I GOT YOUR FRIGGIN' 2 PSI RIGHT HERE: Deflating Deflategate with Science and Logic

I know, I know you have been on the edge of your seat waiting for the engineer/attorney constituents to chime in on the New England Patriots/Tom Brady deflated football controversy.  Yeah, me too.  But since none of my fellow patent attorney geeks have stepped up to the plate (wrong sport analogy), I shall bear this heavy burden of merging Mattock with the Big Bang Theory.  Get your caffeine tablets ready... boredom just might ensue.  

So let's keep tuning out beheadings in the middle east, terrorist in Paris, economic collapse in Russia for a bit longer and put the villainous New England Patriots on trial, but we will use two scary tools that are seldom employed in the court of public opinion: Science and Logic.   Woooooooo.  Nervous yet?

Can 2 psi Just Disappear Without Draining Air from the Ball?

I can hear Johnny Cochran's closing statement right now, “11 of the 12 footballs were under-inflated.  UNDER INFLATED!  If the balls are squishy, there is something fishy!”  Fishy or physicsy? (yes, bad pun – deal with it.  It's my blog).  Since your average concussion prone retired football-player-turned-sports-commentators did not likely take many college physics courses, let's give them a hand in trying to figure out why the football might be squishy.  So I call three witnesses to the stand, "The defendant calls Mr. Temperature, Mr. Pressure and Mr. Volume to the witness stand."

Temperature

A not uncommon analysis I’ve seen online (which is strangely absent from the scientifically challenged minds of ESPN commentators) is demonstrating the relationship between pressure and temperature according to the Ideal Gas Law.  No need to army-crawl under your desks with flashbacks of freshman physics.  I will spare you the fun calculations - and I am not being sarcastic about fun, it is fun to an engineer, it is how we pick up chicks.  I will simply say that the pressure of the football is dictated by the temperature of the air within the ball: PV = nrT (which is one of the easier equations remember to because it looks like the word “PERVERT”).  Using the Ideal Gas Law you can show that if the temperature of the air inside the ball when the football pressure was tested prior to game time was around 70° (a typical interior temperature) and the temperature in the ball dropped to 50° at halftime, this would have drop the pressure in the ball 0.7 psi.  In other words, a ball that was inflated to 12.5 psi indoors would deflate to 11.8 psi outdoors without anyone extracting a molecule of air out of the ball.  Hmmmm.  Suspiciously exculpatory. Though not quite the nearly 2-ish psi deficiency reported in the press, but the defense has yet to rest.

Pressure

What I have seen missing from all analysis is a correct understanding of what the pressure measurement within a football really means.  The pressure in the football is actually a combination of the atmospheric pressure plus the pressure measured at the pump (gauge pressure) .  So if the pump says 13 psi, it is actually lying. What the pump is doing is it is assuming an average atmospheric pressure and shows you how many pounds per square inch (psi) above that assumed atmospheric pressure you are.  So with an assumed atmospheric pressure of 14.5 psi and a measured gauge pressure of 13 psi, the total pressure in the football is 27.5 psi. What no one seems to acknowledge is that the atmospheric pressure is not constant.  Nope it changes.  And changes a lot in bad weather.  In fact, on game day the atmospheric pressure was nose-diving faster than the Russian ruble. Here is the chart of the atmospheric pressure at the Boston airport for the past week, including last Sunday.

Doesn't the chart for Sunday look like your 401(k) in 2008?  So clearly the atmospheric pressure was dropping and dropping fast!  By my calculations, the atmospheric pressure drop from the early Sunday morning to the end of the day would result in a ball measuring .5 psi less.  Some quick numbers (I did convert the units from inches mercury to psi for your convenience):

Atmospheric Pressure Early Sunday (14.93 psi) plus Gauge Pressure (12.5) = 27.43

Atmospheric Pressure Late Sunday (14.48 psi) plus Gauge Pressure (12.5) = 26.98

In other words, because the atmospheric pressure dropped, the apparent gauge pressure at the pump would measure lower as if the ball had been deflated.  Now true, the pressure measurements were not a full day apart. But they were far enough apart to decrease the pressure in the ball by a measurable amount. 

Volume

"Volume? Volume! How can the volume in a football change?" The answer is ‘not very much, but enough to matter.’  You may have noticed that it was raining during the game on Sunday – OK it was pouring!  It is not uncommon for leather to stretch when wet.  It doesn't stretch much, but stretching 1% is a very conservative number. So what happens to pressure within a football if the leather stretches 1% on a rain-soaked day? You simply roll in a 1% change in the radii of an ellipsoid volume calculator and compare it against the un-stretched volume through the Ideal Gas Law.  Interestingly, my calculations say the pressure would drop by about .5 psi with some very minor stretching to change the volume of the football. 

So if you roll in the changes in the balls' gauge pressure from pregame to half-time, you can see that it is possible that the pressure within the ball could decrease 1.7 psi without O.J. Simpson sneaking into the Patriots ballroom and deflating all but one of their footballs.  But let's not rest the science alone, there are other witnesses I would like to call to the stand.   Let's start with the referees. 

Whose Fingerprints Were All Over the Murder Weapon?

One of the key arguments that Tom Brady is lying is how on earth would he NOT have known the footballs were under-inflated. After all, he touches them every play, doesn't he? Well no, he doesn't. If you count the other team’s time of possession and special teams, he probably only touches the ball 40% of the time. There IS someone, on the other hand, who does touch the ball at the beginning and end of every single play; It is the officials!  In fact, they are also the ones in charge of confirming that the footballs are the correct pressure.  So don't you think they would have noticed something on their own? Moreover, not only did they have contact with the Patriots footballs, but they also were handling the Colts footballs too.  They would have been able to actually compare the differences in the feel between two sets of footballs wouldn't they? So I ask you ladies and gentlemen of the jury, if the referees, tasked with ensuring that the balls are the correct pressure and being able to compare the two different sets of footballs, did not notice anything amiss with the footballs on their own, how is it somehow damning evidence that Tom Brady didn't either? 

Is Being Allusive to a Loaded Press Conference Questions Somehow Incriminating?

I've heard some commentators being critical of Tom Brady for not directly answering some of the media’s questions during the press conference.  In law school they like to give an example of a leading and prejudicial question that you just should not ask. The example they like to give is, “Mr. Smith, just how often do your beat you wife?”  You cannot give and unqualified answer to that question without making some incriminating admission. Now let's look at a couple of the probing questions asked to Tom Brady.  And I figure I’d throw in how I would have had Tom answer these questions if he were a Smart-A with an engineering/law degree.

Q: “When and how did you supposedly alter the balls?”  Sorry, the word "supposedly" does not somehow magically make this a neutral question. If I did not alter the balls, how on earth would I know the answer to when and how I didn't do something?  Next question doofus.

Q: “Is Tom Brady a cheater?” No one had called me a cheater before you. Thanks for the epitaph.  Next!

Q: “Do all quarterbacks doctor the balls and have you done anything differently from anyone else in the league?”  So you want me to say that I “doctored the balls” despite the fact that I repeatedly said that I didn't alter the balls in any way.  Nice doctored question dude.

Q: “Are you comfortable that nobody did anything?” Isn't doing nothing doing something? I'm sorry, could you be more vague? I don't want to implicate "anybody," or was that "nobody" of doing "something" or "nothing" or "anything" or whatever.

Q: “You said you didn't want the balls to be touched after you approved them. You didn't notice that 15 percent of the air was out of the ball when you started using it? It didn't strike you during the first half?”  First, the footballs were measure to be under pressure at the end of the half, not when I started using them.  Also, your percentage calculation is wrong.  You are only looking at the gauge pressure and forgetting the atmospheric pressure within the football.  I know you reporters struggle with science, but the actual number is closer to 7%.  Our state sales taxes higher than that. So nope, sorry. Didn't notice that 7%.

The 'BUTT FOUR' Test!

The last legal test to apply to the situation is the "but for" test.  The test go something like this 'but for the ball being under-inflated, the Patriots would have lost the game?'  This was a pretty easy one to answer.  Strangely, after using football inflated to spec in the second half, Tom Brady's completion percentage went UP!  Even though the rain got heavier.  So even comparing just the second half of the Patriots' play with the entire game played by the Colts, the Patriots still seriously kicked the Colts BUTTS and scored FOUR touchdowns in the second half alone. There's your "butt four" test right there.

So ladies and gentlemen of the jury, love them or hate them, the explanation by the Patriots that they had no idea how the footballs became under-inflated might be more reasonable than previously believed.  And more to the point, who cares?  It is a game, with a ball, squishy or not. And if you're saying a few psi or a few grams of air would have change anything on a rainsoaked January day New England, you are either nuts, a diehard Colts fan, or a sports broadcaster paid to create controversy out of a game where a bunch of guys toss around a squishy ball.  

So in closing, I'd like to say to Johnny Cochran, "If your cheating claims are full of crap, ain't nobody nobody got time for that!"