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AVERAGE SALARY AND CONTRACT LENGTH IN MAJOR LEAGUE BASEBALL:
WHEN DO THEY DIVERGE?
Josh Meltzer* Department of Economics^ Stanford University May 2005
ABSTRACT
This paper investigates the ways that various measures of player performance have different impacts on the outcomes of salary determination and contract length in Major League Baseball using contract data from 2002. Because average salary and contract length are jointly determined, a two-stage least squares is used to estimate each as a function of the other andvarious performance metrics. The results show two primary areas of divergence for contract length and average salary. The first comes from young improving players who are likely to get long-term contracts at low annual salaries. The second comes from players with chronic injuries, whose salary is not affected by their injuries but who will tend to get shorter contracts than they otherwise would. This second effect was not apparent from the first-stage regression,demonstrating the importance of the two-stage least squares methodology for analyzing contract length and average salary.
- (^) I would like to thank my adviser Roger Noll for his valuable advice and guidance throughout this process. I would also like to thank John Abbamondi for comments on an earlier draft and Edward Vytlacil and Geoffrey Rothwell fortheir helpful suggestions about the empirical model. All the errors are my own.
INTRODUCTION
Major League Baseball provides a unique opportunity for examining the behavior of employers in offering contracts because of the wealth of data about the individual performance of players. Whereas for most industries it is very difficult to gauge the value of a worker and to compare one worker to another, every action of a baseball player is documented and factored into the employer’s decision. Researchers have paid a significant amount of attention to what determines player salary, especially with the advent of free agency after the Basic Agreement in
- Much less attention has been devoted to the other half of baseball contracts: the number of guaranteed years. In this paper, I will investigate what determines the length of player contracts in Major League Baseball (MLB). Typically, salary and contract length rise together, but what are the exceptions to this relationship? For what types of players would we expect to see long-term contracts for a relatively low average salary? For what types of players would we expect to see short-term contracts for large average salaries? What are the factors that are affecting salary and length differently? These are all interesting questions that have seen little scholarly attention up to this point. Unlike in other major sports leagues like the National Football League, MLB contracts are guaranteed.^1 Players must be paid by their teams even if they do not perform up to expectations or if they are injured and cannot play. If a player is released, the team must still pay
(^1) Many contracts also make use of various forms of options. There are club options, which are like call options for a team on the player. Player options allow the player to have control over whether he returns at apreviously agreed salary. There are also mutual options, to which both the player and the team have to agree. Many long-term contracts have options attached at the end, after a number of guaranteed years. However,just one option year, with rare cases of two option years. The options take various forms, and are sometimes there is usually automatically triggered if the player achieves certain performance incentives. Although options have become moreprevalent in recent years, most players in Major League Baseball are still playing under a guaranteed contract.
Performance and Market Uncertainty There are two major sources of uncertainty: performance and market uncertainty. Unlike the performance of a manufacturing employee, for example, which one would expect to remain relatively constant over a number of years, perhaps improving with experience, the performance of Major League Baseball players exhibits substantial variation. Players who are All-Stars in one year may not be the next year, and vice versa. Many players have a period of one season or several seasons when their performance varies dramatically from their career averages. There are two major explanations for performance uncertainty. The first is that each player has a constant but unknown underlying level of performance, and that any changes in performance are mere statistical fluctuations around this level. For example, let us suppose that a given player has a 3 in 10 chance of getting a base hit in any individual at-bat. We would expect that player to be a career .300 hitter. However, we would expect to see fluctuations around this mean level. On a short-term basis, we would expect to see substantial variability in the player’s performance. On a given day, the player may go 0 for 5 or 5 for 5 at the plate, but the underlying level remains the same. As the time period increases, we would expect to see a more constant level of performance. However, even over the course of a season, we may see substantial fluctuations in player performance that are simply due to chance. Albert and Bennett (2001) ran a simulation imagining that a player’s true on-base percentage was .380. Over the course of 100 seasons, there was an 88-point differential between the player’s best and worst seasons, assuming that the underlying level remained constant. As this illustrates, random chance is a major factor affecting variation in player performance. The second explanation for performance uncertainty is that the player’s underlying level of performance changes over the course of his career. Some of this may be predictable. One
would expect that experience would cause players to improve over the early parts of their careers and then decline as they age. However, other less predictable factors can also affect a player’s underlying level of expected performance. These include the effects of injury, coaching and personal upkeep. Injury provides a powerful explanation for the uncertainty of player performance. Many players are forced to miss games during the season because of physical injuries sustained on the field. Injury history can be useful in attempting to predict the likelihood of a player becoming injured in the future, but there remains a significant element of chance. Some types of nagging injuries, like a shoulder injury for a pitcher, recur many times and can be taken into account when negotiating contracts. Other injuries are flukes, as when a player breaks his leg diving for a ball. These are the types of injuries that can happen to any player regardless of physical fitness. Ken Griffey Jr.’s career provides a compelling case study of the possible effects of injury. In February, 2002, he signed a nine-year $116.5 million deal with the Cincinnati Reds after ten consecutive All-Star appearances with the Seattle Mariners. Over the three years before he signed his contract, he averaged more than 159 games played and more than 53 home runs per season. He signed his contract at the age of 30, generally considered the beginning of a player’s prime. In the five injury-plagued seasons since then, he has averaged just 92 games played and 21 home runs per season. We would not expect injuries to affect only the number of games played, however. It is generally assumed that player health, although difficult to measure, has a tremendous effect on performance. Even if a player does not actually land on the disabled list (DL) and miss games, a decline in performance may be due to a more mild injury. Over the course of a 162-game season, players sustain many mild injuries or experience mild recurrences of more serious past
uncertainty of player performance is something that must be taken into account in contracts. Both the players and the teams face competing risks. If players sign short-term contracts, they risk getting injured and being unemployed in the future. Because even the minimum salary in baseball, at $300,000 in 2003, is much higher than the average salary in the country as a whole, loss of employment for a player is likely to lead to a very large loss in income. However, if players sign long-term contracts, they lose the opportunity to sign for more money in the future if their performance improves. Teams face the opposite set of risks. If they sign a player to a short-term deal, they risk having the player improve and being forced to either sign that player to a higher contract in the future or have the player leave for another team. If they sign a player to a long-term deal, they risk having the player get injured or having his performance decline and being forced to continue to pay that player. Traditionally, researchers have assumed that, for players, the risk of short-term deals is greater than the risk of long-term deals. Given the risk of career-ending injuries and the enormous fall in income that such an injury would entail, players want to guarantee a future stream of income. However, teams have a portfolio of players with which to diversify their risk and thus are more willing to bear this performance risk than players (Lehn 1982). Consequently, they are in a position to offer players additional years in exchange for a lower contract. However, they will still tend to offer shorter contracts to players with higher perceived performance uncertainty (Maxcy 2004). It is important to note that teams may act differently towards the risks associated with performance decline from injury as opposed to from other causes. Teams are able to protect themselves against the risk of injury by purchasing insurance. Teams often purchase injury insurance for their players, especially for the most expensive ones. It has recently become more
difficult to get insurance policies that cover very long contracts, but teams can purchase a new insurance policy after the first one expires (although the new policy will have new premiums based on more recent injury history). Typically, the insurance policy pays the player’s salary, or a portion of the salary, if the player is on the DL. In this way, teams are insured against player injury. Fluctuations in performance, however, are not covered by these policies and thus may be a greater source of financial risk for the teams. Maxcy (2004) hypothesized that better players will tend to get long-term contracts because they are less risky than worse players. This is not because the level of their play fluctuates less but because even a downswing would probably keep them above a certain “replacement level” at which teams would want to substitute a different player but could not because of being saddled with a long contract. This logic is sensible, although evidence from baseball suggests that teams do not always follow it. Paul DePodesta, the general manager of the Los Angeles Dodgers, said: A very small percentage of the players in the big leagues actually are much better than everyone else, and deserve to be paid the millions. A slightly larger percentage of playersare actually worse than players who are stuck in the minors, but those guys usually aren't the ones getting the big money. It's the vast middle where the bulk of the inefficiency lies -- the player who is a 'known' player due to his major-league service time making millions of dollars who can be replaced at little to no cost in terms of production with a player making close to the league minimum (quoted in Lewis, 2005). Here, DePodesta suggests that many players who are below the replacement level are being kept in the Major Leagues. DePodesta is part of a new wave of general managers who rely heavily on statistics (he was a Harvard economics major). Theo Epstein of the Boston Red Sox, J.P. Ricciardi of the Toronto Blue Jays, and Billy Beane of the Oakland Athletics are examples of other general managers who place a heavy emphasis on statistical analysis. These new general managers may be trying to clear up many of these inefficiencies, but for now there remain
teams may weigh the respective risks differently in different situations, and it is difficult to reach a clear theoretical conclusion about how players and teams will act. Empirical results can help to reveal how they are acting in practice.
LITERATURE REVIEW
Much of the scholarly research on baseball came in the aftermath of the signing of the Basic Agreement in 1976 which allowed players to become free agents for the first time. Free agency essentially allowed players to receive the market value for their services, as opposed to the old system when they were forced to accept whatever their teams chose to pay them. This sudden change gave economists an opportunity to analyze the effects of allowing the free market to determine contracts and they jumped at the opportunity. A great deal of research has gone into investigating the effect of free agency on the size of player salaries (Chelius and Dworkin, 1982; Hill and Spellman, 1983; Raimondo 1983). This research has universally found that the advent of free agency led to a substantial rise in salary. These studies focused exclusively on salary, however, and ignored the importance of contract length. More recently, several researchers have investigated the length of baseball contracts. Kahn (1993) used a fixed effects approach on longitudinal data to look at the effect of arbitration eligibility and free agency on salary and contract length. He found that both arbitration eligibility and free agency raise average salary, but only free agency raises contract duration, while arbitration eligibility has no effect. There are several reasons to try to expand on his results, however. His vector of explanatory performance metrics relied entirely on career averages, which are probably less good predictors of performance than more recent measures
like three-year averages. Furthermore, in Kahn’s data, the average contract duration was 1. years. My more recent data has an average duration of 1.79 years, even excluding contracts over five years. The increase in contract length in the decade since Kahn’s work suggests that there may have been changes in the process of contract negotiation over that period. Additionally, Kahn limited his focus to the effect of free agency and arbitration eligibility and did not investigate whether there are other factors that affect salary and contract duration differently. Finally, Kahn ran separate regressions for whites and blacks, although research has not shown any evidence of racial discrimination in baseball salaries (Kahn 1991; Sommers 1987). Maxcy (2004) used a binary choice probit model to determine which players are getting long-term contracts. He regressed length of contract on a host of performance metrics, including slugging percentage. Maxcy found that players who are the most likely to be replaced are the least likely to get long term contracts. These include older players, who will deteriorate more quickly, and mediocre players who are more likely to fall below the replacement level. There are a couple of potential problems with his analysis, however. First, the binary choice probit model indicated only whether a player got a long-term deal but did not distinguish between those deals. Given that a two-year deal is probably more similar to a one-year deal than to a five-year deal, this methodology seems somewhat lacking. Second, he did not include salary in his regression, which is likely to be an important factor and jointly determined, as I will discuss later. Krautmann and Oppenheimer (2002) addressed the interaction of contract length and salary more explicitly. They looked for a compensating effect between salary and length. Given that players tend to prefer both larger and longer contracts, Krautmann and Oppenheimer hypothesized that players will accept a tradeoff between the two. In order to test this empirically, they regressed salary on contract length and other factors, using a two-stage least
METHODOLOGY
Data I decided to limit my research to hitters. The primary reason for this is that pitching statistics are less universal than hitting statistics. There are two main types of pitchers, starting pitchers and relief pitchers. Within relief pitchers, there are middle relievers and closers. Although hitters are composed of many different position players, at the plate they are all measured the same way. For pitchers, statistics like wins, innings pitched, and saves are highly dependent on the type of pitcher. Krautmann, Gustafson, and Hadley (2001) found that pitchers cannot be aggregated together. However, to run different regressions on different types of pitchers would lead to a dangerously small sample and less universal results. Furthermore, many pitchers act as both relief pitchers and starters over the course of a season, requiring an arbitrary cutoff to categorize them as one or the other. Given these difficulties with pitchers, I have opted to focus my analysis on hitters. The data consist of all contracts of hitters as of the end of 2002. Although 73% of the contracts were signed in 2002, they go back as far as 1997. The data were gathered from a variety of sources.^2 I dropped any players who had no Major League experience as of 2002, since they had no performance history at the Major League level. I also dropped any players with contracts greater than five years, since these outliers might skew the overall results. There are three main categories of data: contract details, player characteristics and team characteristics.
(^2) The contract data were taken from the website, http://www.bluemanc.demon.co.uk/baseball/mlbcontracts.htm. This website has since been taken down, but can still be accessed through this website,http://www.archive.org/web/web.php. The contract information was confirmed by looking at newspaper reports of contract signings when available. The data on days on the disabled list were generously provided by Major LeagueBaseball. The performance statistics were taken from The Baseball Archive Database Version 5.2, which is available at http://www.baseball1.com, and from the Baseball Guru database, which is available athttp://baseballguru.com/bbguruol.html. A sampling of the statistics were confirmed with data from ESPN.com to ensure accuracy. Age was calculated as of opening day of 2003 based on the dates of birth available on ESPN.com.Payroll information was acquired from the USA TODAY Salaries Database, available online at http://asp.usatoday.com/sports/baseball/salaries/default.aspx.
Table 1: Variable Definitions AVGSAL Average salary over the duration of the guaranteed contract, including guaranteed bonuses and option buyouts LENGTH Number of guaranteed years in player’s contract OPSAVG Average of on-base plus slugging percentage over the three years prior to signing contract OPSCHANGE Change in OPS in final year before contract over OPSAVG PAAVG Average number of plate appearances over the three years prior to signing contract PAUP Dummy variable indicating if the plate appearances in the final yearbefore the contract increased by more than 100 over PAAVG ALLSTAR Number of All-Star selections in three years before signing contract GOLDGLOVE Number of Gold Gloves won in three years before signing contract DLFEW Average number of days spent on the disabled list over the three years before signing contract if the average is less than or equal to 15 days or 0 if the average is greater than 15 days DLMANY Average number of days spent on the disabled list over the three years before signing contract if the average is greater than 15 days or 0 if the average is less than or equal to 15 days HEALTHY Dummy variable indicating if the player spent 0 days on the disabled list in the year before signing contract AGE Player’s age as of opening day on the first year of new contract AGE^2 Player’s age squared CATCHER Dummy variable indicating if the player is a catcher SHORTSTOP Dummy variable indicating if the player is a shortstop OF Dummy variable indicating if the player is an outfielder FREEAGENT Dummy variable indicating if the player was a free agent when the contract was signed ARBITRATION Dummy variable indicating if the player was arbitration eligible when the contract was signed HIPAY Dummy variable indicating if the team’s payroll was in the top five LUX Dummy variable indicating if the team’s payroll was in the top fiveand the contract was signed after the 2002 season LOPAY Dummy variable indicating if the team’s payroll was in the bottom five POP Population of team’s metropolitan area as of 2000
The contract details consist of the number of guaranteed years (LENGTH) and the average salary (AVGSAL) over those guaranteed years. Team options and mutual options were not counted, but player options were considered to be guaranteed years (Player options allow the player to decide whether to exercise the option and remain on the team, so they are even better than a guaranteed year from the player’s standpoint). Although team and mutual options were
the game.^4 Basic statistics like batting average and runs batted in have given way to a host of advanced statistics, each vying to encapsulate the productivity of a hitter in one number. Given the likely multicollinearity of most offensive statistics, it is sensible to use only one statistical measure of productivity. I have chosen to use on-base plus slugging percentage (OPS). On-base percentage measures how often a player reaches base, a combination mostly of walks and hits. Slugging percentage measures the number of total bases divided by total at-bats. It therefore takes power hitting into account. The sum of these two statistics provides one number which includes both hitting for power and ability to reach base, the two most important components of hitting. Slugging percentage has traditionally been a popular statistic to measure the productivity of hitters (Krautmann and Oppenheimer 2002; Maxcy 2004), but OPS is likely to be a better measure since it includes the on-base component. Albert and Bennett (2001) found that OPS produces a “far-superior” (p. 166) model for predicting team runs per game than either slugging percentage or on-base percentage individually. Given that on the offensive end, teams are attempting to maximize the number of runs scored, it would follow that teams would value the OPS of individual players in the same manner. Students of the game could debate endlessly the single best statistic for measuring a hitter’s productivity. I have chosen OPS, which is generally agreed to be a very good measure. For those not familiar with the statistic OPS, it will be useful to look at the summary statistics from the data. The average OPS in my sample is .754. An OPS of over 1.000 is typically considered an excellent year, and over .900 is still a very strong performance. An OPS below .650 would be considered a poor hitting season. The variable OPSAVG is a three-year average of OPS before the contract was signed.
(^4) For an excellent discussion of the history of statistics in baseball, read The Numbers Game: Baseball’s Lifelong Fascination with Statistics by Alan Schwarz.
Table 2: Summary Statistics of Sample
- AVGSAL 2.437 3. Variable Mean S.E.
- LENGTH 1.789 1.
- OPSAVG 0.754 0.
- OPSCHANGE -0.003 0.
- PAAVG 350.481 194.
- PAUP 0.237 0.
- ALLSTAR 0.209 0.
- GOLDGLOVE 0.081 0.
- DLFEW 3.078 4.
- DLMANY 35.728 18.
- HEALTHY 0.758 0.
- AGE 29.148 4.
- AGE^2 865.829 244.
- CATCHER 0.165 0.
- SHORTSTOP 0.081 0.
- OF 0.338 0.
- FREEAGENT 0.433 0.
- ARBITRATION 0.290 0.
- HIPAY 0.155 0.
- LUX 0.112 0.
- LOPAY 0.160 0.
- POP 6.122 5.
amount of time on the DL, however, each additional day that the player is injured is likely to have a greater effect on the team’s assessment of the player’s future health. For this reason, I created a piecewise function for days on the DL, using the two variables DLFEW and DLMANY. DLFEW represents days on the DL if the player averaged less than 15 days on the DL over the last three years. I am expecting that DLFEW will not be significant for the length regression, as teams will largely ignore rare injuries. DLMANY represents the days on the DL if the player averaged more than 15 days on the DL over the last three years. I expect that DLMANY will be significant, reflecting teams’ concerns about chronic injuries.^5 The dummy variable HEALTHY indicates if the player spent no time on the DL in the year before signing his contract. None of these measures will pick up minor injuries that may cause a player to miss a few days in the lineup or adversely affect a player’s performance without requiring the player to sit out any games. These are less likely to affect a team’s decision to sign a player, however, since their primary concern is likely to be chronic injuries that could cause a player to miss significant playing time and also because teams may not be aware of minor injuries if the player plays through them. I have included All-Star selection over the previous three years as another performance measure. All-Stars are selected because they are among the top performers at their position in the first half of the season. Fans select the All-Star starters, while managers selected the reserves until 2003.^6 Popular players are sometimes elected even when their performances do not seem to merit selection. However, this popularity is a factor that teams may take into consideration when signing a player’s contract, given increased attendance at games, etc., so All-Star selection
(^5) I also ran the regressions assuming that days on the disabled list had a linear effect on contract length and salary, and although the results held using either method, the results were stronger using the piecewise disabled listfunction, as would be expected from the manner in which teams evaluate players. (^6) Starting in 2003, players voted to select the All-Star reserves. All of my data is from before 2003, though, so this is not relevant to my research.
should be a powerful predictor of contract size and length. All-Star selection also takes into account the total player package, including speed and defense and perceived leadership qualities, all of which are attractive to teams but difficult to include as independent variables, for reasons I will discuss later. Another equally important consideration is how far back to consider past performance. Do teams value consistent performance or are they satisfied with a breakout contract year? In order to measure consistent performance, I have included three-year averages of performance statistics, which is fairly standard in baseball research (Krautmann and Oppenheimer, 2002). I have also included OPSCHANGE as the deviation from OPSAVG in the last year of the contract. Additionally, I have included a dummy variable, PAUP, which indicates if plate appearances increased by more than 100 in the final year over PAAVG. Together, these will provide both a measure of a player’s historical averages and his trend in performance, both of which are likely to matter to teams signing him to a contract. However, PAUP may also be useful in isolating a particular class of players that may be likely to get relatively long-term contracts at relatively low annual salaries. These would be young improving players. These players are not likely to get large salaries, often because they are not in a strong bargaining position. If the player is arbitration eligible, the team knows that it can sign the player to a one-year deal for a reasonable price.^7 However, teams may have an incentive to guarantee long contracts for two reasons. First, if they expect the player to improve significantly over the term of the contract, they can lock that player in at a lower rate and avoid paying raises every time the player comes up for arbitration. Second, if they can sign the player
(^7) It is important to note that in practice, it is generally believed that some players get higher salaries under arbitration than they would as free agents. Although the economic theory would predict otherwise, arbitrators virtually alwaysgive players raises, while free agents sometimes take pay cuts. As a group, free agents still get substantially higher salaries than those eligible for arbitration, but it is important to note that free agency does not unambiguously raise aplayer’s salary over the salary that would have been given under arbitration.
