scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Pay, Productivity and Aging in Major League Baseball

TL;DR: This paper examined trends in player productivity and salaries as players age, finding that the best players peak about two years later than marginal players, and development and depreciation of ability appear to be more pronounced for players with the highest peak ability levels.
Abstract: Using panels of player pay and performance from Major League Baseball (MLB), we examine trends in player productivity and salaries as players age. Pooling players of all ability levels leads to a systematic bias in regression coefficients. After addressing this problem by dividing players into talent quintiles, we find that the best players peak about two years later than marginal players, and development and depreciation of ability appear to be more pronounced for players with the highest peak ability levels. Within-career variation, however, is less pronounced than between-player variation, and the talent level of players within a given quintile will typically remain lower than the talent level for rookies in the next higher quintile. Free agents are paid proportionately with their production at all ability levels, whereas young players' salaries are suppressed by similar amounts.

Summary (2 min read)

Introduction

  • After addressing this problem by dividing players into talent quintiles, the authors find that the best players peak about two years later than marginal players, and development and depreciation of ability appear to be more pronounced for players with the highest peak ability levels.
  • To illustrate the extent of the bias produced by traditional ordinary least squares (OLS), the authors run regressions estimating separate salary and performance paths for each talent quintile.

III. Data

  • The Baseball Archive database, version 5.3, edited by Sean Lahman (www.baseball1.com) contains season-by-season data on player performance, salaries, and many other variables that would serve as useful controls in a structural analysis.
  • There is also a large literature in personnel economics that studies reasons why salaries may vary from MRP under competition.
  • Production that increases with playing time, the use of OPS provides conservative estimates of within-career variation.
  • Failure to account for the positional differences would mean that shortstops and catchers would be significantly over-represented in the lowest ability quintile, while first basemen would be under-represented.

IV. Career productivity paths

  • 11 Indexed OPS controls for systematic changes in the league-wide OPS level at each position across seasons.
  • The use of player-seasons as the unit of measure, coupled with the longer career lengths of high-ability players, means that there are fewer players in the top (5th) quintile than in lower ones.
  • IV.A. Productivity paths with respect to Age.
  • The associated Chow F-statistic shows that the improved explanatory power of the model, from 0.2 to 40.0 percent of the variation in ability, is statistically significant.
  • While the authors previously observed an overestimated peak with the pooled regressions using age, the estimated peak from the pooled regression is vastly overestimated, at nearly 9 years of experience, due to earlier retirements of lower ability players.

V. Career Salary Paths

  • Table 4 shows annual arithmetic mean and geometric mean salaries in MLB each season from 1985 to 2005.
  • The intuitive structural break between 6 and 7 years of experience is used to indicate the approximate date of passage into free agency.
  • The regression results in Panel A of Table 5 show that experience alone explains over half of the indexed log-salary ratio (hereafter, “adjusted salary”) for players in their first six seasons, as their salaries increase with ability to contract.
  • 18 To solve the mechanical problem of below-average salaries yielding negative ln results, the authors adjusted to formula to represent percent salaries.

VI. Pay and Productivity

  • Due to the multiple adjustments and instances of indexing the authors have applied to the raw data to assist their analysis of the age trends in performance and in pay, it is unclear what the “efficient” ratio of their constructed estimators would be in an ideally functioning labor market.
  • For this reason, their discussion of pay and performance will be of a relatively heuristic nature.
  • While it is true that the structural causes of changes in the ratio may go undetected with this method, the magnitude of the change in ratio will still be correctly measured.
  • The increased variation in the data points in the right tail is likely due to reduced sample sizes in each conditional mean.
  • The ratio analysis both confirms earlier findings regarding the underpayment of inexperienced players, and adds the novel finding that MLB free agents are paid approximately their MRP not just on average, but throughout the talent distribution.

VII. Summary of findings and future plans

  • Quintile data permit exploration for differing rates of skill development and deterioration for players of different levels of peak ability, and comparison of the variation in a player’s ability across his career to the variation of talent within the league.
  • But as the ratios are only varying between 0.83 and 0.93, this says more about the stability of the ratios for the other quintiles than about erratic pay ratios for lower ability players.
  • Due to partial truncation of the left tail of the sample, young MLB players within a given ability quintile will debut at a productivity level similar to or above the peak ability level of players in the next lower quintile.
  • As in previous literature, the authors find that salaries of young players are suppressed below those of similarly talented older peers.
  • Being able to correctly estimate rates of productivity increase and decline allows competitively negotiated salaries to more closely approximate subsequent productivity, helps managers to make more cost-effective personnel decisions, and assists the calculations of rents in imperfectly competitive labor markets to inform industry-wide policy or regulatory decisions.

Did you find this useful? Give us your feedback

Content maybe subject to copyright    Report

Munich Personal RePEc Archive
Pay, productivity and aging in Major
League Baseball
Turner, Chad and Hakes, Jahn
31 July 2007
Online at https://mpra.ub.uni-muenchen.de/4326/
MPRA Paper No. 4326, posted 01 Aug 2007 UTC

1
Pay, Productivity and Aging in Major League Baseball
Jahn K. Hakes
Albion College
and
Chad Turner
Nicholls State University
July 31, 2007
Contact information:
Hakes: jhakes@albion.edu. 517-629-0419.
Address: Dept. of Economics, Albion College, 611 E. Porter St., Albion, MI 49224.
Turner: chad.turner@nicholls.edu. 985-448-4194.
Address: Dept. of Finance & Economics, Nicholls State University, Thibodaux, LA 70310.

2
Abstract
Using panels of player pay and performance from Major League Baseball (MLB), we examine
trends in player productivity and salaries as players age. Pooling players of all ability levels
leads to a systematic bias in regression coefficients. After addressing this problem by dividing
players into talent quintiles, we find that the best players peak about two years later than
marginal players, and development and depreciation of ability appear to be more pronounced for
players with the highest peak ability levels. Within-career variation, however, is less pronounced
than between-player variation, and the talent level of players within a given quintile will
typically remain lower than the talent level for rookies in the next higher quintile. Free agents
are paid proportionately with their production at all ability levels, whereas young players’
salaries are suppressed by similar amounts.
Keywords: Major League Baseball (MLB); career dynamics; player salaries and performance;
quintile analysis

3
I. Introduction
The correspondence between salaries and worker productivity is a central issue in labor
economics. Due to the abundance of performance and salary data for athletes in professional
team sports, a great deal of empirical work has studied salary patterns in baseball and other
sports, with sub-fields examining salary discrimination and the salary effects of arbitration and
free agency, among other topics.
1
Although this path has been trod frequently, we believe there
is still room in the literature for exploration yielding new insights.
Our contribution is to use quintile analysis to examine how productivity patterns vary
between cohorts of players with similar ability and see how well the labor market accommodates
ability variation in setting salaries. To illustrate the extent of the bias produced by traditional
ordinary least squares (OLS), we run regressions estimating separate salary and performance
paths for each talent quintile. This technique will reduce the tendency of pooled regressions of
salary or productivity on experience to yield a “flatter” time profile than is actually the case.
2
The primary advantage to studying productivity in MLB is the abundance of quantitative
data on multiple components of individual performances. Sabermetricians, statistically-minded
members of the Society for American Baseball Research (SABR), have produced a great number
of performance metrics derived from these components in an attempt to quantify production on a
single dimension. The peformance measure we utilize is OPS (on-base percentage plus slugging
average). While some of the sabermetric alternatives are preferable to OPS in specialized
1
In baseball, the majority of this research stems from the seminal work of Scully (1974). Kahn (1991) summarized
the early racial discrimination literature, which has since expanded to include analyses of coaching discrimination in
MLB (Singell [1991]), the NFL (Madden [2004]), and the NBA (Humphreys [2000], Kahn [2006]). Marburger
(1994, 2004) looks at final offer arbitration in MLB, while Zimbalist (1992), Kahn (1993), Vrooman (1996) and
Miller (2000), among many others, look at the salary effects of free agency in baseball.
2
We note this technique is not the same as quantile regression, although both terms have a common element of
placing greater analytical weight on particular centiles of a distribution.

4
scenarios, the more widespread acceptance of OPS is worth the potential very small cost in
efficiency for our purposes.
In Section II, we discuss the econometric problems involved in career path estimations,
and how quintile analysis mitigates some of those problems. Section III discusses the data set
used and our empirical method. Section IV looks at player productivity over the span of a career
and Section V presents career salary paths. Section VI offers findings on the crude relationship
between pay and performance in each league, while Section VII summarizes our findings and
details our plans for further research.
II. Variation of Individual Characteristics Over Time
II.A. Career Paths in Productivity
Ordinary least squares regression is a tool so familiar to empirical economists that its use
to study relationships such as that between player salaries and years of experience is virtually
reflexive. We do not wish to combat the intuition that regression analysis is an appropriate tool
here – especially as we will use that technique for our own modeling – but rather to note an
observational deficiency in the data that in the absence of correction would lead to biased
estimators.
We can model the abilities of players in a top tier professional sports league as
individuals in the extreme right-hand tail of the ability distribution for playing that sport. To
obtain a roster spot, a player must have an ability level above “replacement level.” A
replacement level player has ability only marginally above that of the top player not contracted
to play in the league, and typically is a benchwarmer or part-time fill-in at the top level, or a top

Citations
More filters
Journal ArticleDOI
TL;DR: This paper applied quintile regression methodology to player pay and performance data from the 1985-86 to 2005-06 seasons of the National Basketball Association (NBA) and found that the highest ability veteran players suffer the most salary suppression relative to the lesser ability players in their debut-year cohort, indicating rents have been transferred from the most able players to players of lesser abilities.
Abstract: We apply quintile regression methodology to player pay and performance data from the 1985-86 to 2005-06 seasons of the National Basketball Association (NBA). In addition to confirming a finding from Hakes and Turner (2007) of systematic bias in pooled OLS regressions of career paths for salary and productivity, the quintile analysis presents two important results regarding NBA salary structure. Unlike Major League Baseball (MLB), the highest ability veteran NBA players suffer salary suppression relative to the lesser-talented players in their debut-year cohort, indicating rents have been transferred from the most able players to players of lesser abilities. Also, while young NBA players in general suffer from salary suppression relative to free agents, as is well-reported in baseball, our regression results show that the highest-ability young players suffer the most salary suppression, and that the effects of the rookie salary cap in the 1995 NBA Collective Bargaining Agreement depressed salaries for young players of all ability levels.

3 citations

Journal ArticleDOI
TL;DR: This article analyzed changes in contract length and dollar value across players of different ability levels, at different points in their careers (contract status), by position, across CBA agreements, and further examined if new stadiums and new television deals impact contract terms.
Abstract: Long-term deals are one tool that both players and franchises use to manage risk. That tool has been much discussed and empirically tested with respect to player shirking, and has more briefly, and only theoretically, discussed with respect to reducing variance in future payrolls. Our work looks at how patterns of use of long-term contracts are affected by changes in contracting rules established through collective bargaining and by expected changes in franchise revenue streams. To accomplish this, we have assembled the most complete dataset of MLB player contracts to date. We analyze changes in contract length and dollar value across players of different ability levels, at different points in their careers (contract status), by position, across CBA agreements, and further examine if new stadiums and new television deals impact contract terms. We confirm the earlier finding that player performance is systematically higher during contract years than during the early portion of a long-term contract. We also find that inclusion of contract length information significantly reduces the unexplained variation in player salaries.

3 citations

01 Jan 2013
TL;DR: This study develops an approach to estimate proper salary level for players in Major League Baseball by analyzes the performance and contractual salaries of free agencies on the year before signing the contract during 2006-2010 in MLB, and combines with neural networks technology to evaluate players’ actual performance and their salaries.
Abstract: Relevant studies in economics point out that an appropriate salary structure is good for an organization to improve the productivity of the staff in the organization. In sports businesses, Major League Baseball (MLB) gathers top baseball players of the world in the competition, player’s performance may not only affect the personal performance and performance of the team, more importantly, but also have profound impact on the business operation of the tem and the league. Therefore, it’s very important both to the players and the team whether the team can provide proper salary to the players to ensure their best performance. In this regard, this study develops an approach to estimate proper salary level for players. The approach analyzes the performance and contractual salaries of free agencies on the year before signing the contract during 2006-2010 in MLB, and combines with neural networks technology to evaluate players’ actual performance and their salaries. According to the preliminary experimental results of this study, the initial accuracy rate of this prototype model is 77.778%. Several issues relevant to the results are also discussed for the continual improvement and development of the model and the research.

1 citations

Journal ArticleDOI
TL;DR: In this paper , the authors employ data from 331 NBA players over the 2020-2021 season to develop multiple linear regression models for analyzing appropriate player salaries, including Ordinary least squares, Ridge regression, Lasso regression, Elastic net regression.
Abstract: The National Basketball Association (NBA) is one of the four major professional sports leagues in the United States and holds substantial economic value. Since the creation of the NBA, the issue of NBA player salaries has become increasingly relevant and the disproportionate salaries of players has emerged as a challenge that obstructs the growth of the league. This paper will employ data from 331 NBA players over the 2020-2021 season to develop multiple linear regression models for analyzing appropriate player salaries. The multiple regression analysis was conducted using basic and advanced data of players as independent variables, which include dozens of variables such as player's age, player's number of games, and player's average score, and player salary as dependent variable. In order to analyze the results more accurately, several types of multiple linear regression models are used in this paper: Ordinary least squares, Ridge regression, Lasso regression, Elastic net regression. The outcome of the regression model for NBA player salary will contribute to enhancing the commercial worth of the NBA and provide constructive input to the league and the team. This research found investors place higher significance on players' three-point shooting proficiency, defensive abilities, and teamwork capacity, which aligns with the current playing style of the NBA.
Journal ArticleDOI
TL;DR: This paper showed that the compensation of free agents reliably reflects the run value contribution of each player, regardless of the source of those contributions (walks, singles, and home runs), suggesting that the labor market for batters in Major League Baseball operated efficiently across the entire sample period.
Abstract: Moneyball ( Lewis, 2003) claimed that data analytics enabled savvy operators to exploit inefficiencies in the market for baseball players. The economic analysis of Hakes and Sauer (2006) appeared to show that the publication of Moneyball represented a watershed, after which inefficiencies had been competed away. In both cases analysis focused on composite statistics such as on base percentage (OBP) and slugging percentage (SLG). This paper relies on a more structural approach, associated with the statistical analysis of Lindsey (1963) which identifies the run value of each individual event in a game. Using a dataset of every event in every game from 1996 to 2015, we show that run value of each event can be accurately calculated, as can the run value contribution of each player. We show that the compensation of free agents reliably reflects the run value contribution of each player, regardless of the source of those contributions (walks, singles, and home runs). We find this was true both before and after the publication of Moneyball, suggesting that the labor market for batters in Major League Baseball operated efficiently across our entire sample period.
References
More filters
Posted Content

680 citations


"Pay, Productivity and Aging in Majo..." refers background or methods or result in this paper

  • ...In comparison with traditional salary models following Scully’s (1974) example, this model is extremely sparse....

    [...]

  • ...In order to compare productivity across a wide range of positions, we focus on hitting productivity, and have 7 Our omission of the traditional set of controls from the Scully (1974) style models is intentional....

    [...]

  • ...…Albion College, Albion, MI 49224, USA e-mail: jhakes@albion.edu C. Turner (&) Department of Finance and Economics, Nicholls State University, Thibodaux, LA 70310, USA e-mail: chad.turner@nicholls.edu 1 In baseball, the majority of this research stems from the seminal work of Scully (1974)....

    [...]

  • ...However, we will compare our broad-brush results to those from adaptations of the canonical Scully (1974) model in Sect....

    [...]

  • ...Previous attempts to compare player productivity to compensation have followed the seminal theoretical work of Scully (1974). Using a two-stage model, team revenue is shown to be primarily determined by team wins, establishing that the production of wins is the player’s marginal physical product, and that the revenue accruing to the team from a player’s performance statistics determine his marginal revenue product....

    [...]

Journal ArticleDOI
TL;DR: This article reviewed studies of racial and ethnic discrimination in professional sports and briefly examined gender differences in pay among professional tennis players, finding evidence of salary discrimination and customer discrimination against blacks in basketball, and positional segregation on the basis of race or ethnicity in baseball, football, and hockey.
Abstract: This paper reviews studies of racial and ethnic discrimination in professional sports and briefly examines gender differences in pay among professional tennis players. Many of these studies include far more extensive controls for individual ability and performance than typical studies of discrimination that use labor force data. The cited studies show evidence of salary discrimination and customer discrimination against blacks in basketball, and positional segregation on the basis of race or ethnicity in baseball, football, and hockey. More limited evidence is found for the existence of salary discrimination and fan discrimination against French-Canadian hockey players and fan preferences for white baseball players. Finally, at several Grand Slam tennis tournaments, the money prize for the women's winner is somewhat smaller than that for the men's winner, despite some evidence that the women's matches draw at least as much revenue as the men's matches.

262 citations


"Pay, Productivity and Aging in Majo..." refers background in this paper

  • ...Kahn (1991) summarized the early racial discrimination literature, which has since expanded to include analyses of coaching discrimination in MLB (Singell 1991), the NFL (Madden 2004), and the NBA (Humphries 2000; Kahn 2006)....

    [...]

Journal ArticleDOI
TL;DR: In this paper, the effects of eligibility for free agency or arbitration on compensation and contract duration were investigated using longitudinal data for major league baseball players, where eligibility is based on experience and better players are kept long-term.
Abstract: Using longitudinal data for major league baseball players, this paper estimates the effects of eligibility for free agency or arbitration on compensation and contract duration. Becaus e eligibility is based on experience and better players are kept longe r, a fixed effects approach is used. Arbitration and free agency eligibility both raised annual compensation; however, only free agen cy raised contract duration. The free agency findings are consistent wi th Nash bargaining; however, additionally considering the arbitration results suggests the "winner's curse": duration rises only when a team might lose a player. The auction market is thus avoided. Copyright 1993 by MIT Press.

122 citations


"Pay, Productivity and Aging in Majo..." refers background in this paper

  • ...Marburger (1994, 2004) looks at final offer arbitration in MLB, while Zimbalist (1992), Kahn (1993), Vrooman (1996) and Miller (2000), among many others, look at the salary effects of free agency in baseball....

    [...]

  • ...edu 1 In baseball, the majority of this research stems from the seminal work of Scully (1974). Kahn (1991) summarized the early racial discrimination literature, which has since expanded to include analyses of coaching discrimination in MLB (Singell 1991), the NFL (Madden 2004), and the NBA (Humphries 2000; Kahn 2006)....

    [...]

Journal ArticleDOI
TL;DR: This article examined racial differences in professional basketball player salaries to determine whether the 20% premium paid to whites in the mid-1980s has persisted into the 1990s and found that whites receive a significant premium (18%) at the upper end of the salary distribution.
Abstract: Racial differences in professional basketball player salaries are examined to determine whether the 20% premium paid to whites in the mid-1980s has persisted into the 1990s. OLS and tobit regressions indicate no difference between white and black salaries, controlling for player and team characteristics for the 1994 - 95 season. However, censored quantile regressions show substantial racial differences at certain points in the salary distribution. Whites earn less than blacks at the lower end of the distribution, although the difference is not statistically significant, and varies with minutes played. In contrast, whites receive a significant premium (18%) at the upper end of the salary distribution. These findings are consistent with a form of consumer discrimination in which sports fans prefer to see white star players, all else equal.

116 citations


"Pay, Productivity and Aging in Majo..." refers methods in this paper

  • ...For an early example that uses quantile regression to examine salary discrimination in the NBA, see Hamilton (1997)....

    [...]

Journal ArticleDOI
TL;DR: This article found that hitters' salaries during this period did not accurately reflect the contribution of various batting skills to winning games, and that knowledge of its existence, and the ability to exploit it, enabled the Oakland Athletics to gain a substantial advantage over their competition.
Abstract: In his 2003 book Moneyball, financial reporter Michael Lewis made a striking claim: the valuation of skills in the market for baseball players was grossly inefficient. The discrepancy was so large that when the Oakland Athletics hired an unlikely management group consisting of Billy Beane, a former player with mediocre talent, and two quantitative analysts, the team was able to exploit this inefficiency and outproduce most of the competition, while operating on a shoestring budget. The publication of Moneyball triggered a firestorm of criticism from baseball insiders (Lewis, 2004), and it raised the eyebrows of many economists as well. Basic price theory implies a tight correspondence between pay and productivity when markets are competitive and rich in information, as would seem to be the case in baseball. The market for baseball players receives daily attention from the print and broadcast media, along with periodic in-depth analysis from lifelong baseball experts and academic economists. Indeed, a case can be made that more is known about pay and quantified performance in this market than in any other labor market in the American economy. In this paper, we test the central portion of Lewis’s (2003) argument with elementary econometric tools and confirm his claims. In particular, we find that hitters’ salaries during this period did not accurately reflect the contribution of various batting skills to winning games. This inefficiency was sufficiently large that knowledge of its existence, and the ability to exploit it, enabled the Oakland Athletics to gain a substantial advantage over their competition. Further, we find

108 citations

Frequently Asked Questions (1)
Q1. What are the future works in this paper?

In their future research, the authors will conduct a similar analysis using player productivity and salary data from the NBA, in which imperfect competition in the labor market persists even for veteran players. The authors will also extend their analysis to identify systematic aging trends in productivity of baseball pitchers and test whether the rates of player deterioration are structurally stable across decades.