I live in Massachusetts, home of the National Football League team the New England Patriots.  I admit to being a fan, being raised as a Minnesota Viking by two enthusiastic parents.  The Vikings have been to two super bowl 5 times (and lost 5 times, ouch).  Since 1980, I have lived in Massachusetts where the Patriots know how to win the whole thing.  Does that method involve cheating?

Right now there is an open mystery with regards to the Patriots.  When they played the American Football League Conference Championship game, 12 of the footballs the Patriots used were under-inflated.  How can this be?

Two hours and fifteen minutes before the game, the referees take each team's 12 game balls and check the pressure on each ball.  Each ball must have a pressure between 82,124 and 93,079 pascals.  Metric units looks silly in this context.  In America, we use our rebranded no-longer-British units, that is 12.5 pounds per square inch and 13.5 pounds per square inch.  Each team is to supply 12 game day footballs.  If the weather is bad, they are required to supply 24 footballs which both teams did due to the rain.

On Friday, the NFL released a report on their initial investigation.  They have interviewed 40 people and got access to many forms of communication (cell phones and computers) over a period of three days.  They confirmed that the referees checked with gauges all 48 balls 3 times (not the usual practice which is just pre-game).  First, 2 hours and 15 minutes before the game.  At that time, all 48 balls were in compliance.  Then at half time.  All 12 game day footballs for the Patriots were not compliant.  All 12 of that bad weather balls were compliant, as were all 24 of the Indianapolis Colt footballs.  How much under pressure is not known to me the blogger.

The number being "leaked" is 2 psi.  Did someone round up?  Were there rough approximations involved?  "It was suppose to be 13, but was one was under 11, so 2psi (12.5 - 10.9 = 1.6)."  But like with all numbers, one really needs to know the both the actual average and the variance.  I am interested to know the variance of air pressure before the game to that of the twelve balls at halftime.  Why?  Well, if New England had this fetish for hitting 12.5 psi for example, and all 24 where within 0.2 psi of that goal, no exceptions, but the deflated halftime footballs were all over the map, from 10.3 to 11.2, that would require the imprecision of a human being.  Conversely, if the variance was the same in both situations, it lowers the odds of a person manually deflating the ball.  People can perfect cheating, so a good deflater would have to have a precise deflation process (probably a special tool for the task).

At halftime, the refs got the Patriots game balls up to the right pressure.  The game was played.  At the end, the refs measured all 48 footballs, and all 48 were in compliance.  That indicates there were no defective Patriots game balls, ones chosen because they had leaks.

The Human Intervention Hypothesis

The simplest model is that a person on the Patriots staff deflated the footballs.  This requires sticking a needle into each of the twelve footballs.  This could not happen casually on the sidelines since it would be trivial to catch on camera.  All the players would know too because this is how they make their living.  There are hundreds of fans who are close to the bench, able to watch everything ("What is the ball boy doing to all the footballs?").  If a ball boy did regularly deflate the footballs, that would require a room somewhere between the refs have the footballs and the path out into the public stadium.  The doctoring operation would require at least a few minutes since it has to be repeated twelve times.  There are few people and few places where that could happen.  I am sure the investigators could narrow down the suspect the Monday morning, it is not that hard a puzzle.

What is not simple about this model is the issue of labor.  Who takes the job of a ball boy at the NFL?  It some ways, it is like the job of an altar boy at a church.  In church, an altar boy carries the Body of Christ to the priest to hand out to the people at mass.  Each of the footballs is signed by a ref as good for the game.  The ball boy cares the focus of the entire game out to the field where it is given to the priest of the Patriots, Tom Brady.  The masses adore the play on the field (at least in this game).

Tom Brady would have had to sit down with one of these ball boys (who I believe are actually men, past the teen years, but I am not sure) and instructed him on how to cheat.  Tom himself could not be deflating the ball - too many cameras constantly on him.  He may well have not had contact with all 12 balls after the signoff by the ref.

Could one of the ball boys taken on the task?  Certainly.  Such a person would have to be a complete, ethical slime bucket.  There are people like this.  Gee, it has a fresh signature from the ref it is compliant, now I poke a needle in, and voila, that is no longer the case.  This has to be cheating, but everyone cheats.  There are people who can live with this.  "I am doing Tom (first name basis-friend) a favor. I'll do anything for Tom."

Altar boys get spiritual compensation.  Ball boys get paid, but I doubt it is very much.  In the ball-boy-cheater hypothesis, the poorly paid ethical slime bucket is being quiet.  Yup, it can happen, the vow of silence.  But he also now has information that could be turned into money, a big, six-figure sum.  Imagine a story with the headline, "How the Patriots Cheat, My Tale", before the Super Bowl.  The storyteller should be able to negotiate a payed tell-all confession for more than six figures.

I admit to believing the stories Lance Armstrong told for a long time. His lies were what I wanted to hear.  I knew Lance as a fierce competitor on the bike.  He was also a jerk off the bike, at least to friends and family.  Tom Brady is every bit as fierce during the game.  Sorry, he is a swearing jerk.  In the game before, he yelled at the ref something nasty.  Only later did I learn that he got poked in the eye another player, so it made some sense.  Brady has a game-day induced psychosis.  On the off days, he goes back to laid-back, football nerd.  Study, study, study, go to bed by 8:30pm.  He is married to a supermodel and has a couple of kids.  Lots of people - who do not play him on Sundays - say he is a nice guy.

If the ball boy confessed his sins to an NFL lawyer, this case is simple.  If with all the film, we have clips of "something" being done to all twelve balls, again, it is a simple case.  This is why the NFL thought it would only take a three day data sweep to figure the case out.  It may be more complicated.  Every day that passes without someone selling out to a website makes me think there may not be a person guilty of this obvious crime.

The Pre-Game Process Hypothesis

The Patriots handle their game day footballs one way.  They may handle their extra twelve another.  And the Colts have their own system.

We know that Tom Brady likes his footballs on the low side.  Being hyper competitive, imagine he asks for 12.5psi exactly.  On a wet day, the ball boys try to make the starting balls compulsively dry as well as hitting the 12.5psi.  They do not bother to do anything with the 12 bad weather balls, they are not going to be used.

In contrast, the Colts have to do things different for this hypothesis to be valid.  Maybe Andrew Luck likes it right in the middle, 13.0psi.  Their equipment team keeps the ball in a trunk outside.

There is a Reddit post on this subject where they go through the Guy-Lussac's Law (I prefer the ideal gas law, PV=nRT).  One needs to deal with absolute temperatures (go Kelvin) and pressures.  But the air is not ideal, this is a leather football.  And it is rainy outside, not inside.  The pressure in a barometer drops when it rains.  The guy doing the calculation on Reddit shows a drop of 1.4psi could happen to a game ball, dropping it to 11.1 from 12.5 psi.

An experimentalist has jumped into the game from Pathfinder Regional Vocational Technical High School.  They have real temperature and pressure gauges.  They took a football at 13.3psi and 72 degrees and dunked it in a bucket of water.  In under three minutes, it had dropped to 11.9psi and 52 degrees. Cool, the experiment agrees with the theory!  The temperature at halftime was certainly lower than the start (46 degrees apparently)

The footballs for the Colts had a similar experience.  They remained compliant for all three measurements.  Did they start at 12.5?  Or at 14.0psi like Aaron Rogers likes?  Did they go down from start to the halftime?  If so, how much?  All of those bits of information are known to the NFL investigators and not to me.  If the traveling Colts keep their footballs outside, bringing them to the refs after a quick check, then I would expect the pressure not to change from the start of the game to halftime.  I would expect the variance in the pressure readings not to change for the Colts for any the three sets of reading.  If the variance is big only for the Patriots footballs at halftime, someone on their staff has altered the game day footballs.

The Gate in Deflate-Gate

One thing known for certain by the NFL is who and when did the refs inform after their halftime measurement.  If it was up to me, I would go up to the head coach, Bill Belichick and let him know that the balls were not up to standard.  I would tell Tom Brady too, 11 out of 12 were illegal.  But I am not an NFL ref.  No doubt they were in contact with "New York", NFL headquarters.  They decided to tell them or not.

Both Brady and Belichick claimed that they first heard about the issue on Monday morning.  I "heard it live", how Brady laughed off the under-inflated footballs.  If they were told at the game about the issue, that kind of cover-up should get them fired.  Like, on the spot.

I look forward to the NFL report.  I don't think this is a hugely complicated case.  The Pre-Game Process hypothesis would require way more work to justify the conclusion.  Everyone would suspect the NFL was going easy on the Pats.

Update

After I posed this blog, Bill Belicheck held a news conference on this subject. He said emphatically that no one in his organization deflated the footballs. What was even more interesting was that he directed his staff to do a number of experiments with footballs. A simple one was to see if they could tell the difference between balls inflated with one psi different. Nope. How about two? Sometimes the players could tell. But they also got it wrong, thinking the lower pressure ball was the high one, a smaller fraction of the time (the raw results were not available).

The entire pre-game prep process was repeated. This time the air pressure was checked along the way. Their method of preparing the ball raised the pressure by about one psi. They do hand off the ball to the ref a 12.5, asking the crew to keep it there. Belicheck also claimed that there is a variance in the [cheap] gauges the NFL uses. When the ball goes from the controlled indoor environment - near the equipment room, not some specially heated, dry location - to the outdoors, the pressure does drop (I think he said 1.5psi, consistent with the theory and experiment cited above). He probably was not able to simulate the rain component. It was nice to hear the scientific method applied to this situation.

The case remains open for the NFL investigators and by extension myself. Both the Colts and the Patriots "bad weather" footballs remain controls. There needs to be some material way they were treated differently.

Update 2

NFL refs treat the psi test as a pass/fail thing. They did not write numbers down. Looks like my hope for analyzing the variance is out.