Academic journal article Journal of Sport Behavior

The Decline of the .400 Hitter: An Explanation and a Test

Academic journal article Journal of Sport Behavior

The Decline of the .400 Hitter: An Explanation and a Test

Article excerpt

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 batted .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 of 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 of human performance and a wide gap existed between the poorest performers and the best ones at that time. Today that range in baseball hitting is less variable. [As an aside, Gould maintains that a Wade Boggs is close to the limit of performance and could have batted well over .400 during the earlier days of baseball.] The standard deviation has declined because the participants in the sport have gotten so much better. Paradoxically, the departure of the .400 hitter is a sign of better athletic performances overall. Gould (1986, p. 62) says:

Paradoxically, this decline [variation] produces a decrease in the difference between average and stellar performance. Therefore, modern leaders don't stand so far above their contemporaries. The myth' of ancient heroes - the greater distance between average and best in the past - actually records the improvement of play through time.

With statistics, through a transformation process, we can compare performances of top hitters at different times. The formula for such standardization is z = (raw score-arithmetic mean)/standard deviation.

In the 1910, 1940 and 1970 decades the means and standard deviations were .266 and .037, .267 and .033, and. 261 and .032, respectively. As examples, Cobb batted .420 in 1911, Williams batted .406 in 1941, and Brett batted .390 in 1980. The respective standard scores (z-scores) for these stellar performers were 4.16, 4.21, and 4.03, respectively. Since 99%+ of all batting averages fall within plus and minus three standard deviation units of the mean and since these three individuals are all at least four standard deviation units above the mean, there is indisputable statistical evidence that Cobb, Williams, and Brett were spectacular hitters. …

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