The NFL's science-free smear campaign

So apparently the NFL has decided that they cheaty cheater New England Cheatriots have been cheating again, deflating footballs during games in order to gain some sort of advantage.  There are several problems with their campaign of accusation, though:

1. In cold weather, footballs lose air pressure.  (This is a consequence of what is known as Guy-Lassac's law from physics.)
2. Nobody on the team will admit to having done this.
3. Apparently they have no videos showing this happening.
4. It's not clear who had an opportunity to do this.
5. At least nominally, the balls were in the custody of the game officials.

But since this is matter involving the Patriots, fact-finding takes a back-seat to a PR assault.  So after Belichick and Brady denied on Thursday knowing anything about this incident, somebody at ESPN decided that what they needed to do is make the front-page story on ESPNBoston "Don't Believe Brady".  I kid you not.

Sadly, it is nearly impossible to find any reliable facts about this issue.  The only information we have from the league is in the form of a leak to Chris Mortensen, published Tuesday at 11 p.m.  Of course, Mort's story is more like a clearinghouse for rumors than anything else.  It also contains the "information" that these balls were re-inflated and used in the second half.  But it also contains the "information" that these balls were taken out of play and replaced by the second bag of 12 balls.  The article reports that a radio station in Kansas City has reported that the Colts' footballs were tested and passed the test.  But when I look at the radio station's website, all I find is a link back to the Mortensen article.  

It's unclear that the Colts' balls were tested at all.  This really ought to be something that the NFL should address.  If the balls were not tested, that does serious damage to their argument.  I would contend that all the balls should be under-inflated by halftime.  The fact that we have no data about the Colts' balls suggests that they were not tested.

So, let's get to the gas laws.  If we presume that a football doesn't leak between testings, the basic equation is P/T = k, i.e. there is a constant ratio between the air pressure of the ball and the temperature.  The temperature here is not in Fahrenheit, or even Celsius, but rather Kelvin, i.e. relative to absolute zero.  And pressure is not the pressure seen using a gauge, but rather the absolute pressure of the air  inside the ball.  What's the difference?  Well, the pressure gauge only measures the difference between the air pressure outside and the air pressure inside.  At sea level, the atmospheric pressure is about 14.7 psi.  That's not an exact number: it was a stormy day in Foxboro, and that means the air pressure was slightly lower than that.  But we won't worry about that.  

If we run through the calculations (see http://www.advancedfootballanalytics.com/index.php/home/research/weather/222-deflate-gate-and-pv-t-k) we'll see that under fairly tame assumptions the balls must have lost at least 1 psi.  And these calculations don't include the effect of adiabatic heat.  Brady, by all accounts, likes balls that are slightly under-inflated.  So I think we can assume that these balls were inflated right before they were given to the officials.  What is adiabatic heat?  Well, when a ball is inflated, it is likely that its heat increases as the extra air meets the fixed volume.  (My understanding is that this is noticeable when you inflate a bicycle tire.)  

So, ultimately what we have here is a league jumping to conclusions without having much in the way of rigorous science being done.  And it's likely that they have botched the job.  We don't know exactly what they've done, because for some unknown reason they have yet to release any information.  We don't know what temperatures the footballs were at, we don't know if any control group was used, and we don't know if any prior tests had ever been done on footballs.  My guess is that the league has never done halftime testing based on the presumption that the air pressure should not have changed.  

Indeed, the combination of rules in place require that footballs be used even they are low pressure.  Teams are not allowed to keep footballs warm on cold days.  And that brings us to an incident when the Panthers played the Vikings last fall.  Sideline attendants were seen putting footballs under heaters to keep them warm.  This was seen on TV.  This is, according to the current rule intepretation being thrown at the Patriots, "tampering."  Nobody on either team was fined or disciplined.  A warning was issued.

If we are to believe some of the news reports (again, unsourced), the Colts thought that the Pats had underinflated footballs at their previous meeting in Indy.  If this is true, let's note how the Patriots have been treated differently than the Panthers and Vikings.  The Panthers and Vikings were given a warning and told to stop.  The Patriots have been treated, in contrast, like criminals - antagonists that need to be caught cheating.  This smacks of Goodell's long-standing bias against the Pats, which was certainly exacerbated when Bill Simmons recently publicly called him a liar.  But, ironically, there is less evidence against the Pats then there was against the Vikings/Panthers.  

The league needs to go public with what they think they know, and why they think they know it.  Right now they seem to be reduced to approaching the entire case with a  presumption that cheating must have happened.  What they should do is simply pump up some footballs and see what happens.

These college students in Massachusetts did exactly that.

http://blog.masslive.com/patriots/2015/01/deflategate_patriots_footballs.html

They started with a football inflated to 13.3 psi.  After being in a bucket of cool water for two minutes, the pressure dropped to 11 psi.