21 January 2015

More on Deflate-Gate

I was invited by Geoff Brumfiel of NPR's All Things Considered to comment on the controversy surrounding under-inflated footballs used in the AFC title game between the New England Patriots and the Indianapolis Colts.  The Pats won in convincing fashion, 45-7, but a dark cloud now palls the game, so much so that the silly "gate" suffix has been used.  After something like 20 minutes conversation with Geoff Brumfiel, a few of my comments made it to air and into the accompanying story.  That story and an audio link may be obtained here.  What I wish to do in this space is elaborate on what appears in the story by repeating some of my comments to Geoff Brumfiel that did not make the final cut.

Bad weather, like the rain and wind in the Pats win over the Colts, will make a quarterback desire a better grip on the ball.  Water on the ball, after all, reduces friction between the ball's surface and the quarterback's hand.  Anyone who has ever tried to palm a basketball, but finds one's hand just a wee bit too small, has noticed that palming the ball becomes easier if the basketball is slightly deflated.  Deflating a football slightly allows for better grip, too.

Losing a little air reduces the ball's mass.  How much?  Well, a normal football has nearly 98% of its mass in the non-air material that comprises the ball.  Only a little more than 2% of the ball's mass is from the air.  Of course, the ball's volume displaces air, leading to a buoyant force that matches the weight of the air displaced.  NFL balls are supposed to be at a gauge pressure of 12.5 psi (pounds per square inch) to 13.5 psi.  Note that gauge pressure is the pressure above atmospheric pressure, which is about 14.7 psi.  An example I described that did not make it to air is to assume that a ball is under-inflated by 2 psi.  Accounting for atmospheric pressure, that amounts to about a 7% loss in pressure.  The ball's weight loss, however, is less than 0.2%.  A less massive ball decelerates faster than a normal ball, but the mass loss in my example is too small to have much effect.

Referees are supposed to inspect balls used in games.  A referee sets the ball on the field before the start of each play.  As I told Geoff Brumfiel, an under-inflated ball may not have been noticed by a referee hurrying to place a ball on a play or two, but should have been noticed if balls used for most plays were under-inflated.  Nobody wants to think conspiracy when trying to figure out what happened, just like nobody wants to think a referee is incompetent or that a team cheated.  Given that both quarterbacks used the game balls, both should have had the same advantage that would have come from better-to-grip balls that may have been under-inflated.  Andrew Luck, however, had such a terrible game for the Colts that any advantage would have gone to Tom Brady, the quarterback for the Pats.  Luck's game, however, does not excuse any possible cheating.

We will have to see what comes of all this silliness.


  1. Each team has thier own in play balls. However, Temp affects pressure. Assume 60°F and ball pressure is 12.5psi. At 50°F ball pressure drops to 10.5psi. This assumes vloume is constant which obviously is not correct. But i dont have ball to test how much ball circumference changes with pressure.

    1. The 2 psi number I gave was based on my calculation of having a ball at 13 psi (gauge pressure) at 20 C taken out to 0 C. The temperature change gives rise to a 1.9 psi drop in gauge pressure, which I simply rounded to 2 psi. I don't know if refs check balls in a comfy locker room and then take them outside. Surely enough football has been played in cold weather that such considerations wouldn't be taken into account. I do wonder how the balls were retested. If they were tested at the same temperature as they were before the game, and the pressure is now lower, air leaving would be the explanation.