Quantifying the performance of baseball players has become popular with the advent of fantasy and rotisserie leagues, but analytical methods remain haphazard and results a matter of dispute. Rasch measurement offers a solution which I investigated with Elias Sports Bureau data on the Chicago Cubs. These data were used to construct conjoint linear measures of Cubs player abilities and the difficulties of the plays necessary to achieve success as a batter.
The counts of plays occurring during each player's at-bats for the 1990 season were transformed into a matrix of log-odds-ratios. Each ratio indicates the probability of a play occurring when the play was possible and there was no other successful outcome. Each row of the matrix represents a player. The row mean estimates a linear measure of his ability. Each column represents a method of getting on base, a play. The column mean estimates that play's difficulty. The origin of the measurement scale was set at the difficulty of getting on base.
The map lays out the abilities of the players and the difficulties of the plays. Singles are the most frequently occurring successful at-bat outcome so they are the least difficult play. Notice that the scoring value of the plays are out of order with their difficulties. A triple is harder than a home run, even though a home run has more scoring value.
Even the best batters are a quarter logit less able than getting on- base is difficult. Thus even the best batter has less than a 45% probability of getting on-base when coming to bat. Dawson and Sandberg are two of the best players in Major League Baseball, a fact supported by this analysis. On the other hand, among Cub fans the common but clearly misconceived opinion is that Grace was above average and better than Smith, and that Wynne, in the twilight of his baseball career, was below average. To the contrary, the map documents that Grace, Smith and Wynne were about the same in ability.
Such erroneous perceptions emphasize why quantitative analyses like this are needed in baseball - to shed light on circumstances that even the management of a professional baseball club find obscure.
Triple + 3.5 + + + + + 3.0 + + Home Run + + + 2.5 + + + + Double + 2.0 + Stolen Base + + + + 1.5 + Base on Balls + + + + 1.0 + + + Single + + 0.5 + Players: + + Most Proficient: + On Base + 0.0 + + Dawson Sandberg + + Villanueva Clark Dascenzo + -0.5 Dunston Grace Smith + Wynne Walton + Salazar + Girardi + Ramos + -1.0 Wilkerson Least Difficult: Least Proficient:
Baseball Plays and Players, P Fisher Rasch Measurement Transactions, 1991, 5:2 p.142
|Rasch Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
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