Defining athletes by statistics: the magical .300 batting average
In sports, athletes are often defined by their performance statistics. Sprinters are defined by their best time in a particular race, soccer players are defined by the number of goals or assists, and basketball players are defined by the number of points they score per game.
In the sport of baseball, the traditional method of measuring batting performance is the batting average defined by the number of hits divided by the number of opportunities. Generally, a .300 batting average is thought to be a benchmark for hitting quality and players really desire a season batting average exceeding .300.
In a recent New York Times article Alan Schwarz talks about research by several University of Pennsylvania professors about the psychological importance of hitting .300.
This phemomena can be demonstrated by looking at the season batting averages of all baseball hitters in the past 50 seasons. I collected the batting averages for all regular players since 1960 who had at least 300 opportunities to bat. For each player, I rounded the batting average to three decimal spaces as commonly done in professional baseball. The figure displays a line graph of the frequencies of the batting averages between .290 and .310.
This graph shows the importance of the .300 mark in baseball. Batting averages slightly smaller than .300 are unlikely but a batting average of .300 is very likely. Athletes might like to say that the performance statistics are not important, but there are patterns in this data that suggest otherwise.
One of the most famous baseball players in history was Mickey Mantle who was a star when I was growing up. In his last season, Mantle had difficulty hitting due to injuries and his batting average was .237, dropping his career batting average to .298. The fact that his career average dipped below was supposedly Mickey Mantle "biggest regret" in his baseball career.
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Philip Howard
One possible explanation is managerial decisions and players' desires towards the end of the season. The majority of teams will be out of contention for the playoffs by the last week or two of the season. Players who are just below .300 will lobby the skipper for continued opportunities to bat, in the hope of raising their average. Players who are at .300 or just above will often be all too happy if a reserve or upcoming young player bats in their place, as a single game where they play and get 0 or 1 hits in 4 plate appearances could cost them their .300. So, if there is prestige associated with hitting .300, and there are low-cost ways to preserve an existing .300 or strive to raise an average in the mid-high .290s, you have a practical explanation for this very interesting pattern.
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cbb3
When, if ever, is a batter in baseball "due" for a hit or better? Does it hold, for example, that if a batter has a certain batting average and has not had a hit in a certain number of "at bats" that he is "due"?
Or, is this batter not any more "due" for a hit from one bat to the next? Or at least no more probable than his batting average?
And thus, what is the statistical significance of the "batting average"?
Thank you....
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