The Bell Curve Triumphs Again
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:
significant is going on down there at the bottom of
American politics," White House political adviser Karl
Rove told me."
By Donald Lambro, The Washington Times, May 29,
I`ll bet he did!
deal with this mirage next week (again). Let`s look at
another recent example of media innumeracy: the golf
With a mere
six hours of web-searching and spreadsheet jiggering, I
was able to publish an article on UPI called
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."
exactly what she did.
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.
her cut-missing was celebrated wildly in the media, it
confirmed my assessment: she couldn`t make a living on
the men`s tour.
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).
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.
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.
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
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
are essentially the study of differences, including
human differences. In his recent
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.
"London School" demonstrated that the proper way to
compare people`s performances is not absolutely, but
relatively, typically in terms of a
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
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
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
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.
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.
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
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
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.
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
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
So the real problem for
the LPGA is that young girls don`t think golf makes them
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
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.
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.
[Steve Sailer [email
him] is founder of the Human Biodiversity Institute and