It seems to have begun with a story in the Boston Globe mentioning that the New England Patriots won the coin toss at the start of their football game, 19 out of the last 25 times. The story just pointed out that the Pats had been lucky in the coin-toss department, and discussed their strategy when they do so.

But CBS Sports decided to call it an “impossible clip.” The insinuation of cheating was evident. It didn’t take long for NESN and Boston.com to jump on the accusation bandwagon. Hell, the innuendo has even spread to the Charlotte Observer.

These stories only prove two things. 1: Prejudice — meaning “pre-judice,” i.e. judge first, investigate later; 2: When it comest to statistics, a little bit of knowledge is a dangerous thing.

The “impossible rate” idea is based on the fact that if you flip a fair coin 25 times, your chance of getting 19 or more “heads” (or tails if that’s what you like to call) is 0.00731665. It’s a straightforward application of the binomial distribution, something those with a *little* knowledge can do. Since that’s about one chance in 137, let’s start spreading rumors with made-up names like “flip-gate” and “coin-gate” — they *must* be cheating, right?

Wrong. As someone who has a *lot* of knowledge about statistics, I can tell you there are a bunch of problems with this “analysis.”

Let’s start with the fact that 1 out of 137 is a far cry — a very, very, very far cry — from “next to impossible.” Some journalist making that kind of exaggeration isn’t a far cry either — it’s par for the course.

Let’s mention that there are 32 teams in the NFL. If *one* of them flips a coin 26 times, the chance of 19 or more “heads” (or tails if that’s what you prefer) is about 1 out of 137. If all 32 of them flip a coin 26 times each, what are the odds that at least one team will get 19 or more? A helluva lot greater than 1 out of 137.

The biggest problem of all is: *cherry picking*. I have no blame to lay, or fault to find, with Jim McBride at the Boston Globe, he was just pointing out a streak of good luck. But the other idiots ran with it, without even thinking about something that’s kinda obvious to those of us who know a lot about statistics. Namely, this: that when someone says “19 out of the last 25” it’s overwhelmingly likely that the **26th** was **not**.

Chances are, McBride picked 25 because that was a run of good luck. But if the Patriots had also won the 26th, he’d have talked about 20 out of 26, not 19 out of 25. He picked 25 *because it was the run of good luck*. Statistically, when you choose your sample *because of the result it gives*, it’s called “cherry-picking.” The salient point is that it *throws off the statistics*.

That’s an issue I’ve discussed often, in relation to climate data. Climate deniers do it all the time, for the purpose of giving the wrong impression. Because it does.

I doubt the Boston Globe article was trying to give the wrong impression. Nor did they; the Patriots have indeed had a run of good luck. But those others ignored the *hard* part of statistics, probably because they don’t really know what they’re doing. They saw a chance to impugn the New England Patriots, and they jumped on it.

Back in 2011, the New York Times mentioned in an article that 11 games into the season, the Cleveland Browns had lost *all 11* coin flips. They also pointed out that the probability of that is a mere 1 out of 2048. But to their credit, they did *not* have the temerity to accuse the rest of the NFL of some giant conspiracy against them. Hey — maybe they even have some people working for them who *do* know more about statistics than a *little*.