Shrinkage Calculation / Patriots Deflate-gate / Are the Patriots guilty? (Blog #65)


We are straying off the subject of college football a bit and venturing into the NFL. Unless you have been living under a rock, you know that the most popular subject on sports radio was whether or not the New England Patriots deflated the 12 game balls they are given during the game. Specifically, 11 of the 12 balls at half time were 2 psi under the required pressure at half time and the other was close to being under pressure.

So what gives? Why the scandal? Is this a bunch of hot air?

The Rule

The rule states that each team shall provide 12 balls that are to be measured 2 ½ hours before kickoff. The pressure in the balls must be between 12.5 to 13.5 psi.

The Accusation

Eleven of the twelve of the Patriots ball were under the required pressure at halftime.

So did the Patriots deflate the balls? Were rules broken?

The answer is yes, that rules were broken, but the Patriots did not break the rules.

What? The Ideal Gas Law explains it all.

Émile Clapeyron discovered the Ideal Gas Law in 1834. We won’t go into the derivations of this law1, but it can be used to predict what happens to the pressure of an object when its temperature is decreased and its volume stays constant.

We calculated what the pressure of the balls should have been at half-time. We assumed the balls initially were at a room temperature of 75 F and were measured at that temperature. We assumed the temperature on the field was 35 F and that the balls would have reached this temperature by half-time.

Based on our calculations:

  • A ball inflated to 13. 5 psi would be at 11.4 psi at half-time.
  • A ball inflated to 12.5 psi would be 10.5 psi at half-time.
So the eleven balls are the unaltered balls. THE NEW ENGLAND PATRIOTS ARE NOT GUILTY.

Should Indy be fined?

If the Colts balls were within specification at half-time, someone must have altered the balls during the game. Given the heat the Patriots have taken, yes, the Colts should be fined. What do you think? Please comment via the button below.

Shame on the journalists, announcers, and most of America

So to graduate college, journalists don’t have to know elementary science? What about the retired football players who went to college to such schools as Harvard and Notre Dame? Shame for shame.

1 – nRT = PV see for more details.

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