Deflategate: Controversy is due to Scientist Error

I’ve submitted an article entitled “New Light on Deflategate: Critical Technical Errors” pdf to Journal of Sports Analytics. It identifies and analyzes a previously unnoticed scientific error in the technical analysis included in the Wells Report on Deflategate. The article shows precisely how the “unexplained” deflation occurred prior to Anderson’s measurement and disproves the possibility of post-measurement tampering. At present, there is insufficient information to determine whether the scientific error arose because the law firm responsible for the investigation (Paul, Weiss) omitted essential information in their instructions to their technical consultants (Exponent) or whether the technical consultants failed to incorporate all relevant information in their analysis.  In either event, the error was missed by the NFL consultant Daniel Marlow of the Princeton University Department of Physics, by the authors of the Wells Report and by the NFL.




Much public commentary about the Deflategate controversy has been about the Ideal Gas Law. However, contrary to many misconceptions, Exponent fully accounted for deflation according to the Ideal Gas Law.  However, they observed that there was “additional” loss of pressure in Patriot balls for which they could identify “no set of credible environmental or physical factors”.   The Wells Report said that this “tends to support a finding that human intervention may account for the additional loss of pressure”:

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.

While Exponent did not expressly quantify the additional pressure loss – a very peculiar omission,  it was approximately 0.35 psi, as compared to an observed pressure loss of approximately 1.4 psi, due to changes in temperature and the balls becoming wet offset by slight warming during intermission.  Drawing on information in the Exponent Report (see article for details), for Patriot balls (left two columns) and Colt balls (right two columns), the figure below compares estimates of the impacts of cooling (Ideal Gas Law) and wet footballs to observed deflation during the intermission plus an allowance for warming during intermission.  Information for Colt balls reconcile almost exactly, but there is a discrepancy of about 0.38 psi for Patriot balls. This discrepancy is almost exactly equal to the bias of referee Anderson’s Logo Gauge (orange) – a coincidence that should alarm any analyst of this data (including Exponent, Marlow and Wells).


Figure 1. Reconciliation of Patriot and Colt pressure drops. In the right column of each pair, estimated warming through the intermission is added to the observed pressure drop to estimate the pressure drop at the start of the half-time intermission. In the left column of each pair are shown the pressure drop for dry balls (limegreen), an estimated average additional drop for wet balls and, for Patriot balls, the additional deflation arising from re-setting pressure after gloving.

Simulation of Patriot Ball Preparation

The newly identified error pertains to Exponent’s simulation of Patriot ball preparation for the AFC Championship Game – an issue originally pointed to by Patriot coach Bill Belichick at his press conference of January 24, 2015.

In their simulation of Patriot ball preparation, Exponent set football pressures to 12.5 psi, then vigorously rubbed the balls (“gloving”) for 7 to 15 minutes before stopping.  They observed that pressures increased about 0.7 psi, but that the effect wore off after 15-20 minutes – effects shown in their Figure 16 (shown below). From this analysis, they excluded Patriot ball preparation as a potential contributor to the additional pressure loss.


Figure 2. Exponent Figure 16. Original Caption: The pressure as a function of time while a football is being vigorously rubbed.

However, Exponent’s simulation neglected an essential element of Patriot ball preparation. According to the Wells Report (WR, 50), Patriot equipment manager Jastremski set football pressures to 12.6 psi after the vigorous rubbing.

Jastremski told us that he set the pressure level to 12.6 psi after each ball was gloved and then placed the ball on a trunk in the equipment room for Brady to review. [my bold]

The detail that Jastremski set pressure after gloving is not mentioned in the Exponent Report, only in passing in the Wells Report.  Exponent’s failure to mention this detail makes one wonder whether Paul, Weiss might have failed to transmit this detail to Exponent. The detail is critical: footballs so processed will have pressures of 12.1-12.2 psi at room temperature, about 0.3-0.4 psi below the NFL minimum of 12.5 psi.  This is illustrated in the re-statement of Exponent Figure 16 shown below, which illustrates the setting of pressure to 12.6 psi of footballs warmed by gloving, with the subsequent loss of pressure to 12.1-12.2 psi as the balls return to room temperature. The resulting amount of under-inflation is almost exactly equal to the amount of “unexplained” Patriot loss in pressure.football_fig16_with_gloving_transients

Figure 3. Re-statement of Exponent Figure 16. Red: Exponent transient shows effect of rubbing to increase pressure, together with a decline after rubbing stopped. Black: shows reduction in pressure from re-setting to 12.6 psi, followed by transients as ball temperature returns to room temperature. Twenty seconds allowed for setting gauge in above transients. Dotted vertical lines show 7-15 minutes from start of rubbing reported by Jastremski. Logo gauge values of 12.5 and 12.6 psi are shown on right axis, deducting the bias of ~0.38 psi.


“Logical Inferences” on Gauges

The battleground issue in scientific analysis of Deflategate has concerned which gauges were used by referee Anderson for pre-game measurement.  Exponent argued that, “despite the remaining uncertainty, logical inferences can be made according to the data collected to establish the likelihood of which gauge was used [by referee Anderson]”, a conclusion with which I agree, though the above analysis changes the conclusions.

Referee Anderson had two gauges, one of which (the Logo Gauge) measured about 0.38 psi too high, while the other gauge (the Non-Logo Gauge) was accurate.  It was observed almost immediately (MacKinnon, 2015; Hassett et al 2015) that the additional deflation of Patriot balls could be explained if Anderson had used the Logo Gauge for pre-game measurement of Patriot balls, a hypothesis that was consistent with Anderson’s own recollection that he had used the Logo Gauge.  However, Exponent argued that other information led to the “logical inference” that Anderson had used the Non-Logo Gauge for measuring both Patriot and Colt balls. They stated:

Walt Anderson recalled that according to the gauge he used (which is either the Logo or Non-Logo Gauge), all of the Patriots and Colts footballs measured at or near 12.5 psig and 13.0 psig, respectively, when he first tested them (with two Patriots balls slightly below 12.5 psig). This means that the gauges used by the Patriots and the Colts each read similarly to the gauge used by Walt Anderson during his pregame inspection.

Exponent had obtained dozens of gauges (all new gauges similar to the Non-Logo Gauge), none of which had a bias similar to the Logo Gauge.  From this information, they argued that it was “very unlikely” that both the Patriots and Colts could have had gauges that were “out of whack” (the term used by Wells) similarly to the Logo Gauge and therefore concluded that Anderson had used the Non-Logo Gauge for pre-game measurements.      This conclusion was endorsed in the Wells Report, with Wells’ being particularly vehement about the conclusion in the Appeal Hearing, comparing the possibility to a “lightning strike” – a term that he liked and used twice.

Wells was particular emphatic that use of the Logo Gauge was a “scientific” finding (rather than a conclusion from circumstantial evidence). Wells told Goodell:

The scientists, the Exponent people say they believe based on their scientific tests that the non-logo gauge was used.

Wells invoked “science” to explain away Anderson’s recollection of using the Logo Gauge as follows:

Look, this is no different than a case where somebody has a recollection of X happening and then you play a tape and the tape says Y happened. Now, the person could keep saying, well, darn it, I remember it was X. But the people are going to go with the tape. I went with the science and the logic that I had three data points. And that’s what I based my decision on.

Goodell was swayed by Wells’ vehemence and his decision expressly included the following finding on gauges:

There was argument at the hearing about which of two pressure gauges Mr. Anderson used to measure the pressure in the game balls prior to the game. The NFLPA contended, and Dean Snyder opined, that Mr. Anderson had used the so-called logo gauge. On this issue, I find unassailable the logic of the Wells Report and Mr. Wells’ testimony that the non-logo gauge was used because otherwise neither the Colts’ balls nor the Patriots’ balls, when tested by Mr. Anderson prior to the game, would have measured consistently with the pressures at which each team had set their footballs prior to delivery to the game officials, 13 and 12.5 psi, respectively. Mr Wells’s testimony was confirmed by that of Dr. Caligiuri and Professor Marlow. As Professor Marlow testified, “There’s ample evidence that the non-logo gauge was used”.

This reasoning is valid if the pressures were set without rubbing (the Colt balls) but leads to exactly opposite conclusions for Patriot balls.

Because the Patriot rubbing protocol resulted in the balls being under-inflated by approximately 0.35 psi at room temperature,  the only way in which Anderson  could have measured them above 12.5 psi was if he used the Logo Gauge.  This is based on exactly the same form of logical inference used by Exponent, but without their erroneous interpretation of Patriot ball preparation.

The corollary is that Anderson inattentively switched gauges between measuring Patriot and Colt balls.  While this seems peculiar, NFL officials did exactly the same thing at half-time – switching gauges between measuring Patriot and Colt balls – despite heightened scrutiny.  If Anderson put the gauge in his pocket after measuring one set of footballs,  it would be entirely random whether he used the same gauge for the other set of footballs.

Although the possibility of Anderson inattentively switching gauges for pre-game measurements was an important possibility (suggested, for example, by Hassett et al, 2015 pdf), at the appeal hearing (Hearing, 369:11), Exponent made the remarkable statement that they had been “told” not to consider such a possibility, which was not raised or analysed in the Exponent Report.  Surprisingly, this admission wasn’t pursued by Brady’s counsel at the Appeal Hearing and it is therefore unknown who gave these instructions or why.


An essential element of Exponent’s report were their comparisons of observed pressures at half-time to modeled transients of pressure changes through the half-time intermission as footballs warmed up, simulations illustrated in a series of figures (Figures 24-30). Remarkably, these simulations contained another error.  The Exponent Report stated that the Logo Gauge had been used to set pressure of footballs to 12.5 psi in Figures 27 and the right panel of Figure 28:

The Logo Gauge was used to set the pressure of two balls to 12.50 psig (representative of the Patriots) and two balls to 13.00 psig (representative of the Colts).

However, Exponent actually used a different gauge (the unbiased Master Gauge) to set pressures to 12.5 psi, resulting in transients that were approximately 0.38 psi higher than under the stated procedure. In the figure below, I’ve re-stated results from their simulations to show transients based on Colt pressures being set with the Non-Logo Gauge and Patriot pressures with the Logo Gauge.  In each case, there is plenty of time during which there is an overlap between observations and modeled transients, contradicting Exponent:


Figure 4.  Re-statement of transients from Figures 25 (Non-Logo) and 27 (Logo), basis 70 deg F, for Colt balls set to 13 psig using Non-Logo Gauge and for Patriot balls set to 12.5 psig using the Logo Gauge. 



The “unexplained” additional loss of pressure can be unequivocally seen to occur as a result of Jastremski setting pressure after gloving, rather than before.  This is a complete explanation, which precludes tampering after referee measurement.

Previous scientific critiques of the Wells Report had observed that Patriot deflation could be explained if Anderson used the Logo Gauge, but had been unable to overcome Exponent’s argument about the improbability of the Patriot Gauge being “out of whack” similarly to the Logo Gauge.  That weakness is overcome in the present analysis.  Correct modeling of Patriot ball preparation yields the “logical inferences” that the Patriot gauge was relatively accurate and that Anderson used the Logo Gauge.

Indeed, it is the Wells Report itself that requires an implausible “lightning strike”. Wells’ analysis requires that, out of all possible target deflations, the amount of Patriot deflation was almost exactly equal to the bias of Anderson’s Logo Gauge.  Any self-respecting analyst should have examined and cross-examined his data when asked to arrive at that conclusion.

Exponent expressly stated that their procedures were based on information provided by Paul, Weiss (Ted Wells’ legal firm).  While descriptions in the Exponent Report generally track descriptions in the Wells Report, the information that Jastremski set pressure after gloving appears only in the Wells Report and is conspicuously absent from the Exponent Report.  With present documents, it is impossible to tell whether Exponent was in possession of this information and neglected to include it in their simulation or whether Paul, Weiss neglected to transmit this information to Exponent. Either way, it is an error that has no place in a professional report.

Without these errors, Exponent could not have stated that there were “no set of credible environmental or physical factors” explaining the additional pressure loss.

Appeal courts are poorly suited to resolve such errors. There is another way to resolve the controversy. The scientific community takes considerable pride in the concept of science being “self-correcting”.  When a scientist has inadvertently made an error, the most honorable and effective method of correcting the scientific record is to issue a corrected report, and, if such is not possible, retraction.  The Deflategate controversy originated in scientific and technical errors and the responsible scientists and investigators should take responsibility. Even at this late stage, Paul, Weiss and/or Exponent and/or Marlow should man up, acknowledge the errors and either re-issue corrected reports or retract. If any of them do so, it is hard to envisage the Deflategate case continuing much further.

Advocate and even policy-makers often like to say that their conclusions are supported by “science”, but Wells’ enthusiastic use of the terms “science” and “scientific tests” as rhetoric to validate incorrect analysis should serve as a caveat

The complete paper is online pdf.


  1. Posted Jun 7, 2016 at 12:38 PM | Permalink

    It sounds as though your conclusion is that the Patriot procedure was to set the pressure to the low end of legal range immediately after gloving, which results in under-inflation. Is that accurate?

    Steve: their intent was to set it at 12.6 psi, at the lower end of the 12.5-13.5 psi range, while not at the very edge.

    • Patrick M.
      Posted Jun 7, 2016 at 1:33 PM | Permalink

      That’s what I’m reading. It looks like a premeditated method to temporarily raise the pressure during testing thus insuring that the balls would be below the legal pressure at game time. Does Volkswagen work for the Patriots?

      • Jon P
        Posted Jun 7, 2016 at 1:55 PM | Permalink

        Why would the Patriots do that, when they knew the officials would measure the game balls later in the day closer to game time and adjust them to within the limits? If not for the fact of Walt Anderson having two gauges and one “out of whack” the whole scenario would never have occurred.


        • Patrick M.
          Posted Jun 7, 2016 at 2:25 PM | Permalink

          Yes, why WOULD the Patriots do that when they knew the officials would measure the game balls later? Oh and it just so happened that the referee had two gauges one of which just happened to be biased high exactly the same amount that the balls were “deflated” by AND the ref just happened to use the biased gauge for the Patriot’s balls and not for the Colt’s balls? Tell me again about lightning striking…

        • Steve McIntyre
          Posted Jun 7, 2016 at 2:33 PM | Permalink

          however, one cuts it, there is a coincidence here.

          But before speculating on Patriot motives, you have to have an accurate idea of what actually happened and its effect. In my opinion, it is as certain as can be that Jastremski set the pressure to 12.6 psi after gloving. It is also certain as can be that the Wells Report failed to analyse the effect of that procedure, instead simulating something that they didn’t do. Are you agreed so far?

          It is also certain as can be that the effect of the JAstremski procedure is that the footballs were slightly under-inflated (~0.35 psi) when they returned to room temperature. This explains the observations.

          If you want to argue that the Patriots were culpable for what actually happened, you’re entitled to make that argument, but it’s a different argument than charging them with tampering with the footballs after measurement by the referee.

        • Patrick M.
          Posted Jun 7, 2016 at 2:46 PM | Permalink

          Steve, you are the statistical expert. What are the odds of randomly finding a gauge with exactly the right bias to offset the under inflation? Now calculate the odds that that biased gauge shows up in the referee’s pocket on game day. Now calculate the odds that the ref “inadvertently” uses the biased gauge only on the Patriot’s balls.

          Take your time. I have to go win the Powerball Lottery…

          Steve: since Anderson had two gauges, one of which had a bias of 0.38 psi, the odds of him using that gauge on Patriot balls would be 50%. He presumably had used the gauge in other games. What are the odds of him using the Non-Logo Gauge on Colt balls: 50%. The ex ante odds of that combination are 25% – not implausible. Afterwards, I’m saying that we can deduce that that’s what happened.

          Going into it, there’s no way that Patriots could know about Anderson’s gauges. So I don’t think that there is anything intentional about the slight under-inflation. If you think that it was intentional, then, as you say, Powerball.

        • Patrick M.
          Posted Jun 7, 2016 at 3:00 PM | Permalink

          No, no, no, you can’t say finding a gauge with the right bias is 50%:

          The article states:
          “Exponent had obtained dozens of gauges (all new gauges similar to the Non-Logo Gauge), none of which had a bias similar to the Logo Gauge.”

          You’re a Patriot fan aren’t you…

        • MikeN
          Posted Jun 7, 2016 at 9:41 PM | Permalink

          I don’t think it’s a coincidental match either, but for different reasons. I doubt the accuracy of the simulations that Exponent did for wet balls, as to how well they matched real game conditions. It involved misting of footballs in a controlled environment.
          The NFL took measurements throughout the year, and I think it is likely that if those numbers had confirmed the data in the Wells Report they would have been made public by now.

    • Jim p.
      Posted Jun 8, 2016 at 1:15 PM | Permalink

      Your new light on deflategate article is excellent (you might just want to proofread it closely and watch for paragraph redundancy) The logic and analysis are the best I have seen. Do Ted Olsen, Kessler and the Patriots have it?

  2. Don B
    Posted Jun 7, 2016 at 1:29 PM | Permalink

    Steve, have you received a response to your submission?

  3. Steve McIntyre
    Posted Jun 7, 2016 at 2:24 PM | Permalink

    In my opinion, there is zero chance that the procedure was “premeditated” to yield lower inflation. As discussed in the article itself, the procedure for the AFC Championship was not their usual procedure using leather conditioner. Because of worries about rain, they used an older manual gloving method that had not been used in Jastremski’s tenure. None of them thought about the slight deflation since the purpose of the gloving was the texture.

    Also, additional deflation at this stage would get picked up by any referee using an ordinary gauge. They could hardly have expected that Anderson would have a faulty gauge.

    Compelling evidence that they were unaware of the effect is the failure of Patriots (or anyone else) to offer this explanation in the Appeal.

    • Patrick M.
      Posted Jun 7, 2016 at 2:33 PM | Permalink

      Steve stated:
      “Also, additional deflation at this stage would get picked up by any referee using an ordinary gauge. They could hardly have expected that Anderson would have a faulty gauge.”

      The article states:
      “Exponent had obtained dozens of gauges (all new gauges similar to the Non-Logo Gauge), none of which had a bias similar to the Logo Gauge.”

      So I ask, is it not very peculiar that a gauge with just the right bias would happen to be used by the ref for only the Patriot’s balls?

      Up until now I had thought the whole thing was not worth pursuing, but now it looks very suspicious. There are too many coincidences lining up for this to be chance.

      • Steve McIntyre
        Posted Jun 7, 2016 at 2:41 PM | Permalink

        Anyway one cuts it, there is a coincidence. Once the gauge goes in the referee’s pocket between team measurements, it is 50-50 whether the same gauge or different gauges. So it’s not problematic that different gauges are used. It happened at halftime as well.

        Simply following the Patriot procedure through logically, one can see that it results in ~0.35 psi below 12.5 psi. We also know that Anderson’s Logo gauge was 0.38 bias. Looks like a coincidence to me.

        Are you suggesting that Patriots used a gloving protocol intentionally designed to under-inflate by an amount to match Anderson’s gauge? (This is the implication of the Wells Report.) That seems very farfetched to me.

        • Patrick M.
          Posted Jun 7, 2016 at 2:50 PM | Permalink

          Clearly Anderson had to be in on it. There is nothing farfetched about handing Anderson a gauge, (and some money), and telling him to use this gauge for the Patriot’s balls.

          Steve: there’s no evidence of such a conspiracy nor was such a conspiracy charged. On the contrary, Wells found that Anderson was very credible. There is also no evidence that 0.35 psi can be detected, while differences in texture can. When presented with evidence that contradicts the NFL’s original conspiracy theory against the Patriots, you are now concocting a new and more far-reaching conspiracy involving payoff to Anderson. You’ve gone full Lewandowsky.

        • Jon P
          Posted Jun 7, 2016 at 2:54 PM | Permalink

          lol @ Patrick

        • Patrick M.
          Posted Jun 7, 2016 at 3:06 PM | Permalink

          This stuff happens all the time. You still have your statistician’s hat on. Take that off and put on your detective’s (deerstalker), hat. Like I said, I had no real interest in this until you laid it out clearly in this article that there was an unbelievable sequence of coincidences that created the perfect storm around the poor Patriot’s. Yeah right. I prefer Occam’s razor. It’s not necessary for there to be ANY coincidences here…

        • MikeN
          Posted Jun 7, 2016 at 9:33 PM | Permalink

          I think he’s joking.

        • Patrick M.
          Posted Jun 8, 2016 at 8:37 AM | Permalink

          Me joking? Only slightly. If you look at the facts, the most straightforward answer is Anderson was in on it. It’s probably something like a 1 in 10,000 chance that Anderson has the biased gauge and only uses it on the Patriot’s balls. (Since the report states that “dozens” of other gauges were tested and were not biased like Anderson’s. I take that as at least 24 other gauges, then there are the two gauges in Anderson’s pocket. So that makes it, at best, a 1 in 26 chance that Anderson has a biased gauge and then a 50% chance he pulls it out his pocket for the Patriot balls and 50% chance he doesn’t pull it out of his pocket for the Colt’s balls.)

          Steve: I am unconvinced by your Anderson conspiracy theory and so we’ll have to disagree.

        • Patrick M.
          Posted Jun 8, 2016 at 8:47 AM | Permalink

          One more thing, the 1 in 10,000 doesn’t even take into account the odds that the bias complements the underinflation in amount and direction exactly. That’s where I think the odds will really grow. I bet you could go through hundreds, maybe thousands of gauges before you’ll find another one with the same bias.

        • Posted Jun 8, 2016 at 9:11 AM | Permalink

          Patrick M. –
          Your inference that Anderson participated in a conspiracy is, shall we say, idiosyncratic.

          Steve: This sounds like Kornheiser and Wilbon on Pardon The Interruption’s What’s The Word. Shall we say…. Lewandowskian.

        • MikeN
          Posted Jun 8, 2016 at 4:07 PM | Permalink

          Regarding the testing of other gauges, what they appeared to have done was to acquire lots of other new gauges, and found no discrepancy, and concluded therefore that it is highly likely that all other gauges held by other teams are similar to the new gauges they acquired and tested, and not like the errant gauge held by the referee.
          So your 1 in 26 or any other low odds cannot be calculated from the data in the report.

          Steve: with no information on Anderson’s gauge, I would say that the ex ante odds of Anderson measuring Patriot balls with a gauge with 0.38 psi bias are vanishingly small. But ex post, knowing that he had two gauges, one of which had a 0.38 psi bias, the odds are 50%. What’s to argue about?

        • MikeN
          Posted Jun 8, 2016 at 4:41 PM | Permalink

          He’s arguing that the probability is very low for Anderson to have such a gauge to begin with, therefore conspiracy. I think it is possible that there are many such gauges with this bias, and that Exponent’s conclusion of rarity is not valid.

          Steve: I’ve thought about this argument, largely because it sidetracked Kessler and Snyder. Exponent’s failure to survey old gauges was ludicrous, but the contemporary argument by Snyder and Kessler that the Patriot gauge was biased similarly to the Logo Gauge was no more than speculation. The analysis here entails that the Patriot gauge was accurate BTW. If it had bias similar to the Logo Gauge, then Anderson would have picked up the under-inflation even with the Logo Gauge. So that precludes Snyder and Kessler’s speculation.

          In the analysis presented here, it doesnt matter.

        • joe
          Posted Jun 8, 2016 at 5:48 PM | Permalink

          Is there any information on when they (the nfl) discovered that the gauges had the differences in calibration?

          Steve: it first became public in the Wells Report. Exponent figured it out from the half-time measurements; I would place their knowledge in February.

        • MikeN
          Posted Jun 8, 2016 at 9:31 PM | Permalink

          I agree it is just speculation. Only say that it is not valid to conclude rarity based on the testing done.

        • Patrick M.
          Posted Jun 9, 2016 at 7:52 AM | Permalink

          MikeN said:
          “He’s arguing that the probability is very low for Anderson to have such a gauge to begin with, therefore conspiracy. I think it is possible that there are many such gauges with this bias, and that Exponent’s conclusion of rarity is not valid.”

          Yes, my point is that the chance that the gauge with the needed bias is in Anderson’s pocket is the long shot.

          If Exponent’s statement about the rarity of the gauge with the bias is wrong, then my argument fails. But if someone were to test “dozens” of gauges and find none that have a bias of that magnitude then my argument is strengthened.

          p.s. I have no issues with Steve’s analysis of the situation. My issue is with how the situation came to be in the first place, (i.e. the long shot I mention above).

          Steve: some words trigger moderation. I agree that the odds of the “out of whack” gauge are vanishingly small ex ante BUT not ex post when you know that he had two gauges. I agree with MikeN that the Exponent survey of gauges was abysmal, but my guess is that a gauge with a 0.38 psi bias would be rare even in a better survey – so this was a debating point, rather than one fatal to the case. For a major decision, it wouldn’t have been that hard to ask Exponent to do a more thorough survey and eliminate the issue or not. But according to my analysis, the Patriot gauge was accurate and the topic ultimately a distraction.

        • MikeN
          Posted Jun 10, 2016 at 3:40 PM | Permalink

          Steve, you speak of a .38 bias being unlikely. Is it necessary to have a .38 bias? Wouldn’t .4 be enough?

        • DonM
          Posted Jun 12, 2016 at 11:28 PM | Permalink

          In New England we call arguments like Patrick M’s saying Anderson colluded – PDS (Patriots Derangement Syndrome). Some NFL fans from other regions are obsessed with the idea that the only way the Patriots win so often is a result of cheating. They can not conceive of an alternative.

          Steve: it’s similar to climate scientists and jihadis being obsessed with the idea that Koch brothers/Exxon are issuing instructions to climate sceptics and lukewarmers.

  4. Posted Jun 7, 2016 at 2:31 PM | Permalink

    Another factor that might be relevant is condensation: If the balls were inflated in a warm, humid locker room, and then taken onto a cold field, some of the moisture in the balls would have condensed, thereby decreasing the pressure even further. I haven’t quantified this effect, but I suspect it’s perceptible.

    Bill Nye the Science Quack made a YouTube video in which he invoked the Gas Law to argue that it only accounts for half the claimed deflation. However, although he remembered that temperature has to be measured relative to absolute zero, he forgot that pressure has to be measured relative to a total vacuum. Since atmospheric pressure is about 14.7 psi, this means that 1 psi is not 1 out of 12.5, but 1 out of 27.2, so that it was he, not Belicheck, who was off by a factor of about 2.

    To “prove” his point, Nye placed some footballs in a refrigerator to cool, and then afterwards squeezed them to determine that they hadn’t lost the requisite amount of pressure. Sad!

    As further “proof” of the correctness of his pronouncements, while the balls were cooling, he went on a tirade, mugging into the camera, about the perils of atmospheric CO2 and global warming.

    Steve: Nye’s comments were foolish. However, it is the Exponent Report that matters to the decision. While Goodell has borne the brunt of the criticism, he had a report from professionals saying that there was unexplained deflation; and the attempted rebuttals, which did not understand the after-gloving issue, were weak. I’d rather than get into non-Exponent related issues.

  5. mpainter
    Posted Jun 7, 2016 at 3:26 PM | Permalink

    Steve, one issue I have never seen addressed is the drop of approximately 0.1 psi in atmospheric pressure from the pregame period to half time. This drop is verifiable via nws station data at the airport (Norwood?), from the day of the game. The pressure data is hourly, I believe. I commented on this last time. This is the rain that began at game time (rain = lower pressure).

    Here is the point: a drop in ambient atmospheric pressure should produce a corresponding drop in ball pressure, unless I missed my physics.

    • Posted Jun 7, 2016 at 3:31 PM | Permalink

      I think that would go the other way —

      The absolute pressure inside the ball is not affected by the outside pressure (unless the ball can expand or contract perceptibly). However, the gauges measure pressure relative to atmospheric. So if atmospheric falls by .1 psi, the measured pressure goes up by the same amount.

    • mpainter
      Posted Jun 7, 2016 at 3:57 PM | Permalink

      Hu, remember that temperature fell from pregame to half time, with a corresponding drop in ball pressure., so the balls would have contracted, slightly (volume drop). I’m thinking that a drop in pressure would allow an adiabatic expansion of the balls and a volume increase with a pressure drop. I will own that I am no expert in these matters. Interesting, but ticklish.

      Steve: I’m declaring this off-topic to this post.

      • mpainter
        Posted Jun 7, 2016 at 4:59 PM | Permalink

        I am astonished. The topic involves the Ideal Gas Law. You should perhaps clarify which aspects of that Law you will/will not permit comment on, because your post touches on this in your charts and elsewhere.

        Steve: I’ve got new material in the article and want to keep focus on that, if you don’t mind.

      • MikeN
        Posted Jun 7, 2016 at 9:35 PM | Permalink

        This was covered in previous posts on the subject, here and at the Blackboard.

    • Posted Jun 8, 2016 at 6:14 AM | Permalink

      When pressure is measured relative to absolute zero pressure, it is called absolute pressure. On the other hand, pressure measuring devices often use gage pressure, which is measured relative to atmospheric pressure. Standard atmospheric pressure at sea level is 101.3 kPa or 14.7 psi.
      [ … ]
      For example, when the driver’s manual for your car suggests that you keep your tires at a pressure of 30 psi, it is refering [sic] to the gage pressure. This is equivalent to 44.7 psi absolute pressure.

  6. Scott Scarborough
    Posted Jun 7, 2016 at 4:07 PM | Permalink

    If you think that a football player can tell the difference between 0.35 psi inflation pressure in a football I’ve got some swamp land for sale for you in Florida!

  7. Kevin Qualters
    Posted Jun 7, 2016 at 5:33 PM | Permalink

    THank you for an excellent and thorough assessment.

    My suspicion from the onset is that the Patriots may have used a technique such as ” gloving” to induce a transient condition to their liking. Of course I don’t know if they did this, snd if so, was it intentional or circumstantial.

    Either way, I am certain there is no rule against it. And even if they did this, it is far less onerous than blatant moves used by other teams (such as heating balls on the sidelines) that resulted in nothing more than a letter from the NFL Office.

    • mpainter
      Posted Jun 7, 2016 at 5:42 PM | Permalink

      Kevin, are you forgetting that the the referee checks ball pressure? What advantage to the Patriots if the referee inflates the balls to whatever pressure that he likes?

      • Kevin Qualters
        Posted Jun 7, 2016 at 6:32 PM | Permalink

        Like I said, I have no evidence either way. But other information has come out that as a whole, PSI checks done by officials were very lax. I would assert that the evidence presented from this case bears it out. The Patriots may have tried it because they thought they could get away with it.

        For the record I am a Patriots fan, and if they did try to game the system a bit and did not tamper with the balls after the inspection, I have no issues with it at all.

        Steve: the charge was that McNally tampered with the balls in the washroom after inspection by referee.

        • Kevin Qualters
          Posted Jun 7, 2016 at 8:51 PM | Permalink

          A charge which I did not think the Patriots would be stupid enough to try to pull off, nor which is there a shred of evidence that shows that they attempted.

          As I said, at most they may have tried a little gamesmanship to gain a competitive edge, or make them feel like they had a bit of an edge. No different than most athletes in most sports. Certainly not a hanging offense.

          Some people might say that if that’s true, than why not just own up to it. Considering the circumstances & circus surrounding this fiasco, it is understandable ad to why they would do no such thing, especially given the ridiculousness of the punishment being suggested.

  8. MikeN
    Posted Jun 7, 2016 at 9:37 PM | Permalink

    > Exponent fully accounted for deflation according to the Ideal Gas Law.

    It really bugs me to hear Patriots owner Robert Kraft still talking about how the NFL ignored physics to reach their conclusions.

    Steve: Kraft and others are entirely correct that there was something wrong with the analysis. They are more right than the people who havent doublechecked and triple checked analyses that led to the odd conclusion that Patriots deflated balls by such a small amount and a small amount that matched the Logo Gauge bias so exactly. The word “physics” to Kraft might incorporate more than the Ideal Gas Law.

    • MikeN
      Posted Jun 8, 2016 at 4:09 PM | Permalink

      I’ll check, but I’m pretty sure he used ‘Ideal Gas Law’ in a statement made this year.

      • MikeN
        Posted Jun 8, 2016 at 9:32 PM | Permalink

        I personally believe that when the league made their decision, they did not factor in the Ideal Gas Law. They admitted that publicly. They had a full year of being able to observe Tom Brady play with all the rules of whatever the NFL was, and make any judgments there. We have laid it out pretty straightforward. And now it’s up for them to decide.

  9. MikeN
    Posted Jun 7, 2016 at 9:38 PM | Permalink

    Tom Brady’s lawyer Mr Kessler came very close to explaining this exact situation at the appeal hearing with Goodell, but he appears to have confused himself while making the argument and dropped the line of questioning. I wonder if it could have changed anything.

    Steve: I discuss this exact incident in the article itself, describing it almost identically. Check it out. I think that the question was accidental, but a correct response from Caligiuri could have changed the outcome.

    • MikeN
      Posted Jun 8, 2016 at 4:10 PM | Permalink

      Yea, I’ve wondered if the lawyer really did come up with that argument or just stumbled into it. Caliguiri can’t make a correct answer to a question so poorly asked.

      Steve: it looks to me like he stumbled into the question. If he’d understood the question, he’d have stuck to it like a bulldog. On the other hand, if Caligiuri had answered the question as asked (and it wasn’t worded all that badly IMO), he would have opened up a door which Kessler might have been able to go through.

      • MikeN
        Posted Jun 8, 2016 at 4:43 PM | Permalink

        If he stumbled into that argument, that suggests a great deal of quick thinking on his part, and perhaps with an accurate answer he would have been able to see it through.

      • MikeN
        Posted Jun 8, 2016 at 4:44 PM | Permalink

        The question does look fine. I just remember the entire line of argument as poorly asked. If he stumbled into it, then that is a different matter.

  10. Posted Jun 7, 2016 at 10:56 PM | Permalink

    Excellent observation Steve! I’ve just posted a workbook on DeflateGate Physics which notes the same problem. See , Investigation #1. I think the flawed deduction by the Exponent scientists probably colored their entire thinking in the report. Coupled with correcting Figure 27, which as you have observed in the past does not follow the Ideal Gas Law, this makes a conclusive argument against the idea of any tampering. I also created an Interactive Simulator (includes Evaporative Cooling, error estimates, etc) — which I hope to put up tomorrow — that allows people to try various starting conditions on their own to correctly generate those charts, and you can see that there are solutions that completely work for both the Patriots and Colts balls together, similar to your “restated transients” chart above. This is the solution the Exponent folks should have found. Excellent job! Thanks.

  11. Posted Jun 8, 2016 at 6:59 AM | Permalink

    Very nice work as usual. I’m completely convinced.

  12. Gary
    Posted Jun 8, 2016 at 7:55 AM | Permalink

    Yet this matters not in the slightest. The intent of the investigation was to find a way to hobble the Patriots’ success, which has been accomplished with a $1M fine, loss of two draft picks, and suspension of their star quarterback for a quarter of the upcoming season. Truth doesn’t matter, power does to those who benefit from it.

    • Steve McIntyre
      Posted Jun 8, 2016 at 9:21 AM | Permalink

      I’ve always tried to avoid editorializing about motives. It’s not that I’m unaware of motives or that I think that they don’t matter, but they are hard to prove and reasonable people can disagree about what motives they believe other people to have.

      There are also limits to what professional people will do. There are a number of ways in which Exponent’s error in the simulation of Patriot ball preparation could have arisen. While I am very critical of Daniel Marlow’s work, I do not believe that his original motives were venal or that he was party to a plot to “hobble” the Patriots.

      Similarly, however mercenary Exponent may be, I do not believe that they would make this sort of error deliberately.

      I think that the error in the simulation of ball preparation arose through a mistake on the part of Paul, Weiss in omitting an important detail in their instructions to Exponent or through a mistake on the part of Exponent in omitting an important detail in their simulation. Everything else follows from that.

      Armed with Exponent’s report, there were lots of people ready to pile on, but that should not distract from technical analysis which can and should be resolvable.

      • mpainter
        Posted Jun 8, 2016 at 2:12 PM | Permalink

        “Similarly, however mercenary Exponent may be, I do not believe that they would make this sort of error deliberately.”


        Litigation and science are similar in ways.
        They both present evidence, argue from points of law or principle, cite precedents, etc.
        But lawyers have a code they must adhere to, enforced by the court and the bar. Science has no such code or enforcement.

        How does a grunt scientist merit a raise at Exponent, I wonder?

        • Steve McIntyre
          Posted Jun 8, 2016 at 3:59 PM | Permalink

          One of the limitations on conduct by NFL consultants, including Paul Weiss, is that they probably had duties of care to impacted third parties, in a Hedley Byrne sense (under its equivalent U.S. tort cases). I’ve seen some not-particularly-well-informed commentary speculating about defamation claims, but that would founder on public figure and lack of actual malice (in libel sense). In my opinion, Exponent and Paul, Weiss would be more vulnerable to a tort action on negligence, i.e. that the error by Paul, Weiss and/or Exponent was negligent and breached a Hedley-Byrne duty of care to Brady and the Patriots. The higher the ostensible standing of the specialists, the more culpable.

      • Posted Jun 8, 2016 at 3:39 PM | Permalink

        On motives, what I like best from this model is that aside from fitting the facts better than any other description, and being a simple explanation,
        it ends up with the most people telling the truth. Nobody directly involved was trying to cheat, or deliberately trying to destroy one another.

        Jastremski was just trying to do his job, gloving, inflating and measuring the ball pressure. The effects of timing on ball pressure heating and cooling meant nothing to him at the time.

        Anderson was just trying to measure all the balls, and happened to choose one out of his two gauges which was inaccurate.

        From Exponents descriptions, it appears they were spoon fed the data from Paul, Weiss, and didn’t always have the full picture. This led to their mistaken conclusion. Fig 27 was probably just a mistake done by a tech switching graphs around, or an experimentation mistake, or simply overlaying the wrong chart. It is hard to see the problem because the pressure differentials are small, so the mistake was simply overlooked (with unfortunate disastrous consequences).

        When the dust finally settles on DeflateGate, it is good to see a scientific explanation that fits the known facts, is not ambiguous, and the mistakes that were made were understandably human. I believe that will be the one that survives.

        • Steve McIntyre
          Posted Jun 8, 2016 at 4:19 PM | Permalink


          You say:

          From Exponents descriptions, it appears they were spoon fed the data from Paul, Weiss, and didn’t always have the full picture.

          As I discuss in more detail in the article, it’s possible that Paul, Weiss left out an important detail or that Exponent had the detail, but failed to analyse it correctly. Either way, there’s an embarrassing professional error. If the NFL league office was at all sane about this, it would give them a way out by blaming the people who should be blamed: Paul, Weiss and/or Exponent and/or Marlow.

          On the other error:

          This led to their mistaken conclusion. Fig 27 was probably just a mistake done by a tech switching graphs around, or an experimentation mistake, or simply overlaying the wrong chart. It is hard to see the problem because the pressure differentials are small, so the mistake was simply overlooked (with unfortunate disastrous consequences).

          Exponent’s position on this is trickier. See the longer discussion in the article. The issue was very clearly raised in the Appeal Hearing. When confronted, Caligiuri took the position that the figure was calculated correctly. Kessler ought to have pursued him on the corollary that the procedure was described wrong in the report but got diverted into the dead end of whether the Patriots could have been using a biased gauge as well – as speculated at the time by Snyder (as an attempted rationale for the Logo gauge) instead of squarely confronting Caligiuei on the implied mispresentation in the report.

          One way or the other, Exponent should have issued a correction to something.

          I notified Marlow of the Figure 27 error last August and notified Wells of the error in late June.

        • mpainter
          Posted Jun 8, 2016 at 7:22 PM | Permalink

          It also squares with referee Anderson’s recollection that he used the logo gauge to measure Patriot ball pressure. This is going to cause some problems for Paul, Weiss and Exponent, it seems. Recall, Exponent rejected the possibility that Anderson had used the defective logo gauge.

    • MikeN
      Posted Jun 8, 2016 at 9:37 PM | Permalink

      I’m not sure if that was their original motive, or perhaps a related we think they’re guilty so who cares about the details, but at this point I think they have a motive of sticking to the punishments. Admitting they are wrong would be a big black eye. Plus the current legal issue is not over DeflateGate, but whether the league and the commissioner can apply penalties like this. They have been losing regularly in court with large penalties being thrown out. Whether Tom Brady plays a few games is irrelevant to their desire for the extra power.

      • Gary
        Posted Jun 9, 2016 at 7:12 AM | Permalink

        The original intent of the investigation was to weaken the Patriots, but you’re right that now it has become a power struggle between the Commissioner and the player’s union. The Court took scientific analysis out of it with the last ruling that upholds the suspension on contractual language grounds. Steve has done a masterful job with this forensic dissection, but it’s too late to have any influence on the case.

        Steve: as I observed, appeal courts are not the right place to sort this out. I think that the scientists have a moral duty to correct the scientific record though. If Marlow, for example, recanted, it would change the entire dynamic.

        • mpainter
          Posted Jun 11, 2016 at 4:59 AM | Permalink

          I disagree that the “appeals court took scientific analysis out of it” as a legal issue.
          The media reported that the decision cited “compelling evidence that the balls had been tampered with”. This “evidence” is the Exponent report.

          The adage that “judges like to rule on technical grounds but in accord with the facts of the case” comes to mind here. It seems that the appeals court was convinced that there was a crime.

        • Gary
          Posted Jun 13, 2016 at 9:35 AM | Permalink

          Living in the heart of Patriots country has provided me with 18 months of intense coverage of the issue. Local media has examined this daily for every angle of unfairness. National media has been more superficial. If truth were the objective then the physical evidence meticulously spelled out by Steve would eventually exonerate the team. But when the case got to the appeals courts, the argument had become about legal process, not the exculpatory evidence. It had become a labor dispute, not a rules violation issue. So yes, the courts are a terrible place to determine scientific fact. And yes, honest scientists should correct the record, but it’s rare that they do.

        • Steve McIntyre
          Posted Jun 13, 2016 at 1:18 PM | Permalink

          the problem is that appeals courts don’t want to re-litigate facts determined by an arbitration or they run the risk of every arbitration being appealed to the courts. Similarly, they will be reluctant to determine that an arbitration process was unfair or else they will get every arbitration appealed to the courts on the grounds of the process being unfair.

          No good can come of this as long as Marlow, Exponent and Wells are adamant in their dishonourable conduct of failing to correct errors in their research record.

        • mpainter
          Posted Jun 13, 2016 at 10:29 AM | Permalink

          imo, Brady’s only chance is to present to the court the finding in this post, the certainty of which is obvious and easily apprehended by any court. No crime, no culprit. I wonder if Brady will ever understand that he now has victory in his grasp, if he only addresses the science aspects of this case, and forgets about labor law.

        • mpainter
          Posted Jun 13, 2016 at 11:04 AM | Permalink

          Of course, if Daniel Marlowe of the Princeton University Department of Physics behaves responsibly and ethically, he will notify the NFL of his error in the science analysis he provided the NFL, as their paid consultant in the matter. This will end the affair in Brady’s favor.

        • Joseph W.
          Posted Jun 16, 2016 at 12:12 AM | Permalink

          [T]he problem is that appeals courts don’t want to re-litigate facts determined by an arbitration or they run the risk of every arbitration being appealed to the courts.

          Also, the Federal Arbitration Act strongly favors arbitration agreements, and makes it very difficult to relitigate issues. So even if the courts were eager to crowd their dockets with re-litigated arbitration issues…and I never saw a court that seemed eager to crowd its docket at all…they’d be up against a longstanding Act of Congress.

        • Steve McIntyre
          Posted Jun 16, 2016 at 12:53 PM | Permalink

          We have a similar setup in Canada. It came up in Canadian litigation involving concussions from professional football (though the Canadian Football League limps along and does not have deep pockets.) Arland Bruce, a recently retired football player, is suffering concussion syndrome, but his attempt to move his claim from arbitration to the courts was refused:

          His illustrious football career over, Bruce soon became the face of concussions and football in Canada. He began to suffer escalating headaches, memory loss, confusion, personality changes, paranoia and delusions, according to interviews and court documents in a suit against the Canadian Football League and its nine clubs that was filed in British Columbia in July 2014.

          Speaking of which (And OT), I’ve watched the first three installments of OJ: Made in America. Thus far, there’s nothing in the program about concussion syndrome, but watching OJ’s evolution, you sure have to wonder. Young OJ (high school, college) seems to have talked his way out of controversy and to have been rather free of dark angriness. He seems to have been a loyal teammate – his insistence on appearing with his entire offensive unit after breaking the 2000-yard record seemed genuine and a complete contrast in unselfishness with, say, Cristiano Ronaldo.

          But by the time that he was 40 or so, he was a jealous domestic abuser. If he’d had such traits when he was younger, you’d think that his friends would have had stories that held meaning in retrospect. The absence of such stories in the narrative sure suggests to me that his paranoia and rage might be connected to CTE.

          Also, the clips and accounts of his early career show just how many hits he must have taken when young. He was carrying the ball far more than any modern back. The coaches also talk about how “durable” he was. I cannot imagine that someone who carried the ball as much as him wouldn’t have had “his bell rung”, but then, eager to please, gone back onto the field. He must have had lots of head hits.

          The narrative of the mini-series seems to be more interested in how the trial fit into the racial politics of the day and jumped from OJ the popular and successful player to OJ the wife-beating monster without wondering why. The doctor who publicized CTE thinks OJ suffers from CTE.

          It would sure be an interesting twist to the NFL concussion case if CTE could be shown in OJ.

        • Joseph W.
          Posted Jun 16, 2016 at 1:36 PM | Permalink

          Also OT but then, it’s your T, isn’t it? When I was a military defense counsel, the base where I worked became “joint.” That meant the Air Force Security Forces took over some of the police duties for the Army half of the base. I remember them telling me that their greatest surprise was how many domestic abuse cases they were getting out of the Warrior Transition Unit. This unit is specifically designed to house Soldiers with serious injuries…including a fair number of traumatic brain injuries (TBI).

          I saw one or two cases myself where a Soldier seemed to change character after even one bad TBI…usually in the direction of losing self-control. So, yeah, it’s possible, though not proven (some abusers can be very glib and wear the mask a long time).

        • Posted Jun 17, 2016 at 9:58 AM | Permalink

          Steve 6/16: “The narrative of the [OJ] mini-series seems to be more interested in how the trial fit into the racial politics of the day and jumped from OJ the popular and successful player to OJ the wife-beating monster without wondering why. The doctor who publicized CTE thinks OJ suffers from CTE.”

          A very interesting possiblity! I hope OJ asks to have an autopsy after his death to determine if this might have been a factor in his erratic behavior.

        • mpainter
          Posted Jun 17, 2016 at 10:13 AM | Permalink

          OJ had a good job with ABC Monday Night Football as a member of the telecast crew. That did not last and I have wondered why.

          If OJ has concussion syndrome, he certainly can show a justification for indemnity from the NFL, it seems.

        • Posted Jun 17, 2016 at 3:00 PM | Permalink

          Or maybe Nicole and Ron’s families should sue the NFL?

        • mpainter
          Posted Jun 17, 2016 at 7:51 PM | Permalink

          An interesting thought, Hu. Liability for OJ’s condition entails liability for his deeds.

        • Posted Jun 18, 2016 at 9:14 AM | Permalink

          I think it should also be considered that The Juice may have been introducing mood/behavior altering chemicals into his system for a significant length of time.

          In other words, The Juice wascould have been Juicing.


  13. Posted Jun 8, 2016 at 10:15 AM | Permalink

    I once did an analysis of the mathematics of the old (pre-2015) BCS college football ranking system, specifically of how its design led to Oklahoma getting one spot in the 2008(?) national championship game, over Texas, a highly controversial decision. That year Texas, Texas Tech and Oklahoma all tied for the Big 12 South title, each team going 1-1 against the other two, and so the conference used the BCS rating to determine who would play in the B12 championship game, which in turn determined who went on to the national championship game. It was a pretty elementary problem, involving the conversion of a real-number rating to an integer ranking.

    Never wrote it up but I guess I could still use it as example to illustrate the basic problem, which is still widespread in various ranking systems.

    Steve: I vaguely recall similar sorts of comparison in game theory and even microeconomics theory of utility. BTW I’ve noticed some interesting recent uses of bayesian binomial regression – a topic of interest in ecology – in baseball statistics. The examples make the bayesianism easier to understand. I’m planning to work through some examples.

    • Posted Jun 11, 2016 at 10:45 AM | Permalink

      Hmmm, sounds interesting, maybe that will alter my growing anti-bayesian stance 🙂

      I’m also quite interested in league and schedule structures and their effect on who makes end-of-season tournaments, and in the structure of those tournaments themselves (e.g. this post: I find this to be an interesting and very overlooked topic.

      I also get far more comments when I post about sports than about science, which I guess should tell me something.

  14. Dan Backman
    Posted Jun 8, 2016 at 2:04 PM | Permalink

    Great analysis and write up of how Jastremski’s gloving and subsequent setting of pressure to 12.6 psig resolves the issue of Anderson’s use of the Logo gage and explains the pressure discrepancy. The gloving explanation was posted on as early as August 2015; see link (or text address) below. The reddit poster indicates that he/she distributed it to the media via twitter … it’s truly unfortunate that the idea didn’t get more exposure so that it could be refined and expanded upon earlier by you or others.

    Thanks again for your in-depth analysis!


    P.S. apologies if I messed up the link.

    Steve: thanks for this link. You’re right. The reddit poster figured out the Exponent error on Jastremski ball simulation. I wasn’t aware of the link before, but I’ll add a link when I revise the article.

    Steve: It turns out that Climate Audit reader davem1964 figured out as early as July 1. I’m not sure why I didn’t twig to it then. I think that it might be that there was the issue with the transients that needed to be cleared up as well to make the point solid.

    • MikeN
      Posted Jun 8, 2016 at 4:14 PM | Permalink

      Steve posted about the gloving in July, referring to a reader comment, which might have been mine in June, thought I got the details wrong.

  15. Dan Backman
    Posted Jun 8, 2016 at 2:09 PM | Permalink

    Oooops – sorry, I didn’t expect that the actual reddit post would be included. The post is an archieved post from 10 months ago. I understand if you delete it owing to the excessive real estate it is consuming on your site.


  16. eloris
    Posted Jun 8, 2016 at 3:40 PM | Permalink

    Do we know that Jastremski measured the pressure immediately after gloving, and not after a long enough period that the additional pressure would have worn off?

    • Dan Backman
      Posted Jun 8, 2016 at 3:59 PM | Permalink

      Eloris –

      Testimony from Jastremski, the equipment guy, indicates that “he set the pressure level to 12.6 psi after each ball was gloved and then placed the ball on a trunk in the equipment room for Brady to review”; indicating that set ball pressure immediately after it was gloved. At the time he provided this testimony it appears unlikely that he understood the “ideal gas law” or how his testimony might influence the investigation either positively or negatively. To understand why I believe this, just look at his test messages with McNally.


      • MikeN
        Posted Jun 10, 2016 at 7:31 AM | Permalink

        Dan, while that is the most likely meaning, it could be interpreted as a pressure check after all the balls are gloved. That always struck me as the more likely explanation, because Jastremski probably has others doing the gloving. He might check the pressure as each is done, or as each set is done. If there was one person gloving each football, then the result is the same.

  17. EdeF
    Posted Jun 9, 2016 at 6:54 AM | Permalink

    I had not heard previously about the gloving of the football, this new analysis makes sense to me. I just don’t get all the uproar over 0.35 psi. Seems to me to be in the noise in a game that can be played in rain or snow, heat or cold………..on grass.
    The era (error) of false precision.

    Steve: the Professors’ Amicus Brief makes this point very well. They observe that thousands of games have been played with footballs below 12.5 psi without the NFL being concerned.

    • mpainter
      Posted Jun 9, 2016 at 12:44 PM | Permalink

      Exactly, Steve, which lends weight to the charge that Goodell targeted the Patriots. Your above analysis can be presented with cogency in a legal context, but there is no guarantee that Kraft will act on it.

      At a very minimum, the conclusions of Exponent are rendered invalid. They certainly have erred.

    • Gdn
      Posted Jun 9, 2016 at 10:25 PM | Permalink

      The Professors Amicus shows graphs that make clear that games are regularly played with footballs that are under 11 PSI, even when starting at 13PSI…and that the known natural variation from temperature alone is about 6 PSI.

      The graphs show that with 12.5 PSI starting conditions for the Patriots footballs stated by the referee and presented in the Wells report, that after November 1st, it is pretty rare for footballs to be within specs for outdoor games.

      All of those QBs on television commenting about whether the Patriots QB should have known they were under-inflated – they played multiple games with footballs well outside of NFL specifications and don’t seem to have noticed – some with a majority of outdoor games in their career having lost at least 1.5 PSI.

  18. jddohio
    Posted Jun 9, 2016 at 1:18 PM | Permalink

    As I pointed out in a previous thread the scientific evidence is important, but there is another potential explanation that is not favorable to Brady or the Patriots. It is possible that deflation was incompetently attempted but not achieved. In such a case, the actions of the Patriots would be akin to attempted burglary. See my comments on (easy way to find them is search for JD on the web page)

    The fact that McNally couldn’t remember why he took a detour to the bathroom almost immediately after the event, is highly suspicious. (See my comments on link above) Also, highly suspicious is Brady destroying his cell phone just prior to meeting with the Wells investigators. If I was innocent, I would want people to see my cell phone records. (keeping private non-football related communications) I definitely wouldn’t destroy it. If there were exculpatory communications in his cell phone (such as “What in the hell is going on here?), he wouldn’t have destroyed it.

    Almost certainly, the two points I am making here were highly influential with the two appellate judges who sided with the NFL. The judges may not be scientifically knowledgeable, but the two incidents I cited are similar to what judges see all the time.


    • mpainter
      Posted Jun 9, 2016 at 1:44 PM | Permalink

      JD, your version will fly only if you are convinced that McNally deflated the football’s and that he goofed by the same fraction of a psi on each of 12 footballs. How are going to sell that?

      • jddohio
        Posted Jun 9, 2016 at 2:10 PM | Permalink

        Mpainter: “your version will fly only if you are convinced that McNally deflated the football’s and that he goofed by the same fraction of a psi on each of 12 footballs.”

        My version flies if McNally lied. If he was doing nothing improper, he had no reason to lie. The circumstances strongly indicate that he lied. Also, he could have very well deflated the footballs by the same amount — just not as much as he hoped. If McNally couldn’t deflate the footballs consistently (taking the negative viewpoint with respect to the Patriots & Brady), then Brady wouldn’t have asked him to do it. Brady has no interest in footballs that are inconsistently administered.


        • mpainter
          Posted Jun 9, 2016 at 2:29 PM | Permalink

          Yes, because of inconsistencies in McNally’s answers, you tag liar on him. I have yet to see a full transcript of questions and answers. In any event, your supposition of “liar” is tantamount to an assumption of guilt. There is a circulatory in your views that is less than convincing.
          In the final analysis, you convict on the basis of supposed inconsistencies from an unrevealed interrogation.

          No doubt that such an argument as yours could be presented in court. But study carefully Steve’s post. His analysis is very tight, very cogent, no weaknesses. It is proof that McNally did not lie.

        • Steve McIntyre
          Posted Jun 9, 2016 at 2:33 PM | Permalink

          actually, the variation IMO counts against McNally deflation as well. Exponent did simulations of surreptitious deflation by novice deflators and obtained ~0.73 psi deflation with negligible standard deviation. Exponent disregarded this experiment.

        • mpainter
          Posted Jun 9, 2016 at 2:48 PM | Permalink

          Hard to imagine that of 12 footballs, McNally goofed on everyone. What is more credible is that he gauged the balls at 12.6 psi immediately after gloving and that psi subsequently dropped. This is documented.

      • mpainter
        Posted Jun 9, 2016 at 2:36 PM | Permalink

        But, JD, Steve’s post is proof that McNally did not lie, or it surely can be presented as such. I feel assured that the points contained in this post can be readily apprehended by any reasonably intelligent court. That is crucial, imo.

    • mpainter
      Posted Jun 9, 2016 at 1:52 PM | Permalink

      Also, I think Brady was justified in protecting his privacy against the intrusion of the likes of Goodell and his henchmen. This cell phone business looks unsavory from the viewpoint of Brady. You might argue poor judgment on Brady’s part, but Brady was entitled to do so, imo. When does this start to look like a fishing expedition to you?

      • jddohio
        Posted Jun 9, 2016 at 2:14 PM | Permalink

        Mp “Brady was entitled to do so”

        I would agree that he is entitled to protect his privacy. However, if his cell phone exculpated him, he had the right to waive his rights. He destroyed the cell phone, which strongly indicates that there was nothing exculpatory on it.

        “When does this start to look like a fishing expedition to you?” Once McNally was seen going into the bathroom and forgetting why he went the very next day, I think the NFL had every right to investigate. Wouldn’t call this a fishing expedition. Would state it was a very incompetent investigation.


        • mpainter
          Posted Jun 9, 2016 at 3:14 PM | Permalink

          And what if Brady already felt “exculpated”, that his innocence was clear?
          You give the impression of a zealous prosecutor. Which is no fault in a prosecutor, of course.

        • DonM
          Posted Jun 13, 2016 at 12:17 AM | Permalink

          Brady’s lawyers offered to provide text message transcripts between Jastremski and McNally. There were none with McNally as I recall. The NFL told Brady’s lawyer they didn’t want them nor Brady’s phone because they already had Jastremski and McNally’s phones and their texts. It was only later that the NFL asked for the phone and Brady had destroyed it already when he got a new one (reasonably as he will dispose of it, and it likely had lots of personal communication with his wife).

        • Gdn
          Posted Aug 7, 2016 at 5:14 PM | Permalink

          If the destruction of a cell phone – which did not destroy the texts, and which was later shown to not contain relevant evidence – is cause for an adverse finding, how do you judge the NFL violating their procedures and altering the pressures of the footballs in question and then disappearing the Colts and the Patriots gauges?

          If, per league rules, the questioned footballs had been set aside and the 12 backup footballs submitted for this purpose had been substituted for them, much of the exercise would have been relatively straightforward.

          The phone issue is simply red-herring agitprop.

    • Steve McIntyre
      Posted Jun 9, 2016 at 2:30 PM | Permalink

      It is possible that deflation was incompetently attempted but not achieved.

      JD, with respect, that is a completely different theory than Goodell’s finding.

      Also, I think that it is important to determine precisely what conclusions can be drawn from measurements as we have them, prior to trying to interpret messages.

      Given the conclusive evidence that Jastremski set pressure after gloving and that his led to under-inflation of the amount observed, there is no “unexplained” deflation to account for. I also am satisfied that there are gross errors in the technical report that should not exist in a professional report. I also believe that the scientists responsible have a moral and legal obligation to correct errors that they become aware of.

      Accusing McNally of “Attempted Deflation” is an ingenious speculative offence (and IMO dubious), but it’s not the offence that was charged.

      • jddohio
        Posted Jun 9, 2016 at 4:40 PM | Permalink

        Steve Mc. “JD, with respect, that is a completely different theory than Goodell’s finding.”

        I agree with this point 100%. I also think that Goodell is a clown. However, it is not like, I worked hard to come up with my explanation. Rather, as a trial lawyer, when I saw McNally claiming not to have remembered why he went to the bathroom a day later, all sorts of bells and whistles started ringing very loudly. That kind of statement is typical of ones made by not very bright liars who think they are being sophisticated.

        My point is putting aside the strict legalities of the case, there is a lot of smoke indicating that the Patriots were up to no good. What exactly, we will never know because of Goodell’s incompetence and because Brady destroyed his cell phone. To me this case is very different than those criminal cases where someone is falsely accused of a crime and later found to be entirely innocent. Even if the Patriots had been in fact cleared by the courts by the scientific evidence of the nature you have presented, I would still be very suspicious that something had in fact happened. Any 10-year-old should have been able to answer the question posed to McNally but he couldn’t.


        • mpainter
          Posted Jun 9, 2016 at 6:06 PM | Permalink

          JD, immaterial. You seem not to have grasped the significance of the post:
          The Patriot balls could not have been deflated. No crime, no culprit.

        • jddohio
          Posted Jun 10, 2016 at 4:55 PM | Permalink

          MP “JD, immaterial. You seem not to have grasped the significance of the post:
          The Patriot balls could not have been deflated. No crime, no culprit.”

          You seem to have not grasped the significance of McNally’s lies. (Or, if you wish, and want to challenge the investigator’s notes, a substantial chance that he lied.) If he had done nothing wrong, he had no reason to lie about what he did. Irrespective of what the science shows about the pressure of the footballs, there is a major league stink of a skunk in the room with respect to something improper that happened [or could have happened if you want to challenge the investigator’s notes]. Science can’t totally clear McNally or Brady in light of what they both did.

          Also, with respect to Brady destroying his cell phone, it is worth looking at the general principles of evidence spoliation, which, if this was purely a civil suit would apply to Brady. More properly, they apply by way of strong analogy. Wikipedia defines spoliation of evidence as:

          “the intentional, reckless, or negligent withholding, hiding, altering, fabricating, or destroying of evidence relevant to a legal proceeding.[1] Spoliation has two possible consequences: in jurisdictions where the (intentional) act is criminal by statute, it may result in fines and incarceration (if convicted in a separate criminal proceeding) for the parties who engaged in the spoliation; in jurisdictions where relevant case law precedent has been established, proceedings possibly altered by spoliation may be interpreted under a spoliation inference, or by other corrective measures, depending on the jurisdiction.

          The spoliation inference is a negative evidentiary inference that a finder of fact can draw from a party’s destruction of a document or thing that is relevant to an ongoing or reasonably foreseeable civil or criminal proceeding: the finder of fact can review all evidence uncovered in as strong a light as possible against the spoliator and in favor of the opposing party.”

          Thus, under the law negative inferences are generally made when a party destroys evidence. In this case, I think it is proper to make negative inferences again, which prevents the true exoneration of Brady. Also, it is noteworthy that Brady’s destruction of his cell phone was mentioned at oral argument on his appeal.


        • mpainter
          Posted Jun 10, 2016 at 7:40 PM | Permalink

          Well, JD, you seem convinced that McNally lied. I would have to see original transcripts before I could form an opinion.

          Regarding Brady’s cell phone, you’ve agreed that he had the right to destroy it, and I do not see the applicability of your legal cite to an affair internal to the NFL.
          It seems they the league no right to Brady’s phone. See Gdn comment below, which I consider settles the phone issue.

          Once again, SMc’s post shows that no deflation occurred, hence no culprit.

        • jddohio
          Posted Jun 10, 2016 at 9:05 PM | Permalink

          MP “Regarding Brady’s cell phone, you’ve agreed that he had the right to destroy it.”

          You fail to understand the legal subtleties. For instance, in a civil case, you have a right to invoke the privilege against self-incrimination, but if you do inferences are applied against you. Also, I said that Brady had a right to privacy (its exact scope would be a very complicated issue), but if he (this is a very crude approximation) invokes that right, it still can have negative consequences.


        • mpainter
          Posted Jun 11, 2016 at 3:59 AM | Permalink

          The gloving of the football and subsequent loss of pressure is a procedure and result that can be demonstrated in court with cogent effect. No covert deflation theory is necessary to explain the half-time air pressure measurements. Again, no crime, no culprit.

        • DonM
          Posted Jun 13, 2016 at 12:28 AM | Permalink

          Maybe the part time ball boy just got nervous being in the spotlight of the NFL commissioners office and went brain dead instead of revealing the hidden truth that the reason he went to the bathroom was of all things – to pee. Whatever the reason for his response, or what he actually did in there, we now know as a result of Steve’s article that it had nothing to do with football deflation.

    • MikeN
      Posted Jun 9, 2016 at 2:31 PM | Permalink

      As covered then, you still haven’t accounted for the fact that these aren’t verbatim quotes but summaries from notes.

    • MikeN
      Posted Jun 9, 2016 at 2:37 PM | Permalink

      Yes, JD let me emphasize the new thing being discussed here. Even if your theory is all true, then it contradicts the facts in evidence.

      Jastremski gloved footballs, then set to 12.6 PSI. Stated in Wells Report.

      Footballs will lose pressure after gloving. Determined by Exponent analysis.

      Referee measures footballs as 12.5 PSI, with good gauge, some a bit lower. According to previous, these should have been around 12 or 12.1 PSI. FIRST CONTRADICTION

      McNally takes footballs into bathroom and deflates them by some amount. Based on Exponent analysis around .4 PSI.

      Now footballs should be at 11.7 PSI. However, according to halftime measurements this is not possible. SECOND CONTRADICTION (really just a cascade of the first contradiction)

    • Gdn
      Posted Jun 9, 2016 at 10:47 PM | Permalink

      You do understand that when you send texts to a person, that both you and they have copies, and for some applications (especially Android) there are additional copies as well? And that the service providers, while allowing the actual contents of the texts to age out of memory a few days after they are confirmed to be delivered, keep the metadata about the texts – such as who sent a text to whom, at what time and date?

      In the case of this case, the NFL had full access to the recipients of the texts that were under NFL investigation, as unlike Brady – whose phone was personal – McNally and Jastremski had NFL/team issued phones which the NFL actually had authority to confiscate. When Wells asked for communications from Brady’s phone, Brady’s counsel asked Wells for the authority for his request for private electronic communications, and Wells and co never responded further, and there was no complaint or further dispute on behalf of the NFL over that discovery issue until after the Wells report was released. Later, the metadata was used to confirm that all of Brady’s texts with Jastremski were in the NFLs possession, and that there were no communications with McNally via Brady’s phone.

      This is a sidetrack to the topic at hand, but apparently needs explained at least this much.

      • mpainter
        Posted Jun 10, 2016 at 6:20 AM | Permalink

        So Goodell smeared Brady over the cellphone issue.

      • MikeN
        Posted Jun 10, 2016 at 7:35 AM | Permalink

        A key point of evidence was Jastremski texting McNally ‘Talked to him last night. Said you must be under a lot of stress to get them done.’
        However, no contact between Brady and Jastremski ‘last night’.

        Steve: I’d prefer that people not re-litigate the texts in this thread and stick to science issues. Reasonable people can disagree on the texts, but I believe that the data has been misinterpreted and that this misinterpretation can be identified.

        • Posted Jun 10, 2016 at 9:19 AM | Permalink

          Reasonable people can disagree on the texts, but I believe that the data has been misinterpreted and that this misinterpretation can be identified.

          I couldn’t help thinking of this emphasis when I read this earlier of another self-funded sleuth:

          I recently met Blaine Gibson in Malaysia.

          This is a man who is now dedicating himself to travelling the globe, finding possible pieces of MH370.

          He doesn’t get involved with the conspiracy theories, he just wants to find evidence.

          Richard Westcott, BBC transport correspondent, going rather further in his endorsement than the equivalent environment scribbler might do about our host.

    • Posted Jun 19, 2016 at 5:00 PM | Permalink

      jd – “Also, highly suspicious is Brady destroying his cell phone just prior to meeting with the Wells investigators. If I was innocent, I would want people to see my cell phone records.”

      Inspecting one’s cell phone and inspecting cell phone records are two different issues. I am not a millionaire as is Brady, but I am quite well off, and I would not surrender my cell phone and risk certain financial information being stolen/hacked; however, cell phone records would gladly be revealed. I can’t remember exactly, but I recall Brady did offer to provide the latter information.

      • mpainter
        Posted Jun 19, 2016 at 8:42 PM | Permalink

        It’s an obvious smear by Goodell and I’m surprised that someone of JD’s background has swallowed it.

    • MikeN
      Posted Jun 20, 2016 at 7:20 PM | Permalink

      JD what opinion do you have about the NFL’s not providing the results of the measurements they took of footballs during the season?
      Is this something you would advise Brady’s team to mention during its appeal?

  19. Alan Watt, Climate Denialist Level 7
    Posted Jun 10, 2016 at 8:28 AM | Permalink

    I’m only interested in this topic tangentially, so perhaps I’ve missed it, but where in all the discussion of who to blame is failure of the NFL to provide their referees with certified calibrated guages considered? If the commissioner is going to suspend a championship player for four games because a ball was underinflated by 0.35 psi, what’s the appropriate punishment for using a guage that is off by 0.38 psi, or more to the point, even having an inaccurate guage that might be used? For that matter, what should the penalty be for not even knowing whether the official gauges are accurate?

    If you’re going to make a major issue out of a small difference in inflation pressure, there is no excuse for not having verified accurate gauges. The underinflation, however it resulted, should have been caught before the ball was ever put into play. That it wasn’t is 100% the fault of the league.

    Steve: the NFL’s theory is that there was tampering with the balls post measurement by the referee. And that this tampering resulted in deflation by the amount of the bias of the referee’s gauge. There is a consensus of 31 of 32 NFL owners on this point- 97%.

    • mpainter
      Posted Jun 10, 2016 at 11:08 AM | Permalink

      “..100% the fault of the league” meaning Goodell, of course, as the fellow in the driver’s seat.

    • Alan Watt, Climate Denialist Level 7
      Posted Jun 10, 2016 at 11:09 AM | Permalink

      Perhaps flogging a dead horse, but what would we say about suspending an athlete for doping even after it was established that some of the instruments in the testing lab had a reporting error greater than the amount of banned substance detected, and the lab could not establish with certainty which instrument was used to declare the athlete guilty of doping?

      What 32 out of 32 owners should believe is that it is far better to avoid a problem than establish guilt after the fact. If the NFL had done its job so officials had certified instruments, an unintentionally deflated ball would have been detected before it could have any effect on the game outcome.

    • MikeN
      Posted Jun 10, 2016 at 11:44 AM | Permalink

      I wonder what the consensus would be if you polled the owners’ true thoughts on the matter.
      How many will say maybe, but better to punish the Pats regardless.

  20. Posted Jun 10, 2016 at 12:51 PM | Permalink

    Does anyone know what the button on the side of the gauge stem is for? The Exponent explanation isn’t too clear. Is it to reset the gauge to current atmospheric pressure? What happens if it’s not used properly?

    I notice from the Exponent report that needles on both gauges were damaged. The shaft of the “non-logo” gauge needle was badly mangled and broken off at less than .8″ from the base of the needle. The “logo” gauge needle was conspicuously bent at the bottom of the shaft, but at least straight beyond the bend, and about 1.4″ long beyond the base. New Tachikara needles are 1.61″ long, including the base, consistent with the “non-logo” needle. They cost $5.99 for a package of 20, so it’s inexcusable that the refs didn’t use undamaged needles. But it would be an obvious choice to use the less damaged “non-logo” gauge if the NFL couldn’t afford new ones.

    The damage is most evident in the overview photo (Figure 2). In the detail of just the needles, the gauges are turned in such a way that the bending is least obvious. The report says that there was inconsequential “slight bending”, and doesn’t mention that the “non-logo” needle is actually broken.

    • Posted Jun 10, 2016 at 12:53 PM | Permalink

      “But it would be an obvious choice to use the less damaged “non-logo” gauge if the NFL couldn’t afford new ones.”

      Make that “But it would be an obvious choice to use the less damaged “logo” gauge if the NFL couldn’t afford new ones.”

    • MikeN
      Posted Jun 10, 2016 at 3:45 PM | Permalink

      Hu, one of the explanations given for discussions about providing needles is that the referees needed them for their gauges.

      • Posted Jun 11, 2016 at 10:19 AM | Permalink

        Thanks, Mike. It’s interesting that Exponent reported finding “debris” in the stem of the “non-logo” gauge that had the broken needle. The needles are supposed to have a rounded, solid tip that will slide through the “gland”, and two holes on the sides of the tip to let the air in. But the broken “non-logo” gauge’s needle instead had a jagged hole at the end that would have likely “cored” the gland instead of sliding through it. IMHO, this is the likely source of the “debris” in the gauge’s stem.

        Any ball that was measured by the “non-logo” gauge would therefore have a damaged gland that would be prone to leaks, and should not have been put in play. This gauge’s measurements could also have been off because of any gland debris still in the needle.

        In the calibration exercise, the needles were removed and the gauges screwed directly to a manifold that was also connected to a high-precision Omega brand master gauge, so that any debris in the needle would not have affected the readings. It is not clear from the report whether the debris in the stem was removed before or after this calibration, or whether the lab inspected the needle for debris.

    • H Davis
      Posted Jun 11, 2016 at 2:56 PM | Permalink

      These gauges are usually used for measuring tire pressure as the valve stem thread is the same as the needle thread. If the tire pressure is too high pressing the button will let a little air out of the tire (or football) without having to remove the gauge and then apply some other instrument to depress the tire valve. The gauge itself depresses the tire valve allowing air from the tire to escape into the gauge for the measurement. Which, by the way, removes a tiny amount of air from the tire with each measurement. For a car tire this amount is negligible but for a football maybe not, especially if several measurements are made by repeatedly inserting the needle into the football…..

      • Gdn
        Posted Jun 11, 2016 at 7:25 PM | Permalink

        Exponent page 31 shows that the act of measurement takes a very precise .01 PSI each time.

      • Posted Jun 11, 2016 at 11:07 PM | Permalink

        Thanks, H Davis — it would make sense that the button is to release excess pressure from the ball. I see now that on p. 52 of the Wells report, two underinflated balls were indeed purposefully over-inflated “because it is hard to be precise when adding air”, and then Anderson “used the air release valve to reduce the pressure down to 12.5 psi.”

        What still confuses me, however, is the statement in n. 22 on p. 20 of the Exponent report that “One data point is excluded from this analysis because during testing an Exemplar Gauge was improperly re-zeroed when a non-zero pressure was being applied.” How is this re-zeroing done?

        In any event, these gauges are not designed to measure tire pressure, and in fact say “Ball Pressure Gauge” on the face. The “logo” gauge only goes up to 15.00 psi, and the “non-logo” one only up to 19.95 psi, both too low for tire pressures.

        You can, however, buy a “logo tire gauge” online for just $5.99 with your favorite NFL team logo on the side! (The logo on the deflategate “logo gauge” is a red Wilson W sticker on the back, and not the logo of the manufacturer or a team.)

        As Gdn points out, Exponent did find that each measurement reduces the pressure by only about .01 psi, and so would not have been a factor.

        • curious
          Posted Jun 12, 2016 at 6:04 PM | Permalink

          Hugh – just a guess but I think it is likely the re-zero function will be an electronic action rather than a physical one.

        • Posted Jun 13, 2016 at 12:08 AM | Permalink

          Curious —
          Thanks. I see now on p. 17 of the Exponent report that indeed the gauges are zeroed to current atmospheric pressure by powering them off and then back on. So I guess they forgot to do this one the one observation they threw out. I guess this would only make a difference if the atmospheric pressure changed while the gauge was in use.

          There are still 5 Patriots logo tire gauges left, at !

  21. Posted Jun 11, 2016 at 11:50 AM | Permalink

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

  22. Navy Bob
    Posted Jun 12, 2016 at 10:02 AM | Permalink

    Excellent job as always Steve. What I find most galling though is the unbelievable incompetence of the high-priced Kessler law firm. They probably charge at least $1000/hr, not to mention presumed additional charges for investigators, their own experts, etc. Yet they were unable to see this now obvious contradiction? As commenters have noted, at least one blogger did, along with your commenters long ago, yet despite all the millions Kessler vacuumed in from the players’ association, he couldn’t conduct a sufficiently thorough investigation to notice this point that others determined for free? Doubly galling is his statement, “The facts are too confused here. I’m just going to drop this subject.” Like it was too far beneath him to try to earn his pay.

    Steve: I think that much more blame accrues to Wells and/or Exponent for making the error and then not owning up to it. In fairness to Kessler on this, I noticed the issue in a comment in early July, but don’t seem to have seized the full significance. If I didn’t seize on it, it would be hard for Kessler to pick it up, as lawyers tend not to have the time or aptitude for this sort of analysis. I’m trying to understand why I didn’t grab it at the time. I might have moved to another file. Also one has to get rid of the error in the transients to make this the critical issue. I also looked at variability soon after – an issue that I didn’t address in my article, but which I ought to have, as my analysis on this was pretty good IMO.

    • James Peterson
      Posted Jun 13, 2016 at 3:23 PM | Permalink

      Thanks for your continuing efforts. Can you get your paper to Olsen, Kessler and the Patriots? Thanks again!

    • MikeN
      Posted Jun 13, 2016 at 5:38 PM | Permalink

      I don’t think Kessler should be faulted too much. If he hadn’t asked the questions, it is possible Steve never catches on to it. I had been telling people how Tom Brady’s lawyer messed up, but didn’t catch the significance of how much until Steve posted about it.

      I was focused on this is an alternate explanation, but didn’t grasp the significance that they had contradicted themselves and blew their whole theory up.

      Steve: Kessler’s questions had nothing to do with my analysis. I re-read hearing in light of what I’d figured out. Mike, yes you were very early in picking up this detail. I’m still puzzled why we didn’t twig to it being such a critical issue. I’m thinking that there were a lot of issues in play and it takes a while to sort them out. Also Exponent Figure 27 purported to show that there was an issue even with the Logo gauge. Until Figure 27 was shown to be invalid, the Logo issue was somewhat secondary. And by the time that it was shown to be invalid, it was more or less Berman ruling time, so the topic got dropped. I’m not sure of this sequence but it must have been something like that.

    • MikeN
      Posted Jun 14, 2016 at 1:45 PM | Permalink posted about the gloving in August, and it was a minor point, presented as a possible explanation. If Kessler had read that site carefully, he would have gotten it as one commenter mentioned it there in late May, pretty clearly.

  23. Posted Jun 14, 2016 at 11:39 AM | Permalink

    Steve —
    It’s taken me a while to figure this out, but you’re clearly right — there’s no evidence that the Patriots deflated the balls after Anderson checked them, since he could well have used his biased “logo” gauge.

    There is one point that you perhaps do not emphasize enough, however: You quote the Wells report that Jastremski “set the pressure level to 12.6 psi _after_ each ball was gloved and then placed the ball on a trunk in the equipment room for Brady to review” (your bold), and then state, “The detail that Jastremski set pressure _after_ gloving is not mentioned in the Exponent Report, only in passing in the Wells Report.”

    However, there are in fact not just one but two important details here: Jastremski did not just glove the balls and then set the pressure levels _afterwards_. Rather, he gloved _each_ ball and then set _its_pressure level before placing _it_ on the bench. If in fact he had gloved all the balls and then set all the pressures, as I perhaps would have done, most if not all of them would have returned to room temperature before being set, as demonstrated by Exponent Figure 16. From a procedural point of view this would make sense, since there were two separate jobs to be done, and this is evidently what Exponent envisioned.

    However, from an organizational point of view, it makes much more sense to prepare each ball fully, one at a time, so that there are only two categories of balls — new ones and ready ones. If they had all been gloved first, that would create a third category, which would be hard to keep straight in a busy equipment room before a big game, particularly if there were interruptions. So if Jastremski did as he said, _each_ would still have been warm when he checked it. But by the time Brady had approved them and Anderson got to them, they would have cooled, per Figure 16.

    Jastremski probably didn’t realize that the rubbing would create a noticeable pressure gain. But even if he had, he would not have tried to game the rules by doing this, since it would have just annoyed Anderson to find all the balls short when he got to them. He had no way of knowing that Anderson would happen to own a defective gauge with just the right bias to let them pass.

    The “logo” gauge is no longer on the market that I can find, and so is probably an older version of the very similar “non-logo” gauge. Perhaps it was accurate when new, but had just drifted off over the years. I was thinking at first that perhaps it was a cheap and inaccurate knock-off of the “non-logo-type” gauge, but it seems if anything to have been a little better made, since it has a screen in the stem to keep debris of the sort that might be caused by using a broken needle out of the mechanism.

    The brass-stemmed “non-logo-type” gauges with a Tachikara trademark on the face are more expensive ($32.83 at Walmart) than very similar black-stemmed digital gauges with Tachikara on both the face and the stem ($17.99 at Kohl’s). Very similar-looking black-stemmed Tachikara analog gauges are even cheaper. But it appears that Tachikara, a ball company, is not sole vendor of these gauges, since Exponent acquired its apparently identical (except for the Tachikara trademark) “exemplar” gauges from Wilson. We don’t know if the “exemplar” gauges from Wilson had the same Wilson W logo sticker on the back as the “logo” gauge.

    In the future, the rules should specify at what temperature the ball pressure should be checked, gauges should be checked for accuracy at least annually, and broken or bent needles should be replaced immediately.

    At a minimum, Anderson owes Brady an apology, since it was his defective vintage gauge that caused the whole imbroglio. And of course, if he is indeed a scientist, Prof. Marlow should read your report and either show where you’re wrong or recant.

    • MikeN
      Posted Jun 14, 2016 at 1:36 PM | Permalink

      Hu, is there any mention as to whether Jastremski did the gloving personally, or if this was done by others? If the latter, then the gloving would have finished for all of them within a short time of setting the pressure.

    • Gdn
      Posted Jun 14, 2016 at 7:37 PM | Permalink

      “In the future, the rules should specify at what temperature the ball pressure should be checked, gauges should be checked for accuracy at least annually, and broken or bent needles should be replaced immediately.”

      If they want to keep up the facade that the pressure matters that precisely.

      The rules that the NFL uses do not appear to have come from deliberation, but rather from the manufacturers recommendation for the care of the football – from some unknown time prior to 1940.

      If you want to see how silly the NFL position is that the pressure actually matters beyond what annoys the QB, see the Scientist Amicus, Appendix B. No one ever cared enough before to bother to measure during or after a game.

      Click to access physics-professors-deflategate-filing.pdf

      Aside from pretention, no real reason to care now.

      • mpainter
        Posted Jun 15, 2016 at 5:52 AM | Permalink

        I agree. Ball pressure is of no consequence and the NFL tacitly acknowledges this by never checking pressures during play. The present ludicrous situation is the result of Goodell’s peculiar obsessions. Strange that the owners allow him to indulge such fantasies.

      • Posted Jun 15, 2016 at 11:18 AM | Permalink

        Sports are full of arbitrary and even silly rules. The issue here is not whether this is a good rule, but whether science proves that one team tried to cheat by breaking it.

        The 21 disinterested scientists who signed the May 24, 2016 Amicus brief that you cite conclude that it does not. Curiously, none of Marlow’s Princeton colleagues were among them. Marlow was evidently hired by the NFL to make a case against Brady, and according to online reports, has been advised by the NFL’s attorneys not to comment on the science. He is still on the Princeton faculty, and was formerly Chair of the physics department.

        However, the brief does not address the very subtle point that bothered Wells and that Steve has resolved here — How could it have been possible that the Patriots and Anderson came up with essentially the same pre-game pressures if Anderson used the biased “logo” gauge, since it would seem to require that the team had a gauge with essentially the same bias as Anderson’s. By an admittedly remarkable coincidence, the discrepancy is just what can be accounted for by the way the balls were innocently prepared. This may be a “lightning strike”, but the world is full of dead trees and at least one pro golfer who are testimony that stuff sometimes happens.

        • Steve McIntyre
          Posted Jun 16, 2016 at 12:32 PM | Permalink

          One of the difficulties faced by the lawyers is that it’s difficult for them to form an independent judgement distinguishing between an actual solution to the problem and a supporting brief from 21 eminent professors which doesn’t. And yet the point is simple enough that a non-scientist can verify the point.

  24. MikeN
    Posted Jun 18, 2016 at 10:55 AM | Permalink

    “disproves the possibility of post-measurement tampering.”

    This is not the case. It only does so, with the assumption that Exponent’s other reported observations are correct. If the simulations reported by Exponent are wrong, then no conclusion can be reached, other than the report contradicts itself.

  25. Rick
    Posted Jun 19, 2016 at 1:09 PM | Permalink

    I was in the local tire shop the other day and a distraught man came in with 2 guages and told the owner that his tire guages couldn’t agree and were giving 2 different readings for his tires.
    “Well” said the shop owner, “which one do you like better?”
    “I like this one”, said the man showing the guage in his right hand.
    “Well” said the owner, “make sure that’s the one you always use”
    Good advice.

  26. MikeN
    Posted Jun 23, 2016 at 8:56 PM | Permalink

    On Bill Simmons’s new show, Ben Affleck goes on a profanity-laced tirade against the NFL. It is unfortunate that both of them describe it as 8% deflation.

  27. MikeN
    Posted Jun 28, 2016 at 7:18 PM | Permalink

    Steve, no commentary on NAS report 10 years later?

  28. MikeN
    Posted Jul 7, 2016 at 12:03 PM | Permalink

    JDOhio, any comment?

    “When asked if there was a transcript of the interview, Comey stated that there wasn’t one because the interview wasn’t recorded, but there was an analysis of Clinton’s interview.”

    • Posted Jul 9, 2016 at 12:00 PM | Permalink

      Comey and Clinton are way OT for this thread, even if the thread is somewhat of a disgression for the blog.

      • MikeN
        Posted Jul 12, 2016 at 5:58 PM | Permalink

        My question is somewhat on topic for this thread, or at least with JD’s prior comments, and I suspect he would answer on topic.

      • MikeN
        Posted Jul 12, 2016 at 6:03 PM | Permalink

        To be clear, what I was asking had to do with an ongoing argument among JD and others about the statements made by McNally, where I brought up that the investigators never made any direct recordings or transcripts, so any quotes are from summaries made from notes taken during the interview.

  29. JD Ohio
    Posted Jul 9, 2016 at 9:34 AM | Permalink

    Have very low opinion of what transpired. Explained in detail in comment that is in moderation.

    • kim
      Posted Jul 10, 2016 at 12:47 AM | Permalink

      In the early days Steve frequently had to restrain me from talking politics or religion. Now and then he still does.

      He has shown a real tour de force keeping the two out of a climate blog. Perhaps unique.

  30. Another Ian
    Posted Jul 11, 2016 at 3:42 PM | Permalink


    FYI if not already mentioned

  31. Posted Jul 16, 2016 at 3:31 AM | Permalink

    Brady gives in. Sad day. Do not understand why your (and others’) analysis didn’t win the day.

    • MikeN
      Posted Jul 16, 2016 at 6:03 PM | Permalink

      The appeals court was not adjudicating scientific details. Roger Goodell’s appeals hearing, Tom Brady’s lawyer came close to making a key scientific point of exoneration, but got confused.

      Also, scientists were not able to weigh in, as data was not made available in a timely fashion.
      Perhaps Steve can find errors in hockey stick paper in days or even hours, but Exponent was a little outside his experience.

      • Posted Jul 16, 2016 at 11:55 PM | Permalink

        But the people involved must know they were wrong. How can they stay silent? I would lose everything and live on the streets before bahaving so dishonorably.

        • MikeN
          Posted Jul 17, 2016 at 8:55 PM | Permalink

          What makes you so sure they know they are wrong?

        • MikeN
          Posted Jul 23, 2016 at 11:29 PM | Permalink

          Prominent sportswriter Joe Posnanski has declared Tom Brady innocent. I think he is the most prominent non-Boston writer to do so.

  32. Posted Sep 22, 2016 at 6:51 PM | Permalink

    Hey Steve,

    Have you seen article in NYtimes on Exponent and Wells Report? Total fluff piece, they don’t answer any of the issues you’ve raised with their analysis.

    They posted a response to critiques on their website yesterday also – seems lacking to me. here’s the link…

    • Posted Sep 24, 2016 at 10:19 PM | Permalink

      An unfortunate set of articles. We all hoped that when past the initial hubbub, the Exponent scientists would break their silence, review the critiques of their report, and acknowledge their mistakes. This shows they have not. They have missed the significance of the timing of Jaremski’s measurement relative to the rubbing of the footballs (see Steve above), and apparently still stand behind Fig 27, despite its rather outrageous error.

      These two mistakes alone completely refute their analysis.

      And there are other mistakes – statistics, calibration, and inconsistencies in the results they measured which are unanswered. And this doesn’t even address the more fundamental question which the 20-30 prominent scientists raised in their amicus brief to the court of how they could attribute the level of significance they did to their experimental results.

      I’m disappointed …

  33. Chris
    Posted Oct 5, 2016 at 12:51 AM | Permalink

    Congrats on your mention at Steve!

    • mpainter
      Posted Oct 7, 2016 at 9:51 AM | Permalink

      Sports Illustrated, so the issue is not dead yet. Unfortunately, most SI readers probably cannot follow the intricacies of reasoning in the article. But the author has stature and cannot be dismissed as inexpert. He has called on Exponent to answer.

    • Navy Bob
      Posted Oct 7, 2016 at 9:07 PM | Permalink

      It’s long overdue for Steve’s analysis to get the publicity it deserves, but I found it odd that Taylor only alludes to Exponent’s mistaken assumption that Jastremski set the balls’ pressure before the rubbing procedure without stating it explicity. The rubbing procedure is mentioned in only one sentence, with no reference at all to the pre- vs post- timing of the pressure setting, yet Steve has shown it’s THE key error that when corrected completely exonerates the Patriots. It’s maddening that no journalist (and I use the term loosely for sports writers) or engineer writing in a major publication like Sports Illustrated has restated this critical point as clearly and conclusively as Steve has.

  34. Posted Oct 8, 2016 at 3:23 PM | Permalink

    Unfortunately we are past the time when there is much interest in the Physics of the footballs, but I am grateful that SI did put out the report, and did reference the good physics that has been done here, which stands in stark contrast to the Exponent news item.
    For a tongue-in-cheek review of the Wells report, which nominates the report for the Journal of Irreproducible Reports, you can look at this article:

  35. EdeF
    Posted Nov 10, 2016 at 4:39 PM | Permalink

    Flying home out of Las Vegas yesterday I happened to see a sign advertising a CSI Tour based on the popular TV show.
    That and DeflateGate got me to be thinking about the plot of a new TV series……CSI-PSI.

  36. Posted Nov 16, 2016 at 5:31 PM | Permalink

    Tom Brady alludes to DeflateGate in an ad:

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