Follow-Up: The Evidence for Non-Tampering in 2 Pictures

The last post on the cognitive and statistical biases in Deflate Gate included a visual of the “Logo Gauge” scenario that was added to the post based on the timeline provided on page 70 of the Wells Report. In that post I discussed the problems with the Colt balls, but failed to include a visual for the scenarios. Such a visual, for both the Logo and Non-Logo Gauge readings, clearly demonstrate how similar the Colts balls are to the Patriots balls relative to what a given ball’s PSI should be at a given time.

Below are the measurements taken at halftime, both from the “Logo” gauge and the “Non’Logo” gauge. Each line is the expected PSI of the balls (blue for Indianapolis, gold for new England) as they heat up during the locker room period. The dots are the actual measurements of the balls. Note the differences between the actual balls and where we expect them to be based on temperature and the Ideal Gas Law:

Deflate Gate Logo Scenario

Deflate Gate Non Logo 12.95

The projections use the following assumptions: The temperature indoors was 71 pre-game, 48 degrees outdoors with an atmospheric pressure of 14.636; The balls were indeed measured in order (this is alluded to but not explicitly stated); It took 3 minutes in the locker room before testing began (an average of the 2-4 min guess made by Exponent); It took 25 seconds to test a ball (Exponent’s 4-5 min estimation for measuring Patriots balls produces a range of 22-27s); It took 3.5 minutes to re-inflate the Patriots balls (again, an average of Exponent’s 2-5 min estimation); It took just over 90 seconds to pack up and leave, using the assumption that packing would take less time than set up;The Patriots balls were all of the same wetness, following a “wet” curve estimated by Exponent’s wet test; The Colts balls were all of the same dryness; Most importantly, that every Patriot ball was exactly 12.5 PSI pre-game and every Colt ball 13.0 PSI pre-game, as claimed by referee Walt Anderson.


Notice how the Colts balls are “shifted down” below where they should be in a similar manner to the Patriots balls. It’s likely the measurements reflect natural variance we see in measuring actual game-play footballs, as both Patriot and Colts balls aren’t where we’d “expect” based on the assumed parameters Exponent uses and the Ideal Gas Law. (This variance can come from the operator or from other subtle environment factors not captured by temperature and atmospheric pressure. It can also come from the balls not all being perfectly 12.5 pre-game, as well or the temp not being exactly 71 degrees F.) We can say this for two major reasons:

  1. Some Patriots balls are above where we’d expect them based on a 12.5 PSI pre-game measurement and the Ideal Gas Law
  2. 7/8 Colts balls are also below where we’d expect them based on a 13.0 PSI pre-game measurement and the Ideal Gas Law

The Colts balls are actually the best evidence for the Patriots, as they are the only four other footballs ever measured at halftime of a game and they show a departure from what’s expected despite not being tampered with. (Note: Here I’m not arbitrarily treating Colts ball #3 as a transcription error as Wells does.)

Screen Shot 2015-05-20 at 3.38.52 PM

This essentially exonerates the Patriots in the Non-Logo scenario, which is what Exponent used to reach its conclusion. Because in that scenario, three of four Colts balls are more than 0.5 PSI under the expected range, with one of four about 0.75 PSI below expected. 7/11 Patriot balls were more than 0.5 PSI below expected with 5/11 more than 0.75 PSI under expected. As stated in the last post, Exponent overlooked this because they ignored the variable of time (the balls heating up) and presented all balls as being measured at the same time.

The final post in this series examines the statistical improbability that there was any tampering during Deflate Gate.

EDIT: Reader “George” astutely noted that simply increasing the indoor temperature pre-game by a degree or three, due to a slight temperature discrepancy between the HVAC and the actual room temperature (from bodies giving off heat in the room) helps explains much of the slightly below-expected values from both teams. In that case, each team’s expected PSI line would be shifted down slightly, helping to explain the results of both sets of balls, as shown below: 

Deflate Gate Logo 74 Degrees


5 thoughts on “Follow-Up: The Evidence for Non-Tampering in 2 Pictures

  1. If you look at the fine print you’ll notice that Exponent specifically adjusted pre-game temperatures to ensure the Colts’ balls fit their curve. For non-logo data they used 69 degrees, but switched to 67 degrees for logo data. They also bewilderingly make the claim that the Colts balls were measured BEFORE the Patriots’ balls were reinflated (flying in the face of logic, since the officials “ran out of time” while measuring the Colts.

    (This entire analysis has been amazingly level-headed, by the way. Thanks for that.)

  2. The footballs were not inflated in a temperature controlled room but in an adjoining room.
    I think this matters for Exponent’s calculations because they took measurements when the outside temperature was 19F

    Gameday it was 50F.
    Wouldn’t the gameday temperature of the adjoining room be higher when there is a 20 degree or less differential compared to a 40 degree differential?

    • Yes — if you see the science wiki you’ll notice that the colder temperatures pre-game start to make the Colt balls deviate more and more from what is expected. That, combined with the logic that the HVAC was 71-74, and filled with people on game day (50 degrees) versus an empty room set to 71-74 without people on a 19 degree makes it quite unlikely that any ball temperature pre-game was actually 67 degrees. Furthermore, note that small perturbations in temperature don’t really matter that much for what is being alleged by the league and Wells.

      That’s the beauty of this from a scientific perspective — we do not have precise measurements, but we don’t NEED precise measurements. Just like we don’t know whether the Patriot balls were measured at 2 minutes or at 4 minutes into the locker room period…it just doesn’t matter, unless you believe that a tenth of a PSI can demonstrate the difference between tampering and non-tampering. At that point we might as well be arguing over a millimeter of illegal cleat height.

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