Page 14 Spring 1988

The
following paragraphs were not initially directed towards juggling, but
have been rewritten with the recently emerging juggling talent in
mind. The theme of this article is the claim that today's best
jugglers are not as prodigious as most IJA members believe. "But
Lucas can juggle five clubs for more than thirty minutes," you
say. "But Gatto can juggle seven clubs at such an early
age."
Although
these two jugglers are quite skillful, it can be argued that they are
not necessarily unusual. To understand juggling prowess, or the
superior skills of any endeavor, I focus on the batting averages of
major league baseball players. It is well known to experts of baseball
trivia that the last major league baseball player to hit over .400 in
a single season is the great Ted Williams. In 1941, Ted singled,
doubled, tripled, and homered his way to a .406 batting average.
Although
others before him had hit over .400, no one has since achieved this
monumental feat. What has happened to batters during recent decades?
Are batters getting worse? Is pitching getting better?
Stephen
Gould, the noted Harvard biologist, addresses these questions in the
August 1986 issue of
In other words, the average batting average has been relatively constant, while the highs and lows have shifted towards the norm. If baseball players have improved over the years, as most experts suggest, then pitchers and batters must have improved by roughly the same amount to maintain the relatively constant average batting average.
But
what caused baseball talent to improve? And why have the highs and
lows of batting averages shifted towards the norm eliminating the .400
hitters?
I
believe I know the answers to both of these questions. Consider the graph which
plots the number of baseball players vs. baseball talent. Plots A and
B are Gaussian curves which reveal talent distributions for two groups
of players who are available to the Major Leagues.
An
available player is defined as an American male who plays the game of
baseball, or has played baseball in his past, and is between the ages
of 18 and 40. Of
Notice
that for each curve there are more players of average ability than
there are at the two extremes. If the population of group A is four
times that of group B, then at each level of talent there are four
times as many baseball players in group A than there are in group B.
Or, from a mathematician's point of view, the area under curve A is
four times the area under curve B.
Now
assume group B is the number of players available to major league
baseball during the 1920's, and group A is the number of players
available to major league baseball today. This arbitrary assumption
means that today there are four times as many available players than
there were during the 1920's. Since major league baseball players are
the most talented players of either available group, they are
represented by the shaded regions at the high-end of the Gaussian
distributions.
If we also assume that the number of baseball players in the major leagues has not changed through the years, then the shaded areas under curves A and B are equal.
Two important conclusions can be made after observing the shaded areas:
1) When the major leagues select players from a larger available group, the average ability of a major leaguer improves (the average major leaguer not to be confused with the average available player is graphically located near the center of a shaded region), and;
2)
as demonstrated by the narrowing of the shaded region under curve A,
the deviation about the average major leaguer shrinks as more players
become available (which is the same as stating that the major leaguers
become more evenly matched in talent). |