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Stephen Jay Gould (1986), an evolutionary biologist, studies the evolution of systems. That is, he studies the nature of variation and change in various phenomena. One of the "systems' he studies is baseball. He addresses the query, What has happened to the .400 hitter?" In 1897 Wee Willie Keeler batted .432; in 1924 Rogers Hornsby batted .424; and in 1941 Ted Williams battled .406. No baseball player since Williams--over a half century ago--has hit at a .400 or better clip.
Why has the .400 hitter become extinct? Baseball aficionados have argued that night baseball, grueling schedules, dilution talent, and improved and specialty pitching have all contributed to this decline. Gould (1986), while not denying these factors may have had an impact, argues that such reasoning is based upon a false assumption. He says that the .400 hitter is not a thing or a phenomenon and proposes two related reasons to explain this extinction: (1) human performance in some activities, e.g., hitting in baseball, is approaching the outer limits of human capacity, and (2) systems tend to an equilibrium as they improve. Another way of looking at the .400 hitter is to view it as representing the extreme right hand tail of a normal distribution. In order to understand why the .400 hitter is nonexistent today one needs to look at the entire distribution of batting averages over time.
To paraphrase Gould's (1986) argument: For the past 100 years the average (arithmetic mean) batting average has hovered around .260. What has happened is that the standard deviation (a measure of variability) has declined in almost law-like fashion. The standard deviations over the past one hundred years have, in fact, steadily declined. Importantly, the arithmetic mean has remained fairly constant but the standard deviation has gotten smaller.
Why has the standard deviation declined? According to Gould (1986), the standard deviation has decreased because all athletes--pitchers and hitters--have gotten better. Unlike clock sports that have an absolute standard, batting in baseball reflects the limits of human performance. That is, there is only so much a body can do to achieve perfection. Further, there is a dynamic and delicate balance between hitting and pitching in baseball. The batting feats of the greats of yesteryear, performed close to the limits...