Lies, Damn Lies, and Sports-Page Statistics

Consider this scenario: a jar sits on a table with 12 marbles in it: eight red, four black. Now imagine randomly drawing one marble from the jar, then putting that marble back in the jar and repeating this process six times. Of the six marbles you draw, how many would you expect to be red?

The sensible answer is, of course, four. Two-thirds of the marbles in the jar are red, so we would expect two-thirds of the randomly chosen marbles to be red. If you did this exercise many times in real life, you would often get a result other than four, but you can expect four to be the most common result.

Now consider this headline about the NFL playoffs from the front page of the Sports section in today’s Washington Post: “Being Rested Has Become More Like Being Rusted.” The evidence on which the article hangs is a table showing that four of the last six Super Bowl winners played in the playoffs’ first round; only two of the six eventual winners were top seeds that had earned first-round byes. The implication is that a first-round bye actually puts teams at something of a disadvantage. As retired 49er Randy Cross puts it in the story’s money quote,

I was so amused with all the talk about the number one seeds. Who wants to be a number one seed these days? When do they ever win any more? That just puts a bigger target on you. Do you want to be on a roll or do you want to be rested? Being rested has become more like being rusted.

Retired Buffalo Bill Mark Kelso spins a similar story:

If you have some issues with injuries, it’s nice to have that first weekend off. But if not, I like to have that continuity of playing and keeping things in the same routine. I like the idea of playing that opening weekend…Teams like New Orleans, with the precision in the passing game, I think it’s good for them to play the opening weekend. It could give them an advantage early in the game the next weekend over a team that didn’t play.

Uh, guys? Twelve teams make the playoffs each year, and the four of those that are top seeds–one-third of the playoff field–get a first-round bye. If the eventual Super Bowl winner were picked at random from those 12 teams, then how many of the past six winners would we expect to have played in the first round? Four. Hey, wait a minute…

Six seasons is way too small of a sample to infer much of anything, and maybe there’s a glimmer of story in the fact that a pass in the first round doesn’t seem to give the top seeds any enduring advantage. But inferring a distinct disadvantage from a tiny sample that matches what we’d expect to see from a random draw in highly competitive league? Now that’s a stretch.

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