Danger Zone
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The Statistical Improbability of Deflate Gate
1. The Cognitive and Statistical Biases of Deflate Gate
3. Follow-Up: The Evidence for Non-Tampering in 2 Pictures
These arent the best 3 articles debunking Deflategate, but they are 3 great articles by the same person.
I posted these out of order, because the 5/22 article is one I hadn't seen before and want to bring to people's attention.
The 5/17 article has some of the best expressed refuting of the Deflator texts and other logical fallacies I've read.
Although it’s far below “statistical significance,” 75.3% might sound like a lot. But what is that number actually saying? For that, we have to look at the observed difference in the averages to put this into perspective: there’s a 75% chance that the 0.3 PSI difference is not simply from variance and is part of a different population (i.e. tampered balls).
- The best-case statistical scenario for the Patriots is that Walt Anderson used the Logo Gauge pre-game, that the balls were measured at 2 minutes, each took about 22 seconds to measure and that the officials took 5 minutes to re-inflate the balls (labeled “Early Start, Fast Measure, Long Inflate” above). That produces a mean where the Patriots balls are higher than the Colts, meaning it’s impossible for the Patriots balls to come from a population that is inherently lower than the Colts balls.
- Three of the six scenarios in which the Logo Gauge was used pre-game completely exonerate the Patriots
- The worst-case scenario for the Patriots is that Walt Anderson used the Non-Logo Gauge in the pre-game, and that the balls were measured at 4 minutes, each took 27 seconds to measure and that the officials took 2 minutes to re-inflate the balls (labeled “Late Start, Slow Measure, Quick Inflate” above). That produces a p-value of 0.247, which means that if our assumptions are true, there is a 75.3% chance the Patriots balls come from a different population.
Depending on the distribution, 0.3 PSI could easily be 99.99% likely to come from a different sample…which would suggest, what? There’s a 99.99% chance that the Patriots systematically released an average of 0.3 PSI per football? And that’s the worst-case scenario? That strains common sense.
1. The Cognitive and Statistical Biases of Deflate Gate
b. “Help the Deflator”
The Globe article takes exception to the Patriots explanation that Jim McNally referenced himself as the ‘deflator’ because he is a big fellow and wanted to lose weight. The author, Ben Volin, responds “It’s hard to find a rational-thinking person in the country who buys this answer.”
That’s just ignorant. And understandably — the science of thinking isn’t exactly taught in high schools.
Volin is under the impression that his mind isn’t heavily anchored to the context of deflating footballs, when for months, he’s only associated the term deflator with this issue. He, like most of us now, probably can’t even think of the word “deflate” without thinking of PSI and footballs. From a cognitive standpoint, that’s predictable.
2. But not necessarily accurate.
Prima facie the texts reflect incriminating language to those who have been loaded up with the idea that there was a tampering ploy in place. Once the mind has decided what the “deflator” refers to, it has a hard time accepting a counter explanation without a larger sum of evidence. But again, that’s a recipe for false conclusions and simply a predictable function of the brain’s desire to create certainty instead of ambiguity.
Conversely, if I told you that two jocular workmates came up with strange terms to needle each other with, and those terms were related to the actual work they did every day, would you think that’s strange? It’s possible, without any additional evidence (see section 3 and 4 below), that he calls himself the “deflator” because he regularly tampers with footballs on Sunday. There are also a myriad of other possibilities for that one text message, especially given McNally’s texting habits and propensity for wild language and nonsensical statements (e.g. “what’s up dorito dink?”)
People use jargon specific to their vocation all the time, and do so in extending humor or personalizing phrases. On the outside (with no context) these references seem meaningless or are misinterpreted. That’s the definition of an “inside joke.” It takes one instant of connecting a football losing weight to a person losing weight and voila, an inside joke. (Or, the only recorded instance of McNally referring to his role in a tampering scheme, a scheme that was otherwise never apparently discussed over text.)
3. Follow-Up: The Evidence for Non-Tampering in 2 Pictures
These arent the best 3 articles debunking Deflategate, but they are 3 great articles by the same person.
I posted these out of order, because the 5/22 article is one I hadn't seen before and want to bring to people's attention.
The 5/17 article has some of the best expressed refuting of the Deflator texts and other logical fallacies I've read.
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