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A Statistician Reads the Sports Pages

Now that I have three children (ages 5, 7, and 9) in Little League, I enjoy seeing the differences between the current Little League experience and the one Iwent through 25 years ago. Some of the chants that the players use have changed; for example, I have not heard "we want a pitcher, not a bellyitcher," But there are some sayings that have stood the test of time; I still hear "A walk is as good as a hit." Although a walk is never better than a hit, there are times when it is as good as a hit. With no runners on base, a walk and a single are essentially equivalent. In general, a single is better than a walk. Despite this, I believe a walk,officiallyknown as "base on balls," is underrated in Major League baseball (MLB). Although, surely a walk is not, on average, as good as a hit, is it close? In this article I study the relative worth of different kinds of results for a hitter in Major League baseball. I develop a model that describes the relative worth of different results and use the model to address how appropriatelysome common measures capture the value ofa player. For example, is batting average a better measure of offensive contribution than slugging percentage? There is also a new measure, on base percentage plus slugging percentage, that is gaining acceptance among baseball fans as a quality measure of a hitter's offensive worth. I also examine how the relative worth of different offensive results have changed over time. There has been a lot of discussion lately about the extreme number of home runs being hit. In the recent offensive explosion in baseball, does the relative worth of a singleshitter change? Because of all the home runs has the value of a home run changed?