A friend of mine who has math and law degrees directed my attention to Deflating "Deflategate," which describes the American Enterprise Institute's thorough debunking of the methodology and conclusions of the Wells report. Authors Kevin Hassett and Stan Veuger conclude:
Our study, written with our colleague Joseph Sullivan, examines the evidence and methodology of the Wells report and concludes that it is deeply flawed. (We have no financial stake in the outcome of Deflategate.)
The Wells report’s main finding is that the Patriots balls declined in pressure more than the Colts balls did in the first half of their game, and that the decline is highly statistically significant. For the sake of argument, let’s grant this finding for now. Even still, it alone does not prove misconduct. There are, after all, two possibilities. The first is that the Patriots balls declined too much. The second--overlooked by the Wells report--is that the Colts balls declined too little.
The latter possibility appears to be more likely.
The entire AEI report can be found here. My friend points to this passage as particularly relevant:
The problem here is that ideally, measurements would have been taken simultaneously for all balls, outdoors, at the end of the half, and with the same gauge that was used before the game. Instead, the balls were taken inside and measured there, but not measured simultaneously. The pressure was checked twice for the Patriots balls (once with each gauge), after which the Patriots balls were reinflated and the Colts ball pressure was measured. Only 4 of the Colts balls (instead of all 12) were measured because halftime ended and the officials ran out of time. The fact that the officials ran out of time is highly material: it implies that the Colts balls were inside a warm room for almost the entire halftime before they were measured and thus had a chance to warm up.
Based on using his mathematical training to evaluate AEI's scientific analysis and on using his legal training to identify the flaws the Wells report's logic, my friend reached the following conclusions, which he permitted me to quote as long as I did not reveal his name (the quoted remarks have been edited slightly for length and clarity, but without changing the analysis and conclusions) :
As I view things, there are several (potential) problems to consider here:
i) From a legal standpoint is there adequate "foundation" to admit the original air pressure results into evidence?; in particular:
ii) Were the original notations/recordings of the individual ball pressures, both before the game, and at halftime, accurate? (Note: I think all commentary I've seen as to this point
iii) The AEI report, quoting/referring to the Wells report, says there were two pressure tester devices (gauges) used, one with an NFL logo on it, one without. The NFL on site official (Anderson) remembers using the "Logo" gauge on the balls before the game. The AEI report says that the Wells report concluded, notwithstanding Anderson's (stated, according to AEI) memory, that Anderson used the non-Logo gauge to run the tests before the game. The AEI report (correctly) notes the significance in the gauge used to test the air pressure before the game because the "Logo" gauge "reports" pressure (apparently consistently, if I'm understanding the AEI report) at .4 pounds per test greater than that reported by the "non- Logo" gauge. For example, if a particular football had been tested using the "Logo" gauge as having 12.0 psi, then presumptively had the same ball been tested instead using the "non-Logo" gauge, then the pressure would have been reported at 11.6 psi.
v) Not trivially, it seems all the Patriots footballs tested at halftime were tested twice. An article by a team from Purdue at Columbus (an initial engineering report [yahoo search terms: "NFL football pressure purdue columbus" will yield a link to "Deflate Gate Examined"]) noted that "The football pump needle made a very poor seal when inflating the football. A noticeable amount of air was felt coming around the side of the needle when inflating the football. The amount of air leaving the football when removing the pump needle from the ball also released a small amount of air each time. The team estimated that with each removal of the valve 0.1 psi was released as we closely observed the behavior of the interaction between the needle and the football. Thus, it could be plausible that if a ball is inspected several times in succession without being inflated could be subjected to a significant loss in pressure and should be noted for further testing."
vi) In light of something I frequently hear engineers say when trying to get a point across: "Do the math." Relevant here, because the AEI report (though rather obliquely and politely) seems to attack the accuracy of the simple math/statistics calculations contained in the Wells report.
OK, all that said, what does this all mean?
In front of a competent judge, the NFL could expect to have significant difficulty in getting the halftime psi results admitted into evidence.
Even if the results were admitted into evidence, I think it unlikely that they would be accorded much evidentiary weight.
In particular, I think a judicial fact-finding might look something like this (what follows is intentionally compressed):
Acting as finder of fact, the Court noted Defendant Brady’s objection to admitting into evidence the reported values of the psi testing of the Patriots’ and Colts’ footballs as measured before the game, and at halftime. The objection was a lack of foundation. The Court admitted the evidence, under the proviso that the Court would later evaluate them “for what they are worth.”
As it turns out, the Court finds they are not worth much.
In particular, the evidence shows that Referee Anderson tested all the footballs before the game using a gauge that reported values--each time, each test--0.4 psi higher than the other gauge used, in part, to measure the footballs during halftime. The Court finds the evidence does not demonstrate precisely which gauge or gauges were used to test each football during halftime. However, it is clear that both gauges were used. Also, it is clear that each “Patriot” football was tested for pressure twice during halftime, while only four “Colts” football were tested for pressure at halftime. Clearly, the Patriots’ footballs were tested first, and there was insufficient time to finish testing all twelve Colts’ footballs.
A significant difficulty in assessing the evidentiary weight of the test results arises from the lack of clarity as to which “gauge” tested each football during halftime. If all of the Patriots’ footballs were tested with the same gauge that Referee Anderson used to test them before the game, then the comparative results between the pre-game and halftime tests are sensible in a “math-physics-engineering” sense. However, if some or all of the Patriots footballs were tested at halftime using the second gauge, then the halftime test results would generate results that would unfairly and incorrectly support a conclusion that the Patriots’ footballs had been improperly deflated after the pregame testing, but before the game started.
Moreover, while the evidence and simple high school chemistry teach that application of the Ideal Gas Law (pv=nrt) mandates a conclusion that both teams’ footballs would have been found to have “lost pressure” between the pregame testing and the testing at halftime, another problem for assessing the weight and meaning of this evidence arises because of the specific circumstances of the halftime testing. All the game balls were taken into the warm “testing” room at halftime for the required testing. Testing on the Patriots’ footballs began immediately. Testing on the Colts’ footballs began after all the Patriots’ footballs had been tested. The evidence establishes that all the footballs that
The end result is that the halftime testing was improperly skewed to support a conclusion that the Patriots’ footballs had been improperly deflated after the pregame testing. The Court finds that the total impact of this improper skewing is contained within a range of 0.6 to 1.0 psi as to each Patriots football. Adjusting the reported results to remove this improper skewing means the Patriots’ footballs did not demonstrate evidence of having been improperly deflated when they were tested at halftime.
To conclude this discussion of the pressure testing and the conclusions that might be drawn from it, the Court notes the criticism the AEI report (and Defendant Brady) level against the accuracy of the statistical calculations contained in the Wells report (and asserted in these proceedings by Plaintiff NFL). While the Court finds the AEI report’s conclusions in this regard to be well founded and accurate, the Court does not rely upon this point to reach its final decision. In other words, the Court assumes, arguendo, that the Wells report’s statistical calculations are accurate.