Measuring Player Loyalty among Baseball's Hall of Famers

By Sommers, Paul M. | Atlantic Economic Journal, March 2007 | Go to article overview

Measuring Player Loyalty among Baseball's Hall of Famers


Sommers, Paul M., Atlantic Economic Journal


JEL L83 * J63

When in April 2006 Johnny Damon (formerly of the Boston Red Sox) appeared in Yankee pinstripes, sportswriter Mike Lopresti lamented: "It's as if the mongoose went over to the rattlesnakes' side" ("Bitter reunion awaits Damon in Boston," The Burlington Free Press, May 1, 2006, p. 7B). The extent to which workers in general (and baseball's Hall of Famers in particular) remain loyal to their original employer is the empirical question that motivates this research note.

Heretofore, the Herfindahl index has largely been limited to studies of industrial concentration and market structure. Here, we consider its use as it applies to the distribution of games played for one or more baseball teams, given by the formula: H =[n.summation over (i=1)] [G.sub.i], where Gi is the fraction of games played for team i. When a ballplayer plays for one team for his entire career, H attains its maximum of 1.0. The value declines (hence, less player loyalty) with increases in the number of teams (during a player's career) and increases with rising inequality in the number of games played among any given number of teams. Unlike the Gini index, the Herfindahl index is sensitive not only to inequality of distribution, but also to fewness. The Gini index would be zero both for a player who played 6 years for two teams and another player who played 2 years each for six different teams. In the former case, the Herfindahl index would be 0.5; in the latter, it would be 0.1666.

The Herfindahl index (hereafter, H) is applied to all of baseball's Hall of Famers who played their last year between 1940 and 1999. Data on the number of games played for each team by each inductee were obtained from Thorn, Birnbaum and Deane's Total Baseball (2004). …

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