Academic journal article Journal of Sport Behavior

Maybe There Were Giants, or at Least Outliers: On the .400 Batting Average Myth and the Absolute Limits of Hitting for Average in Major League Baseball

Academic journal article Journal of Sport Behavior

Maybe There Were Giants, or at Least Outliers: On the .400 Batting Average Myth and the Absolute Limits of Hitting for Average in Major League Baseball

Article excerpt

The demise of the .400 hitter has been postulated to actually be a sign of improved hitting in Major League Baseball. Gould (1996) believes that if hitters have improved, then the variance around annual mean batting averages must be systematically decreasing over time. Decreasing variance makes .400 averages unlikely, even though overall hitting improves. Batting averages between 1901 and 1995 were collected for player-seasons of at least 300 at bats, and regression analysis was used to rigorously test Gould's improvement hypothesis. The evidence does not support the improvement argument. Standardizing batting averages shows that even though not all .400 batting averages were spectacular, the best hitters of today are still not uniformly as good or better than past greats. There has been no improvement over time. Hitting greatness is timeless.

When Ted Williams hit .406 in 1941 there was no reason for anyone to believe he might be the last Major League Baseball player to do so. Why no one has eclipsed the mark in more than fifty-five seasons is the subject of hot-stove anecdotal debate and sabermetric pontificating. Some fans argue the drought proves that the greatest hitters were truly in the past. Their lament is that there will never be another Ted Williams. But more fans probably agree that players today are better hitters than past players were, or at least as good. They claim that Nap Lajoie, Rogers Hornsby, and Ted Williams could not hit as well today as Wade Boggs, Tony Gwynn, and Frank Thomas do. But that creates a paradox. How can today's players be better hitters, but hit for lower batting averages than past greats? Were .400 hitters merely opportunists, while today's sub-.400 performances are truly better? Can the apparent extinction of the .400 batting average be a sign of improved hitting or not? Do the giants of the game walk among us, in the mists of the past, or does every generation boast giants?

Perhaps one of the best recent discussions of the improvement hypothesis as an explanation for the absence of .400 hitting is presented by Stephen Jay Gould (1996). His reasoning may be summarized by two points. First, "(c)omplex systems improve when the best performers play by the same rules over extended periods of time. As systems improve, they equilibrate and variation decreases" (Gould, 1996, p. 112, italics removed). Second, "(a)s play improves and bell curves march toward the right wall, variation must shrink at the right tail" (Gould, 1996, p. 116, italics removed). According to Gould, the variation in batting averages under these bell curves expands and contracts over time around a "rock-stable" mean of .260 (Gould, 1996, p. 99). Variation shrinks, and extreme averages like .400 go away. "The entire game sharpened its standards, narrowed its ranges of tolerance, and therefore limited variation in performance as all parts of the game climbed a broader-based hill toward a much narrower pinnacle" (Goul d, 1996, p. 113). Being a good-field-no-hit player no longer kept you in the game. Better hitters used to take advantage of the sloppier system, but pitching and fielding have improved over time as well, helping shrink the right tail toward the mean (Gould, 1996, p. 114). In other words, the left tail shrinks because fewer and fewer of the hitting dregs make it to the big leagues, and the right tail shrinks because of the overall improved play.

Aggregated individual batting averages measure the overall success hitters have against pitchers, and Gould believes the rises and falls in season mean averages over time signify only relative changes in batting performances, not real improvement or worsening of hitting (Gould, 1996, p. 118). According to Gould, in the game's early days, as it does today, the mean batting average hung close to .260, but back then it fell well below the right wall of human performance, and only a few players were able to excel enough to reach the wall. "(T)hese men stood so far above the mean that we measured their superior performances as 0. …

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