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):
- The interpretation of context-free communication snippets
- The interpretation of memory-based claims
- The statistical analysis of the AFC Championship game measurements
- 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
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.
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.
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  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:
Now here’s the actual data:
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.  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.  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. 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:
- 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.
- 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.
- 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.
- During the October, 2014 game against the Jets, “the deflator” Jim McNally failed to deflate at least some footballs (that were 16 PSI)
- 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.
- 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.
- 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.
- 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
- A lack of understanding around memory likely led the Wells investigators to a number of false conclusions
- The AFC Championship game data shows the following :
- Regardless of what gauge was used, it’s highly unlikely that the Patriot balls were tampered with.
- Exponent reached an erroneous conclusion using poor methodology.
- 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.