The Cognitive and Statistical Biases of Deflate Gate

I’ve been biting my tongue on Deflate Gate, but the scientist in me reached a tipping point today after reading this Boston Globe article analyzing the Patriots rebuttal to the Wells Report. Simply put: Many of the salient parts of this story aren’t being told properly.

This post will analyze key areas of the Wells Report based on the foundations of this blog (cognition in the context of sports statistics):

  1. The interpretation of context-free communication snippets
  2. The interpretation of memory-based claims
  3. The statistical analysis of the AFC Championship game measurements
  4. The lack of coherence in any proposed tampering scheme

Conclusions and a summary are presented at the bottom for those who want to skip over 4,000 words of details.

1. Communication and Context

a. Ambiguity

Essentially, human beings cannot communicate without context. Think about words like transactions. Deposits. Tellers. Now read the following snippet from a conversation:

Person A: “Pick me up by the bank of the river.”

In all likelihood, you thought of a financial institution. Without any context, that snippet is ambiguous. But the mind will rarely interpret it as ambiguous; talking about things related to a financial institution primes the brain to think of a financial institution and thus interpret “bank” as a building with windows and tellers. Most importantly, one’s instinct is to think it’s something, and not think it’s ambiguous. But what happens when we get to see the full conversation?

Person A: “Are you we going rowing tomorrow?”

Person B: “Yes, I’m setting up the boat right now.”

Person A: “Great, so when should we meet?”

Person B: “Let’s say 9. I’ll start at the boathouse.”

Person A: “Pick me up by the bank of the river.”

Person B: “Great — you can just hop on there.”

The conversion is no longer really ambiguous — these two people are talking about an embankment next to the river, not a financial institution.

The majority of the non-statistical case in the Wells Report is based on highly ambiguous texts that were taken out of context. Surely, most people who have been following the story from the beginning don’t think they are ambiguous because most people were thinking about the context of deflating footballs when they read the text messages. They were primed to think this way and as such can no longer see another explanation as even reasonable without oodles of context.

This is a typical case of anchoring and confirmation bias, two of the most powerful mechanisms that govern our decision making. I can shape your opinions by putting information in your head (like the financial institution example above), whether accurate or wrong, and that initial information holds extra weight in your mind (anchoring). Then, once you start to believe something, you start to only look for evidence that supports your story (confirmation bias).

b. “Help the Deflator”

The Globe article takes exception to the Patriots explanation that Jim McNally referenced himself as the ‘deflator’ because he is a big fellow and wanted to lose weight. The author, Ben Volin, responds “It’s hard to find a rational-thinking person in the country who buys this answer.”

That’s just ignorant. And understandably — the science of thinking isn’t exactly taught in high schools.

Volin is under the impression that his mind isn’t heavily anchored to the context of deflating footballs, when for months, he’s only associated the term deflator with this issue. He, like most of us now, probably can’t even think of the word “deflate” without thinking of PSI and footballs. From a cognitive standpoint, that’s predictable.

But not necessarily accurate.

Prima facie the texts reflect incriminating language to those who have been loaded up with the idea that there was a tampering ploy in place. Once the mind has decided what the “deflator” refers to, it has a hard time accepting a counter explanation without a larger sum of evidence. But again, that’s a recipe for false conclusions and simply a predictable function of the brain’s desire to create certainty instead of ambiguity.

Conversely, if I told you that two jocular workmates came up with strange terms to needle each other with, and those terms were related to the actual work they did every day, would you think that’s strange? It’s possible, without any additional evidence (see section 3 and 4 below), that he calls himself the “deflator” because he regularly tampers with footballs on Sunday. There are also a myriad of other possibilities for that one text message, especially given McNally’s texting habits and propensity for wild language and nonsensical statements (e.g. “what’s up dorito dink?”)

People use jargon specific to their vocation all the time, and do so in extending humor or personalizing phrases. On the outside (with no context) these references seem meaningless or are misinterpreted. That’s the definition of an “inside joke.” It takes one instant of connecting a football losing weight to a person losing weight and voila, an inside joke. (Or, the only recorded instance of McNally referring to his role in a tampering scheme, a scheme that was otherwise never apparently discussed over text.)

Just imagine what kind of story can be painted when snippets are taken out of context. The possibilities are endless:

Honestly, I just wanted to slip in Brian Williams rapping. Everyone’s so serious about these footballs that they could use a little Gin and Juice.

c. What happens when you add context?

There are a number of instances of people misinterpreting something without context. I was going to cue up a bunch of examples and research experiments, but we need to look no further than the Patriots inclusion of (alleged) other testimony that was omitted from the Wells Report.

Consider that the report tries to make it look like Brady is bribing McNally with gifts. What the report does not include, according to the Patriots, is that Brady regularly gives comparable gifts to “15 non-player personnel.” This, and many other omissions like this in the report, need little analysis to illustrate the problems with context-free conclusions; obviously it looks quite different if Brady only gives alleged co-conspirators gifts, versus a standard distribution of comparable gifts to a number of people regularly.

Similarly, there was a bit in the Wells Report about “getting a needle.” Without context, many interpreted this as fitting a narrative, as the brain is designed to do. But, when you add the context that McNally was the individual who literally provided needles to the officials for their pre game process, it completely changes the meaning of the text. Again, I’ll leave it up to the reader to guess why Wells left out the context, that according to the Patriots rebuttal, was confirmed by all witnesses involved. (Specifically, that McNally had to return to ask Jastremski for another needle at the request of the officials, and that this practice became, like seemingly everything else between them, a running joke.)

The only difference between these examples and the “deflator” joke is that the full context about the weight-loss joke hasn’t been substantiated by others. However, this is the same cognitive mechanism seen in God of the Gaps thinking. It is a fallacy, and the very problem with context-free thinking, to think that just because we don’t currently have that context that an alternative explanation is improbable or, as the Globe believes, impossible. Especially in the face of all of the other insinuations in the Wells Report being corrected.

2. Memory

There are then a number of other major claims in the Wells Report regarding memory.

a. “I don’t know Jim McNally”

Let’s say my doorman is named Bill. I know his face. I know his voice. I know some of his habits. If I were asked about “William McCluskey” I would have to honestly say “I have no idea who that is.” Both of these things are true — I know a doorman named Bill, and I also don’t know someone named “William McCluskey.”

Only it turns out that these are the same people. I would not be lying to say “I don’t know William McCluskey.” Just like Brady wasn’t lying when he said he didn’t know some lowly locker room attendant’s full name. He did think his name was “Burt,” phonetically similar to his nickname, “Bird,” so Brady was indeed aware of the existence of McNally and even had a name to pair to his face. (I’ll leave it up to the reader to decide if the Wells investigators lacked the knowledge to realize this or intentionally framed it to look like a lie.)

b. “I didn’t do anything abnormal”

Next, there is the trip to the bathroom that McNally took. He was originally asked if he did anything out of the ordinary when transporting the balls from the locker room to the field, to which he answered, “no.” He then later said he went to the bathroom, which the investigators presumed to be out of the ordinary, and thus interpreted McNally as being untruthful. This is a terribly false conclusion.

Assuming he does occasionally go to the bathroom, as he claimed, his answer of “nothing was abnormal” and then later “I went to the bathroom”  is indeed consistent — as opposed to a contradiction — based on his own recollections. Because, for McNally, going to the bathroom wasn’t out of the ordinary. Simply because the investigators find it out of the ordinary doesn’t mean it was for McNally.

c. “I’ve never seen THAT before”

The final issue I’ll discuss regarding memory is referee Walt Anderson’s recollection of the ball location. I once worked across the street from a pink house for a month straight. One day the topic of houses came up. I looked out the window and said “look, they just painted that house pink!” I was informed by many others that the house had always been pink, I’d simply never cared or devoted any attentional resources to it.

It is possible that in his entire career, the AFC Championship game was indeed the only time Walt Anderson remembers the balls “going missing.” (Although it does beg the question of why no one else found it strange that a giant man carried a giant bag of footballs out of the room in plain sight.) But, given that he had been primed before the game to pay attention to the balls for the first time in his career, it is expected that he would suddenly notice things he’s never noticed before. It’s possible that every time Anderson was in New England, or anywhere, that the procedure was equally as lackadaisical as it was during that game…he just never gave any attentional resources to it. Kind of like how that house was always pink.

3. Statistical Analysis and Physics

It is quite clear that no one at the NFL knew anything about the Ideal Gas Law when this story broke. Heck, it’s quite clear most of the public didn’t know about it either. This creates another major bias that is very hard to undo.

Due to the Ideal Gas Law, ever since footballs have been inspected pre game they’ve also been in play at different PSIs. All the time. If we could go back in time and measure balls at half-time of every game, some would be in the 10s, some in the 11s, some in the 12s, etc. People only found the Patriots report abnormal because they had never been introduced to it before. It was a physics problem, and most people, without knowing physics, declared it was abnormal. When explanations of the Ideal Gas Law sprang up on the Internet, people had the same disbelieving reaction that they do now to “the deflator” explanation.

Again, the mind is ripe to do this. We’d like to be measured and cautious and say “I’m not an expert at this so I’ll find out more,” but that’s not how the brain is hardwired to work. By the time the Ideal Gas Law was popularized, people had already made up their mind there was tampering. And it’s very, very hard to undo that. This leads to the aforementioned confirmation bias.

Here’s the thing though — the Wells Report did not present strong evidence that concluded the balls were tampered with, or even likely tampered with. Amazingly, the report tries to bury this finding by making a bunch of assumptions in an attempt to say that it was possible there was tampering, when the “more probable than not” interpretation from any scientist would have to be the opposite conclusion: that it was more probable than not there was no tampering, and that the ambiguities around game day measurements leave open some possibility of foul play, although even that is stretching it.

Analyzing the Wells Report Data

This issue has been discussed in great detail, but I want to translate some numbers to demonstrate why the Wells language is the opposite of what it should be based on the data. The Exponent team commits all sorts of scientific faux pas, such as presenting p-values based on a nonsensical dataset that is literally the best looking data they have to support tampering. (Amazingly, despite all their assumptions, this is the only area of the report they perform such statistical tests.)

So why is it so disingenuous to compare the Colts averages to the Patriots? Primarily because the Colts balls were measured after the Patriots, so they had ample time to recalibrate to the new indoor temperature, raising the air pressure with every minute that passed. Exponents own graphs (fig 22, page 203) show a ~1.0 PSI increase in pressure expected in the Indianapolis balls after 10 minutes indoors…but they make no attempt to adjust the data and retest. From a methodological standpoint, this is astounding. This wouldn’t pass an undergraduate peer review.

A 12.5 PSI football, with all other factors being equal (which they weren’t), is expected to be at 11.32 PSI given the game-day conditions in Foxboro (including an atmospheric pressure of 14.636.). Similarly, we’d expect a 13.0 PSI football to be 11.8 PSI when it entered the locker room at halftime. However, as the balls heat up in the locker room after coming off the field, they will rapidly increase in PSI as shown below. All of the Patriots balls were apparently measured first — with perfect instruments, and excluding the effect of water, we’d expect those balls to be about 11.5 PSI after 2 minutes indoors, when measuring could have started, and [edit] based on time estimations, the highest ball would be about 12.2 PSI.

Meanwhile, starting the Colts measurements at the 10 to 11 minute mark, we’d expect their balls (13 PSI pre game) to measure in the 12.8 to 12.9 range. In other words, in 10 minutes indoors, the Colts balls would have almost completely returned to pre game levels, while a large chunk of the Patriots balls would be significantly closer to outside-condition measurements.

Now, that 11.32 number does not include water, which changes the volume of the ball and has an additional effect on the pressure. Exponent seems to contradict themselves here, stating first that they couldn’t observe any volume change in a wet ball (thus making water moot). However, in their “spraying” test, where they simulated outdoor conditions with wet balls, they clearly find a difference between wet and dry balls. Again, significant because the Patriots balls were wet and the Colts balls were protected in a bag and unused at the end of the first half. Below are the expected readings based on time indoors and dry/wet conditions:

Figure 22 of the Wells Report

Figure 22 of the Wells Report

Now here’s the actual data:

Screen Shot 2015-05-16 at 4.38.08 PM

Note that we wouldn’t really ever expect to see a reading below 11.2, according to Exponent, even with water involved. So, unless something else needs to be incorporated, something beyond the factors we’ve examined would have additionally deflated the footballs per Clete Blakeman’s readings. (Assuming that it’s just simply not transcription error or gauge inaccuracy.)

Amazingly, it turns out something else does need to be incorporated: Walt Anderson possessed a gauge that read roughly 0.3-0.45 PSI below the other gauge. Exponent believes his gauges were consistent — something in science we call “reliability” — despite not being accurate. The Patriots expressed concerns about reliability when they pointed out that the intercepted football measured 11.45, 11.35 and then 11.75 using the same gauge on the sideline, although Exponent did indeed test the gauges in question and found them to be fairly reliable. We’ll assume they are reliable (consistent) for the rest of the post, although this is clearly an area that could create additional variance in the readings.

The Logo Gauge (Higher readings) Scenario

Anderson claims to have used the higher gauge to take the pre game measurements. Why does this matter?

  • If we examine just the presumed logo gauge measurements between pre game and halftime, only the 4th and 10th Patriot ball fall just below our expected floor (by 0.2 and 0.3 PSI, respectively).
  • If we examine just the non-logo gauge measurements and assume Anderson used the logo gauge pre game, then we’d expect something like a floor of 10.9 PSI without water involved, and thus probably nothing below 10.7 PSI. There, the 4th ball is right on the cutoff and the 10th ball 0.2 PSI below.

In other words, if you believe Walt Anderson, then almost all of the Patriots balls were found to be in a range that demonstrates non-tampering. Not the opposite.

From what I’ve seen about variability in measurements, I’m not comfortable chalking up 0.2-0.3 PSI on two balls to “tampering” factors outside of gauge reliability, transcription error, or some other subtle natural effect (i,e. additional water) that we aren’t accounting for. [edit] This hunch is confirmed when analyzing the data in greater detail. Heck, the sample size of this experiment is really 1, because we’d need to test balls at halftime for a handful of games to see if there are readings that also fall just outside the range predicted by Ideal Gas Law or if that is indeed abnormal, even by a small amount. (That’s where you’d publish a p-value, FYI.)

For instance, the Colts 3rd ball measures 12.95. Exponent believes this is a transcription error because it would be the only instance of the Non Logo Gauge measuring higher than the Logo Gauge. Simply introducing this kind of measurement variability essentially puts every Patriot football measured within the expected norm.

In other words, if the Logo Gauge was used pre game, it’s most likely the Patriots balls were not adjusted or tampered with.

The Non-Logo Gauge Scenario

Now, there’s another major issue that Exponent also skirts over. If the Non-Logo Gauge were used in the pre game, then how does one explain the Colt’s readings on that gauge? Indy’s four balls assumed to be measured at halftime by the Non-Logo Gauge exhibited PSIs at 12.7, 12.75, 12.5 and 12.55. However, look at the dry temperature curve presented above. Those balls should all clearly be above 12.8 PSI.

If the Non-Logo Gauge were used pre-game, then something doesn’t add up with the Colt’s balls.

In other words, using Exponent’s (arbitrary) decision to discount Anderson’s claim that he used the Logo pre-game and assume he actually used the Non-Logo gauge, then the Colt’s balls have the exact same problems (to almost the exact same degree) that the Patriots balls exhibited. [edit] Indeed, the Colts balls are either approximately 0.2 or 0.35 PSI higher than the Patriot’s balls on this gauge, depending on when the Colts balls were measured.

In conclusion, assuming we believe the (unrecorded) pre game measurements of 12.5 for Patriot balls and 13.0 for Indianapolis balls, the data shows that

  • if Anderson used the Non-Logo Gauge in the pre game, the Colts balls were also slightly below where they should be based on the physics
  • if Anderson used the Logo Gauge, the Patriots are essentially exonerated

Contrary to Exponent’s conclusions, their procedure is not reasonably scientific because it’s predicated on Anderson’s recollection that the Patriots balls were 12.5 and Colts balls were 13.0. (Memory is unreliable.) There were also no consistent (or repeated) measurements standards and no controls, such as measuring the balls at the same time. With that said, since we can safely assume the Colts didn’t tamper with the balls, that the Colts balls exhibit the same minor failure to align with the Ideal Gas Law and other physics factors as the Patriots balls do.[edit] It’s actual highly improbably that there was tampering whether Anderson used the Logo or Non-Logo gauge, and the claim from Exponent that the Non-Logo gauge implies tampering is based on the statistically invalid practice of ignoring the time and variance in the data.

4. Is there a plausible explanation for Wells’ claim?

Despite reading a good deal of reaction to this story, I have yet to encounter a coherent explanation for what is being alleged. The Wells Report is quite careful not to author such a story, using vague language instead. But let’s actually spell out what they are alleging:

  • Walt Anderson was wrong about what gauge he used in the pre-game, thus the Patriots have some under inflated footballs because of tampering
  • According to Wells, eight of their footballs seem under-inflated by (approximately) 0.5-0.6 PSI on average, with the lowest football being about 1.0 PSI below expected
  • Those footballs were deflated by Jim McNally in the 100 seconds he was in the bathroom with the balls
  • McNally has done this regularly since at least 2013, because he calls himself the “deflator”

In order to believe the above story, one also must believe the following:

  1. Brady would have to figure out at some point in time that he preferred balls just under 12.5 PSI, in the 11.5-12.0 PSI range.
  2. Brady determined that the difference between 11.5-12.0 PSI and 12.5 PSI was so great that he felt he needed to ask an employee to tamper with the footballs, and not even risk under inflating them and hoping they passed inspection.
  3. However, Brady could only tamper with the footballs at home. He’d be using footballs that were so different in his mind that they were worth tampering with at home…but on the road, he would be out of luck. Despite this, he’s better on the road than most NFL QBs.
    • Note that this makes the Indianapolis Colts claim that the Patriots used deflated footballs in Indianapolis during the regular season essentially impossible.
  4. During the October, 2014 game against the Jets, “the deflator” Jim McNally failed to deflate at least some footballs (that were 16 PSI)
  5. Tom Brady, after blowing up on the sideline about the quality of the footballs during that game, performed the following as a charade to protect the cover-up:
    • Brady (allegedly) in front of others, declared he wanted balls at the low permissible range (~12.5 PSI) before giving them to the referee. (Even though McNally was already deflating balls…so why would they not already be at the low range to save McNally time in his deflation process?)
    • Brady brought a rule book to the officials to show them 12.5 PSI balls should not be touched…even though he knew McNally was going to alter them.
  6. Furthermore, Brady would have to go through the charade of inspecting the balls pre-game in front of other people, knowing that these would not be the balls he would playing with. His true pre-game ritual was one of the following:
    • He secretly inspected footballs at some 11.5-12.0 range and then told the staff to inflate them to 12.5 so he could stage a second, phony inspection in front of others every game (right before the balls are delivered to the officials), while no one noticed him missing or sneaking away during this period, OR
    • He simply inspected them at 12.5 for tack and feel, knowing that once he let out a little air, the PSI would be where he wanted it. This explanation assumes that he is both so meticulous about PSI that we wanted less than a pound of PSI (which no human can seemingly detect) out of the ball and simultaneously does not think there would be a tactile difference between a 12.5 and 11.5 PSI ball that he needs to actually inspect the real ball-condition he will play with.
  7. Jastremski and Brady are either horrible at tampering — setting balls to 12.75-12.85 instead of the lowest permissible 12.5 before the Jets game (which would make McNally’s work harder), or they did indeed start at 12.5 pre-October, 2014 and decided to make up a story to tell the investigators that they used to inflate to 12.75-12.85 so Brady could plausibly deny ever knowing about PSI before October, 2014.

I have yet to see Wells, or anyone, make sense of this convoluted, contradictory set of events that must have had to happen according to their meaning of the “deflator” text and allegations about regularly deflating footballs. Which of the following conclusions seems more likely to you?

Conclusion A: Tom Brady figured out that he really liked footballs just under the legal limit, decided not to have his equipment team slightly under inflate balls to hope they would pass a lackadaisical NFL inspection process (the technique Aaron Rodgers told Phil Simms about), but instead set up an elaborate process to take just a little air out of the balls. But only at home. And Walt Anderson forgot what gauged he used…so he took another tenth or two of PSI out of the balls.

Conclusion B: Walt Anderson correctly remembered what gauge he used, footballs can have incredibly small perturbations outside what we’d expect based on just temperature and pressure and Jim McNally was indeed referring to “deflating” his waist.

Can anyone reconcile these issues? Because Occam’s Razor says Conclusion B is a significantly more — excuse me — Conclusion B is “more probable than not.” Yet despite this, recent polls suggest that a majority of the country believe the Patriots cheated…without actually being able to offer up a coherent story for how the events in the Wells Report make sense. There is evidence in the report that needs to be reconciled with the alleged claim because it seemingly contradicts the claim or relies on less-than-likely dependencies.

Conclusion

  1. A Lack of context and predictable cognitive biases can make text messages appear as they aren’t, and make alternative explanations less believable than they really are
  2. A lack of understanding around memory likely led the Wells investigators to a number of false conclusions
  3. The AFC Championship game data shows the following [edit]:
  4. People are comfortable claiming tampering despite the story from the Wells Report lacking coherence and requiring the following to be true:
    • Brady would have discovered he feels a large enough advantage in slightly deflating, when no one else seems to be able to tell the difference
    • He would have been OK with using different (non-deflated) footballs, on the road, despite leading the 2006 rule change to create uniform preparation for QBs at home and on the road
    • Despite tampering only being carried out at home, Brady’s performance has been better on the road.
    • Despite his better road performance, Brady still went through with tampering by carrying out a phony inspection in the locker room before every game (because those would not be the conditions of the balls he would use post-McNally deflation.)
    • After the October, 2014 game against the Jets, Brady extended the charade by providing a copy of the rulebook to the officials before games, knowing full well that McNally would deflate below 12.5 anyway.

PS Please don’t use this post to disparage others. It’s designed to educate, regardless of your opinion or rooting allegiances.

32 thoughts on “The Cognitive and Statistical Biases of Deflate Gate

  1. -the intercepted football measured 11.45, 11.35 and then 11.75 using the same gauge on the sideline
    Actually, no. From the Wells Report, footnote 36, page 65:
    “We believe that [James] Daniel located and used the pressure gauge supplied by the Patriots [to measure the football intercepted by D’Qwell Jackson]. We further believe that this is the gauge that John Jastremski considers his normal gauge. It has not been located since the day of the AFC Championship Game. It should be noted that we have not relied upon the air pressure measurements of the intercepted ball in any respect in reaching any conclusions set forth in this Report.”

    So apparently, neither the logo nor the non-logo gauge was used on the intercepted ball. There are also a number of troubling questions about the two teams’ game-day gauges which I discuss here: http://emailwagon.blogspot.com/2015/05/what-happened-to-teams-game-day-gauges.html

    The three different measurements of the intercepted ball introduce the possibility that “operator variability” affected the readings, and not by a small margin, either. Now, it is true that on page 26 of the Exponent report, we read of a sort of mini-experiment in which five individuals measured 11 equally-inflated footballs using the non-logo gauge, and all measurements were within 0.05 PSI of each other. Based on these results, Exponent rejected any potential effect that operator variability may have had on the pre-game and halftime measurements. But I have a couple of problems with this experiment:

    1. Only the non-logo gauge was used for the experiment. So how do we know there was no variability with the logo gauge?
    2. More importantly, Exponent did not test the Patriots’ game-day gauge. In fact, as I mention in the article linked above, they claim they can’t even FIND the Patriots’ game-day gauge! So how do we know the Patriots’ gauge doesn’t have any operator variability, or any other kind of variability? Don’t the varying measurements of the intercepted ball seem to suggest some kind of technical problem with the Patriots’ gauge? And if the gauge was faulty, wouldn’t this necessarily mean that the Patriots’ footballs might not have been exactly 12.5 PSI before the game, and, that being the case, doesn’t that by extension invalidate Anderson’s claim that the balls were all similarly inflated when he received them? How could the Patriots’ balls have had such similar PSI readings, if their gauge was so unpredictable?

    • Thanks for adding this detail. By “same gauge” I meant within-gauge variability, not necessarily the logo/non-logo gauge. Good points about Operator Variability.

  2. “After the October, 2014 game against the Jets, Brady extended the charade by providing a copy of the rulebook to the officials before games, knowing full well that McNally would deflate below 12.5 anyway.”

    Another thing to add to this is:

    “The Patriots produced two game-day security guards employed by Team Ops, a
    security and guest services company affiliated with the Patriots, to support McNally‟s account.
    Rita Callendar, who was stationed just outside the Officials Locker Room on game day, said that
    she estimates that McNally takes the game balls to the field by himself roughly 50% of the time,
    and that the other times he walks with or in close proximity to Richard Farley. Paul Galanis,
    who was stationed just outside the entrance to the Patriots locker room, across the corridor from
    the top of the center tunnel, said that it was routine for McNally to walk to the field with the
    game balls unaccompanied. He estimated that McNally goes to the field approximately 10% of
    the time with game officials and approximately 25-30% of the time with Richard Farley, and the
    other times he is walking by himself. ”

    So even at the home games he only deflates 50% of the time?

  3. As a former stats guy as a Quality Control Engineer, a former data group supervisor, former programmer, and presently a business and financial analyst and modeler, with 3 degrees from RPI, I was curious how Exponent analyzed the data.

    I would call their work a stats hack job.

    I see no one seems to have noticed a clever trick that Exponent used to help assure that use of one of the gauges would fall outside the expected psi levels. Here is what Exponent did.

    On page 40 of the Wells Report it was stated that beginning with the Bears game on October 26, 2014, Jastremski set all the game balls to 12.6 psi. This was done in a room that would have been controlled by the HVAC system which was set to keep the room temperature at 71 to 74. Given that prep work before Tom Brady chooses the game balls includes vigorous rubbing (i.e., gloving – see page 50 of the Wells Report), it is highly probable that the room temperature would be mostly higher than the HVAC goal of 72.5 due to the amount of heat that would be given off by the prepping, and by the breathing of Jastremski and anyone else who may have been in the room. Presumably the HVAC system kept track of what it did, so it would be rather easy to check. And even if the HVAC records do not exist, it is really a trivial manner to run a duplicate test in either the same room, or in a room that closely mimics the room.

    So the first significant playing with the numbers that Exponent did was to continually say that the Patriots footballs were set at 12.5 psi pre-game. No they were not! They were set at 12.6 psi! This is important because as using 13.0 psi for the Colts footballs shows, the larger the psi that you start with, you get a slightly bigger psi change as the temperature changes (see Table 10 on page 39 of the Exponent report). It is not much, but it exists.

    For purposes of illustration, I will assume the best case for the Patriots, because that is what Exponent allegedly also did during a test (see number item 4 on page 49 of the Exponent Report) to “to maximize the window for the Patriots footballs to reach the average pressured recorded at halftime on Game Day”.

    Therefore, I will assume that the Patriots footballs were set to 12.6 psi by Jastremski at a room temperature of 74. The 24 footballs (12 game and 12 backup) were then given to Walt Anderson by McNally for testing and approval in the officials room.

    Before proceeding, let me provide some psi numbers using the Ideal Gas Law. Here is the affect of a 1 degree change in temperature on the pressure value assuming constant volume and an average sea level atmospheric pressure of 14.696 psi (looks to be the basic assumptions used by Exponent):

    (a) Starting at 12.5 psi gage reading at 67 degrees, then each 1 degree drop will cause a 0.0516 psi change
    (b) Starting at 12.5 psi gage reading at 68 degrees, then each 1 degree drop will cause a 0.0516 psi change
    (c) Starting at 12.5 psi gage reading at 69 degrees, then each 1 degree drop will cause a 0.0515 psi change
    (d) Starting at 12.5 psi gage reading at 70 degrees, then each 1 degree drop will cause a 0.0513 psi change
    (e) Starting at 12.5 psi gage reading at 71 degrees, then each 1 degree drop will cause a 0.0513 psi change
    (f) Starting at 12.5 psi gage reading at 72 degrees, then each 1 degree drop will cause a 0.0511 psi change
    (g) Starting at 12.5 psi gage reading at 73 degrees, then each 1 degree drop will cause a 0.0511 psi change
    (h) Starting at 12.5 psi gage reading at 74 degrees, then each 1 degree drop will cause a 0.0510 psi change

    So what does the above mean? Namely, that over a small temperature range, every 1 degree change in temperature has to result in about a 0.05 psi change in pressure.

    According to page 52 of the Wells Report, Walt Anderson obtained mostly 12.5 psi readings for the Patriots footballs with 2 of the 24 below 12.5 psi, and 2 at 12.6 psi.

    So given that 83% of the footballs were at 12.5 psi, it is quite reasonably to assume that the greater majority of the Patriots footballs experienced a 0.1 psi drop from where they were originally set.

    Therefore, the temperature of the area where Walt measured the footballs would have had to be 72, unless you do not want to believe the Ideal Gas Law.

    Now, on the surface this seems to contradict the 67 to 71 temperature range for the ref’s shower area (see page 48 of the Exponent Report) where the footballs were tested. However, when Exponent took these measurements, I will be willing to guess that they did not have the official’s room packed with people. And unless one does not believe in Physics, if it gets hot in one area of a room, the colder part of the room will heat up rather quickly so that the room reaches a state of equilibrium. And this would happen before the HVAC would kick-in once the ambient temperature surrounding the thermostat sensed above a 74 air temperature. The Exponent people made a bad science conclusion that somehow a room at a higher temperature with a lot of people moving around in it would somehow not cause a cooler area of the room to not heat up. This is another simple experiment that can be run by watching the security camera videos and duplicating what was happening over the same amount of time, and then taking temperature measurements.

    So since this is a fun-and-jolly example, I will believe in the Ideal Gas Law and what Walt Anderson said the psi measurements happen to be, and say that the actual temperature of the area of Walt Anderson measurement was 72.

    Now, at what temperature did Exponent run its “game day simulation”? Why, of course, at 69 (see page 42 of the Exponent Report). One other reason that this temperature is tough to justify has to do with the claim that the relative humidity in the officials room was at 20% at half-time (see page 42 of Exponent Report) and presumably the same pre-game since Exponent said that they fixed the humidity at 75% for on-field simulation and 20% for half-time. According to US testing, at 20% relative humidity, 69 seems like 64 (see http://www.infoplease.com/ipa/A0001434.html), while 72 feels like 67. I would think that someone would have asked for the heat to be raised if the shower area was at 69. It would seem to me that it was more likely that given the number of people in the room that the relative humidity was higher than and that the temperature was higher than 69. I say it was closer to 72.

    So the simulation done by Exponent should have been run at 72 for the official’s room. This would have further dropped the observed psi by roughly 0.15 psi. Thus, the wet football values would have been about 11.27 psi minus 0.15 psi or 11.12 psi.

    SIDE NOTE: Exponent never separately tested the affect of wetness on the psi of a football as an environmental test. They buried it as part of a simulation that had flawed environmental conditions. I wonder if they actually did do this test (it was a logical thing to do as wet footballs did result from rain) and found that the results “hurt” their analysis so they never included it as part of their report?

    Gee, the Non-Logo Gauge average was 11.11 psi (see Table 5 on page 8 of Exponent Report).

    Just by testing using the best case for the Patriots, which Exponent allegedly claimed they did later in their tome, with the correct initial psi and temperatures, and suddenly it does not matter which gauge was used to measure the footballs.

    In other words, I wish we could see the testing notes kept by Exponent, and would it not be special if they purposely set the test temperature at 69 because they knew that setting it too high would kill their proposition that the environment could not explain the drop in psi.

    Well, I just showed that it could, using either gauge.

    What a joke this hack job report happens to be.

    Another group should run the scenarios I proposed above as a counter test.

    Another thing. The temperature gradient was 72 to 47. When I use 72, I get a pressure drop to 11.22 psi using the Ideal Gas Law and without accounting for wetness. At 71, I get 11.27 psi. At 70, 11.32 psi and at 69 I get 11.37 psi. This latter number mimics the Exponent results perfectly (see Figure 22 on page 44 of the Exponent Report). That is amazing to so perfectly match the Ideal Gas Law. Makes one pause as reality usually does not match test results so perfectly. Wonder what the more accurate van der Waals equation would generate as the theoretical values?

    • Thanks for the contribution George. I had the same thought about any difference between the HVAC reading and the actual room temperature. For simplicity, I did not plot multiple scenarios based on temperature as you did. However, a 74 to 48 degree change, independent of wetness, predicts an 11.18 ball (again, without wetness involved).

      To me, this is an issue that helps answer “why are all the balls, including the Colts, slightly off?” Which, again, is a much more likely answer than the Patriots deciding to take 0.3 PSI out of footballs…

      • Chiming in several weeks later to point out that for the transient analysis of the logo gauge data they actually used a starting temperature of only 67 degrees (69 was only used for the non-logo gauge. They changed the temps because they didn’t like where the Colts balls were falling on their curve. This also would’ve been affected by their troubling assumption that the Colts’ balls were measured before the Patriots’ balls were reinflated at halftime.) They also came up with their 67 to 71 range by going back on a day when it was 18 degrees colder to take their measurements, and that room isn’t heated or cooled.

        • To add to this: On pg 208 (48 of Exponent), it says the HVAC is set to a 71-74 degree range in the official dressing room. It will only kick in if the temperature strays from that range. But the balls were gauged in the pre-game in the shower area which is “not actively heated or cooled.” Clearly, the HVAC setting has a strong affect on the temperature of the shower room, and thus to use 67 degrees as a gauging temp in the pre-game is a potential problem. Here’s why:

          The Colts say they set their balls to 12.9-13.05. Walt says he remembers all the balls at 13. What happens to a 13.0 ball at 71 degrees when moved into a 67 degree room? It drops to 12.8 PSI. But Walt says 13. The Patriot balls would have been 12.3 *shrug* It’s just strange to think it’s likely that there was 4 degree difference on game-day that day between the two rooms, and using a highly improbable scenario as your single testing parameter is not a good idea.

          Furthermore, as has been noted, the HVAC only kicks in during a range. It’s more likely the room was warmed up by the bodies. Exponent did not simulate this. (Amazingly – I have no idea what the background and credentials are of their “scientists” but the Paul and Weiss group should get their money back.) So while it was as high as 71 degrees on that day, the game-day temperatures were likely warmer. If we open up the possibility of say, 69-73 degrees as a measurement temp in the pre-game, we’d see the following expected PSI’s (relative to the 71 degrees we’ve been using):

          69: Both teams balls ~0.1 PSI higher
          70: Both teams balls ~0.05 PSI higher
          71: Current assumption
          72: Both teams balls ~0.05 PSI lower
          73: Both teams balls ~0.1 PSI lower

          Tinkering with all the parameters in the equation (pre-game temp, measurement time, what log was used, etc.) There’s no way to get both sets of balls to be perfectly predicted by the Ideal Gas Law…which is EXACTLY what we’d expect. Why? Because the balls had different wetnesses. I use a blanket wetness curve provided by Exponent, but in all likelihood every ball is a few tenths off (up to 0.7 PSI according to one group) based on wetness. This explains why both groups are on order of 0.2-0.3 PSI below what we’d expect on the Logo Gauge, no matter what way we slice the data.

  4. One also needs to see the other “games” that Exponent did to appreciate the cleverness of getting around the fact that it is extremely unlikely that any tampering was done to the Patriots footballs.

    On pages 22 to 23 of the Exponent Report they show the effect of ambient temperature on the accuracy of the Logo, Non-Logo, and Exemplar gauges. Something interesting happened when the results were plotted (see Figure 9 on page 23). The two old Game Day gauges had the pressure readings DROP as the temperature increased while all the new Exemplar gauges had the pressure measurements increase. They acted opposite of each other! How is that possible? One reason could be that as a gauge gets used and older, its ability to read pressure correctly changes. If Exponent noticed this unusual behavior they ignored it and then noted that they saw about a 0.04 psi reading differential, or the reading resolution of the gauge, and then IGNORED this actually significant number by claiming that this change would not have “materially changed the readings generated”. That is bull logic based upon Exponent’s reported test data. It would have been possible to have a reading DROP as the temperature increased. And I had pointed out that a 1 degree temperature change will cause a 0.05 psi change. Thus, a 1 degree change in the temperature could have generated 0.09 psi change in the read pressure. That is a HUGH effect and not insignificant like Exponent tries to claim!

    Exponent’s own tests show that when a gauge gets used a lot (i.e., older) there can be a drift of psi readings as high as 0.75 psi for the Logo gauge and as high as 0.1 psi for the Non-Logo gauge (see pages 26-29 of Exponent Report). Exponent hypothesizes that the drift was caused by large repeated uses by them. Exponent then claims that by making equations to map controlled laboratory Logo, Non-Logo, and Master Gauge readings that this will somehow magically correct all the drift. This is not necessarily true for varying reasons. This equation also does not account for measured gauge error such as indicated in my prior paragraph, human operator error, and any number of other factors. One can easily show that in combination a 0.04 psi error here, and another 0.04 psi error there, and another 0.02 psi error here and a temperature gradient error causing a 0.15 psi error here adds up to a possibility of a 0.25 psi error. That is a LARGE possible error.

    As I noted earlier, Exponent cleverly got rid of what they claim were insignificant possible errors. No they are NOT if we are talking about possible multiple 0.02 psi to 0.04 psi changes. The Non-Logo gauge reading ranged from 11.85 psi down to 10.50 psi for the Patriots footballs. The Logo gauge reading ranged from10.90 psi to 12.30 psi. That is, a reading difference of 1.35 psi and 1.45 psi respectively. Thus, a single 0.04 psi error equals about a 3% error. Have this along with just the temperature gradient error noted earlier by me and we are talking about up to a 14% error factor. And this is not inclusive of all possible error factors, some of which Exponent tested for and gave us data to look at.

    That type of error factor is gigantic when it comes to statistics.

    I am sure a stats geek could put together all the error ranges for the various known measured tests and determine a likely pressure range that may have been possible to have obtained. My gut says that all the readings obtained would have a high likelihood of falling within this psi probability range. And least we forget that outliers exist, many not easily explainable. And statistically one can test if one reading of a group of readings is not consistent and thus probably should be treated as an outlier.

    The Exponent Report “looks” so good to the typical non-scientific person. So far, many, many science geeks seem to be poking holes in it, to the point that non-geeks are even admitting that the Exponent Report is suspect and does not “prove” much to a high degree unless one plays games with the data.

    That alone should put suspect of a scheme to deflate footballs as one of the cornerstones of the Wells Report is that environmental factors alone “more probable than not” could not explain the pressure drops observed.

    Since many have easily showed that if the Logo gauge had been used and not the non-Logo gauge, a 50-50 possibility and actually a higher probability because the measuring refs said he thought he had used the Logo gauge, how in the world does one get away with saying “more probable than not” when the probability is less than 50-50? You get to say it if you are trying to “prove” something that is likely not, and most others say, “your right” even though you are most likely wrong.

  5. Could you guys out there please explain to me how the converted Master gauge equivalents for the Logo gauge and Non-Logo gauge readings almost magically wiped out the stated pressure reading differences between the two gauges? Is it not weird that after supposedly converting to a Master gauge equivalent, that the pressure difference goes from 0.38 psi to 0.12 psi for the Patriots footballs, and from 0.39 psi to 0.11 psi for the Colts footballs.

    I would have thought that no matter what one converted into, that the relative psi measurement difference of at least 0.35 psi would have had to remain? Exponent’s own tests indicated this (see page 20 of Exponent Report). So how in the world could supposedly converted to a Master gauge equivalents not have the same net psi difference?

    Throughout the Exponent Report, and consequently throughout the Wells Report, it is noted that the Logo gauge consistently reads at least 0.35 psi higher than the Non-Logo gauge (see Footnote 37 on page 67, Footnote 41 on page 69, and page 116 of the Wells Report; and see Item Number 5 on page XI, on page 20, on pages 26-27, on page 29, on page 44, and Item Number 5 on page 65 of the Exponent Report).

    On page 20 of the Exponent Report, Figure 7 was shown to indicate that all the testing gauges used would have a linear change in its pressure reading as the pressure reading of the Master gauge went from 8 psi to 14.5 psi. OK.

    On page 22 of the Exponent Report, Figure 8 was shown to indicate the standard deviation of the gauge pressure readings. They then indicated that “The Logo Gauge was noticeably different in manufacture and therefore omitted from this part of the data analysis” and used this as justification for not including the Logo Gauge variability.

    Oh, I see. The plotted data including the Logo gauge probably showed a big variation which would have made it more difficult to play the analysis games they were playing, so they just eliminate the entire Logo data set. Would seem not OK.

    Then they used this data as part of the analysis that will affect the analysis of the Logo gauge? Would seem not OK.

    And even with this data manipulation we are see standard deviations up to roughly 0.125 psi in the measured pressure range. As many know, standard deviation is a measure of the amount of variation in a set of data values.

    Most people assume a normal distribution of the data set, and merrily calculate from there. However, per Figure 6 on page 20 of the Exponent Report we see that the plot of the gauge-to-gauge variation at a 13 psi fixed pressure looks more like a flattened Poisson distribution with a low point of 12.55 psi, a high point of 13.2 psi, and a peak of 12.9 psi. This figure also shows that the within gauge variability was pretty tight.

    Per Figure 8, at 11 psi the standard deviation runs from 0.095 to 0.125 psi and at 12.5 psi the standard deviation runs from 0.11 psi to 0.12 psi. So using 0.11 psi as the average standard deviation in being more than fair.

    That says that for a normal distribution for measuring an actual 11 psi pressure, 68.2% of the readings should be in the range of 10.89 psi to 11.11 psi and 95.4% of the readings should be in the range 10.78 psi to 11.22 psi, and 99.6% of the readings should be in the range of 10.67 psi to 11.33 psi.

    However, the Exponent data itself suggests more of a Poisson distribution with the readings being pushed downward in the probability data set.

    The purpose of the above discussion is to show that what Exponent did was to try to translate the rather wide possible readings distribution set of either the Logo (wide) and Non-Logo (narrower) to the Master (tight). I contend that how they tried to do it was mathematically weak because they NEVER accounted for the variability of the actual readings themselves.

    Statistically it is possible that all the Logo gauge readings could have been off by 0.33 psi and still fall within the distribution profile. It is not highly probable that all 11 Logo readings were off by 3 sigma, but given the data supplied by Exponent, and the gauge resolution being only 0.05 psi, and all the possible factors than can change what one reads as the gauge pressure (each degree of ambient temperature change causes 0.05 psi change, variability of the gauge itself causing 0.11 psi or more change, the gauges exhibiting a 0.04 psi drop in pressure reading as temperature increases, human measure error of up to 0.05 psi, gauge repeatability drops as the gauge gets older and used more and some drift could happen even though Exponent claims none was expected to have happened, and different amounts of water on the football will change the pressure in the football by varying amounts), the measurements taken during half-time are possible.

  6. I have been checking various standards regarding the mapping of non-calibrated instrument data back to a master calibrated instrument.

    As far as I can find, that is a practice not supported by the standards.

    Part of the reason has to do with traceability back to an accepted standard such as those kept by NIST in the US and ISO/IEC internationally. There is no such traceability regarding the gauges as no calibration data was ever generated for the Logo and Non-Logo gauges until Exponent attempted to do comparative analysis with a Master gauge. In other words, one cannot back calibrate to a Master gauge.

    From what I can tell from the data provided, Exponent dropped consideration of data that did not fit neatly into a narrative scenario. In other words, Exponent selectively choose data and cleverly tried to explain away why the other data should be ignored.

    As has been noted before, comparing Colts data with the Patriots data and not taking into account the time and temperature effects is down right sneaky. Much of the data analysis done by Exponent on the half-time gauge reading as reported in the beginning of the Exponent Report is somewhat of a farce.

    Exponent spent all kinds of effort from pages 5-12 analyzing the Colts and Patriots half-time gauge reading never once accounting for the fact that the readings were done at different times (Colts after the Patriots), that as a result the Colts footballs had a significant amount of extra time to gain back pressure due to the temperature difference between outside and inside, that different amounts of football wetness can cause significant pressure difference in a football, and the small sample sizes with no prior controls.

    The bottom line is that the Exponent Reports looks good, but in reality it is weak.

    • It’s quite weak and doesn’t look good at all — they produced a p-value for data clearly confounded by time, and then instead of running further analysis simply drew a picture and said “if the lines don’t cross, it’s impossible” — which is simply wrong (it assumes 0 variance in measurement, and completely biases a dry ball measured later in the locker room period to “intersect” at some point.) They attempt to claim 0 variability in measurement with the 3 paragraphs at the top of pg 186, claiming, as you have mentioned, that their study produced no measurements outside 0.05 psi variability. Such a result STILL does not demonstrate no measurement variability (either from operator or something inherent in the gauge) because at that precision, there will be up to +/- 0.05 PSI variability per measurement. Not to mention that it contradicts the actual data that the produced…including the Colts balls.

      I have been thinking about the Master Gauge though, and re-read some of the sections, namely pg 178, pg 204 (fig 22) and pg 205. I believe here is where the sleight-of-hand comes into play that the researcher in me has a hard time accepting as an innocent methodological error:

      Pg 205 reads: “it was necessary to determine what the averages recorded on Game Day (generated by the Logo and Non-Logo Gauges) correspond to on the Master Gauge. Or, put another way, if the Logo/Non-Logo Gauges were used to measure the pressure inside a football, what would the Master Gauge read when measuring the same football?”

      But methodologically speaking, this is not necessary at all! Exponent cannot simultaneously contend that the two gauges are reliable (consistent) in their measurements, and then contend the gauges need to be normalized, because the “true” PSI is irrelevant. This then allows Exponent to create a NEW transient curve (fig 24, pg 210) that is FAR kinder to the 4 Colts measurements, instead of simply comparing Logo-to-Logo readings and Non-Logo-to-Non-Logo readings (which is what I did). This is a very sneaky translation that I did not catch the first time reading the report, but it literally allows for their “visual proof” to be true. T

      This, along with not not running any statistical test on the data when time is included, allows Exponent to quite literally paint a picture of “tampering is more probable than not,” when the data screams the opposite. Basically, if they used the transient curved that they themselves produce on pg 204, their picture would look quite different.

  7. Great analysis. Would love to know more about the author. I hope Brady’s team has delved into this as completely. Sadly, most of the Harpies in the media haven’t even read Wells let alone any analysis of it.

  8. There is also another error that Exponent did by trying to convert to a Master Gauge equivalent.

    If one is to convert to a Master Gauge equivalent (a waste of time as we have noted), then one has to convert ALL the gauge readings used in the analysis and then re-run all the tests to match everything or else one has apples-to-oranges comparisons which are invalid.

    What do I mean by ALL the gauge readings?

    There was another set of gauge readings upon which the analyses are based that were also done with the Logo and/or the Non-Logo gauge.

    That was the pre-game readings done by Walt Anderson.

    You also have to convert these readings to a Master Gauge equivalent in order to do apples-to-apples comparisons.

    The reason is obvious, or at least should have been to all these “great” analysts at Exponent.

    If the Logo gauge was used by Walt Anderson, then the 12.5 psi he read was actually 12.15 psi (assuming the mid-point difference as provided by Exponent). Then the basis to compare the half-time gauge readings from the Logo gauge when converted to a Master gauge equivalent had to go from 12.5 psi to 12.15 psi. And all the test data that was measured would also have to use this same basis in order to get valid values to be able to compare. Then one has an apples-to-apples comparison and analysis.

    So doing any conversions to a Master gauge would have required Exponent to do an entire new set of data across the board using a different basis.

    Exponent obviously did not do that.

    Thus, much of their Master gauge equivalent analyses can definitely be shown to be invalid as one cannot compare a converted set of data against a set of data not converted.

  9. To re-state what I posted elsewhere.

    One can pretty definitively prove to an extremely high likelihood that Walt Anderson really did use the Logo gauge as he recalled he did.

    All the information to prove it is in the Wells Report and the Exponent Report.

    On page 49-50 of the Wells Report it is described how the Patriots game balls are gloved for 7 to 15 minutes and then right after the pressure is set to 12.6 psi.

    This proves that Walt Anderson had to use the Logo gauge. How so one may ask.

    Exponent tested the effect of gloving a football (see page 34 of the Exponent Report). Rubbing for 20 minutes will raise the psi by 0.7 because the temperature of the air in the football will increase (by about 14 degrees if one wants to believe the Ideal Gas Law indicating that every 2 degrees of temperature change results in 0.1 psi change).

    Looking at the chart shows that when the Patriots gloved the footballs, the psi in the footballs went up somewhere between 0.4 psi and 0.6 psi as the temperature within the footballs rose between 8 and 12 degrees.

    Based upon the same chart, the football will cool down and lose 0.1 psi after roughly 2 minutes. One could safely presume that 2 minutes is more than enough time to take a just gloved football and set its pressure at 12.6 psi.

    However, this psi had to be set against a temperature in the football that probably was 6 to 10 degrees higher than the ambient temperature.

    Therefore, as the Exponent chart shows and their discussion indicates, at least 30 minutes passed after the Patriots had gloved and set the pressure of the footballs before they were given to the refs. Thus, all the footballs had to have dropped in pressure by 0.3 psi to 0.5 psi and thus had a pressure of 12.1 psi to 12.3 psi when given to the refs.

    It does not take a genius to see that adding 0.3 psi to 0.4 psi (see page 44 of Exponent Report which indicated this as the psi error range of the Logo gauge) to values in the range 12.1 psi to 12.3 psi can easily get 2 footballs under 12.5 psi, 2 footballs at 12.6 psi, and all the rest at 12.5 psi (see page 52 of the Wells Report).

    So, the Logo gauge had to have been used by Walt Anderson as he had recalled (see page 52 of the Wells Report), or else he could not have gotten the readings he remembered given how the Patriots footballs were prepped and when they had the pressure set to 12.6 psi.

    Also, the conclusions by Exponent that Bill Belichick was wrong about the effect of gloving the footballs is provably wrong. Bill Belichick was correct. And the process used was cross verified during the “investigation” and noted in the Wells Report itself (see pages 49-50).

    One has to wonder how so many people at Exponent cannot read English and translate simple language into a rather simple procedure. And how the Exponent people conveniently missed the FACT that the Patriots footballs had their pressure set after gloving the footballs. Did they do that on purpose or are we to believe that so many “smart” people cannot understand the following:

    “Jastremski told us that he decided to prepare another full set of game balls, and that, by mid-Sunday morning, he had removed the initial preservative from 24 new footballs, brushed them and treated them with dirt. He and other members of the equipment staff then “gloved” the footballs, spending between 7 and 15 minutes vigorously rubbing each ball. According to Brady, this created a set of game balls “where most of the tack on the ball ended up coming from the leather receiver gloves.” 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.”

    Makes one wonder…

    • Very compelling George.

      I am considering a post that details more methodological problems with Exponent. However, I’m frankly a bit tired of this subject. 🙂

      • Understand.

        This is also very frustrating how Wells and Exponent together essentially went out of their way to destroy the characters of three people, ignoring things, and making things up as they went along.

        I, and I assume others, would find it very enlightening if you could detail the many methodological problems with Exponent.

        Hopefully you will decide to do one last posting that will effectively tie-up the loose ends so everyone can understand just how bad a job Exponent did, and for what I imagine was many hundreds of thousands of dollars in fees and expenses reimbursed.

        What a regrettable sham by these people.

    • George, there’s another piece of HUGE evidence I noticed with this that demonstrates how unlikely it is Anderson used the Non-Logo gauge in the pre-game. (Making it all the more stunning that Exponent just decided he used the Non-Logo gauge). I mentioned in the original post I wrote on Deflate Gate, but I just noticed this: Here are the average readings of the Colts balls relative to our expected 13.0 PSI football as it heats up across all the simulations I presented in the “Statistical Improbability” post:

      Non-Logo, Inflate Patriots then Measure Colts: Avg. 0.46 PSI below expected, almost 0 variance (lowest was 0.44)
      Non-Logo, Measure Colts then Inflate Patriots: Avg. 0.29 PSI below expected, std 0.7, min 0.19, max 0.40

      Remember, inflate Patriot first is more likely. But even if that somehow didn’t happen, the Non-Logo gauge is ~0.19 PSI farther from what physics would expect that the Logo. In the scenario where the Patriots balls were inflated before the 4 Colts balls gauged, you’d have to explain nearly 0.5 PSI of air (at 71 degrees). One can get ~0.15 PSI of air back by changing the pre-game measurement temp to 74 degrees, or perhaps slightly more if wetness is included. But either way, it’s still more likely based on the physics that the Logo gauge was used in the pre-game (i.e. the LOGO GAUGE is the gauge that is more inline with physics for the control group.)

      • Thanks.

        It should be noted that Exponent’s game simulation is invalid when run at 12.5 psi for the Patriots footballs. Thus, all their data using the game simulation is biased.

        Since it can be shown to an extremely high degree of likelihood that Walt Anderson’s memory is not faulty, and that he had used the Logo gauge for pre-game measuring of football pressures, then at a minimum the game simulation should have started at the approximate real football pressure since the gauges used were proven to be in error. When measured against a calibrated Master gauge, the Logo gauge measured too high by 0.3 to 0.4 psi and the Non-Logo gauge measured too low by 0.07 psi (see page 20 of the Exponent Report in the Appendix).

        Thus, at least 12 game simulations should have been run:

        (1) Patriots footballs at 12.1 psi and Colts footballs at 12.6 psi.
        (2) Patriots footballs at 12.2 psi and Colts footballs at 12.7 psi.
        (3) Patriots footballs at 12.6 psi and Colts footballs at 13.1 psi.
        (4) Each of the above run at 70, 71, 72, and 73 starting temperatures.

        This set of data would have presented the most likely, and provably possible, environmental scenarios for both gauges.

        Even doing approximations of expected values based upon the results for the one game simulation Exponent did do (which itself can be compared to expected values using the Ideal Gas Law and wetness pressure factors), one can easily show that the measured half-time football pressures fall within the data probability surface.

        So, as long as one does not play games, including twisting facts as much as 180 degrees (Exponent sets pressure before gloving while the Patriots sets pressure after gloving), the data screams that the Patriots footballs had no tampering and that environmental conditions and gauge variability (i.e., non-calibrated gauges are inherently unreliable) explain the pressure changes in the Patriots footballs (and the Colts footballs as chemistry applies to them also).

        The Exponent “study” and the Wells “investigation” were hack jobs and not independent attempts to determine what happened.

        The Exponent “study” stating that the environment did not cause the football pressure changes seen was a key to allowing Wells to be able to stitch together a few text messages and present an implication that “tampering” had occurred. No proof, just insinuation.

        I presume that as long as Tom Brady has his 4 game suspension lifted (essentially an over $2 million fine), he will not pursue a court case to the end. Even if filed, an out-of-court settlement can be arrived at before all the interesting stuff shows up in court. But would it not be special if a few questions like the following can be heard out in court:

        (1) Did the Wells lawyers not give the Patriots gloving process to Exponent?
        (2) If Exponent was given the Patriots gloving process, why did they switch when the football pressure was set?
        (3) If the Wells lawyers did give the Patriots gloving process, but it occurred after they had done their initial tests, why did Exponent not re-run their tests once they knew that the real gloving process was opposite to what they ran?
        (4) Who did the Exponent/Wells people contact, when were the contacts, and what was mentioned in the contacts (and responses from the contacts)?

        Since Wells was not hired as a lawyer but as investigators, the communications between any party are not privileged and thus open to a Discovery court order.

        It would be very interesting to see said communications.

  10. My take on methodology and related issues.

    (1) The pre-game prep procedure of the Patriots footballs was not tested by Exponent

    This could be because:

    (a) Paul Weiss, et al (i.e., “Paul Weiss) lawyers never gave it to Exponent.
    – If that happened, Paul Weiss did not do its fiduciary responsibility and they could be in trouble, possibly even criminally.
    – This seems unlikely to have happened as Exponent would have no way to do their gloving tests.
    (b) Paul Weiss lawyers gave procedure to Exponent.
    – This lets Paul Weiss off the hook as potentially doing anything wrong unless they restricted Exponent from using it except for trying to disprove Bill Belichick’s comments that gloving affects the football pressure.
    (c) Exponent decided not to use as part of game football analysis except for a very narrow use to try to disprove Bill Belichick statement that gloving affected football pressure.
    – This calls into question Exponent’s chain of analysis and many of its conclusions.
    – Possibly could be considered a fiduciary responsibility issue although not as cut-and-dried as if Paul Weiss had not given them relevant information.
    – Among the conclusions given by Exponent that could have been called into question if a proper test had been done were the discounting of Bill Belichick’s results that gloving could have affected the football pressure, that Walt Anderson’s memory was correct in that he did use the Logo gauge, and that the starting psi of both the Patriots and Colts footballs were likely less than 12.5 psi and 13.0 psi by between 0.3 and 0.4 psi due to the reading errors shown to exist in the Logo gauge.

    (2) Exponent’s initial analysis of the half-time football pressures did not account for time, that over time the pressure changes due to temperature, and football wetness pressure effects.
    – This calls into question why Exponent did this when later in the report they tried to account for these factors.
    – Why do an improper analysis knowing that the results would be statistically biased?

    (3) No environmental tests were done on footballs at different temperatures and football pressures
    – This was one of the key environmental conditions that was known to affect football pressures, yet this test was not done. Why not?
    – This test would have validated the presumed accuracy of Exponent’s day game simulation. Why not done?

    (4) Improper use of Master gauge for comparisons
    – There were three situations that the Logo gauge was used (and arguably the Non-Logo gauge also): pre-game, half-time, and after-game.
    – The after-game values were rejected for any analysis.
    – The pre-game values were ignored and arbitrarily set at 12.5 psi and 13.0 psi based upon Walt Anderson’s recollections even though Exponent had proven that both the Logo and Non-Logo gauges gave different pressure reading when compared to the Master gauge.
    – Only the half-time values were mapped to the Master gauge and the way that Exponent used was to shrink the actual tested discrepancies between the gauges to a smaller number.
    – By not also converting the pre-game values to a Master gauge mapping, Exponent made an apples-to-oranges comparison which is statistically invalid.
    – By doing what Exponent did, they biased the statistical results by using an invalid statistical mapping.

    (5) Pressure was shown to be highly sensitive to both temperature and football wetness but only one extensive game simulation test was performed.
    – Exponent ran the game simulation assuming that the starting football pressure were 12.5 psi for the Patriots and 13.0 psi for the Colts. This can be easily contested as an invalid assumption for the reason that both the Logo and Non-Logo gauges were proven to give invalid pressure reading when compared to a highly calibrated Master gauge.
    – It can be contested that the shower room temperature pre-game was at least 71 if only based upon Exponent own testing which in and of itself could be questioned as iffy unless they simulated game day room conditions which could be roughly gathered from security tape footage.
    – Choosing 69 rather than 71 for the formal test can cause a minimum of a 0.1 psi change in expected pressure readings which for this situation is a very large error factor. Exponent’s later attempt to account for the possibility of a 71 temperature is weak versus having done a formal test. Proper methodology would require the actual test when it is relatively easy to do, as is the case here.
    – The game simulation done effectively tested a Master gauge initial pressure against Logo and Non-Logo gauges that were known to be significantly different than the Master gauge. That is another apples-to-oranges comparison which is an invalid statistical methodology.
    – Thus, a proper set of tests should have been run while using the probable “real” pressures in the footballs for the Logo gauge scenario (initial pressure at 12.1 to 12.3 psi based upon the testing of the Patriots pre-game procedure or 12.2 psi based upon what Walt Anderson said it thought was the reading of 12.5 psi; plus Colts “real” pressure was then 12.7 psi), the Non-Logo gauge scenario (12.4 psi for the Patriots and 12.9 psi for the Colts), and the Master gauge scenario if desired although not necessary (12.5 psi for Patriots and 13.0 psi for Colts).
    – Both the Logo and Non-Logo scenarios would have to be converted to a “real” value range based upon the Exponent prior shown statistical variability of each gauge when compared to the Master gauge.
    – Now one has an apples-to-apples game simulation.

    I am sure that there are more methodology errors in the Exponent Report, but the above are pretty bad by themselves.

    Hopefully others will feel free to comment.

  11. As noted in prior post, with the Logo gauge use, the game simulation should have been run for the end points of the Logo gauge reading error range, or 12.10 to 12.20 psi. Not using the actual pressure biases the results. You then re-map the simulation results to the Logo gauge error and one can then compare apples-to-apples.

    The barometric pressure during the game was roughly 29.62 which equals 14.55 psi as the atmospheric pressure to add to the gauge pressure.

    At 12.10 psi, a football that goes from 67 to 48 per the Ideal Gas Law would expect on average to see the pressure drop to 11.14 psi.
    At 12.10 psi, a football that goes from 71 to 48 per the Ideal Gas Law would expect on average to see the pressure drop to 10.94 psi.

    At 12.20 psi, a football that goes from 67 to 48 per the Ideal Gas Law would expect on average to see the pressure drop to 11.23 psi.
    At 12.20 psi, a football that goes from 71 to 48 per the Ideal Gas Law would expect on average to see the pressure drop to 11.04 psi.

    One also has to account for the pressure drop caused by the footballs being wet. From Exponent’s tests it look like the wetness effect causes the pressure to drop more as the football is heated as can be seen in Figure 22 on page 44 of the Exponent Report. When brought into the ref’s room at half-time, the wet football pressure effect was about 0.1 psi. Four minutes into half-time the wetness effect was a little over 0.1 psi. Four minutes later and the wetness effect jumps to 0.2 psi.

    Per Exponent, they said that the Ideal Gas Law indicated that the range of pressures was 11.32 psi to 11.52 psi when the temperature was in the range of 67 to 71 for the refs room’s area where the footballs were measured.

    So, using the best case scenario for the Patriots (71 to 48, actual football pressure 12.10 psi, wetness factor of 0.20 psi, Logo gauge high by 0.3 psi) to the worse case for the Patriots (67 to 48, actual football pressure 12.20 psi, wetness factor of 0.10 psi, Logo gauge high by 0.4 psi) the expected range at the time that the Patriots footballs were measured at half-time would have been from 11.14 psi to 11.53 psi.

    Checking the half-time readings shows that the Patriots footballs with the Logo gauge had readings that ranged from 10.90 to 12.30 psi with an average of 11.49 psi.

    Obviously, the Patriots footballs fall within expected ranges with the Logo gauge.

    So, by Exponent testing the gloving effect opposite to what the Patriots said they did, a cascading effect resulted in Exponent being able to claim that the Non-Logo gauge was used.

    Ergo, the gloving test looks to be the key to debunking the Exponent Report and consequently the Wells Report. Everything else is really superfluous and argumentative.

    It should be relatively easy and not costly at all for an independent lab to actually test what the Patriots did. In fact, one would not even have to break-in the footballs to demonstrate that Exponent made a key wrong conclusion that gloving had no affects by the time the Patriots footballs were given to the game refs.
    _________________________________________________

    Exponent tested the gloving after setting the football pressure. The Patriots did the opposite of setting the football pressure after gloving. From pages 49-50 of the Wells Report:

    “Jastremski told us that he decided to prepare another full set of game balls, and that, by mid-Sunday morning, he had removed the initial preservative from 24 new footballs, brushed them and treated them with dirt. He and other members of the equipment staff then “gloved” the footballs, spending between 7 and 15 minutes vigorously rubbing each ball. According to Brady, this created a set of game balls “where most of the tack on the ball ended up coming from the leather receiver gloves.” 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.”

    Of course, the really interesting question after one proves the Physics that setting the pressure shortly after gloving a football would lower this pressure once the football finishing cooling down, is why did Exponent not test gloving the way the Patriots said they used it?

    Without a court case this probably will never be known.

    If Paul Weiss, et al (I.e., “Paul Weiss”) never gave Exponent the gloving procedure noted in the Wells Report even though they knew it, that has got to be a breach of their responsibility and calls into question the independence of the entire investigation.

    If Paul Weiss did give the gloving procedure to Exponent, and Exponent did not use it in its tests and used a provably very different procedure, that would seem to be a breach of their responsibility and calls into question what they did throughout.

    There are other variations of what happened, but in any scenario, Paul Weiss and/or Exponent look pretty bad.

    If either of the above turn out to be true, would the action raise to the level of “actual malice” which is the key legal condition that Tom Brady would have to prove in order to win a defamation lawsuit?

    For John Jastremski and Jim McNally who are not public figures, they would have an easier time proving defamation (i.e., libel). All they would have to prove was that the statement was false, caused harm, and was made without adequate research into the truthfulness of the statement. If either of the above scenarios of not providing/using key information during research were true, then one could see how the two of them have a reasonable libel case.

  12. I am reposting a shortened summary of my last post because it is important to note that one simple independent test can prove that Exponent lied about the effect of gloving on the pressure of the Patriots footballs. This is the keystone conclusion, as without this lie, Exponent could not “assume” that Walt Anderson’s memory was wrong and in reality he actually, provably, had to have used the Logo gauge.

    By Exponent being allowed to lie, and apparently getting away with it, we have the defaming of 3 people, and smearing of an organization.

    Boy, do I hope this gets to court, so, hopefully, the truth as to what Exponent did can be broadly exposed.
    ___________________________________________

    A keystone question is why did Exponent not follow the Patriots gloving procedure but use a completely opposite procedure to do its testing? Because without this switch, Exponent would not have been able to play the games it did during its analysis.
    ___________________________________________

    (1) Per the Wells Report the Patriots Gloving Procedure (pages 49-50) was:

    – Glove footballs
    – Set pressure

    (2) Per the Exponent Report in Appendix 1 of the Wells Report (pages 33-35), the Exponent Gloving Procedure was:

    – Set pressure
    – Glove footballs

    (3) Exponent’s football gloving test was the opposite of what the Patriots had done.

    (4) A simple, inexpensive test by an independent testing organization can prove that Exponent was wrong in its conclusion that gloving did not have long term pressure effects on the Patriots footballs when using the actual Patriots gloving procedure.

    (5) The gloving pressure effect is a keystone conclusion. Without Exponent switching the Patriot’s gloving procedure, their data analysis, their game simulation, and their conclusions would fall apart. And the Wells Report would similarly fall apart.

    (6) Since it would be proven that the Patriots did nothing wrong, would the NFL punishments for the Patriots, Tom Brady, Jim McNally, and John Jastremski have to be rescinded? I would hope so.
    ___________________________________________

    Did Paul Weiss, et al (i.e., “Paul Weiss”) purposely withhold the Patriots gloving procedure from Exponent?

    If yes, why?

    If yes, no matter what the reason, then Paul Weiss is guilty of aiding the creation of a lie.

  13. The game day data is garbage and insufficient for any conclusions. The initial pressures are not known, the gauges used uncertain and uncalibrated, the temperature of the balls and degree of wetness unknown, variance of measurements unknown because of single measurements and uncertain conditions. As Kessler has stated, this is an argument akin to how many dancing angels are on the head of a pin nonsense.

  14. I have only gotten interested in this lately, and believe that there are a number of studies that can explain the Pats/Colts pressure differences w/o tampering. However, I would like to raise one thought that I think is new. For the ordering of the pressure measurements given in the Exponent study the third highest measurement is first and lowest is next to last. I think that a lot of the variability in the Pats’ data is because they were warming up. Say a given ball was measured by ref. A, then by ref. B and then ref. B inflates the ball. They then go on to the next ball until they run out of time. This would take about 45 sec. per ball and (given a few minutes to set up) use all the available time. (The extra measurement does take extra time because it’s being done in parallel.) So the Pats’ balls would be warming up and increasing in pressure during the 7 to 8 minutes of the measurements. The first balls measured would be low compared to the mean and last ones would be high. You can see from the decay portion of Fig. 16 of the Exponent report that a ball will recover roughly 75% of its original pressure in 8 minutes. This scenario would also explain the wide scatter/range in the Pats’ measurements, which strikes me as quite high for balls that all started close to 12.5 psi.

  15. It is impressive how incredible dumb people are when it comes to Deflategate. Or should I say how desperate people want to believe that Jim McNally purposely deflated footballs while going to the bathroom after taking the footballs from the referee’s locker room.

    Exponent’s restroom deflation tests published in Appendix 2 shows that nothing other than natural deflation could have happened.

    The Ideal Gas Law also has to apply to the footballs after they allegedly had air removed. I trust everyone does believe in nature? If everyone does, then extra air could not have been removed by Jim McNally in the restroom based upon Exponent’s published test results.

    No fancy statistics. All anyone has to do is apply simple first grade math to demonstrate this using Exponent’s own testing as reported in Appendix 2 of the Wells Report.

    Please read the following, and you can easily see for yourself that Exponent PROVED that Jim McNally could not have let out air from the footballs while in the restroom.

    And this restroom test also proves that Exponent’s analysis in Appendix 1 is wrong and their conclusion that nature did not cause the observed pressure changes is also WRONG.

    Below is in addition to the FACT that Exponent improperly indicated that gloving footballs had no long term affect on pressure (it does) by not testing the Patriots gloving process, and that Exponent made a serious logic error trying to “prove” that the Non-Logo gauge was used by Walt Anderson (it was not – Walt provably used the Logo gauge).
    ______________________________________________________________

    So that everyone is on the same page, let me boil down the Deflategate science into the following three simple sentences:

    – The pressure in a football changes when the football is placed in a colder or a hotter temperature than what the football is in now.

    – Every 1 F (i.e., “Fahrenheit”) of temperature change causes about a 0.05 psi change in football pressure either up (hotter) or down (colder) per the Ideal Gas Law.

    – The pressure of a football is lowered by being wet by 0.1 to 0.3 psi per Exponent game simulation study.

    As one can see, simple first grade math can be used to determine what can be expected to happen to football pressure as temperature and wetness changes.
    ______________________________________________________________

    Here are the 3 sets of restroom data that Exponent got by having people try to remove air from 13 footballs as fast as they could while in a small confined room simulating the restroom Jim McNally went into:

    Initial pressure set at 12.5 psi. Calibrated gauges used.
    Set 1 Drop Set 2 Drop Set 3 Drop
    11.806 0.694 11.816 0.684 11.779 0.721
    11.741 0.759 11.740 0.760 11.636 0.864
    11.795 0.705 11.651 0.849 11.773 0.727
    11.714 0.786 11.801 0.699 11.698 0.802
    11.877 0.623 11.730 0.770 11.836 0.664
    11.797 0.703 11.708 0.792 11.568 0.932
    11.688 0.812 11.532 0.968 11.827 0.673
    11.864 0.636 11.833 0.667 11.792 0.708
    11.730 0.770 11.526 0.974 11.848 0.652
    11.577 0.923 11.734 0.766 11.760 0.740
    11.682 0.818 11.779 0.721 11.844 0.656
    11.744 0.756 11.721 0.779 11.717 0.783
    11.585 0.915 11.899 0.601 11.717 0.783

    Set 1: average pressure drop of 0.762 psi with plus/minus of 0.089 psi.

    Set 2: average pressure drop of 0.772 psi with plus/minus of 0.104 psi.

    Set 3: average pressure drop of 0.747 psi with plus/minus of 0.081 psi.

    The above three sets average is about 0.760 psi with plus/minus of about 0.09 psi.

    The temperature difference from the ref shower room to the field was 69 F – 48 F = 21 F or a 1.05 psi further drop.

    Per Exponent’s wetness testing (see page 44 of Appendix 1 of Wells Report), the pressure further drops about 0.1 to 0.3 psi depending upon the time spent in the ref’s locker room during half-time. The average pressure drop is 0.2 psi due to football wetness.

    The Non-Logo gauge reads too low by about 0.07 psi and the Logo gauge too high by 0.3 to 0.4 psi when compared to a calibrated gauge (see page 20 of Appendix 1 of Wells Report).

    Therefore, when the footballs were brought in from the field at half-time, a wet 12.5 psi football could be about in the range of 10.4 to 10.58 psi or an average of 10.49 psi at the one sigma level, and 10.40 psi at the two sigma level.

    Thus, using the Non-Logo gauge, the average pressures would be about 10.42 psi at one sigma and 10.33 psi at two sigma.

    And using the Logo gauge, the average pressures should have been about 10.84 psi at one sigma and 10.75 psi at two sigma.

    However, the actual average pressures readings were 11.11 psi for the Non-Logo gauge and 11.49 psi for the Logo gauge (see page 45 of Appendix 1 of Wells Report).

    In other words, it was IMPOSSIBLE for Jim McNally to have released any air out of the Patriots footballs in the amounts noted in Exponent’s testing and have gotten the pressure readings obtained.

    Now, to have a complete proof that no non-natural deflation occurred, another test would have to be done.

    Namely, is it possible to let out a tiny amount of air from a football, and still be able to get the pressure readings, all in 140 seconds. We are talking about 0.1 psi to maybe 0.2 psi worth of air at most. Without special gauges this would be a pretty tough task to accomplish across 13 footballs with just a simple football needle and a time limit of 140 seconds to finish the entire task. The task is to go into restroom with multiple bags (Jim McNally had multiple bags with him), unzip game balls bag and dump footballs onto floor (should be a sloped floor as that is what the real restroom has), needle each football to no more than 0.2 psi less air and placing them back into the bag, zip the bag, and exit restroom with all bags.

    I can conceive of one possible way it may be possible to remove a very tiny amount of air with just a normal football needle. And if that way causes the pressure to drop more than 0.2 psi, then it would be IMPOSSIBLE for Jim McNally to have removed any air from the footballs.

    To me, this is a waste of time as the gloving pressure and the team locker room to shower room pressure drop is sufficient to prove that natural deflation occurred. However, for completeness one should run this additional test.

    • But they were not interested in finding the truth. If they were, they would have obviously tested the minimal amount of air one can release with a quick needle into the ball. Similarly, they would have done more with wetness instead of their “misting” test. And they would have run more simulations / scenarios.

      Instead, they tried to create a fixed window that the real-world results could not squeeze into, by a small amount, not mention how implausible or insignificant that small amount actually was, and then wax on about how the balls must be below the levels they “should be” even though they based the whole thing on estimations, memory, poor proxies and one or two scenarios.

      More importantly, believing that someone would alter a football by 0.2 PSI, when it’s definitively proven beyond a doubt that NFL players can’t even detect the difference of +/- 1 PSI is like believing that Brady concocted a scheme with the shoe company to make sure his spikes were 0.01 mm longer than the legal spike limit…but only for his home games.

      • The real question is did Exponent purposely “cook the books” to get its results because their testing was not getting the desired end results (i.e., that nature could not explain the observed half-time football pressures)? To me that is scientific fraud.

        Also, was Paul Wiess, et al, kept abreast of what was being done to “cook the books” and given reasons why it was being done? To me that may be collusion to commit fraud.

        Lastly, since Jeff Pash (NFL executive VP and general counsel) was stated as the co-investigator on the Wells Report, was he kept abreast as to what was happening? If yes, then he would be an accessory to the fraud.

        Makes one wonder what is really in all the notes and communications that the NFL refused to make public. The NFL wanted the arbitration hearing testimony sealed, and once Judge Berman made it unsealed, we could see why. Roger Goodell’s final arbitration ruling lied as to what Tom Brady had actually said, and Troy Vincent’s testimony called into question what was written in the Wells Report as to when the alleged deflation issues became known.

        If this occurred in a relatively small amount of testimony, what in the world could be in the voluminous amounts of notes and communications that occurred during the investigation that went from late January to the Wells Report release in early May?

        I would be willing to bet the house that some juicy stuff exists and the NFL wants it buried. Hence, the “independent” investigation becomes a “privileged” investigation.

        I would like to see that designation be able to hold up in a court of law. There is tons of case law rulings that indicates that when a lawyer is hired to do tasks not considered legal advice, then the notes and communications are open to discovery.

        And if any criminal or fraud or similar nefarious acts happen to have occurred, the US Supreme Court has already ruled that “privilege” goes out the window.

        • I agree, but I don’t think we’ll ever see it adjudicated.

          The cognitive scientist in me must point out that the same people who found the entire cell phone narrative so damning to Brady will probably not even bat an eyelash at the NFL hiding its investigation notes, hiding its internal communications and blocking such people from testifying.

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