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That's because as the game gets more competitive and players and techniques improve, there are smaller differences among the top teams.

Closer to you, see Batting Average

Henry Chadwick, an English statistician raised on cricket, was an influential figure in the early history of baseball. In the late 19th century he adapted the concept behind the cricket batting average to devise a similar statistic for baseball. Rather than simply copy cricket's formulation of runs scored divided by outs, he realised that hits divided by at bats would provide a better measure of individual batting ability. This is because of an intrinsic difference between the two sports; scoring runs in cricket is dependent almost only on one's own batting skill, whereas in baseball it is largely dependent on having other good hitters in your team. Chadwick noted that hits are independent of teammates' skills, so used this as the basis for the baseball batting average. His reason for using at bats rather than outs is less obvious, but it leads to the intuitive idea of the batting average being a percentage reflecting how often a batter gets on base, whereas hits divided by outs is not as simple to interpret in real terms.

In modern times, a season batting average higher than .300 is considered to be excellent, and an average higher than .400 a nearly unachievable goal. The last player to do so, with enough plate appearances to qualify for the batting championship, was Ted Williams of the Boston Red Sox, who hit .406 in 1941, though the best modern players either threaten to or actually do achieve it occasionally, if only for brief periods of time. There have been numerous attempts to explain the disappearance of the .400 hitter, with one of the more rigorous discussions of this question appearing in Stephen Jay Gould's 1996 book Full House.

In Full House, Gould demonstrates how one type of statistical misconception leads to misunderstanding of important phenomena. The misconception is paying attention only to the "high score" or extreme value, when a continuous distribution of values exists (what Gould calls a "full house") and is what actually drives the phenomena.

The book focuses on two main examples of this misconception: the disappearance of the 0.400 batting average in baseball, and the perceived tendency of evolution towards "progress" making organisms more complex and sophisticated.

In the first example, Gould explains that the decline of the top batting average does not imply that there has been a decline in the skill of baseball players. Quite the contrary: he shows that all that has happened is that the variance of the batting average decreased as professional baseball got better and better, while the league average remained constant as the game rules changed - together causing the extreme value of the distribution--the best batting average--to decrease as well.



By laying out pros and cons we risk inducing people to join the debate, and losing control of a process that only we fully understand. - Alan Greenspan
by Migeru (migeru at eurotrib dot com) on Mon Jun 14th, 2010 at 03:55:50 PM EST
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