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.
In an earlier article, I pointed out that essential figures in the Exponent report contained (what appeared to be) an important misrepresentation: that transients purporting to represent Logo gauge initialization had not really been initialized with the Logo gauge. The same point was later (and independently) made in a technically oriented sports blog. Exponent’s misrepresentation (“trick”) exaggerated the “decline” – a word that climate readers will be amused to find in discussion of this topic. To effectively defend their client, in my opinion, this was perhaps the most important job for Brady’s technical experts. And, out of all the technical issues, because this issue involved a misrepresentation – be it unintentional or intentional – this was arguably the technical issue with the biggest upside for Brady’s legal team, since misrepresentations have an entirely different legal weight than errors. In today’s post, I’ll look at the transcript to see how Snyder (the technical expert) and Kessler (the lead lawyer) did on this issue. I’ll also suggest a face-saving solution for Goodell.
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The transcript of the Brady appeal before Goodell has been released and it’s astonishing to see how the sausage was made. It raises many issues, one of which I’ll discuss in today’s post. Continue reading →
Goodell accepted Exponent’s finding that the full extent of the decline could not “be explained” and that a “substantial part of the decline” was due to tampering. Goodell says that the Brady side submitted “alternative scientific analyses (including the study presented by economists from the American Enterprise Institute)” and, as an expert witness, produced Dean Edward Snyder of the Yale School of Management, described as an “economist who specializes in industrial organization”. Against them, the “Management Council” produced two Exponent scientists (Caligiuri and Steffey) and the Princeton professor who had originally reviewed the Exponent study.
In today’s post, I’ll return to more typical Climate Audit programming. Upside-down Mann’s mentor, Raymond Bradley, has somewhat surprisingly published an article (Balascio et al 2015) that supports a longstanding Climate Audit criticism of varve proxies. Bradley and coauthors did not report that their interpretation of an important Baffin Island series is upside-down to the orientation used in PAGES2K and numerous AR5 vintage multiproxy reconstructions. It seems that proxies used by the Team are like the Grand Old Duke of York:
And when they were up, they were up,
And when they were down, they were down,
And when they were only half-way up,
They were neither up nor down.
Further to my series of posts on Deflategate, reader chrimony observed that my statistical analysis had shown that it was possible that there had been no tampering, but had not excluded the possibility of tampering. This is a sensible observation, but raises the question of whether and how one could use the available statistical information to exclude tampering. This is analysis that ought to have been done in the Wells Report. I’ve done the analysis in this post and the results are sharper than I’d anticipated.
For Logo initialization, any manual deflation exceeding de minimis of say 0.1 psi can be excluded by observations. For Non-Logo initialization, statistical information rules out “high” deflation scenarios i.e. deflation by more than the inter-gauge bias of 0.38 psi plus uncertainty, including deflation levels of ~0.76 psi reported in Exponent’s deflation simulations. Remarkably, for Non-Logo initialization, the only manual deflation that is not precluded are amounts equal (within uncertainty) to the inter-gauge bias of ~0.38 psi. Precisely why Patriots would have deflated balls by an amount almost exactly equal to the bias between referee Anderson’s gauges is a bizarre coincidence, to say the least. I think that one can safely say that it is “more probable than not” that referee Anderson used the Logo gauge than that such an implausible coincidence.
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In my first writeup, I observed that Exponent’s Logo transients appeared to be bodged too high, even with their unwarranted and adverse use of 67 deg F initialization (Exponent’s “temperature trick”). In today’s post, I’ve taken a closer look at the seemingly questionable calculation of the transients at 67 deg F, showing that the Patriot transients make sense only if initialization for the transients purporting to show Logo Gauge initialization were not actually initialized at 12.5 psi using the Logo Gauge (as stated and as is the purpose of the diagram). My reverse engineering shows that the Patriot dry transient in Figure 27 only makes sense if the Logo Gauge read 12.81 psi at initialization or if the Master Gauge (not the stated Logo Gauge) was erroneously used for initialization. If I’m correct, this is a very significant error – a botch, rather than a bodge – for which one would expect a prompt corrigendum, if not retraction, of the corresponding calculations. In a postscript to today’s post, I’ve attached a note on conversion from Logo and Non-Logo Gauge scale to correctly calibrated Master Gauge scale.
One of the ironies of the NFL’s conduct in this affair is that it can be established that NFL officials (under the supervision of NFL Executive Vice President Troy Vincent) over-inflated Patriot balls at half-time, the only proven tampering with Patriot balls. Brady and the Patriots were unaffected by the overinflation by NFL officials, as they destroyed the Colts in the second half.
Exponent must have noticed the over-inflation by officials, as it is implied by the post-game measurements, but failed to report or comment on it. Their avoidance becomes all the more conspicuous because many of the texts at issue in the Wells Report pertain to an earlier incident in which NFL officials had over-inflated Patriot balls, much to Brady’s frustration and annoyance at the time.
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