NAME: Pay for Play: Are Baseball Salaries Based on Performance? TYPE: Census (see descriptive abstract below) SIZE: 337 observations, 18 variables DESCRIPTIVE ABSTRACT: We consider as our population of interest the set of Major League Baseball players who played at least one game in both the 1991 and 1992 seasons, excluding pitchers. This dataset contains the 1992 salaries for that population, along with performance measures for each player from 1991. Four categorical variables indicate how free each player was to move to other teams. SOURCES: CNN/Sports Illustrated at http://www.cnnsi.com/baseball/mlb/historical_profiles/ _Sacramento Bee_, 10/15/91. _The New York Times_, 11/13/91, 2/23/92, 11/19/92. The Society for American Baseball Research (SABR) at ftp://skypoint.com/pub/members/a/ashbury/sabr/SALARIES /1992_salaries_baseball VARIABLE DESCRIPTIONS: Columns 1 - 4 Salary (in thousands of dollars) 6 - 10 Batting average 12 - 16 On-base percentage (OBP) 18 - 20 Number of runs 22 - 24 Number of hits 26 - 27 Number of doubles 29 - 30 Number of triples 32 - 33 Number of home runs 35 - 37 Number of runs batted in (RBI) 39 - 41 Number of walks 43 - 45 Number of strike-outs 47 - 48 Number of stolen bases 50 - 51 Number of errors 53 Indicator of "free agency eligibility" 55 Indicator of "free agent in 1991/2" 57 Indicator of "arbitration eligibility" 59 Indicator of "arbitration in 1991/2" 61 - 79 Player's name (in quotation marks) SPECIAL NOTES: Players' batting averages are calculated as the ratio of number of hits to the number of hits plus the number of outs. On-base percentage is the ratio of number of hits plus the number of walks to the number of hits plus the number of walks plus the number of outs. A batting average above .300 is very good; OBP above .400 is excellent. An RBI is obtained when a runner scores as a direct result of a player's at-bat. I believe that number of hits serves as a proxy for the amount of playing individuals did in the year. There is a statistic for number of games played available, but this statistic counts any entry into the game, even defensive participation for a single out, the same as participating for the entire contest. STORY BEHIND THE DATA: Baseball provides a rare opportunity to judge the value of an employee -- in this case, a player -- by standardized measures of performance. The question is, what are those characteristics worth? In addition, the economic principle of freedom of movement for employees can be measured; that is, what financial benefit does a person gain if he is able to change employers? Additionally, baseball fans may use their analysis of this dataset, in combination with other similar datasets, to gain insight into the salary structure in Major League Baseball. Additional information about these data can be found in the "Datasets and Stories" article "Pay for Play: Are Baseball Salaries Based on Performance?" in the _Journal of Statistics Education_ (Watnik 1998). PEDAGOGICAL NOTES: This dataset can be useful during a regression course using a text such as Neter, Kutner, Nachtsheim, and Wasserman (1996) or Christensen (1996). The data require a transformation of the response variable and detection and elimination of outliers. In addition, numerous model building techniques may be employed. Students interested in baseball will note the nice interpretations of some of the coefficients, especially the fact that some models point to the newest free agents' being paid less than in previous years, and the players' union winning a grievance over that issue. For more advanced students, the instructor may choose to discuss the interpretation of estimated parameters in models where a log-transformation (for example) is employed. In addition, with the large number of explanatory variables, making future predictions is a difficult issue. REFERENCES: Christensen, R. (1996), _Analysis of Variance, Design and Regression: Applied Statistical Methods_, New York: Chapman and Hall. Neter, J., Kutner, M. H., Nachtsheim, C. J., and Wasserman, W. (1996), _Applied Linear Statistical Models_ (4th ed.), Chicago: Irwin. SUBMITTED BY: Mitchell R. Watnik Department of Mathematics and Statistics University of Missouri-Rolla Rolla, MO 65409-0020 mwatnik@umr.edu