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Do Firms Have Short Memories? Evidence from Major League Baseball
Andrew Healy
Loyola Marymount University
Department of Economics
February 13, 2007
Abstract
When deciding what salary to offer an employee, a firm needs to predict
that employee’s future productivity. Classical theory predicts that firms
will effectively use the available information to set an appropriate salary.
Evidence from major league baseball contracts indicates, however, that
biases influence contracts. Consistent with insights from psychology and
behavioral economics, salaries are affected too much by recent
performance compared to past performance. All organizations do not
suffer equally from short memories. The teams that achieve the most with
the money that they spend also use performance data most effectively.
I. Introduction
A growing, and now large, body of evidence indicates that economic agents often do not
conform to the classical rational model of behavior. In many cases, bounded rationality appears
to best describe behavior (Simon, 1957; Kahneman 2003). Agents often rely on rules of thumb
or heuristics to solve problems, particularly when those problems are complex (Tversky and
Kahneman, 1974). The biases that arise from the application of heuristics may lead to a range of
inefficiencies. One example of a heuristic at work involves limited memory. Psychological
research shows that people tend to primarily remember the most salient events (Mullainathan,
2002). This paper shows that limited memory leads firms to make systematic mistakes in their
salary offers.
Since performance and pay of baseball players are easily measured, the market for
baseball players offers an ideal laboratory for testing for the effects of limited memory on salary
offers (Sommers and Quinton, 1982; Kahn 1993). Also, with salaries are so high, the costs of
any mistakes are amplified; the presence of inefficient behavior in the market for baseball
players would likely extend to other environments where the stakes are lower. Evidence from
Major League Baseball demonstrates that memory-based rules of thumb cause player contracts to
deviate from optimality. Teams reward players for performing well in the immediate past,
ignoring other evidence of a player’s quality from his previous performance. When choosing
salary offers, teams have short memories.
This finding will likely not surprise baseball fans. Many observers have expressed strong
opinions that certain players have received excessively high contracts after only one good
season. For example, Adrian Beltre, a third baseman for the Los Angeles Dodgers, had an
exceptional season in 2004. Despite the absence of any similar success in the preceding years,
the Seattle Mariners offered Beltre a five-year, $64 million contract. The contract paid Beltre as
if he would continue to perform at his 2004 level, but he has instead reverted to his pre-2004
form.1 While other anecdotes also suggest that players are excessively rewarded for performing
well in the final years of their contracts, testing the hypothesis that teams systematically have
short memories requires a comprehensive analysis of players’ salaries.
In this paper, I conduct that analysis. I look at salaries and performance data for all
Major League Baseball hitters who signed free agent contracts from 1985-2004. The data shows
that a player’s performance this year is predicted about as strongly by last year’s performance as
Statisticians often use on-base plus slugging percentage (OPS) to measure a hitter’s performance (Albert and
Bennett, 2001). From 1999-2003, Beltre averaged a .756 OPS with a highest value of .835 in 2000. Then in 2004,
his OPS jumped to 1.017. In the two seasons since, Beltre had a .716 and .793 OPS, respectively.
1
by his performance from two years ago. In contrast, a player’s salary this year depends on his
performance in the previous year about twice as much as his performance from two years ago.
Teams are not equally prone to underweighing past performance relative to recent
performance. Controlling for total payroll, the teams that use past performance data most
effectively win the most games. Perhaps surprisingly, the successful teams weigh previous years
in a similar way to the unsuccessful teams. The successful teams outperform the others by
signing players whose future performance is actually predicted more by recent performance.
What could cause memory-based biases to affect baseball salaries? Previous research in
the psychology of memory offers a compelling explanation. People often access the most salient
memories when making decisions. Reacting primarily to salient memories in this way
corresponds to the availability heuristic (Tversky and Kahneman, 1974; Mullainathan, 2002).
The most salient memory about a player who just had a remarkable season may be his
outstanding season, while other relevant performance data fails to stand out as much.2
Availability could have caused the Seattle Mariners, for example, to believe that Adrian Beltre’s
lone exceptional season more accurately described the player’s skills than his previous five years
of unexceptional play. In general, this sort of behavior could explain why teams fail to take into
account a player’s performance in previous years when making a salary offer.3
In section 2, I describe ways to measure a baseball player’s performance and the data
used in the analysis. In section 3, I present the main empirical results. Section 4 concludes.
2
Psychological research has also shown that individuals remember best events that happened very recently. That
research generally does not apply to my findings, however, since teams appear to rely too heavily on the
performance in the most recent entire season, as opposed to what happened in the immediate past.
3
A related phenomenon, the “hot hand”, can also be understood by invoking the availability heuristic as it applies to
memory. Camerer (1989), for example, finds that bettors behave in an inefficient way by believing that a basketball
team that has had recent success will also have future success. Likewise, Gray and Gray (1997) find that the odds
are skewed towards teams that have had recent success and against teams that have had recent failure. They argue
that football bettors’ behavior “is consistent with the idea that the market overreacts to recent form, discounting the
performance of the team over the season as a whole.”
II. Estimation Strategy
A. Measuring a player’s performance
In this paper, as in previous research, I focus on a player’s contribution towards winning
games, through which the player affects a team’s revenues (Scully, 1974; Sommers and Quinton,
1982; Fort and Quirk, 1992). A team may have other incentives to sign a player, such as a star
player who may sell a large number of tickets but does not commensurately increase the team’s
chances to win games. Even compared to previous research, though, the distinction between a
player’s contribution to winning games and to team revenue is likely less important here because
the goal of this paper is to see how contracts respond differentially to recent as opposed to past
performance.
A variety of measures capture different aspects of a hitter’s performance.4 The number
of home runs that a player hits, a player’s on-base percentage, and his slugging percentage are
three such measures. Previous research suggests that a measure called OPS, the sum of on-base
percentage and slugging percentage, is a reasonable measure of a player’s worth (Albert and
Bennett, 2001). Most of the results on which I focus use OPS to measure a player’s worth. All
of my results, however, do not depend on what measure of player performance is used. Alternate
measures yield similar results.
To formalize these ideas, consider a player i whose OPS in year t is OPSit. I model the
player’s performance as a weighted average of his performance in the previous k years and other
observed factors captured by xit. One plausible component of xit is a player’s age.
OPSit 
4
t 1
  OPS
s t  k
s
is
  xit  uit
(1)
As is standard in academic research on baseball, I will focus on hitters rather than pitchers.
Equation (1) simply states that our prediction of a player’s performance this year is based on his
past performances, with higher weight presumably assigned to more recent years. The error
term, uit, arises because previous performance is not a perfect predictor of current performance.
Take a player’s salary to be a function of his expected performance in year t, so that
Salaryit 
t 1
  OPS
s t  k
s
is
  xit   it
(2)
The error term in the above regression comes from other aspects of player value not captured by
OPS and by any unobserved factor that determines a player’s salary.
Equations (1) and (2) suggest the test that I will conduct in this paper. If teams are
optimally using previous performance information to predict players’ future performances, the
coefficients that relate previous performance to current performance should exhibit the same
pattern over time as the coefficients that relate previous performance to current pay. Suppose we
estimate that if last year’s OPS is 1 point higher, today’s OPS will be 0.6 points higher. Also
suppose we estimate that if the player’s OPS from two years ago is 1 point higher, today’s OPS
will be 0.3 points higher. So today’s performance is twice as sensitive to last year’s performance
as to the performance from two years ago. If management acts optimally, its salary offers will
also be twice as sensitive to last year’s performance as to the performance from two years ago.
B. The Data
Baseball contract data is ideal for looking at whether firms have short memories when
making salary offers because well-measured performance histories are available for all players
To test the hypotheses about management rationality, I utilize data on free agent signings in
Major League Baseball from 1985-2004. In baseball, a free agent may negotiate freely with all
other clubs except his original club. The bidding for certain highly-valued players can be fierce.5
For the analysis, I focus on free agent signings that occur between October and April,
when the regular-season games are not taking place and the vast majority of free agent signings
occur. Focusing on offseason signings allows for a clear comparison between a player’s
performance before and after the contract is signed. Of those signings, the primary regressions
in this paper are based on the 500 observations for which players have played for three years
before signing the free agent contract and have at least 200 at-bats in each of the previous three
seasons.6
The data on players’ salaries and past performances is obtained from the Baseball
Archive.7 The past performance data includes measures of every standard statistic for each
player. I construct a player’s OPS by adding his on-base percentage and slugging percentage.
The salary information refers to a player’s base salary for the given years. To determine free
agent signings, I use the data on baseball transactions compiled by Retrosheet.8
In the analysis, I include year dummies in the estimation of equation (2). The data shows
that the average salary has increased from $500,000 in 1985 to $2.8 million in 2004. Baseball
salaries are also highly skewed, and have become more skewed over time. The median baseball
salaries in 1985 and 2004 were $410,000 and $870,000, respectively. To ensure that the few
very high salaries do not have excessive influence on the regression results, I estimate equation
5
Baseball players gained the right to free agency in 1973. Even since then, it is something of a stretch to assume
that the market for baseball players has been a perfectly competitive one. Owners of baseball teams have been
found guilty of colluding to keep players’ salaries down as recently as the early 1990s. But recent research has
found that baseball players are now receiving something close to their marginal products in wages. None of these
issues has an effect on my main results about whether teams suffer from short memories. If estimation is restricted
to only 1995-2004, instead of 1985-2004, all results main essentially the same.
6
The results are somewhat stronger if the analysis is restricted to the 427 players who are at least 30 years old when
signing the contract, to focus on those players who have finished developing their skills.
7
I thank Sean Lahman for help in accessing this data. It was accessed in August 2006 at http://www.baseball1.com.
8
The transaction data was accessed online in August 2006 at: http://www.retrosheet.org.
(2) using the log of salary as the dependent variable. Results remain essentially the same if
salary is used as the dependent variable instead of the log of salary.
III. Results
A. Testing for short memories
Table 1 presents the results from estimating equations (1) and (2). The first table presents
the results from estimating the regressions for players who have played at least three years before
signing a free agent contract. All of the regressions include year dummies to account for
differences over time in both salaries and the tendencies for hitters to do better as a whole.9 To
account for determinants of a player’s value that are not captured by his OPS, I include lagged
salary in the salary regression.
The table shows that, on average, a player’s performance is significantly less sensitive to
recent performance than is a player’s salary. A player’s performance is predicted about as
strongly by last year’s performance as by his performance from two years ago. The regression of
current performance on the performance from the three previous years gives a coefficient of
0.320 for last year’s performance and 0.280 for performance from two years ago. An F-test
cannot reject the hypothesis that the coefficients are the same (p = 0.595). In general,
performance from two years ago and from the previous year are about equally good predictors of
current performance.
On the other hand, an increase in last year’s performance is about twice as effective at
increasing that player’s salary as better performance two years ago. An increase of ten
percentage points in OPS in the previous year leads to a 35.7% increase in a player’s salary,
9
There tend to be cycles that favor hitting in baseball and other cycles that favor pitching. For example, the leagueaverage OPS in 2000 was 0.762, compared to 0.711 in 1985.
while a ten percentage point increase in performance two years ago only increases a player’s
salary by 19.4%. An F-test rejects the hypothesis that the effect of last year’s performance on a
player’s salary is the same as the effect of performance from two years ago (p = 0.013).
Likewise, performance from three years ago is underused when organizations make salary offers.
Player performance is predicted about twice as strongly by last year’s performance as
performance from three years ago, but last year’s performance predicts salary about five times
more than the three-year ago performance.
Figure 1 displays graphically the stark differences between how past performance
predicts future performance and how past performance is used to determine salaries. It is clear
that management looks primarily at performance from the previous season when setting salary
and that it largely disregards performance from three years ago. That performance could be used
to predict a player’s future productivity, but management fails to do so. By having short
memories, teams fail to effectively use their payrolls to win games.
B. Do Successful Teams Use Past Performance Information More Effectively?
To compare teams, I divide the thirty Major League Baseball Teams into three groups. In
group one are the ten teams that have won more games than their payrolls would predict. These
are the teams that get the most out of the salaries they pay out to players. The teams that have
won about what their salaries would predict are in group two. The teams that have performed
worse than their salaries would predict are in group three. To break the teams down into these
three categories, I regress a team’s wins in a given year on a general functional form of the
team’s payroll. The complete details of how I construct these groupings are in the Appendix.
Table 2 displays the rankings.
By the standard of getting the most wins out of the salaries it has paid out, Oakland is the
best-run team in baseball. Oakland averaged 86 wins per season from 1985 to 2004, even though
its payrolls predicted only 79 wins. On the other end, Tampa Bay has averaged only 65 wins
during its seven years of existence, ten wins less than the 75 wins that its payrolls would have
predicted.10 Notice that there are low and high salary teams in all groups. Due to its high
salaries, the New York Yankees have the highest predicted wins of all teams. They also have the
highest average number of wins, and have done well enough that they rank fifth. In contrast, the
Arizona Diamondbacks are tied for second-highest in predicted wins. Even though they have
won slightly more games than they have lost, Arizona ranks in the bottom group because their
high payrolls predicted more wins.
The rankings in Table 2 make it possible to test for differences in how well-run teams
utilize past performance information compared to poorly-run teams. To conduct these tests, I
estimate regression (2) separately for the well-run teams and other teams. The results are shown
in Table 3.
The teams that use their money most effectively also do a better job of making their
salary offers match up with how past performance data predicts present performance. What sets
the well-run teams apart from the poorly run teams, however, is not primarily differences in
sensitivity of salary offers to recent versus past performance. The differences arise from the
kinds of players that different teams sign. The well-run teams sign players whose performance is
predicted more by last year’s performance than by previous years’ performances. In contrast, the
poorly-run teams sign players whose performance is predicted slightly better by performance
from two years ago than the most recent season’s performance. In other words, the well-run
teams are different from the other teams because they do a better job of identifying which
10
Florida and Colorado entered the league in 1992. Tampa Bay and Arizona entered the league in 1997.
players’ recent performances actually predict their future performances. The data suggests that
poorly-run teams are more likely to base their salary offers on recent performances when those
recent performances have more to do with luck than a player’s quality.11
Figure 2 illustrates these ideas graphically. Panel A refers to the well-run teams (Group
1). Panel B refers to all other teams (Groups 2 and 3). The well-run teams use past performance
data in accordance with how that data predicts future performance. For the players that they
sign, the poorly-run organizations base their salary offers more on last year’s performance
compared to performance from two years ago than they optimally would. Successful teams do
not make memory-based mistakes, while unsuccessful teams systematically make these errors.12
IV. Conclusion
To best use the dollars that they spend on salaries, organizations need to predict how well
players will perform in the future. The data shows that organizations make systematic mistakes
in how they make these predictions. Teams infer too much from players’ performances in the
most recent season relative to performances from earlier years. The organizations that make
these mistakes are the same ones that generally fail to spend their resources well. The best
organizations are also the ones that use past performance data most effectively.
One interesting question that is beyond the scope of this paper is the reason why baseball
player compensation overweighs recent performance relative to past performance. It may be the
case that players are rewarded for good luck in the last seasons of their contract, as previous
research has demonstrated that CEOs are rewarded for luck (Bertrand and Mullainathan, 2002).
Albert and Bennett (2001) show that a player’s performance in any given year reflects a great
11
Alternatively, it may be the case that the weaker teams are more likely to sign players who do not intend to
provide a full effort after signing the new contract.
12
Notice, too, that the R2 for the regression of salaries on past performance is higher for successful teams (.617) than
for unsuccessful teams (.485), indicating that the successful teams’ salary offers depend more on a player’s
performance history than the unsuccessful teams’ offers.
deal of luck. On the other hand, maybe there are certain players who exert greater effort in the
final years of their contracts and teams repeatedly fail to recognize this behavior.13 Future
research can attempt to estimate the extent to which firms are rewarding players for luck in the
final years of their contracts or for the extra effort they put in at the end of their contracts.
Notice that the tendency shown in this paper for teams to excessively reward performance at the
end of a contract would amplify a player’s incentive to try harder in his contract year.
References
Albert and Bennett (2001). Curve Ball: Baseball, Statistics and the Role of Chance in the Game.
New York: Springer.
Bertrand and Mullainathan (2001). “Are CEOs Rewarded for Luck? The Ones Without
Principals Are,” Quarterly Journal of Economics, 116(3): 901-32.
Camerer, Colin (1989). “Does the Basketball Market Believe in the ‘Hot Hand’?” American
Economic Review, 79(5): 1257-61.
Gray, Philip and Stephen Gray (1997). “Testing Market Efficiency: Evidence from the NFL
Sports Betting Market,” Journal of Finance, 52(4): 1725-37.
Kahn, Lawrence (1993). “Free Agency, Long-Term Contracts and Compensation in Major
League Baseball: Estimates from Panel Data,” Review of Economics and Statistics, 75(1):
157-64.
Kahneman, Daniel (2003). “Maps of Bounded Rationality: Psychology for Behavioral
Economics." American Economic Review. 93(5): pp. 1449-1475
Lahman, Sean (2006). “The Baseball Archive,” http://www.baseball1.com
McCracken, Voros (2001). “Pitching and Defense: How Much Control Do Hurlers Have?”
Baseball Prospectus, http://www.baseballprospectus.com/article.php?articleid=878
Mullainathan, Sendhil (2002). “A Memory-Based Model of Bounded Rationality,” Quarterly
Journal of Economics, 117(3): 735-74.
One way to disentangle these two hypotheses is to look at a player’s batting average on balls hit into play.
McCracken (2001) argues that whether a ball that is hit into play results in a base hit is largely a matter of luck. This
fact could be used to see how much the luck component of a player’s performance changes in the last year of his
contract compared to the skill component of his performance.
13
Quirk, James and Rodney Fort (1992). Pay Dirt: The Business of Professional Team Sports.
Princeton, NJ: Princeton University Press.
Retrosheet (2006). “Transactions,” http://www.retrosheet.org.
Scully, Gerald (1974). “Pay and Performance in Major League Baseball,” American Economic
Review, 64(6): 915-30.
Simon, Herbert (1957). “A Behavioral Model of Rational Choice,” in Models of Man. New
York: Wiley.
Sommers, Paul and Noel Quinton (1982). “Pay and Performance in Major League Baseball: The
Case of the First Family of Free Agents,” Journal of Human Resources, 17(3): 426-36.
Tversky, Amos and Daniel Kahneman (1974). “Judgment under Uncertainty: Heuristics and
Biases,” Science, 185(4157): 1124-31.
Tables and Figures
Table 1: How past performance determines present performance and salary
Performance this
year
(1)
Salary this
year
(2)
Performance last year
.320
(.044)
.357
(.038)
Performance two years ago
.280
(.049)
.194
(.042)
Performance three years ago
.157
(.050)
.070
(.043)
Number of observations
500
500
R2
.451
.489
Dependent variable:
Notes:
1) Regression standard errors are in parentheses.
2) A player's performance is measured by his OPS.
3) All regressions include year dummies.
4) Salary is the natural log of salary divided by ten, so that the coefficient gives the effect
of increasing OPS by 0.100 on a player's salary.
Table 2: Ranking teams by management effectiveness, 1985-2004
Mean payroll
millions)
(in Average number
of wins
Average predicted
wins based on
Actual wins payroll
predicted
Group 1:
Oakland (A)
Houston (N)
Washington (N)
Atlanta (N)
New York (A)
San Francisco (N)
St. Louis (N)
Chicago (A)
Toronto (A)
Cincinnati (N)
28.5
34.3
20.4
49.0
62.4
38.5
39.7
32.9
37.7
32.6
86
85
80
89
91
85
85
83
84
82
79
81
76
85
88
82
82
80
82
80
7
4
4
4
3
3
3
3
2
2
Group 2:
Minnesota (A)
Boston (A)
Cleveland (A)
New York (N)
Seattle (A)
Florida (N)
Los Angeles (N)
Anaheim (A)
Pittsburgh (N)
San Diego (N)
24.6
50.2
36.9
46.7
37.7
33.1
49.7
37.0
23.8
29.5
79
86
81
84
81
76
84
81
76
78
78
85
81
84
81
76
85
82
77
79
1
1
0
0
0
0
-1
-1
-1
-1
Group 3:
Milwaukee (N)
Kansas City (A)
Arizona (N)
Texas (A)
Philadelphia (N)
Chicago (N)
Colorado (N)
Baltimore (A)
Detroit (A)
Tampa Bay (A)
25.5
28.7
74.3
42.4
32.9
40.0
48.9
41.2
30.6
38.5
76
77
82
80
77
78
76
77
73
65
78
79
85
82
80
82
81
83
80
75
-2
-2
-3
-2
-3
-4
-5
-6
-7
-10
Notes:
1) Florida and Colorado entered the league in 1992. Tampa Bay and Arizona entered the
league in 1997. Since average salaries have been increasing in baseball, the average
salaries are higher for these teams.
2) The Washington franchise played in Montreal until 2005.
Table 3: How past performance affects salary for well-run and poorly-run teams
Group 1 teams
Performance
Salary this
this year
year
(1)
(2)
Dependent variable:
Group 2 and 3 teams
Performance
Salary this
this year
year
(1)
(2)
Performance last year
.444
(.077)
.386
(.058)
.340
(.050
.399
(.044)
Performance two years ago
.250
(.085)
.246
(.064)
.372
(.051)
.205
(.045)
167
167
369
369
.445
.590
.447
.493
Number of observations
2
R
Notes:
1) Regression standard errors are in parentheses.
2) A player's performance is measured by his OPS.
3) All regressions include year dummies.
0.35
0.4
0.3
0.35
0.25
0.3
0.25
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
0
Last year Two years Three years
ago
ago
Effect on salary
Effect on performance
Figure 1: How previous performance
affects present performance and salary
This year's
performance
This year's salary
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Effect on salary
Effect on performance
Figure 2A: How previous performance affects
performance and salary (well-run teams)
This year's
performance
This year's salary
Last year Two years
ago
0.45
0.45
0.4
0.4
0.35
0.35
0.3
0.3
0.25
0.25
0.2
0.2
0.15
0.15
0.1
0.1
0.05
0.05
0
0
Last year
Two years ago
Effect on salary
Effect on performance
Figure 2B: How previous performance affects
performance and salary (poorly-run teams)
This year's
performance
This year's salary