The Sports Illustrated curse and regression to the mean

Due to overwhelming demand, today’s column is a classic reprint. This originally appeared on 18 January 2008.

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 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. At this point, their picture is shown.

But, lo! In the coming weeks, our poor athlete slumps back to average or even below, disappointing all, and 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 his 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. And I want you to have fun. Which means I don’t want you to go away depressed; so I’ll close by telling you that I am a Lions fan.

1. Dave B

Some consumers, I believe, misunderstand the phenomenon and believe that the tendency of observations to regress towards the mean is the result of some independent force of nature “making” or “dooming” an athlete to fail.

It is perhaps easier and more palatable to understand regression to the mean that way, as a force or curse akin to gravity, than as you correctly describe it; as a probabilistic statement or a prediction.

2. Alan D. McIntire

It’s generally accepted that positive feedback is the best way to get students to improve, but the US Air Force came to the opposite conclusion using data similar to the “Sports Illustrated” model. Of course students improve at an “average” rate. Sometimes performance fluctuates above that rate, sometimes below it. Flight instructors found that when they chewed out a student after a below average performance, they usually improved to average next time. When the student was complimented after an exceptionally good performance, they usually deteriorated closer to average the next time. The conclusion was negative feedback worked better than positive feedback.-

I can recall, when I was still in, two popular hats guys wore when off duty.

The first was adorned with: “Air Force: Another Fine Game from Parker Brothers.”

Second: “Friend don’t let friends reenlist.”

4. Ken

The principal described here, performance “regression to the mean,” is so fundamental that a variety of real-world examples are used to illustrated it. Its also presented early on in “The Drunkard’s Walk, How Randomness Rules Our Lives”: http://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0375424040

They use a baseball example in which some above-average player happened to break Babe Ruth’s record, a statistical unliklihood that was also statistically expected (that is, it was expected to occur with some player or other, sometime or other, relatively soon, though not necessarily that particular player when he actually did). This resulted in a rather loud outcry in the sports-watching community as the new record holder wasn’t as nice & cuddly, in the sports fan’s perception, as the ‘other guy’ that just missed setting the new record.

Which just goes to show that nice guys finish last (another curse…right?).

Hhhhmmmm…..Hindsight being what it is, perhaps someone would like to perform some sort of multi-variate statistical analysis with the Sports Illustrated cover curse to demonstrate that those performers most adversely affected by the SI “curse” are those who are “nicest” (i.e. that those most immune are ‘not so nice’). E.G. what is the conditional probability that a player portrayed on SI’s cover that goes on to perform above average is later is found to have been involved in some scandalous activity or other VERSUS the conditional probability that some player that gets jinxed goes on to live a scandal-free life. Put another way, how prescient is SI at picking players of future notoriety relative to random chance? I bet random chance will result in some pattern that looks spooky.

5. So, did the Packers win or was it the Giants? Or was it the curse that won?

Somehow I think it was the Giants, as I recall a player catching a ball with 1 hand and his head in another game a few weeks later. I also recall that said player was NOT on the cover of SI, meaning that once again the curse was true (try to follow my perverted logic: a) the man who used his head was NOT on the cover of SI. b) the man who used his head performed exceptionally well. c) this was predicted by the curse by avoiding putting the tall dark man with one blue hat on the cover and forcing him to have done something less exceptional, thereby allowing him to have the exceptional performance that may have earned him an all-expenses paid trip to Curseville).

Now can I have that job as a reporter on Global Warming?

6. John Galt

Good Morning Mr. Briggs,

Interesting, your performance curve appears to be maxwellian. Is that necessarily true? Might such performance be non symetrical? Possibily a Lorentz or a Possion distribution. I guess it would depend on how you measure the performance, but wouldn’t is seem that the poor performance tail might be longer than the high end? At the high end, you are approaching the limits of human strength, reaction time, judgement, etc. At the low end, you could be ill or injured, forgotten your contact lens, all the way to being dead (that would be some poor performance).

7. Briggs

John,

Right: this particular distribution is only a cartoon. Real ones will be much different quantitatively, but qualitatively they will be similar.

8. zdudey

I will attest that Air Force fighter pilot training is best encapsulated as a “fear, ridicule and sarcasm” system.