Paul M. Sommers

English

Research Papers in Economics

 
 
 
 
 
 
 
MEASURING PLAYER LOYALTY 
AMONG BASEBALL’S HALL OF FAMERS 
 
 
 
by 
 
 
 
Paul M. Sommers 
 
 
September, 2006 
 
 
MIDDLEBURY COLLEGE ECONOMICS DISCUSSION PAPER NO. 06-12 
 
 
 
 
 
 
 
Department of Economics 
Middlebury College 
Middlebury, Vermont 05753 
 
 
 
 
JEL #: L83, J63                                                                                                                                              2 
                                                                                                                                               
 
MEASURING PLAYER LOYALTY 
AMONG BASEBALL’S HALL OF FAMERS 
 
 
 
 
  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.”  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
i
i G
1
, where  i G  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 six years for two teams and another player who played two years 
each for six different teams.  In the former case, the Herfindahl index would be .5; in the latter, it 
would be .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).  
For the inductees who retired between 1940 and 1999, there was no statistically discernible 
difference (p = .24) between the average H of batters ( batters H  = .755, n = 72) and that of pitchers                                                                                                                                               3 
                                                                                                                                               
 
( pitchers H   = .686, n = 31).  All Hall of Famers who retired between 1940 and 1975, however, 
were more loyal to their teams ( before H  = .785) than were the 37 inductees who retired after 1975 
( after H  = .643) [p = .008].  The difference before and after 1975, a watershed year for free 
agency in Major League Baseball, arises not because batters were less loyal in the post-1975 
period ( before H  = .777,  after H  = .713, p = .311), but because player loyalty as measured by the 
Herfindahl index significantly declined for Hall of Fame pitchers ( before H  =.804,  after H  = .498,  
p = .001).  There was no difference between batters and pitchers in the 1940 to 1975 period 
( batters H  = .777,  pitchers H  = .804, p =.691).  But pitchers were less loyal than batters since 1975 
( batters H  = .713,  pitchers H  =.498, p = .012). 
  Free agency has had an effect on the stability of baseball’s Hall of Fame players.  During 
their careers, Hall of Famers moved more often after free agency than before.  The application of 
the Herfindahl index presented here suggests that player loyalty since 1975 has diminished the 
most for Hall of Fame pitchers. 

MEASURING PLAYER LOYALTY AMONG BASEBALL’S HALL OF FAMERS

http://www.middlebury.edu/services/econ/repec/mdl/ancoec/0612.pdf

MEASURING PLAYER LOYALTY AMONG BASEBALL’S HALL OF FAMERS

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