The scandal du jour in the N.F.L. is “deflate gate,” the recent allegation that the New England Patriots may have under-inflated their footballs in the N.F.C. championship game in order to gain some type of tactical advantage, i.e., better grip on the ball in cold, wet weather. After listening to the breathless chatter about deflate gate, it occurred to me that deflate gate really wasn’t that much different than your typical DUI case. Applying the principals of metrology—the science of measurements—(the very same scientific principles used estimate the accused’s B.A.C. in DUI case) and a dose of common sense, it is evident that there are many holes in this story. Here’s why:
First, the N.F.L. has very specific requirements for game balls, viz.:
The Ball must be a “Wilson,” hand selected, bearing the signature of the Commissioner of the League, Roger Goodell.
The ball shall be made up of an inflated (12 1/2 to 13 1/2 pounds) urethane bladder enclosed in a pebble grained, leather case (natural tan color) without corrugations of any kind. It shall have the form of a prolate spheroid and the size and weight shall be: long axis, 11 to 11 1/4 inches; long circumference, 28 to 28 1/2 inches; short circumference, 21 to 21 1/4 inches; weight, 14 to 15 ounces.
The Referee shall be the sole judge as to whether all balls offered for play comply with these specifications. A pump is to be furnished by the home club, and the balls shall remain under the supervision of the Referee until they are delivered to the ball attendant just prior to the start of the game.
N.F.L. Rulebook, Rule 2, Section 1, Ball Dimensions, found at: http://static.nfl.com/static/content/public/image/rulebook/pdfs/5_2013_Ball.pdf. According to an ESPN source, when the referees tested the balls at halftime of the game, 11 of the 12 balls were found to be two p.s.i. below that range, or 9.5 p.s.i. This “test” is really a measurement of how much air pressure is inside the ball.
Second, the science of metrology tells us that a “measurement” is really just an estimate. No measurement is 100% accurate and, as such, you can never know for certain the true value of whatever you are measuring.
For example, if a person steps on a scale and weighs themselves three times in short succession, they might get three different measurements or estimates of their weight, e.g., 185, 183, and 184 lbs. The uncertainty of this estimate might depend, for example, on the accuracy of the scale (how precise is it, how carefully was it calibrated, etc.), how the person is standing on the scale (are they putting their mass in the same exact position every time or are they placing their mass on slightly different sensors each time, e.g.), and even the vantage point of the person reading the scale (are they looking to one side or the other of the needle to see the result?) This example demonstrates that even a simple scale cannot tell us with 100% certainty how much you weigh, but can provide a useful estimate of your weight, i.e., 184 lbs. plus or minus one pound.
Thus, whether you are talking about estimating somebody’s weight, a person’s B.A.C. or a football’s p.s.i., the really important question is how accurate is the estimate. If, for example, the N.F.L.’s air gauge has an uncertainty of plus or minus 2.5 p.s.i., it would be difficult to determine with any certainty whether the footballs actually were under-inflated, given that the estimate of the ball’s p.s.i. taken at halftime could fall within the acceptable range. It is for this reason that it is imperative to know how much uncertainty there is in any measurement or estimate. Only when you know this information, can you make an informed decision about whether the measurement is fit for its intended use. For example, if your bathroom scale is only capable of estimating your weight within a pound or two, you might be ok with that level of uncertainty; however, if you are the N.F.L. and charged with deciding whether to suspend the star quarterback in the biggest game of the year, because the balls appeared to be underinflated in the previous game, you may require a higher level of accuracy in your measurements.
This seems to be a gaping hole in deflate-gate—how accurate are the N.F.L.’s and the Patriot’s p.s.i. estimates. The accuracy of a p.s.i. estimate depends on a number of factors that have to be taken into account, including, but not limited to:
- the ambient air temperature of the location where the measurements were taken (on the field vs. in the locker room, were the balls stored at room temperature prior to the game);
- barometric pressure;
- whether any air was lost during play;
- how many samples were taken by the N.F.L. for each ball;
- how much air was lost each time a sample was taken;
- how accurate is the N.F.L.’s air gauge;
- when were the air gauges last calibrated;
- how did the Patriot’s p.s.i. estimate differ from the N.F.L.’s and how does the Patriot’s air gauge compare to the N.F.L.’s (if the Patriot’s estimated the p.s.i. at halftime using their gauges, would it match the N.F.L.’s estimate or be within 12.5 to 13.5 pounds)
For more on the science behind calculating p.s.i. see http://www.csmonitor.com/Science/2015/0121/Deflategate-Can-science-tell-us-if-the-Patriots-cheated-video. Without knowing this information, it is impossible to determine with any degree of certainty whether the balls were actually under-inflated, setting aside entirely whether there is any evidence that the Patriots intentionally under-inflated the footballs. In the meantime, anybody that claims to know for certain that the balls were under-inflated is probably full of hot air.