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MatheMUSEments
Batting Streaks
By Ivars Peterson
Muse, May/June 2002, p. 35.
For baseball fans, one of the highlights of last season was
the home-run record set by Barry Bonds of the San Francisco
Giants.
All summer long, newspapers printed charts showing how many
home runs Bonds had hit and how many he would have at the end of
the season if he continued hitting them at the same rate. On
average, Bonds was hitting a home run once every second game. So
his total was likely to be about half the number of games he
played. In the end Bonds played 153 games and walloped 73 homers.
Here's an interesting question. Bonds had a 50 percent chance
of hitting a homer over the course of the season, but were those
his odds for any particular game as well? What if he had a hot
streak? What if you went to a game when he was in the middle of
his hot streak? Wouldn't the chances of his hitting a homer be
higher than even-steven?
Another way to ask this question is to ask whether Bonds was
hitting homers like a tossed coin falls. When you toss a fair
coin, it has a 50 percent chance of coming up heads. Even if you
get heads three times in a row, the next time you tossed the coin
it would still be even odds it would come up heads. Was Bonds's
ability to hit as random as a coin toss, or could he, by eating
his Wheaties or spitting on his hands, force a long run of good
luck?
For each game during last summer's baseball season, economist
Paul Sommers of Middlebury College in Vermont checked whether
Bonds hit one or more home runs and looked for streaks. Bonds had
one stretch of 13 games in which he failed to homer. He had two
stretches of six games in which he hit home runs every time.
You can get streaks when you toss a coin, too. Suppose you
toss a fair coin 250 times. You will probably get two runs of six
heads or more, and one run of seven heads or more. Most people
are surprised by this. When they are asked to write down a long
string of heads and tails that they believe is random, they
rarely include four or five heads in a row, even though such runs
are likely to occur.
Sommers used a statistical formula to find out whether Bonds's
hot streaks were as random as home runs in a coin toss. They were.
How could this be? Maybe so many factors affected his hitting--the
weather, game time, the ballpark, whether the pitcher was right-
or left-handed, and so on--that it wasn't really possible to
predict whether he'd hit a homer in a particular gasme. All you
could say is, based on past performance, his odds were about 50-50.
Somehow that sort of takes the magic out of a streak. But it
doesn't mean Bonds isn't a good player. A lesser player might
have as much chance of hitting a homer as a single die has to
come up as a three (one chance in six).
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