University of Richmond UR Scholarship Repository Math and Computer Science Faculty Publications Math and Computer Science 7-2011 Comparing Hall of Fame Baseball Players Using Most Valuable Player Ranks Paul Kvam University of Richmond, [email protected] Follow this and additional works at: http://scholarship.richmond.edu/mathcs-faculty-publications Part of the Applied Statistics Commons Recommended Citation Kvam, Paul H. "Comparing Hall of Fame Baseball Players Using Most Valuable Player Ranks." Journal of Quantitative Analysis in Sports 7, no. 3 (July 2011): Article 19, 1-20. doi:10.2202/1559-0410.1337. This Article is brought to you for free and open access by the Math and Computer Science at UR Scholarship Repository. It has been accepted for inclusion in Math and Computer Science Faculty Publications by an authorized administrator of UR Scholarship Repository. For more information, please contact [email protected]. Journal of Quantitative Analysis in Sports Volume 7, Issue 3 2011 Article 19 Comparing Hall of Fame Baseball Players Using Most Valuable Player Ranks Paul H. Kvam, Georgia Institute of Technololgy Recommended Citation: Kvam, Paul H. (2011) "Comparing Hall of Fame Baseball Players Using Most Valuable Player Ranks," Journal of Quantitative Analysis in Sports: Vol. 7: Iss. 3, Article 19. DOI: 10.2202/1559-0410.1337 ©2011 American Statistical Association. All rights reserved. Comparing Hall of Fame Baseball Players Using Most Valuable Player Ranks Paul H. Kvam Abstract We propose a rank-based statistical procedure for comparing performances of top major league baseball players who performed in different eras. The model is based on using the player ranks from voting results for the most valuable player awards in the American and National Leagues. The current voting procedure has remained the same since 1932, so the analysis regards only data for players whose career blossomed after that time. Because the analysis is based on quantiles, its basis is nonparametric and relies on a simple link function. Results are stratified by fielding position, and we compare 73 Hall of Fame players up to 2010. We also consider the players on the 2011 Hall of Fame ballot as well as other potential Hall of Fame candidates. The analysis is based on the method of maximum likelihood, and results are illustrated graphically. KEYWORDS: maximum likelihood estimators, quantiles, censoring, order statistics Author Notes: This work depended on the aid of Georgia Tech student Heeseung Moon, who compiled all of the vote data for this analysis. Kvam: Comparing Baseball Players Using MVP ranks 1 Introduction In this paper, w e propose a rank-based statistical estimator for comparing the performancesof top major league baseball (MLB) players who played in different eras, from 1931 to present. Rather than addressing popularbatting and pitching statistics and trying to predict how those statistics could be compared across different eras (see Berry, et al., 1999), w e instead focus on a simple o v e r a l l rank measure: The Baseball W r i t e r s Association of America (BWAA) Most V a l u a b l e Player (MVP) v o t e s . This analysis will belimited to positionplayers, and not pitchers. Although some pitchers are considered for the MVP a w a r d , many baseball writers consider the MVP a position-player a w a r d , leaving the Cy Y o u n g a w a r d as its pitching equivalent. There are v a l i d reasons to use MVP v o t e s for dictating how w e rank players from different eras in baseball. Mainly, baseball statistics have evolved dramatically throughout the y e a r s , and critics who compare players using such statistics risk confounding the effects of player v a l u e with the effects of his baseball era. F r o m 1974 through 1976, for example, Mike Schmidt led the league in home runs, though never hitting more than 38. In 1998, 17 players hit 38 or more home runs. Although the v o t i n g procedure has its drawbacks (discussed later), it serves as a consistent metric for how the public perceives player performanceand v a l u e across a wide range of y e a r s . Starting in 1931, the Baseball W r i t e r s Association of America began a w a r d i n g the MVP a w a r d to players in both the American League (AL) and National League (NL) using a w e i g h t e d scoring system. This is more or less the same form of v o t i n g that is used today, and replaced previous a w a r d s (Chalmers Award from 1911-1915, League Award from 1922-1929) which used an inconveniently c h a n g i n g criteria for a w a r d i n g the MVP. F o r example, the League Award listed only one player perteam on the ballot and American League players could only win the a w a r d one time. F o r this reason, our analysis of MVP v o t i n g is used only for players whose career blossomed after 1930, and as a consequence, leaves out arguably the greatest player of all time, Babe Ruth, who played his besty e a r s between1915 and 1933. T a b l e 1 shows the MVP v o t i n g for the 2010 season. There are 32 v o t e s in the NL, which is t w o for every franchise, and 28 for the AL. Josh Hamilton w o n the AL MVP a w a r d with 358 pointsbased on 22 (out of 28) first place v o t e s , four second place v o t e s and t w o fourth place v o t e s . In the NL, Joey V o t t o w o n with 443 pointsbased on 31 (out of 32) first place v o t e s and one second place v o t e . A first place v o t e is w o r t h 14 points,a second place v o t e is w o r t h 9 points,and v a l u e s decrease pointb y pointafter that. 1 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19 The thesis of this research is based on a simple assumption: no matter how many different statistics can beused to assess the v a l u e of a player on a year-to-year basis, their ultimate v a l u e is bestinterpreted through the v o t e s of experts, and the BWAA MVP a w a r d represents the besta v a i l a b l e ranking procedure of that ilk. The pointtotal, based on a w e i g h t e d ranking system, could bemodeled using nonparametric rank statistics, but w e focus only on the actual rank, treating the outcome as an observed percentileof a v a l u e statistic whose distribution is arbitrary outside its ability to correctly order players according to this unobservable measure of v a l u e . Because of the large variability of productivity betweenfielding positions,w e also focus on comparisons b y position. The data are comprised of 73 players who w e r e elected into the Hall of F a m e and includes players selected b y the V e t e r a n s Committee. All of the data w a s made a v a i l a b l e at Baseball-reference.com, which includes a com- prehensive list of inducted players and information about how each player ranked in MVP v o t i n g in any given y e a r . W e do not include members who played in the 1920s and earlier. The writers who v o t e rely on several sources of information, and mainly lean on batting statistics such as runs batted in, batting percentage, on-base a v e r a g e and slugging percentage. Other factors are considered, as w e l l , including fielding statistics, apparent leadership abilities, and perceived ability to performw e l l in clutch plays. However, rankings can bebiased with the affects of media exposure, home team favoritism, player reputation and writer ignorance. Because of these biases, some past MVP a w a r d s have been controversial, although most critics seem to bein agreement about a w a r d winners in most y e a r s . Discrepancies due to bias becomemore obvious in lower rankings such as candidates who score 50 or fewer points. This is partly due to the attention the writers heap on their first or second c h o i c e , and it might also be due to the difficulty in distinguishing t w o similarly qualified players who have different strengths and weaknesses. F o r example, Ryan Howard, the power-hittingfirst-baseman for the Philadelphia Phillies received only eight v o t e s from the 32 writers, but got an unexpected second and third place v o t e from Philadelphia writers. This placed him one point shy of Martin Prado, the A t l a n t a Braves second-baseman, who received 17 v o t e s , but none higher than fifth.