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 Discover. In this article, Gould shows that while the average batting average among major league baseball players has not shown a long range trend for either increasing or decreasing, the deviation about the average batting average has continually decreased with time.

 

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 course the major leagues accept foreigners, and would probably accept females if they could demonstrate the required talent. Also, players outside the defined age range have played major league baseball. But for the sake of simplicity, I make these approximations.

 

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).