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Andrew Healy, frequent contributor here and at Football Outsiders, is back for another guest post. You can also view all of Andrew’s guest posts at Football Perspective at this link, and follow him on twitter @AndHealy.

For a stats guy, the Wells Report is gripping reading, particularly the appendices provided by the consulting firm Exponent. The conclusion there is pretty simple. Compared to referee Walt Anderson’s pregame measurements, the Patriots’ footballs dropped significantly further in pressure than the Colts’ footballs did. Therefore, even if Tom Brady’s involvement is unclear, a Patriots’ employee probably deflated the balls.

At first glance, that evidence seems pretty convincing, maybe even strong enough to conclude more definitively that tampering occurred. And it is kind of awesome that the officials even created a control group. But there is a problem with making firm conclusions: timing. As Exponent acknowledges, the measured pressure of the balls depends on when the gauging took place. The more time that each football had to adjust to the warmer temperature of the officials’ locker room at halftime, the higher the ball pressure would rise.

And, not surprisingly given the Colts’ accusations, the officials measured the Patriots’ footballs first. This means that the New England footballs must have had less time to warm up than the Indianapolis footballs. Is that time significant? We will get to that, but it does make for a good argument that the Indianapolis footballs are not an adequate control group for the New England footballs. Given the order of events, we would expect the drop of pressure from Anderson’s initial measurements to be lower for the Colts’ balls that had more time indoors at halftime. As the Wells report notes, the likely field temperature was in the 48-50 degree range, compared to the 71-74 degree range for the room where the footballs were measured.

So, how much lower? Here it gets a little fuzzy. The report is clear that the Patriots footballs were gauged first during halftime, but it is unclear about whether the second step was to reinflate the Patriots’ balls or to measure the four Colts’ balls. In Appendix 1 (see p. 2 of the appendix), Exponent notes “although there remains some uncertainty about the exact order and timing of the other two events, it appears likely the reinflation and regauging occurred last.” If events unfolded this way, it would make the Indianapolis footballs at least a better sort of control group.

If, on the other hand, the Colts footballs were measured last, there would have been a significant amount of time between when the last Patriots’ football was measured and when the first Colts’ ball was — i.e., the amount of time it took to reinflate the New England footballs. With a few extra minutes to warm up closer to room temperature, the pressure in the Colts’ footballs could rise towards the levels Anderson measured before the game.

I am not breaking any ground here: Exponent acknowledges this possibility in the scenarios it thoughtfully presents about how natural causes could explain the differences between the Patriots’ and Colts’ footballs (see item 10 on p. XIII of Appendix 1, or the 159th page of the 243 page .pdf). It concludes that the necessary timing conditions are unlikely given the information that was provided to them by Wells’s law firm, but it allows for the possibility. So this seemed to me the most important question after reading the report: Could the observed differences between the Patriots’ and Colts’ footballs come from timing if the Colts’ footballs had actually been measured just before the end of halftime?

To try to answer this question, we actually have a little more information to go on than just the average differences in ball pressure. Specifically, we have the variation in the pressures in the balls. Consider the data from the report on the halftime pressures for the 11 Patriots’ footballs and the four Colts’ footballs that the officials had time to measure. (If you haven’t read the report, the two officials (Clete Blakeman and Dyrol Prioleau) were using different gauges, one consistently reading a little higher than the other. There is one case (Ball 3 for the Colts) where Blakeman’s gauge read lower in the report. The report plausibly argues that the readings may have been transcribed incorrectly, and I switch the readings here accordingly.)

TeamBall #BlakemanPrioleau

First, notice that the effects on the Indianapolis footballs when moved from a colder to warmer environment were not enough to not bring the Colts’ footballs back up to their pregame level of nearly 13.0 psi. Therefore, absent tampering, I think we should expect roughly similar levels of variation across the balls for each team.1

But it won’t take you long to see that it doesn’t appear that way in the table above. The Patriots’ footballs vary, on Clete Blakeman’s gauge, from 10.5 to 11.85 psi, while the Colts balls vary in a much narrower range from 12.5 to 12.95 psi. On the other hand, there are more Patriots’ balls in the sample, so we’d expect the range to be higher. How about the standard deviation for the Patriots’ footballs compared to the Colts’ footballs?


Under Blakeman’s numbers, the Patriots’ footballs had a standard deviation of .402 psi compared to .165 psi for the Colts’ balls. With Prioleau’s pressures, the standard deviations for the two teams are .410 psi and .144 respectively. So the Patriots balls had a standard deviation of pressure more than double that of the Colts. Given the sample size, these differences are not quite significant. Using Blakeman’s measurements, the p-value is 0.17. With Prioleau’s, it is 0.11.

Still, the difference in variation between the Patriots’ and Colts’ balls is awfully suspicious. That piece of evidence has helped tip me, initially a Deflategate skeptic, into the convinced column. There was a wealth of interesting evidence in the Wells Report. But absent video of the Deflator (somehow neither an action hero nor an incompetent central banker) working his magic, the hard proof had to come from the pressure in those 15 balls tested at halftime. Combined with the difference in average pressure levels, the difference in dispersion is hard to dismiss.2

Moreover, that latter difference fits with the theory of how The Deflator committed the crime. With a short amount of time in that bathroom, he could just quickly release a little pressure from each ball. That process would take balls that were roughly equal in pressure at the time of Anderson’s initial measurements and make them more dispersed.

  1. Also note that the Patriots’ balls do not register a clear upwards trend in pressure during the gauging process. []
  2. Although it sure would be nice if the officials had had the time to measure all 11 Colts’ balls to really nail this theory down. []
  • sacramento gold miners

    Two aspects of this case are troubling, Brady’s statements before the Super Bowl, and his lack of cooperation with the investigation. I just assumed Brady would have been more outspoken about his innocence, the way other great QBs would have been, and disclosed everything in order to clear his name. Spygate also plays a role here, because it goes back to a prior question of team misconduct. Back then, the investigation seemed rushed, and the tapes themselves were strangely destroyed. Reasonable fans are still asking themselves if an organization which had been illegally taping meaningless preseason games, would have stopped itself when it came to the postseason. It’s a valid question, and Brady may have more knowledge of that era than was previously thought.

    • Dave M

      SGM, you have your facts wrong on both points. 1. Spygate was about taping defensive signals from the sidelines during the games. The league changed the rule on that, making it illegal. Pats did it in 1st game of year against the jets. Before that, it was legal. So they taped one regular season game illegally and then stopped.

      2. Re: brady presser…go back and watch it. Knowing what we know now, his answers are fine… All the q’s were about why can’t he explain not knowing the balls were 2 lbs lighter in weight. At the time, people were thinking they would feel 2 lbs lighter. He keeps answering that he didn’t feel a difference and he doesn’t have an answer, that he picks the balls he likes pregame and then he’s not involved. He keeps getting asked how its possible he couldnt feel the weight difference. He can’t answer why balls are 2 lbs under because we now know that wasn’t the case and the balls would feel no different than any other cold weather game for any nfl team. Hes struggling to give an answer to a false assumption. Any cold weather nfl game where balls start at 12.5 psi are going to be 11.5 or lower during game. Balls in colts game were worst case .5 psi below that, and of the 4 possible scenarios, that is only one where balls were lower than expected. So its possible there was 0 difference vs every other cold weather game he played in. So he felt no weight difference yet everyone keeps asking how he couldn’t feel they were 2 lbs lighter.

      • sacramento gold miners

        Dave M, respect your opinion, but the Patriots already admitted taping preseason games during that era. I think a reasonable person wouldn’t expect New England to suddenly police itself in the postseason later on. If you still believe it’s ok, I just can’t help you. A number of those postseason wins were by a TD or less, including the Super Bowls. The way the NFL conducted a hurried investigation is very troubling, including the destruction of those tapes.

        Regarding the Brady press conference, he still came off as defensive, and many people feel the same way. I feel the league did the right thing, and taking past behavior into account was justified.

        • Dave M

          respect your opinion also. I am not saying they didn’t tape games. They taping they were doing was legal before 2007, so any team was allowed to tape any preseason, regular season or post season game.. the league made the taping they did (and some other teams were doing) illegal before the 2007 season – pats continued to tape in 1st game against jets after new rule, and were caught. So the taping was legal until the rule change in 2007, where the pats did it in the 1st game of the season, they were caught, and were punished. Here’s Wikipedia explaining spygate: “refers to an incident during the National Football League’s (NFL) 2007 season when the New England Patriots were disciplined by the league for videotaping New York Jets’ defensive coaches’ signals during a September 9, 2007 game.Videotaping opposing coaches is not illegal in the NFL but there are
          designated areas allowed by the league to do such taping. The Patriots were videotaping the Jets’ coaches from their own sideline which is not allowed”

          Here’s a good video summary on what the wells report testing got wrong – http://www.backpicks.com/ – it’s actually more likely that the balls were normal, but even if the balls were 0.3 psi below what they were supposed to be in cold weather, in his presser, brady is trying to explain false assumptions at the time. at the time no one was aware of how cold weather affected drop in psi, and most in the press (and public) didn’t realize that 2 lb psi wasn’t like the weight of 2 pounds – during the questions, none of the press can understand why he couldnt feel the weight difference in the balls. we now know no one could feel the psi weight difference. Of course he’s defensive, he’s being accused of taking 2 lbs out of the balls and not being able to feel the weight drop of 2 lbs. He’s being asked over and over to explain how he couldn’t feel something so obvious, or explain why the balls dropped that much weight.

          it still could be that pats were deflating balls and brady knew about it, but the ball measurements and correct analysis from the colts game doesn’t prove the balls were tampered with.

      • Vega

        A 2 psi difference is NOT a 2 lb difference in weight. 2 lbs of air at standard temp and pressure is 25 cubic feet of air. By that logic, a ball 12 psi ball would have 150 cubic feet of air in it and weigh 12 lbs! See how far you can throw a 12 lb weight. The difference could possibly be felt in the tension of the leather and in the very slight difference in weight. However, it was wet and raining so the water in the leather would negate any small weight difference

      • Cú Chulainn

        Point of fact: The League did NOT chance the rule on taping from the sideline. The commissioner sent a memo saying not to do it. BB felt that if the commissioner wanted to change a rule, he could follow the established process…submit the rule to the rules committee and then to the entire league for a vote.

  • Richie

    Get ready to feel the wrath of Patriots fans in 3…..2……1…..

    • atyler2011

      With that front seven, TB will take notice.

  • Richie

    The hardest thing for me to reconcile in all this is: on one hand, I feel a little appalled that the Patriots would tamper with the game balls after they were inspected. On the other hand, if a team did this in the 1950’s, I could easily picture Art Donovan telling the story about how they snuck in and deflated the balls and everybody has a good chuckle about it now.

    I can’t decide if it’s just “gamesmanship” or outright cheating.

    Did the NFL ever rule on the Cleveland Browns texting on the sidelines during games? Is deflating footballs worse than that?

    • Andrew Healy

      I’m also on the fence about that. Maybe it’s worse than the texting. Is it all that different than extra stickum or illegal pads (like the 70s Raiders used and have popped into my head like Donovan does for you), though? Probably not.

      What Spygate and this have in common is that they seem so unnecessary. Spygate provided very little, if any, advantage to the Patriots. I doubt any deflating helped Tom Brady throw any better, either. Fumbling is a much longer discussion.

      As a Pats’ fan, I just wish they stayed away from this stuff.

      • Richie

        I hope somebody does some deeper analysis on the fumbling to see if there may have been a benefit there. The Sharp blog was very interesting, but I know people have pointed out a lot of problems with that analysis. Up until just now I thought that maybe Brady figured out that it’s easier to avoid fumbling with a softer ball.

        But it occurred to me that Brady likes the feel of throwing a softer ball. Any advantages in the fumbling department might just be a happy coincidence.

      • sacramento gold miners

        The extra stickum used by the Raiders in the 1970s was a different situation, because it was well known in the NFL to the point the CBS pregame show did a feature on the stuff. It was messy and had an odor, and there were other NFL players who just weren’t convinced of the effectiveness of the stuff. When the league outlawed the substance, I think it was Lester Hayes who complained, but that was it. Even when something is a minor benefit, when steps are taken to conceal the activity, it usually comes out in the end. I don’t think the under inflated footballs were the difference in the AFC title game, but the rules still need to be followed. It’s a slippery slope, if we don’t enforce all the rules.

        I do wish the league had done a more thorough investigation on Spygate, because the Pats were involved in a number of close postseason wins, games decided by one critical play, and it would have benefited everyone to leave no stone unturned. I’ve heard postgame audio of another teams’ coach asking Charlie Weiss how they knew what was coming during the game, and that’s not something you normally hear. This was after a regular season game, when Weiss was the offensive coordinator.

      • atyler2011

        Not a Pats but a big TB fan. Agree but they didn’t and probably did not need to in trying to get an advantage. What a shame?

    • Alejandro

      Just on the Cleveland Browns situation, the Browns were fined $250,000 and the GM, Ray Farmer, has been suspended for the first four games for the regular season.

      In that case, a $500,000 fine would be justifiable, in my opinion. I have no clue where precedent would lie in suspensions though, unless you feel like suspending the equipment manager and considering that a punishment…

      • Richie

        I’m going to be irritated if I find that the equipment manager is fined or punished.

        I would think that a punishment similar to the Cleveland situation would make sense – except I don’t think suspending a GM and suspending a starting QB or apples-to-apples punishments.

  • JoeS

    Patriots defenders (I’m not accusing the author here) are quick to point out little points, but, usually neglect the larger picture:

    This isn’t a “one game” thing. There are several reports throughout the season of possible tampering. The texts prove this (and, if Brady’s cellphone had been turned over, no doubt any “debate” would be OVER). At least three teams (Colts, Jets & Ravens) reported suspicions. And, you have to go all the way back to when Brady and Peyton successfully lobbied the league a few years ago to allow teams to tinker with the footballs to show where this all likely began.

    The other point that hasn’t been brought up much is the then-derided theory that the under inflated footballs lead to a statistically significant lower of fumbles for the Patriots. Time to re-open that analysis.

    • ElGee

      Well, let’s re-open it so we can get it right:


      Also, how could the Patriots have tampered against the Colts…the game was in Indianapolis. The Colts equipment men are locker room liaisons. The Ravens are the same team who wanted to say the Patriots cheated for running trick formations. And it was like 10 degrees by the end of that game…Know what a 12.5 PSI football inflated at room temperature would be at 10 degrees? About 9.5 PSI.

      • JoeS

        Every team (Home OR Away) controlled their own balls. So, YES, the Patriots were deflagating on the road, too. Of course, the NFL just passed a rule changing the procedure for next season.

        • ElGee

          I’m lost. Both teams prepare balls BEFORE delivery to the officials. The allegation (and quite a specific one about stopping in the bathroom) is that the balls were tampered AFTER the officials gauged them. How would that possibly happen on the road?

          • JoeS

            Same way it happened at home.

            But, like has been noted – the rules have been tightened going forward.

            The bigger point is that the NFL should never have allowed Brady and Peyton to convince them that this was a good idea in the first place! Imagine if Lebron James could ask for “his” ball when Cleveland was on offense?

            • ElGee

              Hmmm. I feel like you’re not understanding the procedure. There is a window of time after the officials approve the balls before they are on the field (in plain site). For all intents and purposes, at some point in that window tampering must occur. The allegation is that it occurred during transporting the balls from the locker room to the field. There is no ambiguity about this in the Wells Report — the balls are in plain site at all other times, save for the trip to the bathroom.

              But, on the road, there are no Patriot employees in the officials locker room. They could not have access to the balls in that window, short of Mission Impossibling through the ventilation system. Jim McNally, “the deflator,” does not go to away games.

              That makes it impossible to deflate the footballs on the road in this manner.

  • mocha_bob

    In their experiments and analysis, the Colts balls are used as the “control group.” Does that not seem problematic to anyone? It seems fairly obvious that the Colts knew there were going to complain to the NFL (they had already teed it up), and the report contains almost zero discussion about the conditions that their balls experienced prior to the game. When were they delivered to the officials locker room? Why wouldn’t a report which really had a lot of fluff in it, not be more rigorous about the control group that was used to set all the environmental factors associated with the game day simulations. Seems a bit sloppy to me.

  • editstet

    All that has been established here is that the Colts balls reached equilibrium of pressure, which makes measuring their gas pressure easier, while the Patriots balls, all in different conditions of wetness and temperature, never reached equilibrium. So oranges are usually more round than apples, and they are still different fruits. Garbage in, garbage out still rules.

  • ElGee

    Just saw this main article: Here is a video explaining the full data analysis based on what you observe here: https://www.youtube.com/watch?v=Cx0P3NErcNo

    A note on standard deviation — New England does indeed have a higher one, even when we control for difference from expectation. This is certainly likely to be from either water, gauge variability (see the intercepted ball measured in the 1st half) and/or the Colts only measuring 4 balls. It’s also hard to muster up an argument that the variability in the balls is a problem if it spreads in *both* directions…did McNally accidentally insert air into some of the balls?

  • Bill S

    Here is another theory (or the actual explanation) on the wide variance on the Patriots balls as stated by a friend of mine:

    It was a “hot” day in New England that January day (50 degrees that day, but averaging
    20 degrees leading up to that day) and there would have been an “ice cube” of sand and dirt
    directly under the artificial turf that day — and no one in the NFL has thought to consider
    that the temperature of that turf might be less than the air temperature! And then a number of Patriots balls
    rolled around and sat on that wet cold turf during that long final drive leading up to halftime, and the halftime measurements!

    That is why there is such a wide variance in the Patriots balls, and why they were lower in pressure. It is really that simple.

    In their “Game Day Simulation”, the Wells Report forgot to include the Game. The balls sitting on the turf at the line of scrimmage between each play would have cooled off more than other balls. Another note, because of problems with Artificial Turf being too hot on hot sunny days, the turf is designed to bring coolness up from underneath. Check with the manufacturer FieldTurf …

    This also explains the “smoking gun” — the intercepted ball that the Colts equipment manager stuck a needle in an measured a pressure of 11.0psi. They then let it sit outside for 15 minutes, which assuming the Ideal Gas Law would have brought it up to about 11.3psi, and then when they brought it inside, they took 3 minutes before they measured it, and they got 11.45psi, which is exactly the warming that might expected for bringing the ball inside. This is one ball, and more uncertain because of the uncertainty in measurements, but totally consistent with a cold turf field, and the process it went through.

    • Andrew Healy

      Great, great points. The Patriots’ response brought up the different usage in the game, too, and that does make sense as an explanation for the higher variance. I’m mostly back to believing there’s a pretty good chance they didn’t do anything. Almost wanted to write another post about it, even. We’re talking about 0.4 psi tops (still not understood enough). Why you would even bother at that small amount is a good question. And these other factors (e.g. the different usage in the first half) seem like more likely explanations than the Patriots deflating from 12.5 to the almost-imperceptibly lower 12.1-12.2 (which is really what the Wells Report is alleging).

      This would all be so much different if people were not so ignorant of the science. The balls measuring so low at halftime framed the debate that followed. Imagine the horror if people had measured the balls during the Ice Bowl.

      • Richie

        ” I’m mostly back to believing there’s a pretty good chance they didn’t do anything. ”

        Then why did the equipment guy call himself “the deflator”?

        • Andrew Healy

          That one I don’t think means much at all. I thought that was maybe the weakest point the Wells Report made, despite the attention it garnered. He routinely deflated balls from their out-of-the-box level down to where Brady liked them. So he can be “the deflator” without being “the rule-breaking deflator.”

          The texts actually were something I had to overcome to believe that the Patriots did this. These guys text about everything, they have to believe nobody is ever going to see these texts, and yet nobody ever makes an explicit reference to breaking the rules. You can argue they’re extraordinarily careful, I guess. Anyway, “the deflator” is actually a pretty weak piece of evidence, I think.

          • Richie

            It’s hard for me to imagine a guy calls himself “the deflator” and talks about “a lot of stress trying to get them done” if he is operating 100% within the rules.

      • Bill S

        Thanks for understanding these points. I did write this up in more detail here: http://billspencer42.wordpress.com .The cold field is a simple explanation, and it explains all the observations that occurred, unlike the Wells Report which answers some questions, but leaves many more. It is disappointing to me that more people haven’t caught on to it — even the Patriots themselves which see the different usage in terms of hard plays, etc, but haven’t really caught on to the point of a cold field. By now most people have forgotten how cold it was leading up to that game.

  • ssl

    Your analysis is on an interesting track but I feel you stopped too soon. The sample standard deviations of the Colts balls and Pats balls at the end of the game can also be calculated. We can safely assume that the Pats treated their footballs approx. the same way in the first half and in the second (cold earth and all). The comparisons at halftime of the Pats balls versus the same balls at the end of the game after they’ve been re-normalized at the half is very interesting.

    I think it is very compelling evidence that the Pats footballs were tampered with between the ball inspection and the half. It’s a shame this view has gone completely unreported. I think it would kill off a lot of the rhetoric, once we all come to grips with the football tampering. It would bring people face to face with what they’ve been trying to avoid with their countless wacky explanations: and that is Occam’s Razor. It would move things toward actual resolution.

  • Bruce Loescher

    I’m wondering if the time of possession would make a difference, where the patriots had the balls on the field of play and possibly more exposed too the elements than the Colts balls giving the balls more time to deflate