The Wells Report made numerous errors in its scientific analysis of Deflategate. In fact, nearly everything in the transient analyses, shown below, is wrong. This led to an incorrect conclusion that science could not explain the drop in Patriots pressure. However when the errors are fixed, the Patriots footballs can be explained by natural causes, regardless of which gauge referee Walt Anderson used to measure the footballs before the game.

Original Graphs in Exponent Report – Errors Notated

exponent_graphs

Errors in the Graphs

1. Transient Curves Too Low: The transient curves cannot be reproduced using the 71 – 74 degree halftime temperature stated in the report. They can only be reproduced using a 65 – 67 degree temperature, which is not possible given the conditions on game day. (1)

2. Incorrect Averages: The report uses Master Gauge averages in the results, but explains that the two graphs were set by the Logo and Non-Logo gauges, respectively. The charts must use a consistent gauge for each analysis, meaning they must use the Logo and Non-Logo averages instead of Master Gauge averages. (2)

3. Error Bands Too Narrow: The report didn’t take into account the small sample sizes when calculating the error bands for the 4 Colts and 11 Patriots balls. More specifically, Exponent assumed a normal distribution (used for samples greater than or equal to 30) instead of a t-distribution (used for samples less than 30) when estimating the error bands, which improperly narrowed the error bands for both teams. (3)

4. Inaccurate Wetness Effect: The wet curve for the Colts Non-Logo simulation is 0.2 PSI lower than its dry counterpart, but the wet curve for the Patriots Logo simulation is 0.5 PSI lower than its dry counterpart. Wetness should consistently impact footballs regardless of which gauge is used. Additionally, the wet curves should be rising more slowly than the dry curves since wet balls warm more slowly than dry balls, but this is not represented in the graphs. (4)

Corrected Graphs

The corrected graphs below represent what the Wells Report’s graphs would look like without errors. Specifically, each corrected graph uses a halftime temperature of 71 degrees, the Logo and Non-Logo averages, respectively, more realistic error bands, an initial wetness effect of 0.5 PSI, and slower warming for the wet balls.

fixed_graphs

“Where there is overlap between the shaded area bounded by the transient curves and the shaded area of the Game Day averages, the Game Day results are physically plausible.”

– Wells Report, page 214

“Testing [of the Patriots footballs] is likely to have begun no sooner than 2 minutes after the balls were brought into the locker room and was estimated to have taken approximately 4 to 5 minutes (leading to an ending time of between 6 and 7 minutes, and thus, an average measurement time of between 4 and 4.5 minutes, assuming a start time of 2 minutes).”

– Wells Report, page 212

Conclusion

After correcting the mistakes in the Wells Report, the Patriots averages overlap with the transient curves 4 to 4.5 minutes into halftime on both the Logo and Non-Logo transient curves. Therefore there is a scientific explanation for the measurements no matter which gauge was used to measure the footballs before the game.

Click Below for Further Explanations on Each Topic

SOURCES:
1. Deflategate transient analysis, YouTube (Nov 25, 2015), https://www.youtube.com/watch?v=crahIs7d-cs
2. NFL/Brady Appeal Transcript, Case 1:15-cv-05916-RMB-JCF (June 23, 2015), page 185-187
3. Statistical Sampling and Regression: t-Distribution, http://ci.columbia.edu/ci/premba_test/c0331/s7/s7_4.html
4. MIT Professor Debunks Deflategate, YouTube (Dec. 1, 2015), https://www.youtube.com/watch?v=wwxXsElty

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Twitter: @nkistner87

by Nick Kistner