Hitters called “inconsistant” actually hit for the bell curve

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I was fascinated by this Wall Street Journal article examining baseball players’ batting averages because it featured my favorite player, Alan Trammell. Turns out Ichiro Suzuki, Babe Ruth, and Alan Trammell each had a long stretch in their careers where they hit > 10 points off of their batting average in either direction. The author called to their batting averages statistical anomolies.

I wanted to find out if the author was right, or if batting 10 points off your average is no big deal. Some examples of of the best, most consistent hitters:

  • Tony Gwynn: Hit within 10 points in only 3 of 20 seasons
  • Ted Williams: Only 6 of 19 seasons
  • ARod: 6 of 16

Actually, hitting within 10 points is actually not very common.

Then I applied some statistics to the author’s findings to see if he was “in the ballpark.” Let’s use Alan Trammell as an example. The solid blue line is the normal distribution of his expected batting average. The dots are his actual batting average each year. And the red line denotes 1 standard deviation on each side of his average.

Batting average: 1978-1993: .288, standard deviation: .039 (equal weighted). # seasons within 1 standard deviation: 11 of 17

A normal distribution would suggest 68% of his seasons within 1 standard deviation, and actually 65%, which is almost perfect. Trammell is not inconsistent. He’s actually as consistent as the normal distribution itself.

Here’s the same chart for Ichiro. In this case, Ichiro does better than the normal distribution, with 78% of his seasons within 1 standard deviation of his batting average.

These players are not inconsistent nor do they have statistical anomalies.  The range of 10 points is too small.

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