In today’s post, I’m going to show the Deflategate data from a new perspective. Rather than arguing about whether the Patriots used the Logo gauge, I’ve assumed, for the sake of argument, the NFL’s conclusion that the Non-Logo gauge was used, but gone further (as they ought to have done). I’ve “guessed” the amount of deflation that would be required to yield the observations. And, instead of only considering the overall average, I plotted each data point and how the “guessed” deflation would reconcile each data point.
Some very surprising results emerged, one of which raises the question in the title: did McNally inflate one football in the washroom? If the question doesn’t seem to make sense, read on.
Rather than one guess being applicable to all measurements, I ended up needing four different groups each with a different guessed deflation. A “good” guess (i.e. one that “worked”) for the majority of balls (7) was 0.38 psi – an interesting number that I’ll discuss in the post. A good guess for two balls was zero deflation. But for ball #7, it was necessary to assume that it had been inflated by approximately 0.5 psi in the washroom. One ball was lower than the others (0.76 psi) and remains hard to explain. The Wells Report reasonably drew attention to variability, but did not address the details of actual variability other than arm-waving and did not actually show that erratic washroom deflation was a plausible explanation for observed variability.
While the approach in today’s post doesn’t appear conceptual, statistical algorithms, including linear regression, typically solve inverse problems. The spirit of today’s post is approaching Deflategate as an inverse problem. In doing so, I am aware (as Carrick has forcefully observed) that the underlying physical conditions were poorly defined, but people still need to make decisions using the available information as best they can. I think that the approach in today’s post provides a much more plausible and satisfying explanation of the variation in Patriot pressures than those presented by either Exponent or Snyder or, for that matter, my own previous commentary.
Bear with the explanation of context, as the results are interesting.