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7-2011 Comparing Hall of Fame 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 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 . 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, 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, led the league in home runs, though never hitting more than 38. In 1998, 17 players 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 (AL) and (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, , 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. 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 . 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, , the power-hittingfirst-baseman for the 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. Prado and Howard are dramatically dif- ferent in terms of skills they offer their team, and its hard to compare their 2010 player v a l u e s using head-to-head statistics.

DOI: 10.2202/1559-0410.1337 2 Kvam: Comparing Baseball Players Using MVP ranks

American League National League Josh Hamilton, T e x a s 358 Joey V o t t o , 443 , 262 , St. Louis 279 Robinson Cano, New Y o r k 229 Carlos Gonzalez, 240 Jose Bautista, T o r o n t o 165 Adrian Gonzalez, San Diego 197 P a u l Konerko, 130 , Colorado 132 , T a m p a Bay 100 , Philadelphia 130 , T a m p a Bay 98 Aubrey Huff, San F r a n c i s c o 70 , Minnesota 97 Jayson W e r t h , Philadelphia 52 Adrian Beltre, 83 Martin Prado, A t l a n t a 51 Delmon Y o u n g , Minnesota 44 Ryan Howard, Philadelphia 50 , T e x a s 22 Buster P o s e y , San F r a n c i s c o 40 , T a m p a Bay 21 , St. Louis 32 CC Sabathia, New Y o r k 13 Brian Wilson, San F r a n c i s c o 28 Shin-Soo Choo, Cleveland 9 , Cincinnati 26 , New Y o r k 8 , Milwaukee 19 F e l i x Hernandez, 6 , W a s h i n g t o n 18 , Seattle 3 , Philadelphia 12 , Minnesota 2 , Florida 12 , Kansas City 1 , St. Louis 12 Mark T e i x e i r a , New Y o r k 1 , A t l a n t a 11 Brian McCann, A t l a n t a 9 , W a s h i n g t o n 9 Ubaldo Jimenez, Colorado 7 David W r i g h t , New Y o r k 3 , Milwaukee 2 Josh Johnson, Florida 2 , San Diego 2

T a b l e 1: 2010 Most V a l u a b l e Player Ranks and P o i n t s .

3 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19

2 The Model

Our goal is to compare top positionplayers from different eras using their MVP rankings. W e treat the rank as the quantile outcome out of N players that compete for rankings on a y e a r l y basis. Although the n u m b e r of teams and players have increased through the y e a r s , w e will treat N as a constant, based on how w e perceivethe populationof candidates. F o r example, if w e consider only players who achieve 500 or more plate appearances (which is the minimum n u m b e r required to qualify for a batting title), w e are limited to about 150 players from the combined leagues. However, if w e consider all the players throughout the system who are competing for a major league position,N will bein the thousands. W e will focus on this problem more in the next section. Most position players in the MLB Hall of F a m e (after 1931) have received MVP v o t e s in ten or more y e a r s of their career, and achieved top-5 rankings in four or more of those y e a r s . , as the extreme, w a s v o t e d MVP only once, but landed in the top 5 an amazing 13 times, and received v o t e s in 17 y e a r s of his long, historic career. A t the other end of the spectrum, second-baseman , a controversial Hall of F a m e selection, received MVP v o t e s in only t w o y e a r s , placing 8th and 23rd. In our model, w e consider a maximum m = 20 y e a r career for any given player, knowing that few players could actually performat the major league level for even half that time. Suppose a player receives v o t e s in k different y e a r s of his career. F o r any of the k y e a r s in which the player receives MVP v o t e s , w e treat his MVP rank as a quantile for some unobserved quality statistics that could beused to judge the merit of the player’s o v e r a l l performance.F o r any of the m−k y e a r s in which the player does not receive v o t e s , w e treat the quality statistic as censored - specifically, it w o u l d be type-II left c e n s o r i n g , since only the upper percentilesof the quality statistic are observed. T o illustrate, w e will use a classic example of t w o baseball legends and their legion of fans who have debated the same question for fifty y e a r s : Who is better,Willie or Mick? , who played center field for the New Y o r k Giants came up to the major leagues in 1951, winning the NL rookie-of-the-year a w a r d beforeentering military service during the Korean W a r . He returned for his first full season in 1954, winning the NL MVP. His cross-town rival also broke in with the New Y o r k Y a n k e e s in 1951 and w a s constantly compared to Mays (even after the Giants moved

DOI: 10.2202/1559-0410.1337 4 Kvam: Comparing Baseball Players Using MVP ranks to San F r a n c i s c o in 1958) becausebothoutfielders w e r e considered to be the bestplayers in their respective league. Mays w o n t w o NL MVP a w a r d s and received v o t e s in 15 y e a r s between 1954 and 1971. Mantle w o n the AL MVP three times and received v o t e s in 14 y e a r s of his spectacular but injury-plagued career between1951 and 1968. F o r a given player, let v1,···, vk represent the set of MVP ranks achieved during his career. These ranks correspond to the top k unobserved quality measurements Xm−k+1:m,···, Xm:m from a player’s m = 20 y e a r career. The order statistic Xi:m designates the th i smallest observation from the sample (X1,···, Xm). The remaining order statistics (X1:m,···, Xm−k:m) correspond to y e a r s in which the player did not receive MVP v o t e s from the BWAA, possiblybecausethe player w a s not even in the major leagues. The observed quantiles of Xm−k+1:m,···, Xm:m are a simple function of the ordered MVP ranks: N−v+ 1 r = i:m , i = m−k + 1,···, m. (1) i:m N−1

0 1 2 3 4 5 6 7 8 9 10 11 12 13

-0.5

-1

-1.5

-2

-2.5

-3

-3.5

Figure 1: Ordered v a l u e s of -log(v+1), where v is player MVP rank. Three players are plotted across 15 y e a r s : Willie Mays (dashed line), Mickey Mantle (solid line) and Duke Snyder (dotted line).

Figure 1 graphically shows how Mantle, Mays and the other cross- town Hall of F a m e center fielder (for the Brooklyn Dodgers) Duke Snyder

5 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19 compare in terms of MVP ranks. T o make the differences clear, the figure plots the ordered v a l u e s of −ln(v + 1), so each player’s highest rank appear at the left side of the graph and the logarithm causes the top ranks to appear more separated compared to lower ranks. The graph suggests that Mickey Mantle had a brilliant o v e r ten y e a r s , but Willie Mays proved to be bettero v e r a longer periodof time. Duke Snyder, an already-established center field all star when Mantle and Mays broke into the big leagues, had several productive y e a r s with the Dodgers, but his career beganto fade in 1956, just when the careers of Mays and Mantle started booming. Without further refining the model, the player statistics w e propose to use (rm−k+1:m,···, rm:m) are insufficient for effective comparisons between players (even if N is specified). T o make such comparisons possible,w e assign each Hall of F a m e player a parameter θto represent a quality characteristic. Suppose the distribution of the quality statistic for a baseline player is des- ignated F (x). F o r a player with parameter θ, the distribution G(x) of the quality statistic is related to the baseline player using the link function

G(x) = F (x)θ. (2) This is a common link used in semi-parametric analysis and acceler- ated life testing, although it w o u l d bemore common to link survival functions (1 −G(x)) = (1 −F (x))γ, which makes it easier to relate hazard functions. In this case, the link based on the cumulative distribution function is more convenient in forming maximum likelihood estimators in the following sec- tion. Because w e are only observing quantile v a l u e s , without loss of gener- ality, w e can assign F (x) = x, with 0≤x≤1, so that G(x) is the cumulative distribution function for a Beta(θ,1) distribution. Larger v a l u e s of param- eter θreflect higher quality characteristics for the player. This is a semi- parametric analysis, becausethe distribution of the quality measurement is arbitrary, but the link function is specified with an unknown parameter θ.

3 Estimating the Quality Characteristic

F o r a given player w e observe his highest k quantiles (rm−k+1:m,···, rm:m) out of m y e a r s , and m−k of the smallest quantiles are left censored. In most y e a r s , there are no more than 30 players in either league that receive MVP v o t e s , and sometimes fewer than 20. With the t y p e - I I left censored v a l u e s ,

DOI: 10.2202/1559-0410.1337 6 Kvam: Comparing Baseball Players Using MVP ranks

w e essentially have upper boundsfor the missing quantiles, with ri:m≤(N− 30 + 1)/(N + 1), where i = m−k + 1,···, m. T o estimate θ, w e treat the k observed quantiles as observations from the Beta(θ,1) distribution, and m−k unobserved quantiles as right-censored (corresponding to the left-censored quality statistic) at the upper quantile q = (N−29)/(N +1).Finally, our c h o i c e of N will affect model fit, although it will not affect the orderings of the different v a l u e s of θbetweendifferent Hall of F a m e players. F o r example, w e could c h o o s e N so that q w o u l d beat approximately 0.95, meaning that the top 5% of major league players receive MVP v o t e s in any given y e a r . This is satisfied with N = 600. If q increases to 0.99, w e need N = 3000. By c h o o s i n g m = 20, w e are considering a large populationof ballplayers at v a r i o u s stages of their potentialcareer, including time in the minor leagues, or even early retirement. As a consequence, this c h o i c e requires that q will beo v e r 0.95, so N will belarger than 600. Out of the 73 Hall of F a m e positionplayers, the average number of y e a r s a player receives MVP v o t e s is 9.6, or roughly half of their potential 20-year career. Our goal is to c h o o s e q (and N) so that the estimate for θ corresponds to a distribution Gθwith median xˆ 0.50 which is as close to q as possible. That is, when a v e r a g e d across θfor the 73 players, a player has a 50% c h a n c e of receiving MVP v o t e s in any given y e a r . This happens to match up approximately at q = 0.99 (N = 3000) where the a v e r a g e of these 73 medians is 0.987. F o r purposes of this study, then, w e will treat q = 0.99 and N = 3000. Implicit with this model assumption is that, on a v e r a g e , 50% of the player rankings will begreater than 0.99, or in other w o r d s , for a randomly c h o s e n Hall of F a m e player, they are expected performin the top 1% during their best10 y e a r s in baseball. T o estimate θ, w e apply the method of maximum likelihood. The likelihood function, based on a m = 20 y e a r career of a player with quality characteristic θcan beexpressed as

m∏−k ∏k θ θ−1 L(θ) = q θrm−i+1:m, (3) j=1 i=1 where ri:m = (N−vi:m + 1)/(N−1). In (3), L(θ) is based on k observations from a Beta(θ,1) distribution along with m−k left censored observations at q. The maximum likelihood estimator (MLE) for θhas a convenient closed form:

7 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19

−k θˆ = ∑ . (4) − k (mk) log(q) + i=1 log(rm−i+1:m) Based on the Fisher information, w e can estimate the standard deviation of θˆ as

( ( ))− ∂2 1/2 k σˆ ≈ −E log L(θ)|ˆ = . (5) ∂θ2 θ θˆ With a gage of uncertainty, w e have a compelling w a y to rank Hall of F a m e baseball players according to their estimated quality characteristic. As an example, if w e use N = 3000, the Mays v e r s u s Mantle debate is summarized from (4) and (5) as

θˆ σ ˆ Willie Mays 185.2 12.3 Mickey Mantle 139.4 10.0

According to our model, Willie Mays is the superior player, mostly because Mantle shows a quicker decline in performanceafter their careers peaked. Both players ranked in the top six in MVP v o t i n g in their bestnine y e a r s , but Mays continued in the top six for another three y e a r s . It is w e l l known, too, that Mantle suffered from debilitating injuries that hampered him throughout his career, while Mays w a s relatively injury free. The only debate left in this case is how good Mantle w o u l d have beenif he had not tore the cartilage in his right knee while fielding a ball in the 1951 W o r l d Series game against the New Y o r k Giants. Ironically, the ball w a s hit b y Willie Mays.

4 Goodness of Fit

Before giving further credence to the quality estimator, w e will investigate the goodness of fit for the proposed model in (2), based on the Beta distribution. W e test this model in t w o steps. The first step is to see if the observed v a l u e of k is consistent with what the model predicts. If the discrepancies are small enough, o v e r a l l , w e will assume the k observed quantiles are from the truncated Beta(θ,1) distribution, with the m−k missing observations being less than q = 0.99 and not included in the truncated distribution. By doing

DOI: 10.2202/1559-0410.1337 8 Kvam: Comparing Baseball Players Using MVP ranks the test in t w o steps, w e make the goodness-of-fit test simple to compute and easier to understand. F o r all the players in the data, the model does w e l l in matching the actual n u m b e r of times the player received MVP v o t e s (k) and the expected n u m b e r according to the model (Ek). Out of 73 players, only four players have a difference |Ek−k| greater than one: Joe DiMaggio (k=12, Ek=13.7), Willie Mays (k=15, Ek=16.9), Mike Schmidt (k=12, Ek=13.5), and (k=9, Ek=10.2). In each of these cases, the player w a s expected to receive v o t e s in more y e a r s than they actually did, due to the high rankings they received during their prime y e a r s . In the next step, b y treating the observed k as fixed for each player, w e examine the model fit for the truncated Beta(θ,1) distribution. F o r a given player with quality parameter θand m = 20 y e a r s of service, w e have m independent quantile ranks r = (r1,···, rm), of which only the top k are observed: (rm−k+1:m,···, rm:m). Based on the model in (2), the m v a r i a b l e s in r are generated from a Beta(θ,1) distribution, and the elements of r in the set (rm−k+1:m,···, rm:m) represent the k largest order statistics from r. T o test the proposed link model in (2), w e make a convenient as- sumption that the k upper quantiles are actually the observations from the truncated Beta(θ,1) distribution, where only quantiles greater than q are ob- served. T o do this, w e employ the Cram´er-von-Mises test statistic ∫ 2 = (Hk(t)−H0(t)) dH0(x). (6)

In this case, Hk is the empirical distribution function based on the upper k observed player quantiles, and H0 is the left-truncated Beta(θ,1) distribution:

tθ−qθ H (t) = , q≤x≤1. (7) 0 1−qθ F o r every Hall of F a m e player, w e computed the MLE for θand the Cram´er-von-Mises test statistic ψ. W e approximated ψb y treating θas a known parameter, so the computation of the test statistic is more straight- forward (see Chapter 6.3.2 in Kvam and Vidakovic (2008), for example). F o r players who appeared in six or more MVP lists, Cs¨orgoand F a r a w a y (1996) showed the approximation to the Cram´er-von-Mises test statistic

9 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19 ( ) 1∑m 2j−1 2 = + H (r )− (8) 12k 0 i 2k j=m−k+1 is sufficiently precise, for all practical purposes. Out of the 73 players in the data, eight goodness of fit tests produced a p-value smaller than 0.05, and t w o players in particular are associated with test statistics with p-values close to 0.01: Eddie Murray and Joe DiMaggio. Thirteen out of 73 tests have a p-value smaller than 0.10, which is not un- expected if the model is correct. This suggests that o v e r a l l , the model fit is adequate.

5 Comparing Hall of F a m e Players

T o compare Hall of F a m e players, w e have stratified players into the fielding positionsthey w e r e most t y p i c a l l y associated during their career. In Figure 2, the quality statistic θˆ (in terms of a 95% confidence interval) is plotted for nine Hall of F a m e from the modern era. The same 95% confi- dence intervals are plotted for Hall of F a m e members who played first base (Figure 3), second base (Figure 4), third base (Figure 5), (Figure 6) and outfield (Figure 7). This section contains only a brief commentary on the results shown in these figures, and also comments on how rankings are affected b y the model in 2.

5.1 In Figure 2, the estimate for the quality statistic shows that Y o g i Berra, who played for the from 1946 to 1963, is unrivaled among catchers. Berra received MVP v o t e s in 15 y e a r s , winning the a w a r d three times, and having a top five rank in seven of those 15 y e a r s . In the next section, w e will consider the merits of great players who are on the ballot for Hall of F a m e v o t i n g . Because there are so few catchers on this list (at least catchers who stand a reasonable c h a n c e of election) w e will mention , who stands out among this group. His score of θˆ = 56.3 clusters him with and , among the top catchers of all time. The graph does not include Gabby Harnett, also among the top all-time catchers, who played for the between1922 and 1940.

DOI: 10.2202/1559-0410.1337 10 Kvam: Comparing Baseball Players Using MVP ranks

Hall of Fame: Catcher

Ferrell, Rick

Lombardi, Ernie

Lopez, Al

Fisk, Carlton

Campanella, Roy

Carter, Gary

Dickey, Bill

Bench, Johnny

Berra, Yogi

0 20 40 60 80 100 120 140 160 180 Theta

Figure 2: 95% confidence intervals for quality parameter θof Hall of F a m e Catchers

5.2 First Base Figure 3 shows the interval estimates of quality for seven out of eight Hall of F a m e first basemen. It does not include the estimate for (θˆ = 297.5). Because Stan Musial’s career statistics o v e r s h a d o w all of the other 1B players, it is difficult to compare the other players when the graph is scaled to include Musial’s score. Musial not only w o n MVP three times, but w a s runner-up four times and received MVP v o t e s in 18 seasons. Since the Hall of F a m e v o t i n g took its current form after 1930, w e are not able to include t w o of the greatest 1B to play the game: Jimmie F o x x and .

5.3 Second Base Figure 4 shows interval estimates of quality for eleven Hall of F a m e second basemen. While the high score of is noteworthy, the figure shows in a clear w a y how Bill Mazeroski (previously mentioned as a contro- v e r s i a l selection for the Hall of F a m e b y the V e t e r a n ’ s Committee in 2001) scores belowthe other second basemen in this group. Mazeroski w a s never seriously considered b y the sportswriters when it came to MVP v o t i n g , and he landed in the top 10 only once in his career, ranking 8th in 1958 NL v o t - ing. The V e t e r a n ’ s Committee placed more w e i g h t on Mazeroski’s fielding

11 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19

Hall of Fame: 1B

Perez, Tony

Cepeda, Orlando

Garvey, Steve

Greenberg, Hank

McCovey, Willie

Murray, Eddie

Mize, Johnny

0 20 40 60 80 100 120 Theta

Figure 3: 95% confidence intervals for quality parameter θof Hall of F a m e First Basemen abilities and his post-seasonperformance,and specifically on his dramatic game-ending that w o n the 1960 W o r l d Series for the Pirates. Because the data analysis is limited to players from the past 80 y e a r s , other great 2B in the Hall of F a m e are left out, including , , and .

5.4 Third Base Figure 5 shows interval estimates of quality for eleven Hall of F a m e third basemen. Mike Schmidt, who played for the Philadelphia Phillies between 1972 and 1989, w a s not recognized among statistical leaders becausehe w a s a home run leader in an era when not many home runs w e r e hit. He led the NL in home runs eight times, but hit more than forty in only one of those eight y e a r s . During the steroid era (1998 - 2003) it w a s not uncommon for 10 or more major league batters to hit 45 or more home runs in a given y e a r . This aspect of the ranking data shows an advantage o v e r using batting statistics, which can v a r y from y e a r to y e a r and make player comparisons difficult.

DOI: 10.2202/1559-0410.1337 12 Kvam: Comparing Baseball Players Using MVP ranks

Hall of Fame: 2B

Mazeroski, Bill Schoendienst, Red Sandberg, Ryne Herman, Billy Morgan, Joe Doerr, Bobby Gordon, Joe Robinson, Jackie Carew, Rod Fox, Nelie Gehringer, Charlie

0 20 40 60 80 100 120 Theta

Figure 4: 95% confidence intervals for quality parameter θof Hall of F a m e Second Basemen

Hall of Fame: 3B

Hack, Stan

Kell, George

Boggs, Wade

Molitor, Paul

Mathews, Eddie

Brett, George

Killabrew, Harmon

Robinson, Brooks

Schmidt, Mike

0 20 40 60 80 100 120 140 Theta

Figure 5: 95% confidence intervals for quality parameter θof Hall of F a m e Third Basemen

13 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19

5.5 Shortstop Figure 6 shows interval estimates of quality for eleven Hall of F a m e short- stops. In contrast to the 3B graph, the t w o w e a k e s t on this list are recent inductees: and Robin Y o u n t . Cal Ripken, who also played at 3B and holds the consecutive game playing record, actually has a career that goes beyond20 y e a r s with the , and w a s a 19-time all-star. Despite this longevity, his MVP data is adequately modeled using the m = 20 y e a r career upperbound (with goodness-of-fit test statistic p-value larger than 0.10). In terms of future ballots, w e will see that will rank higher than Smith, Y o u n t and Ripken after he is inducted as a Hall of F a m e shortstop. Honus W a g n e r w a s the first shortstop inducted into the Hall of F a m e , and played between1897 and 1917, so is not included in this analysis.

Hall of Fame: SS

Smith, Ozzie Yount, Robin Vaughan, Arky Rizzuto, Phil Cronin, Joe Aparicio, Luis Ripken, Cal Appling, Luke Boudreau, Lou Banks, Ernie Reese, Pee Wee

0 20 40 60 80 100 120 140 Theta

Figure 6: 95% confidence intervals for quality parameter θof Hall of F a m e Shortstops

5.6 Outfield Figure 7 shows interval estimates of quality 27 Hall of F a m e outfielders (not distinguishing betweenleft, center or right field). The graph shows off the great career achievements of Hank Aaron and T e d Williams, t w o of the great- est players in baseball history. Undoubtedly, the particular order implied b y

DOI: 10.2202/1559-0410.1337 14 Kvam: Comparing Baseball Players Using MVP ranks each outfielder’s θˆ statistic will not beagreeable to all experts, and serves to illustrate how our model might performdifferently compared to other mod- els used for ranking player achievement. As an example, T o n y Gwynn, who played for the San Diego P a d r e s from 1982 to 2001, ranks higher than , who many consider to bethe greatest lead-off hitter in baseball history. Henderson w o n the AL MVP in 1990 when he led the Oakland A t h - letics to the W o r l d Series, but Gwynn received MVP v o t e s in more y e a r s than Henderson (12 v e r s u s 8). This suggests that longevity is more highly v a l u e d in this model. The lowest ranked OF here is , who w a s the first black player allowed to play in the AL, following who played in the NL. They bothdebuted in 1947, often playing in front of hostile crowds. His major league career w a s solid if not spectacular, and he received MVP v o t e s in four of his y e a r s with the . He w a s inducted into the Hall of F a m e b y the V e t e r a n s Committee in 1998. , who will beeligible for Hall of F a m e v o t i n g in a future y e a r , w o n the NL MVP seven times. His quality estimate of θˆ = 204 will rank him above all the modern Hall of F a m e outfielders except T e d Williams and Hank Aaron. Along with Babe Ruth, there are other exceptional Hall of F a m e outfielders who played in an earlier era and are not included in this analysis, including T y Cobb, T r i s Speaker, and .

6 Discussion

This model based on MVP ranks has several advantages o v e r traditional regression models that employ a profusion of batting data. Batting statistics can bemisleading becauseso many factors that influence them are ancillary to the actual player’s performance,especially the year-to-year variability in league offense. There are v a l i d criticisms of MVP balloting, but despite the apparent flaws in the system, this model produces a useful link between v o t i n g outcomes from different y e a r s , and implies a fair manner in which to make player comparisons across different eras. By sorting players into fielding positions,w e can see that the threshold for greatness is different for different positionplayers. The median v a l u e for θˆ for the positionsare 46.24 for Catcher, 50.83 for 2B, 64.37 for SS, 66.96 for 3B, 67.42 for 1B, and 69.13 for OF. The data suggest that catchers and second basemen can bev o t e d into the Hall of F a m e without the same frequency of

15 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19

Hall of Fame: OF

Doby, Larry Kiner, Ralph Averill, Earl Ashburn, Richie Williams, Billy Medwick, Joe Slaughter, Enos Henderson, Rickey Snider, Duke Rice, Jim Dawson, Andre Puckett, Kirby Winfield, Dave Brock, Lou Stargell, Willie Gwynn, Tony Clemente, Roberto Yastrzemski, Carl Ott, Mel Jackson, Reggie DiMaggio, Joe Kaline, Al Mantle, Micky Robinson, Frank Mays, Willie Williams, Ted Aaron, Hank

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 Theta

Figure 7: 95% confidence intervals for quality parameter θof Hall of F a m e Outfielders

MVP v o t e s received b y other positionplayers. This is important to note in comparing current Hall of F a m e players as w e l l as players that will qualify for Hall of F a m e election in the future. Figure 8 shows the quality estimate for the top 15 players on the 2011 Hall of F a m e ballot. This is a helpful graph to rank potentialinductees, especially 1B and OF becausethey comprise a majority of the players. As an example, w e can gage Herold Baine’s MVP v o t e s b y noting how far behind he lags from other outfielders such as Larry W a l k e r or Dave P a r k e r . F o r other positionssuch as 2B, SS and 3B, it will behelpful to compare their quality estimates to some recent Hall of F a m e inductees, which can beused to benchmarkquality scores b y position. Currently, there are no catchers ranked high on the 2011 ballot, but w e discussed Mike Piazza’s statistics in the previous section. Figure 9 plots the quality estimates for six shortstops, including three current Hall of F a m e members (Smith, Y o u n t and Ripken) along with t w o shortstops on the 2011 ballot (Larkin and T r a m m e l l ) and current player Derek Jeter. Note, Jeter’s v a l u e can only rise if he receives MVP v o t e s in his remaining active y e a r s , but few expect him have future y e a r s in which he will behighly ranked. If Ozzie Smith represents a benchmarkfor gaining

DOI: 10.2202/1559-0410.1337 16 Kvam: Comparing Baseball Players Using MVP ranks

2011 Hall of Fame Ballot

Baines, Herold

Martinez, Edgar

Larkin, Barry

Trammell, Alan

Raines, Tim

Alomar, Roberto

Mattingly, Don

Murphy, Dale

Gonzalez, Juan

Walker, Larry

McGriff, Fred

Parker, Dave

Palmeiro, Rafael

McGwire, Mark

Bagwell, Jeff

0 20 40 60 80 100 Theta

Figure 8: 95% confidence intervals for quality parameter θof players on 2011 Hall of F a m e Ballot

17 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19

Comparison of SS

Smith, Ozzie

Larkin, Barry

Trammell, Alan

Yount, Robin

Ripken, Cal

Jeter, Derek

0 20 40 60 80 100 120 Theta

Figure 9: 95% confidence intervals for quality parameter θof Shortstops. Hall of F a m e players are plotted with checkerboard pattern, and other players with solid bar. entry into the Hall of F a m e for shortstops, then Larkin, T r a m m e l l and Jeter compare w e l l . This need not bethe case, of course. It is not clear that Larkin or T r a m m e l l belongin the Hall of F a m e group in Figure 6, but Jeter’s inclusion is hardly debatable using these metrics. Figure 10 shows the quality estimates of Hall of F a m e 2B Sandburg, Morgan and Carew along with (on 2011 ballot), Jeff Kent and (on future ballots). F r o m Figure 4, w e saw that Sandberg represents one of the lowest 2B ratings of any Hall of F a m e 2B outside Bill Mazeroski. This fact does not support Biggio’s case for Hall of F a m e in- duction. Kent and Alomar, however, compare w e l l to , who w a s inducted easily in 1990. Figure 11 shows quality estimates for 3B, including t w o current Hall of F a m e players, W a d e Boggs and . Alex Rodriguez, still playing and likely to receive MVP v o t e s in the next y e a r s , has a quality rating that far exceeds the rest of the group and w o u l d place him at the top of Hall of F a m e 3B in Figure 5. is included only becausehis recent death has helped catalyze discussion about his Hall of F a m e c h a n c e s , though his v o t i n g periodis long passed and induction w o u l d require getting sufficient v o t e s from the V e t e r a n s Committee. Edgar Martinez, known primarily as a for the , is often thought to bea 1B, since he played there sporadically during the second half of his career. F o r the purposes of Hall of F a m e v o t i n g , however, he will beconsidered b y the BWAA as 3B.

DOI: 10.2202/1559-0410.1337 18 Kvam: Comparing Baseball Players Using MVP ranks

Comparison of 2B

Biggio, Craig

Sandberg, Ryne

Kent, Jeff

Alomar, Roberto

Morgan, Joe

Carew, Rod

0 10 20 30 40 50 60 70 80 90 Theta

Figure 10: 95% confidence intervals for quality parameter θof Second Base- men. Hall of F a m e players are plotted with checkerboard pattern, and other players with solid bar.

Comparison of 3B

Martinez, Edgar

Santo, Ron

Boggs, Wade

Brett, George

Jones, Chipper

Rodriguez, Alex

0 20 40 60 80 100 120 140 160 Theta

Figure 11: 95% confidence intervals for quality parameter θof Third Base- men. Hall of F a m e players are plotted with checkerboard pattern, and other players with solid bar.

19 Journal of Quantitative Analysis in Sports, Vol. 7 [2011], Iss. 3, Art. 19

While no player ranking method can bedefinitive, these results may help to clear up debates and controversies surrounding player compar- isons, especially for if the players beingcompared did not have overlapping careers. The graphs in this paper serve as the bestsummary of player eval- uation that this analysis can glean from 80 y e a r s of BWAA v o t i n g data.

References

[1] Berry, S. M., Reese, S. P. and Larkey, P. D. (1999) “Bridging Different Eras in Sports” Journal of the A m e r i c a n Statistical Association, 94, No. 447, 661-676.

[2] S. Cs¨orgo,S. and J.F. F a r a w a y , J. F. (1996) “The exact and asymp- totic distributions of Cram´er-von Mises statistics”, Journal of the R o y a l Statistical Society, Ser. B 58 (1), 221-234.

[3] Kvam, P. H. and Vidakovic, B. (2008) Nonparametric Statistics with Applications to Science and Engineering, Wiley, New Y o r k .

DOI: 10.2202/1559-0410.1337 20