William M. Briggs, Statistician

The headlines of today’s New York Daily News is

CURSES!

It seems the New York Giants will play the Green Bay Packers in some sort of sporting event this coming weekend. What makes this interesting is that Brett Favre, the star player of the Packers, has just appeared, much to the delight of the News, on the cover of Sports Illustrated, because the Daily News feels that this appearance will befoul Mr Favre, causing him to fail and so let the Giants win the game.

Got all that?

The News is hoping that Favre will fall pray to the so-called Sports Illustrated curse. What is supposed to happen is that the showing of an athlete on the front cover of that magazine applies a sort of black magic to that athlete’s capabilities, and that he will soon perform badly, or not up to expectations. The SI magazine itself is aware of its supposed talismanic powers, and wrote an article analyzing the statistics of the curse.

They examined 2,456 covers and found 913 jinxes, for a rate of 37%, which they intimate is a number high enough to conclude “something” is going on. Perhaps you think so, too.

Now, even though the editors said they listened to the advice of “sober statisticians” (if you attended any of our meetings, of Bayesians, anyway, you’d realize that this adjective is mistaken), they didn’t really take them seriously. Because it is true that mere numbers can remove the mystery and explain the curse. Take a look at this picture:

This describes that probability that Brett Favre’s performance will be way below, below, average, above average, and way above average. Higher levels of the curve indicate higher probability; the highest probability is for “average” performance. Now, that “average” is Favre’s average, not yours or mine. It applies to his lifetime performance capabilities and simply says that on most days he’ll perform at his average level.

Of course, there is some probability that he’ll perform “Way above” average and, judging by this year’s record, he has so far. But if you had to make a bet, and there is some evidence that people bet on football games, you’d do well to guess his performance in his next game will be just average. There is some correlation from game-to-game, meaning that if Favre played way above average last week, he’ll tend to also be above average this week, but this tendency is actually not that strong, and your best bet is still to say just average.

What about the curse? What happens is that some athlete somewhere in some sport will perform way above average. Sports Illustrated has to have something on its cover and so seeks out those athletes who are doing exceptionally well, and picks from among them the one that outperforms them all. In other words, this particular athlete will have performed way, way above average, a rare event. So their picture is shown. But, lo! In the coming weeks, our poor athlete slumps, disappointing all,? once again proving the validity of the curse.

All that has happened, however, is that the athlete has “regressed to his mean.” The overwhelming probability is for that athlete to perform near their average, which the athlete subsequently does. It’s no slump after all, just a return to regularity.

To say the SI has a “cover curse”, then, is no different than saying a coin has been hypnotized after a “Tail” finally shows up after a successful run of 20 “Heads” in a series of coin flips.

I realize, however, that showing the “curse” to be merely a banal expectation of statistics sucks the fun out of it. I don’t want you to go away depressed, so I’ll close by telling you that I am a Lions fan.

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