Last time we heard about Deflategate on this blog, Warren Sharp compiled some statistics on fumble rates, showing that the Patriots were unusually good at avoiding fumbles. (link, link) I thought the level of analysis was "above average" and remarked that statistical evidence of this type can only get you so far. The metric is indirect, and it does not speak to causation.
The official investigators have now issued their report. New York Times has its coverage here. As one reader commented, this article, currently nearing 800 comments, has more comments than most articles with more serious subject matter. The NYT article is one of the better ones out there on this subject.
Two set of new evidence has emerged.
The first, which is getting most of the headlines and attention, are text messages involving two Patriots employees who discussed their deflating operation. These text messages are highly incriminating for the two involved and for me, also incriminating for Tom Brady, the team's superstar quarterback (who refused to release his own text messages or other correspondence to the investigators). The text messaging evidence shores up the causal evidence in a way that numbers by themselves could never accomplish.
The takeaway from the text evidence is the power of "metadata". Metadata is data about the text messages (sender, recipient, date and time of sending, length, etc.), as distinct from the content of the texts. Metadata went mainstream when the U.S. government was revealed to have been massively scooping up metadata on domestic phone calls, but denied collecting contents of said phone calls (See these coverage, for example). The investigators can use metadata to learn who else is in the circle of insiders, how often they communciate, when they communicate, etc. Notice that these pertinent questions do not require knowing the contents of the text themselves. (This is not to say knowing the contents of at least some of the text messages is important--at the minimum, to zoom in on the relevant texts.)
But these investigators could not determine when the deflator operation started, how often it occurred or the full scope of the operation. This is likely to do with selective disclosure of the text messages by selected parties (e.g. none from Brady).
Another takeaway is the inherent bias in surveillance data. Simply put, you only know what you can measure, and there is much that are not being measured. To get the "full scope", the investigators would need phone records, emails, and even wiretap evidence following the key players around (just kdding).
The second set of evidence is also extremely important to the story but it has received far less attention. One reason I like the NYT coverage is that the reporter gets to this evidence before talking about the text messages. For the first time, I see direct evidence of football tampering. The NFL rule requires footballs to be inflated to between 12.5 and 13.5 pounds per square inch. According to the NYT report, after the Colts raised suspicion at half-time of the Patriots-Colts matchup, all of the footballs were found to be underinflated (below 12.5 pounds), with the minimum vaule of 10.5.
This is the first time I see a clear admission that all of the footballs were underinflated. This is much more convincing evidence that someone tampered with the footballs than any of the fumble analysis.
Further, the referee had already weighed the balls before the game, and at the time, found all of the Colts-supplied footballs to be about 13 pounds, and only two of the Patriots-supplied footballs to be under-inflated.
Once tampering is established, the investigators can move on to finding the cause. Here, they are helped by videotapes from surveillance cameras, and also the texts.
One nitpick about the sentence: 'The report uses the nebulous phrase “more probable than not” several times in making its conclusions.' To a statistician, this is a very precise statement, not nebulous at all! I interpret the investigators to mean there is more than 50% chance. That is the standard of "preponderance of evidence."
FiveThirtyEight has a lengthy discussion of the report. They helpfully showed a screenshot of the measured ball weights: