Today my favorite writer – The Sports Guy – wrote an excellent column about Bill Belichick’s “reckless” call to go for it on 4th and 2 when his team was up by 6, on their own 28 yard line, with just over 2 minutes left to play. Much of the article goes into great detail on the problems inherent with relying on statistics in such a situation (see: Insane angle #1: Statistically, it was right move). But in Insane angle #2, he can’t help but pull out his own statistics to “justify” why the Pats shouldn’t have gone for it.
Unfortunately, The Sports Guy made an all-too-common mistake while doing so – providing a reminder that however dangerous putting blind trust in statistics can be, the problem is that much worse if you don’t understand them properly.
His argument was simple. Indianapolis had already completed two long touchdown drives in the 4th quarter. By punting, New England would have forced them to do it a third time. So, to “prove” his point, he asked someone to crunch the numbers on “the number of times a team started and completed three touchdown drives in the fourth quarter to erase a double-digit deficit and win an NFL game since 2005.” The answer he found was 4 – it happens less than once per season. He then started banging his head on his desk.
It sure looks like a perfectly reasonable, statistically-based argument, but there are some major flaws. The one I’m going to focus on here (another big one is switching from %s to a raw count of a known rare situation, which is almost always an easy but meaningless thing to do) is tied to what’s called the “Gambler’s fallacy” – the belief that deviations from expected behavior in the past are likely to be evened out by opposite deviations in the future. The common example is coin flips, but I’m going to use a basketball analogy – since that’s the Sports Guy’s favorite sport.
Let’s say your playing the Cleveland Cavaliers, and for no obvious reason whatsoever they run a play to get a three-point shot for Shaquille O’Neal – who has only even attempted one such shot in the last decade or so. The defense is so confused by this that they foul him, and he steps to the line. Even though he’s only a 50% FT shooter, he hits the first two. What are the odds of him hitting the third?
Back in March I wrote about a