Thursday, January 29, 2015

Deflategate: a view from Central Europe

Between 1972 and 1974, America was excited about Watergate. Similarly, the most important event that decides about the future of the United States in 2015 is the so-called Deflategate. In fact, Bill Nye the Science Guy has changed his occupation and began to give lectures about Deflategate rather than climate change, his previous favorite scandal that is – as he equally pointed out – approximately equally fatal as Deflategate.

During a semifinal game in a competition ("NFL") revolving around an esoteric sport named "football" although it is in no way "football" in the conventional sense, the team that I would have encountered in Greater Boston for six years, The New England Patriots (yes, if you wake me up at 3 am, I won't tell you the difference between The New England Patriots and The Boston Red Sox LOL), was found to have provided the game with underinflated balls. Well, 11 of the 12 balls had a lower pressure.

(Incidentally, Czechia is excited about low pressure these days, too: the pressure dropped to 970 kPa, close to the February 1989 record of 967 kPa.)

Because their January 18th, 2015 defeat of the Indianapolis Colts, 45-to-7, was apparently a statistical tie that could very well have ended up differently, people keep on repeating questions such as: Were the balls underinflated deliberately, to help the Patriots? Was it just negligence? Did the underinflation result from a low temperature or high humidity? And so on.

I find the spectrum of these questions to be ludicrous.

First, let me mention a few basic facts related to physics that are usually being said in this context. But I have never read the actual answers so what follows is my independent calculation that may suffer from some mistakes (or, on the contrary, that may fix mistakes that are being made by others).

NFL demands the pressure inside the balls to be between 12.5 and 13.5 PSI. America uses medieval units and pressure is no exception. PSI stands for "pound per squared inch" and it is defined the "terrestrial weight of one ancient Roman metallic balance with some post-Christ mass bonus per the area surrounded by four bloody fingers cut from an adult thief of potatoes".

Because some readers may have a hard time to locate all the historical facts, let me mention that 1 PSI is about 0.068 atmospheres or 6.9 kPa; conversely, one atmosphere is about 14.7 PSI. OK, it means that the extra pressure in the ball should be between 0.85 and 0.92 atmospheres. Instead, the pressure was found to be 11 PSI. In order to be compatible with the U.S. conventions, let us use the PSI unit.

The minimum allowed pressure was 12.5 PSI but the actual pressure was 11 PSI. It is about 10% lower. Can you reduce the pressure in the ball by lowering the temperature? You bet. The air (or whatever was inside) is approximately an ideal gas. And they obey \(pV=nRT\). At a fixed volume \(V\), the pressure \(p\) is directly proportional to the temperature in kelvins, \(T\).

To decrease the pressure \(p\) by 10 percent, you need to reduce the absolute temperature \(T\) in kelvins by 10 percent as well. The normal temperature is about \(T\approx 300\,{\rm K}\) which means that you need to cool the ball by 30 °C in order to reduce the pressure by 10 percent. It's a lot but not impossible.

I hope that NASA and Boeing have already learned how to produce a more accurate sphere. ;-)

However, the actual total pressure inside the ball actually wasn't around 0.85-0.92 atmospheres. It's the extra pressure relatively to the environment. So the total pressure in the ball is supposed to be between 1.85 and 1.92 atmospheres, more than twice as much. For this reason, what we need to reduce the (extra) pressure from 12.5 to 11 PSI isn't a 10% decrease of \(T\) but rather (slightly less than) a 5% decrease of \(T\), i.e. something around (less than) 15 °C. Of course it's totally plausible that the pressure was set at a place that was 15 °C warmer than the playground so that the cooling would lead to this deflation.

One may also mention that the humidity affects the pressure. In humid conditions, leather (which is found on the surface of the balls) actually tends to shrink which would increase the pressure. To produce a ball of a lower pressure, you need to inflate it in very wet conditions, when the humidity adds some pressure, and when you transfer the football to less humid conditions later, the pressure goes down.

Great. These are some technicalities.

But my major points – which, as far as I can see, are not being voiced in the U.S. at all – are not quite physics points.

First, I think it's irrelevant what happened with the temperature or the humidity. If the rules say that the pressure should be between 12.5 and 13.5 PSI, then the rules clearly mean the pressure that may be measured on the playground at any moment during the game because that's the quantity that is relevant for the play. So whatever procedure they use to inflate the ball – in conditions where the temperature or humidity is different – must be done in such a way that the pressure will be right on the playground. If the temperature or humidity is changing significantly, it's a job for the serviceman to learn – either theoretically or empirically – what happens with the pressure when he moves it from one place to another, and it's his job to make sure that the pressure is right on the playground.

For this reason, I think that all the discussions about the effect of the temperature or humidity are absolutely irrelevant for the legality of the situation. At most, the Patriots may prove that the serviceman is science-illiterate and he would never think about the effect of the temperature or humidity, and that almost proves that the wrong pressure was due to negligence or stupidity or ignorance of physics – and not the result of an evil intent.

Second, I am convinced that most of the sensible Europeans must be stunned by the same point: Even if the pressure was too low and if it were providing some players (those catching a ball etc.) with an advantage and some players with a disadvantage, both teams should be affected pretty much equally, shouldn't they?

You know, in Europe, some people are playing the real football – "soccer", if you wish – and the weather may be freezing. There stadium may be full of mud or something like that. But those things don't matter much because they affect both teams equally. The weather may be hard but the game is still fair.

Here, we are being assured that if the balls had not been underinflated, the 45-to-7 victory of the New Patriots could have become a loss. Wow. If that's the case, then it is a pretty damning verdict about the American football as a game. If the chance to revert this overwhelmingly clear result by a lower pressure is truly significant, the victory is pretty much decided by the pressure of the footballs!

And if the final score isn't this random or dependent on irrelevant physical quantities, than a team that won 45-to-7 should almost certainly win again when the game is ordered to be repeated, right? So if the game makes sense, the probability that such a thing could matter for the results of the league is tiny.

Just think about it rationally. The people who say that the lower pressure mattered effectively say that the score is a function of the pressure. At 11 PSI, we get 45-to-7 for the New Patriots. At 12.5 PSI which is allowed, the Colts would win. So 1.5 PSI is enough to turn the clear score upside down. If that's so, then obviously 1 PSI – the width of the tolerated window for the pressure, 12.5-13.5 PSI – greatly matters, too.

If it matters in the direction that the critics of the New Patriot promote, then it is very clear that the home team always wants the pressure to be as low as possible, at 12.5 PSI, while the visiting team should do everything it can to make the pressure 13.5 PSI, the maximum allowed value.

As you must have figured out (and you probably knew it long before you were reading this blog post), I don't give an infinitesimal damn who should win. Patriots or Colts, what's the difference? True patriots wear colts, anyway. But what I do care about slightly more is the question whether the American football is a sensible game at all, and the very existence of this Deflategate is rather strong evidence that it is not a sensible sport. Millions of viewers find it plausible that the final score of a match is pretty much all about the pressure of the footballs! That's too bad if it is true. Is it true? An experimental investigation could settle this question. But even before it does, I think it's crazy that so many people may believe that 1.5 PSI in the football is so fatal for the result of every match – and they still care about the results!

Why would a sensible person care which team was able to inflate the balls at the lowest pressure?

Why isn't this meta-point discussed at all? I think that the reason is that the very suggestion that the American football could be a stupid and non-meritocratic game is being viewed as a blasphemy by almost all Americans, isn't it?


  1. The Colts use their own footballs, which were supposedly not deflated. Perhaps this is because they started at a higher pressure 135C, or even inflated theirs outdoors.

    Also, if humid air was used, then they could have formed liquid inside the ball, reducing n.

    Others are saying the rain would have had an effect as well.

  2. kashyap vasavadaJan 29, 2015, 7:41:00 PM

    The whole incidence is funny! Pressure going down because of cold temperatures is a simple high school physics. For cars, tire pressure which should be about 30 PSI routinely goes down by 4-5 PSI in winter especially when car has been parked outside overnight. But if this is just physics, Colts' footballs should have also lower pressure! So it is possible that there is a non-scientific human explanation!!

  3. Lubos,

    American Football has two ways of getting a touchdown(the major scoring mechanism of football that produces the greatest point advantage possible per possession). A player runs it in(usually a running back or quarterback) or a quarterback throws it to a receiver who runs it in or if the receiver is in the end one when he catches it it is a touchdown. If a quarterback throws it and the opposing team member catches it, possession goes to the opposing team(an interception). You could argue that a deflated ball helps the other team make interceptions but interceptions are statistically far more rare than receptions. Football teams have a mix of throwing plays and running plays but depending on the talents of the team make up some teams like the patriots are more throwing teams. The patriots have an advantage especially over a running team(teams whose offensive strength is running the football more than throwing). But the Patriots still have an advantage over other throwing teams like the colts because of the large ratio between receptions and interceptions.

    That being said the NFL should not allow the teams to handle their own balls before the game.

  4. Thanks. Very helpful. But whoever takes care of the footballs, do you agree that the probability that Patriots win the league is a (significantly) decreasing function of the average pressure of the footballs?

    Don't you think that it's bad? A lobby may allow softer balls - a pro-New-England lobby, of course. ;-)

  5. The higher ball pressure isn't good for the Colts. They lost in an almost historic lopsided game.

    The difference between a low pressure squishy ball and a high pressure taut tightly inflated ball is how difficult it is to hold on to. If you drop the ball it's a fumble that the other team can pick up and advance to their goalline.

    Also a squishy ball is easier to catch for the same reason.
    If you want to add a physics component, the hand strength needed to compress the football to carry it securely while 300 lb linebackers are trying to knock you down or take it away, something that I haven't seen many talking about.

    I'm of the opinion that the difference between an 11 psi ball and a 13.5 psi ball isn't enough to change the outcome of a 45-7 thumping.

  6. As a young student in a small Illinois college I was happy to experiment with american lifestyle. So I played "football" with some guys from our dormitory. So on first play our teem thought it was smart to throw the ball to me to catch because it would be unexpected. I was a good goalkeeper, so I caught the ball among three giant Americans. But fell on the ground with three guys on top of me, I thought for few seconds I was transported to a UFO operating table. It is a game of skills, you must know how to judge distances and be agile.

    It was ruled fumble yet I know the guy pulled the ball from my hand illegally. American are honest in general but they can get very nasty in competitions.

  7. Higher is not good for the Colts per se, it is just being used as evidence of the Patriots' cheating.
    Aaron Rodgers of Green Bay prefers high pressure and admits to submitting overinflated and hoping the referees don't let the air out.

    How can you say it is meaningless, when it has revealed Bill Nye's stupidity in a way almost anyone can understand? It is even better than his fake experiment for Al Gore.

  8. Luboš - do a little more study on psig versus psia. The real spec is a standard indenter for grip. Pressure is a poor diagnostic.

    Processed prescription eyeglass lenses were transported in wheeled trucks of aluminum cafeteria trays. Slip elevation given modest vibration was about 10°. Slick lenses and tracking tags separated. Uncle Al added a surface micron of, ah, cleverness. Still slick, surface slip angle was now about 45°. Any coach could quietly get a grip by giving his team the finger.

  9. The whole situation is absurd in the extreme. After every play, at least two or three game officials handle the ball, and theybhave ample opportunity to determine its condition its condition. By putting it play, they assert the ball meets all relevant rules.

    By the way, speaking of medieval units, many European engineers use a system with kilogram-force, kilogram-mass, meter, second units. This is a gravitational system, and F = ma/gc.

  10. Off topic unless you think the universe is topologically a football ;) Heads up! The HFi Planck French website has posted new summary results from Bicep2/Keck/Planck. See the site (in French):

  11. I'm baffled by the whole thing. There may be a social side to the thing -- many Americans just deeply dislike Tom Brady, including people in Boston. Brady is a really talented quarterbak by any measure, he's physically attractive (probably could have been in the movies, for example) and he's married to a gorgeous supermodel who makes more money than he does. They seem to lead a glamorous, perfect life, so I think the hatred of him is mostly envy. I'm not that into the whole thing, people who understand the game well have explained strategies of Am football to me during games and that made it much more interesting to watch, you begin to appreciate the multiple plans in motion at once. Referees have made some terrible calls, btw, that probably determined outcomes of specific games as much as any squishy or plump ball might have. It 's just amazing what a big story this seems to be fore some.

  12. kashyap vasavadaJan 30, 2015, 2:04:00 AM

    Well! I rarely watch any of these games. So I do not particularly want to argue that american football is superior to soccer. But if you want rapid action (violence!!) and scores , you can understand why people may prefer watching american football to watching soccer. In soccer you watch for an hour or so and the score is still 0-0! One thing is true though, football is complete misnomer for american football. The ball is not in contact with foot except when kicking which happens only a few times during the game!

  13. And if they do allow teams to handle their own balls, they should allow for a challenge like they do in hockey for goalie pads and the curve of the stick. In hockey there's a two minute penalty to the team that loses the challenge.

  14. There are many subtleties in American Football, Gordon. It’s not a thinking man’s game like baseball but play decisions are not simple, to give just one example.
    All team sports give us a place to exercise our inborn tribal instincts. We all have these and there are much worse ways to let them out, starting wars, for instance.

  15. Who actually cares? American (and Canadian) football is a supremely stupid game, rivaling golf; not a sensible game like soccer, tennis, or hockey. The only reason fans like it is that it gives them an excuse to get pissed.

  16. Nor a sensible game like curling. Physicist love curling!

  17. Afaik, each team supplies their own balls, about a dozen per game, one of which they use while in possession. When the other team takes possession, they use their own ball, not the Patriots. So the Patriots play with a ball that they had entire control of, a ball which was not then used by their opponents. This provides an opportunity to create an advantage by using an underinflated ball in cold weather, while the opponents use a harder, fully inflated one.
    The Patriot coach is known for pushing the edge of the rulebook in search of advantage, his quarterback has stated that he much prefers a softer ball and the record shows 11 of the 12 Patriot balls were underinflated.

  18. All I have to say is: Go Patriots!

    But I'll also add a bit more - like with all spectator sports, there are lost of idiots involved. Since most people are idiots they can easily associate with mundane things, plus lots of idiots spend a lot of money so it attracts even more idiots that want that money and even an occasional non-idiot.

  19. The fans of the sensible game of soccer have been known to take it way beyond "pissed":

  20. I doubt very much if you could determine the pressure of a ball at 12 + / - 1 psi with your fingers. However, as the ball is made of leather, you could change the texture or feel of the ball easily. The surface of a wet ball will deform quite easily. If there is a waterproof coating on the new ball it can be damaged quite easily. If i wanted to 'work' the ball for better grip in the game then I would overinflate the ball and adjust the pressure down. That would create microcracks in the surface and would allow me to get a better grip on the ball by wetting it without changing the internal pressure of the ball.

  21. Bad punctuation in that first part - sorry about that, I don't know how to edit using this format.

  22. ...sorry about that. I...

  23. I think you would find the game of American football much more interesting if you made note of the similarity of football play diagrams ( to Feynman diagrams. Each diagram is a possible outcome of the collisions between the two teams, and the opposing teams must evaluate the probabilities associated with observing the opposing team's position and momentum. Since the pressure of the football affects its cross section in interactions between the various players, it is of course an important factor in making an accurate model of the system.

  24. Gordon, you are so wrong you have no idea. Football is the ultimate team sport, and plays are choreographed down to the finest detail. The quarterback taking a four step drop instead of a five step drop is the difference between a touchdown and a sack. There are many more such details. Eleven players have to be nearly perfect at the same time to pull off a play. It just looks chaotic.

  25. Once again, it's the Baltimore game and other regular season games that are relevant. It is a near certainty they've done it more than once.

  26. Someone may have already said this but you are making 2 mistakes. 1) each team supplies it's own balls. I.E. the Colts did not play with the Patriot footballs and vice-versa. That's why it won't affect the teams equally. 2) No one thinks the Colts would have beaten the Patriots. The objection is twofold: they probably also cheated in the Baltimore game, which they won on a last minute touchdown, and they have a history of cheating going back years. Belicheat is the coach's nickname, and outside of New England, pretty much everyone else is sick and tired of the Patriots cheating all the time and rarely getting punished.

  27. I saw where they had the lowest season total on fumbles. That could win a couple games I suppose.
    Was that because of underinflated footballs? Or good coaching?
    Water under the bridge.

    OTOH the footballs were all inflated to the correct pressure in the Colts/Patriots game at halftime.

  28. I like curling. Not enough to move somewhere cold, but....
    I like shuffleboard too.

  29. Sorry, if a higher pressure isn't better for Colts, then lower pressure can't be better for Patriots and forcing a lower pressure can't be considered cheating because it doesn't bring anything good for the Patriots.

  30. Thanks for this insightful perspective to what are the likely forces that matter behind Deflategate.

  31. I agree that if the balls pass human tests of authorities, they should be just considered OK and some retroactive questioning should be inappropriate.

    If someone wants to enforce some rules after some measurement shows the pressure outside the interval, well, good for him. The rules are very vague about what should happen in such situations. Such questioning moves the competition from the hands and legs of athletes to the hands and hollow skulls of bureaucrats and that's not good for sports, I think.

  32. That doesn't make any sense. The accusation is that the Patriots cheated with lower pressure, and the Colts did not cheat, and thus were at a disadvantage. Strange new twist is that only the ball the Colts touched was at a low 10.5 PSI, while the other ten underinflated balls were all at the level you calculate.

  33. Apparently the first American football game ever played was in the mid 19th century between Princeton and Rutgers. The game then was more a mashup of rugby and sooccer and much more use of the feet, than how the game is played today (feet only for field goals now). Rutgers beat Princeton 6-4. : )

  34. The teams prepare the balls. They are then given to the ref for inspection and marking. The ref can adjust pressure if he sees fit. 10 minutes prior to the game the refs give the ball to the ball attendant- who is an NFL employee but hired by the team. Security footage shows the ball attendant went into the bathroom for 90 seconds on his way out. So the working theory is that in 90 seconds he dumped the balls out and precisely deflated them, then put them back in the bag. Or he took a piss since he would have to be on the sideline for the next two hours.

    Carnegie Mellon ran experiments here.

    They published what they did as well. Essentially atmospheric conditions would cause 1.2psi, and wetness (it rained during the game) added .7 or so for around 1.9.

    If the team did alter the balls for what is an imperceptible change, or play. It would have to be around .2psi or less. Which is quite ridiculous, and in my opinion the evidence thus far shows nothing more than the NFL wasn't aware of natural pressure changes mid game (they never checked them before). And merely ended up baffled and lashed out like a confused child when they for whatever reason checked pressure halfway through an ongoing game in cold weather.

  35. Nye does an experiment. Thought he would confuse volume with pressure since it's called deflategate, or perhaps he is doing another fake video. Instead...WOW

  36. In my darker moments I think things like "deflater-gate" are calls of "Oh look, a squirrel!" when public attention might embarrass the powers-that-be. In my more cheerful moments I think the media are just as foolish as they appear to be.

    As to athletic contests, everything north of "rock/paper/scissors" has some elements of strategy that aficionados can rave about. If one can be bothered to master such details, few sports are "stupid" (though I can think of exceptions).

    I think this expresses my attitude to the SuperBowl nicely

  37. I have no idea what you're talking about. If some quantity brings the same advantage or disadvantage to both teams, it's clearly irrelevant and doing something with the quantity can't be said to be cheating because it isn't expected to affect the outcome in one way or another.

  38. The two teams are not playing with the same football

  39. All true, but there is the question of why 11 of 12 Patriot balls were below spec and none of the opposing teams'.
    That evidence seems to eliminate natural causes.

  40. Well the simple answer would be that the Colts balls started at 13.5, and Patriots at 12.5. But of course you're correct, the Colts may have tampered with their own balls. Maybe they should be investigated. At this point we don't know if the Colts balls passed, or if they were even tested. We know the Patriots requested the refs set the balls to 12.5.

    There's a host of other possibilities. Prep of the ball is apparently done with grinders and buffers which would heat the balls. The Colts were visiting and took a bus for an hour. Their balls probably were stored underneath. They may have been cold when the refs set them. The air compressor may have been used on Patriot balls. Wetness makes a huge difference according to the experiment, the Patriots balls, could have been more wet. Especially since they were on offense more. There's plenty of possibilities, but the more obvious reason why it's probably not tampering is that once you figure in the temperature we are suggesting that they somehow conspired to take out .3 or .5 psi or less? All in some silly 90 second window? The gauges are barely that accurate.

    There's many factors that effect the balls pressure a nonzero amount besides temperature. It's a rather far fetched to jump to some deflation conspiracy when there's a laundry list of variables that can account for such a trivial discrepancy.

  41. I see your good friend Neil deGrasse Tyson also weighs in on the controversy, but not before having his work checked by a real scientist:

  42. The win! I'm sure they checked and rechecked all the balls this time. Arizona is dry and warm.