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The Bell Curve Triumphs Again
The innumeracy of journalists is a pet peeve of mine. Among other things, it allows them to be manipulated by political consultants. Thus the Washington Times' Donald Lambro just wrote the umpteenth article about how the Republicans are (any day now!) winning blacks and Hispanics over from the Democrats:
"'Something very significant is going on down there at the bottom of American politics," White House political adviser Karl Rove told me."
[GOP's voter inroads By Donald Lambro, The Washington Times, May 29, 2003]
I'll bet he did!
Ah, I'll deal with this mirage next week (again). Let's look at another recent example of media innumeracy: the golf gender gap.
With a mere six hours of web-searching and spreadsheet jiggering, I was able to publish an article on UPI called "How will Annika Sorenstam perform?" the day before the top woman golfer teed it up with the boys at the Colonial Country Club. Here was my forecast, based on her average scores on the Ladies Professional Golf Association courses, which average about five strokes per round easier than the PGA courses:
"So, I predict that if Sorenstam plays this week the way she's played in the rest of 2003, she'll miss the cut by four strokes."
And that's exactly what she did.
She shot what she called one of the best rounds of her life on Thursday (a 71), then regressed toward her mean on Friday (74). She hit a disastrous stretch of five bogeys in eight holes in the middle of her second round, but then she gutted it out and closed with seven straight pars to stanch the bleeding. She still beat 13 men out of 114, so she played extremely well under pressure. Congratulations Annika!
But while her cut-missing was celebrated wildly in the media, it confirmed my assessment: she couldn't make a living on the men's tour.
Sorenstam carefully selected the Colonial tournament because the course suited her, and because its field is limited in both quality (all five of this year's multiple winners—Tiger Woods, Davis Love, Mike Weir, Ernie Els, and Vijay Singh—passed it up) and quantity (about 35 fewer golfers start than in the normal tournament, but the same number make the cut).
Top Washington Post sports columnist Tom Boswell claimed ahead of time that Annika would be a top 100 player the PGA Tour and even win one or two tournaments. Boswell was unusual for a journalist in that he actually tried to use statistics. He took Sorenstam's scoring average on the tour, then adjusted for the greater length of the PGA courses. But, either through ignorance or ideology, he failed to account for the obvious facts that the men play inherently more rigorous courses, and that those links are set up harder, with longer grass in the rough and shorter grass on the greens.
My estimate was that if Annika had been playing on the men's tour all of 2003, her scoring average would be tied for 183rd out of the 185 golfers on the PGA's scoring average list. But the guys down at the bottom are not among the top 185 in the world at present. They are ex-stars like David Duval and Craig Stadler who are invited to tournaments solely because they used to be big names.
I'd guess there may also be 100 minor league golfers who are better than Duval and Stadler (and Sorenstam) right now. Plus, say, 150 golfers in Europe, plus more on the Asian tour and on the Senior (Champions) tour. Overall, Annika is probably about the 300th to 500th best golfer in the world.
That's not bad! But that's also nowhere near as good as you've been hearing from the press. That's because few journalists understand how to think quantitatively about human differences. (Veteran pundit James J. Kilpatrick has rightly argued that the most important course of study in college for aspiring journalists would be statistics.) But if your ideological bias is that everyone is exactly the same, or at least they morally ought to be, you won't be comfortable with the tools developed by the great statisticians.
Statistics are essentially the study of differences, including human differences. In his recent book The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century David Salsburg makes clear that many fundamental statistical techniques were invented by the British hereditarians Francis Galton, Karl Pearson, and Ronald Fisher who were largely interested in studying the inheritance of intelligence—an inquiry that continues to attract furious denunciations even today.
Galton -- who invented fingerprinting, the weather map, and the silent dog whistle—was Charles Darwin's half-cousin. Their common grandparent was the famed doctor and polymath Erasmus Darwin, who had proposed his own version of a theory of evolution. Not surprisingly, Galton was fascinated by how intelligence tends to run in families. In 1869, Galton wrote the first book on subject, "Hereditary Genius." To aid his research, Galton invented the correlation coefficient and the concept of "regression to the mean," which describes how smart parents tend to have less smart children (and, more happily, dim parents tend to have children brighter than themselves). In the 20th Century, Fisher's enthusiasm for Galtonism led him to become not only the most important statistician of all time, but also the leading mathematical geneticist of his era.
Galton's "London School" demonstrated that the proper way to compare people's performances is not absolutely, but relatively, typically in terms of a bell curve.
For example: Colonial's winner Kenny Perry finished at 261, 19 under the par of 280. Justin Leonard was 13 under. Both shot rounds of 61, since conditions at Colonial were easy this year—soft, holding greens, no wind. Shooting 145 for two rounds before being cut, Annika was en route to a four round total of 290, or ten over par. Thus, she projected to be 29 strokes or 11.1% worse than the winner.
Now 11% doesn't sound like all that much. Yet, because of diminishing returns, that's about what you'd expect for a gender gap in sports where the competitors strive against nature rather than against each other. In our 1997 article "Track and Battlefield," sports physiologist Stephen Seiler and I pointed out that the gender gap between the male and female world records in the ten main running events from 100 meters to the marathon averaged 11.5%.
Which is probably why Serena Williams, the world's best woman tennis player, has strongly denied any intention of ever attempting a men's tournament. Annika and Serena are about equally good compared to the rest of the women in their respective sports. If Serena entered a 128-player field, she'd do exactly as well as Annika—fail to make the second round. But, as she well knows from rallying against minor league male players, she'd lose ugly
Here's the difference: an Olympic sprinter can run 100 meters in 10 seconds. I could probably step outside right now in my bathrobe and slippers and run 100 meters in 20 seconds. So, mathematically, he's only twice as good as me. Right? Right?
But if I stepped into the ring with a top boxer for 15 rounds, he wouldn't win ten rounds to my five. He'd win on a one-punch knockout in the first 20 seconds.
Annika can score respectably because she's playing the course. But Serena would be humiliated by a professional male tennis player because she'd be playing him. That's why the Galtonians invented statistical techniques like the bell curve—it's the only way to compare people's performances rationally.
Thinking like a statistician allows you to ask fascinating questions that open up important perspectives on society. For example, I compared Annika statistically to the small, short-hitting, old-timer Corey Pavin. I suggested, based on their scoring averages, that he was at least two strokes per 18 holes better than her. As it turned out, over 36 holes he beat her by seven strokes.
Corey is clearly a better golfer than Annika, but why? It's not because he hits it longer. At Colonial, they both averaged 268 yards off the tee (99th out of 114 players). A major reason is because he has a more delicate feel around the greens. That's a typical sex difference in professional golf—even though women overall tend to have better small motor skills than men at tasks like sewing and typing.
How come? One possibility: men tend to be better at three-dimensional visualization than women. Golf course architects build undulations into greens to test golfers' ability to forecast the gravity-induced curvature of their putts. Some of the male superiority at the short game may be mental.
Also, male pros simply constitute a much more highly-selected fraction of all male golfers than female pros make up of all female golfers. In other words, out of the millions of slightly-built guys who were nuts about golf while they were growing up, Corey Pavin is simply way, way out at the far right edge of the bell curve of talent.
In contrast, it's an understatement that not very many American teenage girls have been obsessed with golf.
Indeed, a major PR problem for the America-based LPGA tour is that fewer and fewer American women are winning tournaments. Why? In Sorenstam's Sweden, and in East Asia, golf is much less unfashionable among heterosexual teenage girls than it is here. (In fact, girl's high school golf in the U.S. is increasingly dominated by East Asian girls, of whom the six-foot-tall Korean-American 13-year-old Michelle Wie is the most promising.)
Golf used to be trendy among young American women. My Mom once gave me a book of golf memorabilia that included lots of women's magazine covers from the 1920s showing young ladies dressed in the height of flapper fashion swinging their mashie-niblicks. In that decade, the great P.G. Wodehouse sold dozens of romantic comedy short stories about beautiful girls who shoot scratch and the duffers who love them to the Saturday Evening Post for bundles of money.
At some point, though, golf stopped being sexy for American girls. Nowadays, the great majority of amateur women players in America are the wives of male players. Typically, they are post-menopausal. Most of the fans at LPGA tournaments are middle-aged or elderly husband-wife couples. The next biggest cohort: packs of burly, crop-haired, gym teacher-looking women who express approval of their favorites' best shots by punching each other excitedly on the shoulders.
(The role of hormones in golf's appeal is a fascinating subject. My wife became highly enthusiastic about playing, and even watching, golf both times she was pregnant with our sons. As soon as the boys were born, however, the oxytocin started flowing and she lost 101% of all interest in golf. This phenomenon is rare but by no means unique.)
So the real problem for the LPGA is that young girls don't think golf makes them look sexy.
I'm not sure that Annika is going to solve that problem. She's added a startling amount of upper body muscle mass. When I saw her at the Nabisco Championship in early 2001, she looked like the slender, attractive young married woman she was. When I saw her again this spring at the Office Depot tournament, she looked like Hans and Franz, the Schwarzeneggerian muscleheads played by Dana Carvey and Kevin Nelon on old Saturday Night Live shows. ("Jah! Ve vill pump you up!") Her upper arm muscles have gotten so big that her arms no longer hang down along her sides like a normal person's.
Clearly, she's worked awfully hard in the weight room, and good for her. Still, I've been burned too many times over the years by naively hero-worshipping jocks who become champions after suddenly sprouting amazing new upper-body muscles: for example, Jose Canseco, Ben Johnson, Ken Caminiti, and Mark McGwire. They are just some of the validated cases of steroid, testosterone, or human growth hormone abusers. I've got a long list of other superstars I have strong reasons to suspect are on the juice.
Women's sports are even more susceptible than men's sports to corruption by chemistry. Females, being naturally less masculine, get more bang for the buck from artificial male hormones. Communist chemists could make East Germany the world's leading power in women's sprinting. But men's sprinting continued to be dominated by highly muscular men of West African descent. To beat Carl Lewis, an East German man would have needed such a massive jolt of steroids that even the pathetic drug tests of the 1980s would have caught him.
So my enthusiasm for Annika's new massiveness is restrained. As, I think, will be the enthusiasm of America's teenage girls.
Conclusion: Journalists don't like to think systematically about human differences – in golf as everywhere else. Yet differences are the most important facts in the social universe. When we ignore them, we make bad policies that hurt real people.