of procedures and standardized pressure measuring equipment to check the pressure of each football used in the NFL before, during, and after each NFL game; and which can be used to compare the pressures in one sample set of footballs to those used in other games between other clubs in other localities.

    We might even think about automating the collection of pressure data through use of onboard pressure measurement micro-devices which transmit a football’s internal pressure data in real time throughout the course of the game, allowing any pressure discrepancies which might occur to be caught immediately, with appropriate corrective actions then being taken as deemed necessary by game officials.

    • mpainter
      Posted Jun 24, 2015 at 8:51 PM | Permalink

      Or we could let game officials provide the game ball, as in days of yore.

  27. Posted Jun 25, 2015 at 6:23 AM | Permalink

    This might help; Rubber and Rubber Balloons: Paradigms of Thermodynamics (Lecture Notes in Physics).

    • mpainter
      Posted Jun 25, 2015 at 7:31 AM | Permalink

      It might help. The problem of the balls cooling evaporatively is a nice problem in thermodynamics.
      How much cooling could you expect of the air inside a wet football per evaporative cooling of the surface of the football, given ambient conditions of circa 20°F higher temperature (than the football) and say, 20% humidity, but no wind, and in circumstances of unquantifiable limited moisture on the ball’s surface?This is a theoretical problem, but best resolved, imho, by a recreation of the conditions experimentally.

  28. MikeN
    Posted Jun 25, 2015 at 9:15 AM | Permalink

    The football pressures were measured in the non-temperature-controlled shower room, adjoining to the temperature controlled room where the halftime measurements were made. The analysts calculated the effect of this on a day with a substantially different temperature than gameday, I think 19F. Could the smaller temperature difference on gameday mean the footballs started at a higher temperature?
    There is also the possibility of showers being used warming up the room.

    • MikeN
      Posted Jun 25, 2015 at 12:08 PM | Permalink

      I think 72, 73F as a starting point should be analyzed as well. Even though there is temperature control in the adjoining room, this is not the inside of a house. There will be plenty of heat loss, and there is a large crowd to increase the temperature.

  29. MikeN
    Posted Jun 25, 2015 at 9:17 AM | Permalink

    Could the ideal gas law calculations be affected by a change in n and V as well, due to condensation inside the football?

    • Posted Jun 25, 2015 at 11:49 PM | Permalink


      Could the ideal gas law calculations be affected by a change in n and V as well, due to condensation inside the football?
      Yes. If someone intentionally pumped in moist air, they could cause the balls to lose pressure at low temperatures and gain pressure at high temperatures. I estimate for a temperature change of 40-70, the effect could be 2 psi or so. If this was done the pressure in the balls would very more than you’d expect based on the idea gas law. So they’d be soft out on a cold field and harder in a warm building.

      • Posted Jun 26, 2015 at 12:22 AM | Permalink

        Correction– I misread the columns. I should have known 2psi was too big.
        The effect of water vapor evaporating could be manipulated to have an effect as high as 0.294 psi. (That’s ~ 2kPa/101kpa * 14.psi. It’s not zero– and a motivated team might use it to achieve on field pressure drops. The NFL method of testing balls would not be well suited to detecting this.

  30. political junkie
    Posted Jun 25, 2015 at 9:45 AM | Permalink

    At the root of this major crisis is the following (possibly apocryphal) background story:

    NFL game balls at one time were supplied by the home team. However, some parsimonious owner got upset by the visitors’ celebrating TD’s by throwing the balls into the crowd and got the league to force visitors to supply their own balls.

    Any truth to this?

    • MikeN
      Posted Jun 25, 2015 at 10:10 AM | Permalink

      No, Tom Brady and Peyton Manning are the reason for the change.

  31. MikeN
    Posted Jun 25, 2015 at 9:57 AM | Permalink

    Walt Anderson said he used the Logo gauge to measure pregame, but this memory was considered flawed by the Wells team, but they thought it was very important to include his recollection that he never lets the footballs go out with just the ballboy.

    The choice of gauges explanation falls apart when you consider the timeline presented by Wells of how the Patriots prepared the footballs. Exponent analyzed the gloving effect that Bill Belichick described in his press conference, and concluded that he was right but the effect wears off in about 30 minutes so it is not important. However, the Patriots footballs were inflated after the gloving, possibly immediately for each football. This would mean the Pats footballs as prepared by the team would have been higher than 12.5 as given to Anderson, according to the Pats gauge.

    • MikeN
      Posted Jun 25, 2015 at 6:40 PM | Permalink

      Correction, the Pats footballs would have been lower than 12.5 according to their gauge, when they gave the football to Anderson.

      Steve: not if their gauge was also biased ~.2-.3 psi as well. If Anderson’s gauge had drifted over time, then something similar would be possible with the Jastremski gauge as well. Note that the Jastermski gauge readings on the intercepted ball were consistent with the Logo gauge tho, as noted in my writeup, there is enough time uncertainty that it could also be consistent with other scenarios if enough time passed

      • MikeN
        Posted Jun 26, 2015 at 12:40 AM | Permalink

        By their gauge, I mean the Patriots gauge. They inflated at 12.0 according to their gauge, but by the time the balls get to the judge the pressure has increased.
        This is if Jastremski’s inflation happened after each ball was finished.

        • MikeN
          Posted Jun 26, 2015 at 12:41 AM | Permalink

          I mean inflated at 12.5 and then the pressure decreases, due to the gloving effect wearing off.

  32. MikeN
    Posted Jun 25, 2015 at 10:14 AM | Permalink

    Here is Bill Nye’s scientific confirmation of the Wells Report.

    Steve: what a bizarre and incompetent performance. If one is to judge Nye’s competence on climate change by his competence on football inflation, it’s not very flattering. It’s curious that he should be so anti-Patriot.

    • MikeN
      Posted Jun 25, 2015 at 12:00 PM | Permalink

      He could argue for either side. However, to continue to get money and attention speaking on global warming, he had to make the right choice. So he went with they are cheaters.
      It’s also possible he forgot all about the chemistry, as his show was 20 years ago.

    • Posted Jun 25, 2015 at 7:50 PM | Permalink

      Bill Nye pontificating about the absence of tornados in Norway:

      (interspersed with a video of a tornado in Norway)

      Nye is Norwegian for ‘No’, which is generally an appropriate response to his pontifications.

    • Gdn
      Posted Aug 1, 2015 at 10:38 PM | Permalink

      So…Nye cooled the balls, took no measurement of the pressure after cooling, and proclaims that he can’t tell the difference in softness between that ball and a pre-cooling ball?

      That is supposed to prove what? To the extent it is evidence of anything, it suggests only that he can’t tell the difference between balls at presumedly 13 PSI at 80F , and those which would be at 11.5 PSI at 51F…which would bolster Brady’s argument rather than his own.

  33. MikeN
    Posted Jun 25, 2015 at 6:03 PM | Permalink

    Another line of supporting evidence used is the difference in variation in the Pats’ measurements and the Colts’ measurements. They declared that having only four Colts measurements mattered, but then they went on to use it.
    If you look at the Patriots measurements and take them in groups of 4, you get 27 out of 330 combinations that have the same range or less than the Colts .40, and another 13 that are range .45.
    Almost half the combinations have a range .65 or less.
    The outliers are the footballs that have the highest pressure.

    • MikeN
      Posted Jun 25, 2015 at 8:35 PM | Permalink

      Almost 1/3 have .65 or less.

  34. MikeN
    Posted Jun 25, 2015 at 6:20 PM | Permalink

    One point of evidence against the Patriots is that the footballs seem be be losing pressure as the measurements are being taken. The same happens with the Colts, but to a lesser extent. The Patriots 3 highest measurements are at spots 1,6,7, while the last 3 measurements are in the bottom 5 PSI including the overall lowest.
    They do not explicitly say the measurements were taken in the order provided, but that is likely.

    Steve: A section on individual measurements would be worthwhile in a longer article. This curious behaviour is one of the reasons why I think that evaporative cooling is important. The Wells Report excluded volume change of footballs as a factor, but left the effect of wetness unexplained. If there was no tampering, then the lower pressures require (under the Ideal Gas Law) that ball temperatures were several degrees lower. The evaporative cooling examples result in similar temperature decreases, so it’s the sort of thing that the Patriot’s defence ought to have worked up on an experimental basis.

    • MikeN
      Posted Jun 26, 2015 at 12:48 AM | Permalink

      They measured the volume on the outside of the footballs and found no change, but I suggested an inside volume change for the gas with water condensation, which would also change the number of moles. Lucia suggested .2-.3 PSI.

      From the report it appears the Pats would have filled with 20% humidity air, so not an issue unless the Colts did something different.

    • Gdn
      Posted Aug 1, 2015 at 10:43 PM | Permalink

      An interesting graph posted showed that the slopes of cooling for the first five Pats balls, the next six Pats balls, and the Colts four balls are all pretty close…which could be suggestive of evaporative cooling as each set was taken out and measured…or randomness.

      The Weiss report did not seem to be able to determine details like this…or even the order of ball inflation and measurement of the Colts balls.

  35. MikeN
    Posted Jun 25, 2015 at 6:30 PM | Permalink

    Beyond the ideal gas law, there appears to be another phenomenon lowering the pressure of the footballs. Look at the postgame measurements. The Pats footballs were reset to 13.0 at halftime, which is the same as what the Colts started with. Yet there is a .7 PSI difference between the two sets of measurements.

    Steve: yes, the post-game is interesting. The Colt balls had another 0.7 psi to go to reach equilibrium. Applying the same amount to PAtriot balls shows that the NFL over-inflated the Patriot balls ABOVE league rules at half-time. That is the only proven tampering. The Wells Report conspicuously evaded any discussion of the full-time measurements. I have some notes on full-time that I meant to include, but didn’t quite finish in time.

    • Joe
      Posted Jun 26, 2015 at 2:26 PM | Permalink

      MikeN – The controversy is that the patriot balls deflated faster than the colts balls for reasons other than a natural process.

      A couple of points which may not apply but are worth noting

      1) as I read the AEI response to the Wells report, the Pat balls were measured first at halftime, so they would be cooler at the time of measurement having less time to warm up indoors and therefore lower psi. (common knowledge among cyclists is that you partly deflate you bike tires before putting the bike into the car to prevent the internal heat from blowing out the bike tires due to the heat build up and resulting increased PSI in the bike tire)
      2) secondly, if the balls are filled with compressed air or machine driven air vs a hand pump, the compressed air will also come with a powdery residue and/or an oil residue which acts to gum up the value seal resulting in faster deflation. Cyclists will often use a co2 cartridge to inflate a new tire when fixing a flat on the road. It is well known among cyclists that the co2 filled bicycle tire will deflate much faster than a hand pumped tire.

      I could not tell from my quick scan of the wells report if a machine pump or a hand pump was used. If a machine pump was used, then the deflation rate will likely be much faster.

      • MikeN
        Posted Jun 26, 2015 at 3:25 PM | Permalink

        By the end of the game, the Pats balls had deflated slower then the Colts, after a halftime reset at 13.0.

        • Gdn
          Posted Aug 1, 2015 at 10:46 PM | Permalink

          By the end of the game, the Patriots balls were over-inflated – including one of the four outside legal specs.

  36. EdeF
    Posted Jun 25, 2015 at 6:59 PM | Permalink

    I love evaporative coolers…..we swear by them out here in the high desert where you have extremely low humidity. If you have a wet ball sitting in-doors near a fan on a winter’s day where the humidity is low, you could get pretty good cooling. Humidity levels east of the Mississippi are generally much higher than out here in the west.
    I guess we all did the PV=nRT thing when Deflategate first came out. I see many cases where the ball pressure can fluctuate as mentioned above. How about keeping a sack full of balls on the sidelines at Pasadena early September when the temp is 102 F. I played tons of football in my youth and never really thought about the ball, it was mainly blocking and tackling that we were concerned with in the old single-wing days. Too much passing now.

  37. Rick C.
    Posted Jun 25, 2015 at 10:17 PM | Permalink

    There seems to be a misconception that Exponent was expected to be or intended to be impartial. The name says it all. They set out to support their paying clients case, regardless of the “facts”. This is what they do.

    • mpainter
      Posted Jun 25, 2015 at 10:24 PM | Permalink

      Well now, this is an interesting thought.

  38. chrimony
    Posted Jun 25, 2015 at 11:40 PM | Permalink

    Steve McIntyre: “the question is whether the Wells Report established technically that it was “more likely than not” that the balls had been tampered with in the AFC Championship game.”

    That is ONE question that you have supplied a negative response to, but the question people ultimately care about is “Did the Patriots intentionally deflate the balls?” In the thread and post you are replying to, I’m judging based on the text messages and video in the affirmative, and this evidence you do not address at all. Thus, while your analysis does not rule out environmental factors, notably, it does not rule out intentional deflation, either.

    By the way, I would have replied to your comment in-place, but it seems at a certain depth replies are forbidden. Yay for crappy technology that can’t match features of Usenet from 30+ years ago.

    • glenndc
      Posted Jun 26, 2015 at 9:25 AM | Permalink

      Mr. Chrimony,

      The video you refer to, as well as the two text messages, are only suspicious in the context of significant deflation having been found. As you acknowledge in your opening sentence, such was not the case, ergo, any video or texting is now decontextualized, and shows nothing of significance other than humans behaving.

    • chuckrr
      Posted Jun 26, 2015 at 9:27 AM | Permalink

      I’ve read the text comments. Before I read them I was under the impression that they clearly displayed evidence of tampering. And when I read them with the associated commentary I could see why some people came to that conclusion. But then I read them and discounted the writers obviously predetermined slant. I could see two guys making jokes about their jobs. Imagine that. I could see the guys in charge of inflating the balls talking about needles. Imagine that. I could see Brady at some point complaining that the balls were over inflated so the guys may have to deflate them and they make jokes about that too. Imagine that. And I could see a guy going to the bathroom. That I don’t want to imagine..

  39. Navy Bob
    Posted Jun 26, 2015 at 8:24 AM | Permalink

    snip – a little OT.

    I was struck in particular by these AEI observations: “Second, the Wells report’s statistical analysis cannot be replicated by performing the analysis as described in the report. Third, the Wells report’s results can (for the most part) be replicated when we use a different, flawed modeling approach that fundamentally differs from the approach described in the report.” That sounded very familiar.

    To Chrimony’s point about the supposed damning nature of the text messages: If the balls’ pressures are within the bounds of what’s expected from natural cooling, then the texts are irrelevant – there’s no crime in the first place. And the texts that some feel implicate Brady refer to his displeasure with balls in a previous Jets game that felt “like bricks” because they were inflated by the referees to near 16 psi – far above the legal limit. In other words, the referees themselves violated the rule in that game. Brady simply wanted to make sure the balls’ psi was at the low end of the legal range.

    Also Steve – that’s a brilliant insight about time perception being different for great athletes – standing still for Brady while lesser mortals have to play rushed.

    Steve: I played a lot of squash doubles with a partner who was a better player than me. He could get to a ball early and had the ability to seemingly check the opposition spots and then hit the ball to the best of three different locations. I used to use compare this skill to Brady, comparing this ability to Brady checking off receivers. By contrast, it always seemed to be that I was rushed by the time that I was hitting the ball. I’m good at anticipating where opponents would probably be and would hit to good spots based on anticipation, but it’s second-string technique in comparison.

    • MikeN
      Posted Jun 26, 2015 at 1:12 PM | Permalink

      Navy Bob, the texts are irrelevant only if the science can eliminate the possibility of deflation. Given the possible different temperature starting points, a small deflation cannot be ruled out, although the lack of variation in the simulation by Exponent might do just that.

      • Navy Bob
        Posted Jun 27, 2015 at 5:46 AM | Permalink

        Mike – have to disagree. All possibility of deflation doesn’t have to be eliminated. Remember the Wells report standard for conviction was “more probable than not.” If there’s only the possibility of a small deflation at one temperature starting point, it wouldn’t even meet that squishy criterion i.e., it would be less probable than not. The texts were too ambiguous by themselves to establish anything. They only constitute “proof” in the minds of those already convinced by the Wells report’s faulty statistics. Or in Henry’s case in Steve’s following post, those consumed by hatred of all things Patriots. Read objectively, the inflation-related texts were referring to Brady’s dislike of illegally OVER-inflated balls. Over-inflation is the only level referred to, not under-inflation.

    • MikeN
      Posted Jun 26, 2015 at 1:16 PM | Permalink

      Not so much checking off but reading the defense early. Mike Lombardi said there was one game where Brady didn’t throw to an open receiver because the receiver should not have been open with the way the defense was playing.
      The Patriots also have an immense system of offensive playcalling that allows Brady to play faster.

  40. Beta Blocker
    Posted Jun 26, 2015 at 9:26 AM | Permalink

    As part of Exponent’s investigation, did they determine if the Patriot’s game balls were part of the same batch supplied by the manufacturer — a batch of footballs which presumably had been manufactured in the same facility on the same day using the same techniques and construction processes?

    Were the Patriot’s game balls tested to ascertain whether or not they were capable of holding a constant pressure under constant environmental conditions?

    Were such tests performed both at the playing field temperature present on game day, and at the higher temperature present inside the locker room on game day?

  41. AndyL
    Posted Jun 26, 2015 at 11:57 AM | Permalink

    Having read this thread and Steve’s article, I come to two conclusions:

    1. The degree to which America and American sport are tied up in legalities is astonishing
    2. These legalities are one possible reason why American sports are barely played in the rest of the world.

    Steve: Seems to me that FIFA is tied up in legalities as well. Basketball is very popular internationally. It also seems to me that rugby and U.S. football are, in a sense, different dialects, rather than completely different sports. I played football at high school, but found it very easy to adapt to rugby when I was at university in England. Even cricket and baseball are, in their way, different dialects though further apart than rugby and football, rather than completely different sports. I played cricket for my college in England, never having played before. Entirely as a fielder, but I still remember scoring 18 runs in the first over that I ever batted. Usually I didn’t bat. I took 6 big baseball swings and got 4 boundaries. Then they put in a spin bowler and I was gone.

    • AndyL
      Posted Jun 26, 2015 at 7:03 PM | Permalink

      Steve, with your ball-skills I’m not surprised that you could successfully transfer from one sport to another.

      In an evolutionary sense, I’d say the related sports have separated into different species – perhaps like dogs and wolves. One could argue the sports are closer, perhaps like horses and donkeys. My main point though was that in this case lawyers are involved in interpretation of the rules of the game. The rules themselves are amazingly legalistic. This is unlike Fifa where lawyers are involved in the organisation and its politics.

    • StuartG
      Posted Jun 27, 2015 at 2:09 PM | Permalink

      OT – Delete if too personal or irrelevant

      Steve according to Wikipedia you attended Corpus Christi College Oxford.
      That means that you played for Corpus rugby 13 years before I did.
      Any thoughts about attending any events for the quincentennial in 2017?

  42. H Davis
    Posted Jun 27, 2015 at 4:00 PM | Permalink

    In football, except for interceptions, the football is handled exclusively by the team inflating it. Why define in the rules what this inflation pressure should be? The inflating team will live or die by its inflation decision relative to its own ball and that will not disadvantage the other team whatever it is.

    • chuckrr
      Posted Jun 27, 2015 at 4:40 PM | Permalink

      I know this is going more off topic so I understand if it’s snipped, but here’s a question that I haven’t heard answered. As you say the opposing team would rarely handle the Patriots footballs. So how did it come about that they would even be aware …if it is true?

    • MikeN
      Posted Jun 27, 2015 at 5:46 PM | Permalink

      Chuck it is because they did intercept.
      H the NFL sets the standard, and you do get an advantage with a lower inflation.

      • H Davis
        Posted Jun 27, 2015 at 6:07 PM | Permalink

        But if the other team can set their inflation pressure as they see fit and they agree that lower pressure is advantageous and set it so, then neither team has an advantage. If they think there is some advantage to a higher pressure they will feel they have the advantage and be happy whether they are correct or not.

        If there’s no rule there can’t be any cheating. Each team selects the inflation pressure that they feel gives them an advantage so both should be happy.

      • chuckrr
        Posted Jun 27, 2015 at 8:05 PM | Permalink

        I find it hard to believe a player that just intercepted Brady would b able to tell. Anything is possible but some defensive player that rarely handles the football intercepts from a hall of famer. Huge emotional high. I don’t think he’s thinking about the ball pressure.

        • Gdn
          Posted Aug 1, 2015 at 10:53 PM | Permalink

          The player that made the interception says that he couldn’t tell. The Colts equipment manager stuck a needle in the ball and brought the result to the attention of a league official.

    • ScottV
      Posted Jun 28, 2015 at 7:31 PM | Permalink

      I agree. Why have a rule about psi in a football. That’s absurd! Let the quarterbacks choose what is right for them. One team will win one team will lose. Why split hairs over it? The world is becoming so regulated that its stifling innovation. Jesus F-Ing Christ!

      • Glenn999
        Posted Jun 29, 2015 at 10:47 AM | Permalink

        Even better. Submit a rule change amendment to allow greater variability to the psi of game balls. I think the most important factor to remember here is that the refs were handling the balls during the first half and weren’t alarmed to the lack of pressure.

        If one of the goals of a football game is to improve the game, then allowing quarterbacks to use balls with a psi to their liking, would seem to improve their throwing ability, and thus the game. It doesn’t adversely affect anyone else on the field either…

      • Gdn
        Posted Aug 1, 2015 at 10:58 PM | Permalink

        The PSI rule for the footballs is a manufacturers (Wilson) recommendation for best results that pre-dates 1940. No one knows exactly when the pressure was put in the rule book, but it was in at least one version prior to 1940, with copies of the rule book since 1940 continuously available.

  43. Posted Jul 2, 2015 at 12:04 AM | Permalink

    I agree with MikeN that the facts in the wells report show the logo gauge was used to gauge pats balls pre-game – the wells report recounts how the pats prepped the balls that AM – they gloved a ball (temporarily raising it’s psi by .5 to .6, according to exponent study), then set the psi to 12.6. Also according to exponent, the increase in psi due to gloving wears off in 30 minutes, so each ball’s psi decreases to 12 – 12.1 by the time they get to Anderson to gauge. If he uses the logo gauge like he recollects, and the logo gauge reads .4 higher than other gauges, then he would get readings of around 12.5 with the logo gauge – imagine that, that’s exactly what he recollects!

    Then when you look at the pats logo gauge readings at half time, there is 0 evidence of tampering.

    So now when Mcnally stops to go to the bathroom on the way to the field, the science points to him actually relieving himself vs. deflating footballs.

  44. Posted Jul 2, 2015 at 8:41 AM | Permalink

    Stan, regarding the Warren Sharp’s fumble analysis, it’s been thoroughly debunked, so Steve may not want to spend time on it. Here are a few websites that have already done the analysis:


    2. Drew Fustin’s analysis also links to 5 other sites

    3. the Backpicks website critiques the wells report science also:

  45. jmarshs
    Posted Jul 15, 2015 at 5:06 PM | Permalink

    I’m late to the party, but what convinces me that tampering did take place is this:

    According to both Exponent and Dr. Marlow, the difference in the average pressure drops between the
    Patriots and Colts footballs is statistically significant. This conclusion was consistent regardless of the
    assumptions made as to which of the two gauges was used to measure the game balls prior to the game and at

    This can be most easily explained by the uncontrolled way in which the balls were haphazardly deflated, without a gauge, in the bathroom. Random amounts of air were released from the Patriot’s balls so they all arrived on the field with different PSI’s.

    Steve: please see earlier posts as the statement: “This conclusion was consistent regardless of the assumptions made as to which of the two gauges was used to measure the game balls prior to the game and at halftime” is untrue. If referee Anderson inadvertently switched from the Logo gauge on Patiot balls to Non-Logo gauge on Colt balls – as happened even under the heightened half-time scrutiny – there is no significant difference. Important technical statements in the Exponent report are simply incorrect, including the one that influenced you and doubtless many others.

  46. Gene
    Posted Sep 20, 2015 at 6:52 AM | Permalink

    An audit needs be done on the statement, “Tom Brady, the greatest quarterback of his generation”. A highly subjective statement. Matt Ryan, Peyton Manning, and Brett Favre are also candidates for such.

  47. Navy Bob
    Posted Oct 18, 2015 at 8:15 AM | Permalink

    Vengeance Bowl game 8:30 tonight – Patriots at Colts.

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