Performance Variation in the NBA:
Guaranteed Contracts and the Contract
Year Phenomenon
Neal Jean
Professor Peter Arcidiacono, Faculty Advisor
Honors Thesis submitted in partial fulfillment of the requirements for Graduation with
Distinction in Economics in Trinity College of Duke University.
Duke University
Durham, North Carolina
2010
2
Acknowledgments
I would like to thank my faculty advisor, Professor Peter Arcidiacono, an avid follower of
the NBA in his own right. Without his insights and ideas, much of the quality of my
paper would not have been possible. I would also like to thank Professor Kent
Kimbrough, who encouraged me to pursue a topic that I was truly interested in and
helped to guide the formulation of my research goals and objectives. My gratitude goes
out to Professor Michelle Connolly who, despite having no prior interest in basketball,
spent hours reading and discussing my paper with me, and helped with everything from
the development of theoretical hypotheses to the empirical analysis. Finally, I am
indebted to my Economics 198S and 199S classmates for their patience and comments.
In the spirit of this paper, all fouls are my own.
3
Abstract
Asymmetric information in the typical principal-agent model may create
incentives for workers to participate in opportunistic or strategic behavior. This paper
examines evidence for the existence of ex ante and ex post strategic behavior in the
National Basketball Association (NBA), where multi-year guaranteed contracts give
players incentive to vary their effort level over the course of the contract cycle. I
hypothesize that players will increase effort in a contract year, the season prior to signing
a new contract, and decrease effort in the following season, with the assumption that
variations in effort are expressed through variations in performance. Player productivity
is found to increase significantly in a contract year, while no evidence is found to support
the presence of shirking behavior. The resulting model may serve to guide NBA teams in
structuring contracts, as appropriate performance incentives built into individual player
contracts could positively influence team success.
4
I. Introduction
In the principal-agent models present in most organizations, inefficiencies may
arise from the creation of long-term contract agreements. Knowing that their future
wages are guaranteed, workers have an incentive to participate in opportunistic or
strategic behavior, generally referred to as shirking behavior (Alchian and Demsetz 1972;
Holmstrom 1979). The moral hazard problem leading to the occurrence of shirking
behavior results from asymmetrical information between the parties involved.
1
In
general, opportunistic behavior may occur under the following conditions:
2
1. The principal and the agent enter into a binding, long-term contract,
through which the agent is compensated by the principal for expending
effort at some cost to himself.
2. The principal’s level of utility or profit is a function of the agent’s
level of effort expended.
3. The principal is unable to monitor the effort of the agent directly.
Under these conditions, the agent may decide that he has sufficient incentive to
strategically vary his effort level. This paper will examine the question of whether this
type of strategic behavior exists in the context of long-term guaranteed contracts in the
National Basketball Association (NBA).
Maxcy et al. (2002) introduces the terminology ex ante strategic behavior and ex
post shirking to describe potential worker behavior under circumstances of asymmetrical
1
Regarding asymmetrical information, Holmstrom (1979) mentions that situations in which the private
actions of individuals affect the outcome distribution have long been recognized for the risk of moral
hazard. Since individual actions cannot be observed and contracted upon, contracts are written without
complete information.
2
As described by Krautmann and Donley (2009).
5
information. Ex ante strategic behavior refers to an increase in effort expended by the
agent prior to the signing of a new contract. In attempting to increase his perceived value
to the principal, the agent seeks to maximize the level of compensation guaranteed him
by the impending contract. Ex post opportunistic behavior, or shirking, is defined as a
decrease in effort expended by the agent once the contract is signed. Since compensation
is then guaranteed, regardless of effort level, the agent has no incentive to continue
performing with maximal effort.
3
A key point here is that the employer is unable to
observe employee effort level directly; if effort-monitoring were possible, the employer
would be able to structure contracts accordingly and guarantee an efficient outcome.
4
Strategic behavior as a result of long-term guaranteed contracts has been widely
cited in academic economic literature and also carries significant real-world implications,
arising in such diverse situations as manufacturing sales, political decisions, nuclear
power plants, and the academic institution of tenure (Krautmann 1990).
56
3
A brief note on terminology: Strategic behavior and opportunistic behavior will be used interchangeably
to describe any type of changing behavior as a result of information asymmetry during the contract cycle.
The term shirking will be used to describe ex post strategic or opportunistic behavior.
Whenever
agents are faced with the incentives created by long-term contracts, they are also
presented with motivation to vary their effort to maximize their own utility. Consider the
example of university professors and tenure: One can imagine that a professor seeking
4
If a principal were able to observe effort directly, he could simply compensate agents directly for the level
of effort that they contribute toward the principal’s production. In reality, the principal must make an
estimate of the agent’s future effort level and productivity that may be unmet by the agent’s actual
contribution.
5
Oyer (1998) examines the impact of incentives as they relate to the sales of manufacturing firms, and
finds that sales are often boosted near the end of the fiscal year as salesmen try to hit their incentive targets
and increase their own compensation.
6
Krautmann (1990) gives an interesting example illustrating the usefulness of being able to distinguish
shirking behavior from the outcome of a stochastic process. He says to imagine a safety regulation scheme
for nuclear power plants that induces the socially optimal maintenance and safety effort. Even with this
optimized system, he argues that accidents can still occur as the result of random processes. In these cases,
regulators would be better served to categorize these failures as random events rather than assigning fault to
and punishing the individual plant, as this would cause the plant to respond by overspending on future
maintenance and accident prevention, rather than simply spending the original, optimal amount.
6
tenure would be very productive, publishing original research on a regular basis, but upon
achieving tenure, might lose motivation and kick back, enjoying the flexible lifestyle
afforded him. We of course hope that most professors are more scrupulous and resist the
temptation to take advantage of the opportunity to exert effort strategically, but this
example makes it clear that such opportunities exist.
7
Professional sports offer an ideal setting to study the incentive effects of long-
term contracts, as players are carefully observed by teams, fans, and media, resulting in
an expansive and thorough set of productivity data that is widely available for analysis.
Already, a number of researchers have utilized the unique environment of professional
sports to search for evidence supporting the shirking hypothesis, with varying results.
8
Most of these studies have focused on Major League Baseball (MLB), as performance
metrics that measure player productivity are more widely agreed-upon in baseball,
although a few have also examined the NBA.
9
7
Stiroh (2007) points out that in other situations involving long-term contract cycles (e.g., professors
working for tenure or politicians seeking election), the inefficiencies caused by incentivized strategic
behavior could be even higher than in the NBA, due to greater information asymmetry and less monitoring
ability.
Perhaps as a result of employing different
empirical specifications, research concerning professional sports has drawn conflicting
conclusions. Stiroh (2007) claimed that there is strong evidence that players engage in
strategic behavior, while many others have refuted the existence of such behavior
(Krautmann 1990; Maxcy et al. 2002; Berri and Krautmann 2006; Krautmann and
8
Krautmann and Donley (2009) give a brief description of the typical study in professional sports. Usually
the researchers examine the player’s performance in proximity to contract negotiations. Conclusions about
the presence of shirking behavior are drawn from the discrepancies between observed ex ante and ex post
performance and expected performance.
9
Berri and Krautmann (2006) remark that baseball has a number of indices that have been designed
specifically to capture the productivity of an individual player in a single number.
7
Donley 2009).
10
The NBA was chosen from among the three major professional sports leagues in
the United States as the league to be studied for several reasons. From a practicality
standpoint, the prevalence of long-term guaranteed contracts in the NBA provides a
textbook setting in which to study shirking behavior––unlike, for example, the National
Football League (NFL), in which large portions of a player’s contract are not guaranteed,
and players can be cut or released at the team’s discretion. The relative scarcity of
performance-based incentives in the NBA also contributes to an environment that would
support the shirking hypothesis.
The goal of this paper is to explore the ex ante and ex post phenomena
of opportunistic behavior in a specific labor market, the National Basketball Association
(NBA).
In terms of impact, the question of whether or not strategic behavior exists in the
NBA is arguably more important, and certainly more complex, than in the NFL or MLB.
Team sizes are much smaller in the NBA, making each athlete—and accordingly, each
athlete’s contract—that much more important to the success of the team. Think back to
the 2006-07 season, when Lebron James carried a team of largely mediocre players all
the way to the NBA Finals, or the next season, when the Celtics’ acquisition of Kevin
Garnett and Ray Allen led to a year-on-year improvement of 42 wins and culminated in
the 2007-08 NBA Championship. Unlike football, in which the vast majority of players
play either offense or defense but not both, or baseball, where most players spend only a
10
Stiroh (2007) found evidence of shirking behavior in the NBA, while studies refuting the shirking
hypothesis have been conducted using both NBA and MLB data. Maxcy (2002) rejects strategic behavior,
citing that the data suggests that mechanisms incorporated into the structure of MLB contracts intended to
prevent players from strategically adjusting their effort seem to be fulfilling their role. Examples of such
mechanisms include performance incentives, team success bonuses, and clauses that allow for
performance-based contract renegotiation.
8
fraction of the game directly participating in the action, basketball is a game in which
players are constantly involved.
11
While individual contributions are generally more important in basketball, an
added layer of complexity arises when one attempts to quantify these contributions.
Compared to baseball, the other prominent arena for studying shirking behavior, player
effort in basketball is notoriously difficult to measure. To illustrate, imagine a baseball
player who is up to bat. Presumably, there are players who care more than others about
whether or not they get a hit, but it seems unlikely that this will affect their effort to hit
the ball. It is debatable whether or not a player can hit a curveball more effectively
simply by trying harder. In basketball, the effect of effort on player performance is
intuitively apparent, though not always easy to discern through statistical analysis. It
makes perfect sense that a basketball player can play better defense by exerting more
effort, getting into a lower defensive stance, and rotating to help his teammates. A player
can also help his team by diving for loose balls or boxing out on offense to earn extra
possessions. Of course, since teams cannot monitor the effort of their players directly—
one of the conditions under which strategic behavior can occur—they must determine
effective methods to indirectly measure player effort.
While on the court, NBA players are continuously
contributing to both the offensive and defensive efficiency of their team. Individual
athletes make a greater impact in basketball than in any other major team sport popular in
the United States.
11
One could make the argument that starting pitchers in baseball are able to affect the outcome of an
individual game to a greater extent than any player in a basketball game. Though it is difficult to quantify
contributions across sports to allow for comparison, intuitively this claim is not without merit. However,
the key is that starting pitchers can influence an individual game. Since most pitchers start once every four
to five games during the regular season, they are limited to affecting the team’s performance at most 25%
of the time.
9
Generally, teams resort to using statistics of player performance as a proxy for
effort. The paradox here, however, is that while an individual can make a greater impact
in basketball than in baseball, basketball is simultaneously a more team-oriented sport. If
a baseball player wishes to improve his performance, he can easily see where he should
focus his efforts. Hitting and fielding, the primary components of the game for most
position players, are largely individual capacities. In basketball, however, the answer is
much less easily defined. Consider two average and equally dedicated NBA players,
Player A and Player B. Suppose Player A chooses to focus on improving his scoring
ability; any improvement in this domain will show up in the box score at the end of the
game. Now suppose Player B concentrates his effort on playing effective help defense or
on boxing out for offensive rebounds; even the most dramatic improvements in these
areas might not be reflected in the statistics. We see here that two players who devote an
equal amount of energy may not appear to benefit the team in equal measure. A
successful general manager, then, must discern a player’s true value to his team in the
face of divergent statistical inputs. Furthermore, how players decide to allocate effort
may change over time. Clearly, these complexities will be problematic in determining an
effective measure of player productivity to be used as a proxy for effort.
The two pieces of literature most relevant to my current research are Stiroh (2007)
and Berri and Krautmann (2006). Both of these studies look for evidence of
opportunistic behavior in the NBA, with Stiroh (2007) concluding that the hypothesis
was strongly supported, and Berri and Krautmann (2006) claiming that there was no
evidence that NBA players engaged in shirking behavior. My research will attempt to
synthesize and build on the methods of Stiroh (2007) and Berri and Krautmann (2006),
10
ultimately arriving at a more effective method of determining the presence of strategic
behavior in the context of NBA player contracts. Two main objectives will be pursued
through this study: First, I hope to evaluate several methods of measuring player
performance and then identify the measure that I believe to be most appropriate for this
study. Second, I will determine whether or not sufficient evidence exists to support the
hypothesis that players engage in strategic behavior, answering the original research
question that was the inspiration behind this study.
Using a playing-time adjusted measure of player performance, I find that evidence
for the contract year phenomenon, or ex ante strategic behavior, does exist in a dataset
that includes more recent observations than those used in the aforementioned studies. Ex
post shirking, however, is not supported by the data, although shirking behavior may be
masked by confounding factors. Additionally, in the course of this study, I develop a
method for separating the interrelated effects of age and experience on player
productivity by measuring experience in such a way that it is no longer perfectly
correlated with the passage of time.
The rest of this paper will be organized as follows: Section II will review the
existing body of literature and discuss its relevance to the current research. Section III
will describe the economic theory of shirking and its implications for my empirical
analysis. Section IV will provide an overview of my data set and discuss any limitations
that it might impose. Section V will establish my empirical specification. This section
will include my expectations for the results of the study, as well as the actual results
obtained. Section VI will conclude the paper, and discuss possibilities for further
improvement and research on the topic.
11
II. Literature Review
Long-term Guaranteed Contracts in the NBA
Shirking behavior has the potential to occur when an agent is signed to a long-
term, guaranteed contract, in which he is compensated by the principal for the
expenditure of costly effort (Krautmann and Donley 2009). The NBA provides a large
sample of these types of situations, as well over half of all players are under contract for
two or more seasons.
12
Stiroh (2007) offers a discussion about why long-term contracts have not been
replaced with alternatives such as incentive-based contracts or short-term contracts.
Instead of fixing future compensation at the moment that the contract is signed, an
alternative to the guaranteed contract would be to offer players long-term, incentive-
based contracts. Incentive-based contracts compensate players for reaching certain
Since contracts in the NBA are largely multi-year and guaranteed,
players could choose to raise their effort prior to signing a long-term contract, then
reduce their effort level substantially after locking in a guaranteed salary for the ensuing
several years. Since opportunistic behavior is associated with the presence of long-term
guaranteed contracts, one may reasonably wonder why the NBA continues to utilize
multi-year contracts. Given that the nature of the industry limits the accuracy of
information that employers can obtain about their workers’ behavior, why wouldn’t they
simply eliminate the types of contracts that promote strategic behavior altogether?
12
Unlike contracts in the NFL, NBA contracts are fully guaranteed (Berri and Krautmann 2006).
Regardless of whether or not a player plays in games, or even if the player is with the team, the team must
continue to pay the player under the original terms of the contract.
12
standards of performance.
13
A reduction in the guaranteed portion of the contract would
motivate players because their pay would then be dependent upon their performance,
rather than remaining fixed, as in the guaranteed contracts that currently prevail in the
NBA. Many NBA contracts already contain performance-based incentives, though these
usually compose only a small fraction of the total value of the contract.
14
Unlike other
professional sports leagues that make extensive use of performance incentives, such as
the NFL or MLB, bonuses in the NBA are generally limited to far less than 25% of the
player’s total salary (Heubeck 2003; Stiroh 2007).
15
Prendergast (1999), in his work on firms providing incentives to their workers,
discusses the benefits and drawbacks of pure incentive contracts.
Consider the example of Peyton
Manning, the star quarterback of the NFL’s Indianapolis Colts. In 2004, Manning signed
a 7-year contract worth $99.2 million. Manning could also earn up to an additional $19
million in contract incentives. Of this total, only $34.5 million was guaranteed money in
the form of a signing bonus. In contrast, contracts in the NBA are almost fully
guaranteed.
16
13
For example, it might be specified in a player’s contract that he would be paid a base salary of $10
million for the season, and incentives of $1.5 million for averaging 20 points per game (ppg), $1 million for
averaging 10 rebounds per game (rpg), and $1.25 million for averaging 5 assists per game (apg). If the
player averaged 19 ppg, 12 rpg, and 4 apg, he would be paid the $10 million base salary plus the extra $1
million for averaging over 10 rpg for a total of $11 million in compensation for the season.
By construction, a
contract that is entirely composed of performance incentives is far riskier than a contract
in which all future payments are guaranteed. It follows that a risk-averse worker would
14
Incentives can be included for achievements that are not purely statistical. For example, a player may
have bonuses written into his contract that would reward him for winning league awards such as the Most
Valuable Player (MVP), or for being voted onto the conference All-Star team or the All-NBA team.
15
Salary structure in the NBA is regulated by the collective bargaining agreement (CBA) between the
National Basketball Players’ Association (NBPA), which is the players’ union, and the NBA. The CBA
distinguishes between “likely bonuses” and “unlikely bonuses” in the incentives clauses included in player
contracts, and state that “unlikely bonuses” cannot exceed 25% of the player’s salary.
16
This would be the limiting case, in which all compensation is contingent on the agent fulfilling the terms
of the incentive clauses written into the contract and there is no guaranteed compensation.
13
require the expected value of the total compensation under a pure incentive contract to be
higher than the amount guaranteed by a fixed-wage long-term contract. This is especially
true in professional sports leagues such as the NBA, where a highly volatile environment
limits the ability of the player to accurately forecast his own future performance (Stiroh
2007). For example, for most players, playing time is distributed at the discretion of the
team’s coach, meaning that there is no guarantee that an individual player will even have
the opportunity to accumulate the necessary statistics to meet their contract incentives.
Additionally, injury is a common and unpredictable limit on the productivity of
professional athletes, and as such, also presents a risk to a player’s compensation. Given
such high levels of uncertainty, if NBA teams wanted to implement incentive-based
compensation schemes, they would have to pay players a much higher average salary to
convince them to accept the increase in volatility from riskless guaranteed contracts. We
can infer that the corresponding productivity gains from increased player effort would not
be enough to offset the increased financial expense of incentive-based contracts for NBA
teams.
Stiroh (2007) also considers short-term contracts as an alternative to long-term
contracts. If teams are worried that players might increase their effort in contract years
and then decrease it after signing a long-term contract, why not make every season a
contract year, and motivate players to play hard every year to earn a lucrative deal for the
next season?
17
17
A contract year is defined here as the last season before signing a new contract. It is in the contract year
that ex ante strategic behavior is hypothesized to occur.
However, this solution of year-by-year contracts is not as ideal as it
sounds. There are many advantages to long-term contracts in the NBA, both for the
teams and for the players. From the team’s perspective, signing a player for the long-
14
term can provide positive returns in excess of the player’s on-court contributions—
professional athletes also serve as commercial commodities. By signing popular players,
teams can create fan interest and develop loyalty among supporters, which over time
results in increased box office revenues, as well as profits from sales of jerseys or other
team paraphernalia. In terms of winning games, keeping players for multiple seasons can
also have positive effects on team performance. It is commonly accepted—and anyone
who has ever played competitive team sports would agree—that players learn to play
more effectively with specific teammates over time, a performance-enhancing
consequence that results naturally when a core group of players stays with a team for
multiple seasons.
From the player’s perspective, long-term guaranteed contracts are preferable to
short-term contracts for the same primary reason that they are preferable to incentive-
based contracts. Simply put, long-term contracts reduce volatility in compensation by
smoothing out the risks posed by injury concerns and other unpredictable circumstances.
Suppose a player is given a choice between guaranteeing a relatively high salary for the
next few years and playing for a new, more profitable contract each season—but at the
same time exposing himself to the risk of not earning any new contracts beyond the
current season, as in the event of a career-ending injury. It is clear that in most situations
the player would choose the guaranteed money over multiple seasons. There are other,
less significant concerns that would predispose a player to prefer longer-term contracts,
such as not having to make new living arrangements if moving to a new city, building a
relationship with the team and city that he is currently playing for, and so forth.
Opportunistic Behavior in the NBA
15
As mentioned before, the two previous studies on incentive effects of long-term
guaranteed contracts in the NBA reached conflicting conclusions. Both provide
significant insights on the topic, and the theoretical framework supporting this paper has
drawn on components of each previous study. We will begin with a review of Stiroh
(2007), in which the author found strong evidence of opportunistic behavior by using
both individual statistics and a composite statistic as measures of player performance.
We will then examine Berri and Krautmann (2006), in which the authors found weak
evidence supporting the shirking hypothesis using the NBA’s measure of player
productivity, and evidence against shirking when using a measure of each player’s
marginal productivity.
The motivating hypothesis in Stiroh (2007) is that imperfect information and
multi-year contracts create an implicit incentive for workers to strategically alter their
effort over the contract cycle. Stiroh defines information asymmetry as the condition
under which an employer cannot perfectly distinguish between effort and ability in his
employees, but rather sees only an indicator that results from a combination of the two.
Using this instrument, the principal must form perceptions about the quality of the agent,
and then structure long-term compensation using these incomplete perceptions. From the
other side of the strategic game, theory tells us that a rational worker should choose to
exert an optimal level of effort in each year of the contract cycle. Returning to the
specific case of the NBA, Stiroh continues to explain that players in their contract year
should choose their effort level by balancing the gains from higher wages in future
contracts with the disutility that arises from increasing effort. Similarly, in the season
following the signing of a new contract, players should have incentives to decrease their
16
effort level. At this point, the cost of exerting effort is not balanced by any marginal
benefit, since compensation levels have already been fixed by the terms of the contract.
Applying these theoretical results, his goals are to test for two indicators that he believes
would support the shirking hypothesis: whether players exert above-average effort in
contract years and whether players exert less effort after the new contract is signed.
In his study, Stiroh (2007) uses contract data from the 2000-2001 NBA season
and player statistics from 1988 through 2002.
18
He estimates the following weighted
OLS regression in order to test his hypotheses:
P, the dependent variable, is a performance metric that depends on the dummy variables
PRE and POST, which determine whether or not the performance occurs in a contract
year or in the season immediately following. NAGE is a standardized measure of the
player’s age relative to the league average, and each of the α’s corresponds to dummy
variables to control for unobserved individual ability, player position, year, and team.
1920
The performance metrics employed by Stiroh (2007) are quite elementary, as the
regression is estimated several times using individual measures of performance, and once
using a composite rating. The following individual statistics were used: points scored,
total rebounds, assists, blocked shots, shots attempted, free throws attempted, and
The shirking hypothesis predicts that the coefficients on the dummy variables PRE and
POST will be positive and negative respectively, showing that performance increases in
the contract year and decreases following the signing of the contract.
18
The year 1988 corresponds to the 1988-99 NBA season.
19
The variable NAGE is used to control for predictable age-related effects (Stiroh 2007).
20
Player position refers to the position that the player primarily plays when he is on the court. Position is
relevant because players who play different positions can be expected to accumulate different distributions
of statistics. Players in this study were classified as guards, forwards, or centers.
tijtpiAGEPOSTPREti
NAGEPOSTPREP
,,
εααααβββ
+++++++=
17
minutes played. The reasoning behind including shots and free throws attempted as
dependent variables is that attempts might be a better proxy for player effort, as the
player is able to control these statistics more directly. The composite rating used was
designed to summarize a wide range of performance statistics and provide a
comprehensive measure of overall performance.
21
Using the composite statistic, Stiroh finds statistically significant evidence of both
performance increases in the contract year and performance decreases in the following
year. Using the seven independent statistics, he discovers that the data strongly supports
an increase in performance during the contract year, but fails to provide evidence for a
decrease in production after the contract has been signed, instead showing that player
performance regresses to the long-run mean. In other words, these results support the ex
ante strategic behavior hypothesis, but find no evidence in the data that players also
display shirking behavior after signing a new contract.
The Berri and Krautmann (2006) study is motivated by the same hypothesis as
Stiroh (2007), namely that opportunistic behavior can occur when there is incomplete
information in the labor contract between principal and agent. Berri and Krautmann
approach the problem differently in several important ways, beginning with the objective
of the research. Instead of searching for evidence of opportunistic behavior both before
and after the signing of a contract, they only look for evidence that supports ex post
shirking behavior.
21
The composite rating is calculated as (field goals made*1.4 + blocked shots*1.4 + free throws made*1.0
+ assists*1.0 + steals*1.0 + offensive rebounds*0.85 + defensive rebounds*0.5 – turnovers*0.8 – field
goals missed*0.6) / (minutes played / 48).
18
The model estimated by Berri and Krautmann (2006) is listed below:
The chosen measure of productivity is the dependent variable, regressed on dummy
variables D2 and D12 for the years of experience that the player has in the NBA, the
change in games played from the previous season to the current season as a proxy for
injury, the years of experience that the coach has, the lifetime winning percentage of the
coach, the change in the number of team wins, a variable that accounts for the roster
turnover, and the dummy variable that indicates that a player is in their first season after
signing a new long-term contract.
22
Berri and Krautmann (2006) note that from prior
work, they have discovered that player productivity is nearly constant over the course of
a player’s career, with two notable exceptions. Productivity increases sharply in the first
two seasons of a player’s career, and then decreases steadily once the player reaches his
12
th
22
The ΔROSTER variable was calculated by first determining which players were on the team in both the
previous season and the current season, adding up the minutes played by those players in both seasons, and
then dividing by the total number of player minutes available in both seasons. This measure was developed
in Berri and Jewell (2004).
year of experience. Therefore, a dummy is included for players with more than 2
years of experience, and another for players with more than 12 years. The change in
team wins variable is designed to account for the impact of teammate quality on player
productivity. The assumption is that a player’s productivity falls with increasing
teammate quality, as his teammates contribute a greater portion of the team’s overall
production.
∆PROD =
β
0
+
β
1
D2+
β
2
D12+
β
3
∆GP +
β
4
CEXP +
β
5
CWPCT
+
β
6
TMWINS +
β
7
∆ROSTER+
θ
1
SHIRKING +
ε
19
The term designated SHIRKING was tested by Berri and Krautmann using three
different variables. In the first model, the simple SIGNED variable was used, a dummy
equal to 1 when a player was in the season immediately following the signing of a new
contract. Next, they tested the interaction with contract length (SIGNED × LENGTH),
and the interaction with salary (SIGNED × SALARY). If the ex post shirking hypothesis
is supported by the data, then we would expect to see a negative coefficient on whichever
variable was being used for the SHIRKING variable in the test. As stated previously,
Berri and Krautmann (2006) found weak evidence supporting the shirking hypothesis
when using the NBA’s measure of player productivity, and evidence refuting the shirking
hypothesis when using a marginal productivity measure, with the additional result that
the coefficients on SIGNED and (SIGNED × LENGTH) were significant, while the
coefficient on (SIGNED × SALARY) was not. From their study, they concluded that
signing a new long-term contract would decrease player productivity by about 2-4%,
while increasing the size of the contract signed had no effect on productivity.
Using the marginal product method of measuring player efficiency, the evidence
obtained by Berri and Krautmann (2006) refutes the shirking hypothesis. They conclude
that in the argument over whether opportunistic behavior takes place in professional
basketball, the answer is largely dependent on the measure of player productivity chosen.
However, they hint that the conventional methods of measuring player efficiency, such as
that employed by the NBA, may be lacking in their ability to fully capture a player’s
contributions to his team’s success. From their implication that the marginal product
metric better represents the productivity of an individual player, we can infer that Berri
20
and Krautmann believe that shirking behavior in the NBA is not supported by the
available data.
III. Theoretical Framework
Testing for Strategic Behavior
The underlying foundation of this paper is the theoretical prediction that the
principal-agent model present in the NBA provides incentives for players to strategically
alter their effort and therefore their performance over the course of the contract cycle.
23
Choosing a Model of Player Productivity
Testing for the presence of ex ante strategic behavior and ex post shirking, terms
introduced by Maxcy et al. (2002), will be the main goal of this study. In theory, players
will exert more effort in the season prior to signing a long-term contract; their incentive
for doing so is the promise of higher compensation over the duration of their new
contract as a result of their increased productivity. In the following season, we would
expect performance to drop; since their salary is no longer tied to their contemporaneous
production, players lose the incentive to play hard and give maximum effort. I will
follow Stiroh (2007) in testing for the existence of both ex ante and ex post strategic
behavior, unlike Berri and Krautmann (2006), which only tested for shirking behavior.
Evidence from Stiroh (2007) hinted that the ex ante effect of increased performance
before a new contract may be stronger than the ex post effect, suggesting that a
statistically significant relationship may be easier to uncover if we test for both instances
of performance variation.
23
The straightforward hypotheses of the principal-agent model in the presence of long-term contracts will
only be reviewed briefly in this section, as they have already been discussed at length in previous sections.
21
The problem with picking a single model of player productivity is that it is
unlikely that we will ever find a combination of performance metrics that perfectly
measures the level of effort expended by an individual player.
24
Although we must control for additional variables regardless of our choice of
productivity measure, I assume here that players will expend effort in a way that helps
their team win. If this assumption is largely true, then by picking a measure of
productivity that is related to team success, we hope to find a reliable proxy for effort. In
this way, we can ensure the consistency and accuracy of the results without an
overreliance on the selection of perfect controls.
Thus, we must choose
some productivity measure that is a function of effort, among other variables, and then
attempt to control for those other variables to the best of our ability. The remaining
variation in productivity—provided we have chosen a valid and thorough set of
controls—can be attributed to fluctuations in player effort throughout the contract cycle.
Furthermore, increases and decreases in productivity in the ex ante and ex post seasons, if
found, will serve as evidence supporting the existence of strategic behavior in the NBA.
As a starting point, I began by comparing the productivity measures used in Berri
and Krautmann (2006). Using the NBA measure of player efficiency as the performance
measure, Berri and Krautmann found statistical evidence supporting the shirking
hypothesis at the 5% significance level. However, this measure of productivity may have
several deep flaws. The NBA measure of player efficiency is calculated as follows:
25
( )( )
NBA
PROD PTS TREB STL BLK AST TO FGMS FTMS= + ++ + −+ +
24
Of course, if this were possible, the hypothetical perfect measure would directly indicate whether players
vary their effort level over the contract cycle, and this study would be unnecessary.
25
The variables in this equation are defined as follows: PTS = points scored, TREB = total rebounds, STL =
steals, BLK = blocked shots, AST = assists, TO = turnovers, FGMS = field goals missed, and FTMS = free
throws missed.
22
We immediately see that there are weaknesses in using this measure of performance.
Because all of the statistics used to construct this overall measure of player efficiency are
weighted equally, we cannot discern the relative value of any single statistic with respect
to any of the others.
26
Berri’s approach to measuring player productivity hinges on the idea that team
performance can be connected to player statistics through marginal productivity. This
idea is developed in Berri (1999), Berri and Jewell (2004), and several other sources, and
then reevaluated in Lee (2008). The general idea is to express team winning percentage
as a function of points per possession employed and points given up per possession
acquired. By differentiating this equation with respect to the independent variables, it is
possible to determine the marginal impact of each individual player statistic. For
example, through this method, it is possible to calculate the contribution toward winning
of a single offensive rebound by a specific player. Summing all the individual statistics
that impact team performance, we recover a formula that is very similar to the
productivity measure used by the NBA:
In an attempt to develop a more robust measure of player
productivity, Berri and Krautmann turn to an economics-inspired model that relies on the
player’s marginal contribution to team winning percentage.
27
)44.0()( FTAFGATOSTLTREBPTSPROD
MP
++−++=
The key difference is that this measure, derived from marginal productivity, punishes
players for shooting inefficiently. By the NBA’s measure, a player can boost his
performance just by taking a large number of shots, but in this measure, each shot attempt
26
For example, we would not expect a missed field goal to have the same effect as a missed free throw.
27
For a more detailed explanation of this derivation, refer to the Appendix of Berri and Krautmann (2006).
23
deducts from the player’s productivity rating, forcing him to make a higher percentage of
his attempts.
28
Adhering to the assumption that players funnel effort into production that
increases their team’s likelihood of winning, the marginal productivity measure of player
efficiency used by Berri and Krautmann (2006) provides the basis for the measure of
productivity that I will use to estimate my regressions. In order to compare player
productivity across different seasons, during which players may not always play the same
number of minutes, I will adjust marginal productivity to account for playing time. The
final measure of productivity used in my base regression will be the player’s marginal
productivity per 48 minutes (MP48), the duration of a regulation NBA game.
29
Choosing Independent Variables and Controls
To control for any factors that might influence a player’s productivity other than
the contract cycle, it is important to choose appropriate independent variables for the
model. As before, I rely on the previous literature to guide my choices of independent
variables. To begin with the most important, a player’s age and experience will clearly
have some kind of impact on his productivity. Surprisingly, both of the previous studies
included either age or experience in their regressions, but neither included both.
Although no explicit explanation is given, I surmise that the authors assumed that age and
experience would be highly correlated, and that including either one would largely
28
Using the NBA’s measure of player efficiency, in order for a player to improve his rating, he must
attempt more field goals while making them at rates above 33% for 2-point FGs and 25% for 3-point FGs.
Since most players in the NBA shoot above those percentages, a player need only take more shots to
improve his productivity. Using the marginal product method, which punishes players for the shots that
they take instead of just the shots that they miss, a player must make at least 50% of 2-point FGs and 33%
of 3-point FGs to improve his rating.
29
Since player statistics are recorded on a per-game basis, I will divide the calculated marginal productivity
by the number of minutes played per game, and then multiply by 48.
24
capture the effects of the other as well.
30
Age is representative of a player’s physical condition, which includes factors such
as athleticism, accumulated injuries, daily wear and tear, and the natural aging process.
As such, I expect the relationship between player age and performance to be generally
parabolic, with performance increasing with age up until some critical age—the average
age at which a player reaches his physical prime—and then decreasing as a player begins
to lose athleticism and feel the effects of the figurative “miles” that he has put on his
body over the course of his career.
However, in theory, age and experience should
have quite different effects on player productivity.
On the other hand, I expect that experience falls under the category of “you can
never have too much of a good thing.” If age is controlled for separately from experience,
I would anticipate the effect of experience on productivity to be monotonically increasing,
although probably with decreasing returns. Upon entering the NBA, it makes sense that a
player would learn and improve quickly, with marginal improvement slowing over his
career, as there remains less and less to be gained from additional experience. As with
age, experience should have a nonlinear relationship with productivity, so both will be
included in the model with first and second order terms.
31
One variable from Berri and Krautmann (2006) that I chose to include in my
model is the change in games played from one season to the next. This variable will
serve as a proxy for injuries, which have a definite impact on player performance. I
30
Stiroh (2007) chooses to include player age in his regression using the NAGE variable, while Berri and
Krautmann (2006) include experience using the variables D2 and D12. It is possible that these variables
are designed to account for the effects of both experience and age together (more likely to be the case with
D2 and D12).
31
Age will be controlled for with variables AGE and AGE
2
while experience will be controlled for with
variables EXP and EXP
2
.
25
expect that if a player is healthy for a larger portion of one season than the previous
season, his performance should also increase, as he generally will not have to deal with
minor injuries that may not stop him from playing, but can still inhibit his productivity.
Finally, it is important to control for the player’s team, the season in which the
performance measure was recorded, and individual player characteristics. Different
teams in the NBA can have widely varying styles of play, not to mention differences in
coaching, so a player’s current team during a given season must also be accounted for.
32
Similarly, league-wide characteristics such as pace and style may also change from
season to season, so it may be important to control for the season in which player
performance is recorded. Individual players will of course have different characteristics;
for example, talent level, commitment, career ambition, and let’s admit it, greed, may all
differ among players. We expect there to be variation in productivity between players
who play different positions, so player position must be accounted for as well.
33
Confounding Variables / Potential Difficulties
Stiroh (2007) discusses at length two confounding variables that he believes will
work against the incentive effects and perhaps diminish the strength of his results. First,
there is a selection effect that determines the population of players who are signed to
long-term contracts. It is in the best interest of each team to make a significant effort to
determine which players are truly high-ability—and thus deserving of long-term
contracts—and which are merely opportunistically increasing their effort level in their
contract season. If teams are at all successful in distinguishing between ability and effort,
then the players being signed to long-term contracts will disproportionately be those who
32
Players can be traded in the middle of a season, so in order to determine a player’s team for a particular
season, I simply chose the team for which the player played the majority of his games in that season.
33
Players are categorized under one of five positions: C, F-C, F, G-F, and G.
26
have high levels of natural ability. This type of high-ability player will have more
potential than a similarly productive player who is producing at that level because of
increased effort, and this potential will likely be expressed through higher levels of future
production, even if effort levels still fall after the signing of the contract. The idea is that
teams try to sign high-ability players who have the potential to continue improving, a
strategy that, if successful, will work against the hypothesized decline in performance in
the year following the new contract.
Another confounding effect might stem from players’ concerns about their careers,
specifically about future compensation. Although compensation may be guaranteed for
the duration of the current contract, all players, particularly younger players, must keep in
mind that they will likely be signing new contracts within the next few years. Even
though their recent effort and performance will not affect their current pay, it could have
adverse affects on their reputation or perceived ability level, which would result in a
lower-valued subsequent contract than they could otherwise earn. Stiroh points out that
this effect leads to two additional testable hypotheses: variation in effort should be
correlated with both the length of the contract signed and the age of the player. The
longer the contract, the less the player has to worry about negatively impacting future
contracts, and the older the player is, the smaller the proportion of his career he has left to
worry about.
It is important to note that both of these confounding effects, the selection effect
and future career concerns, are hypothesized to act in the opposite direction of ex post
shirking. Thus, we theorize that evidence for performance increases during contract
27
seasons may be easier to uncover than evidence for shirking in the season following the
signing of a new contract.
IV. Data
Both Stiroh (2007) and Berri (2006) take their contract data from the USAToday
website, as do I. This source provides the annual salary, the total value of the contract,
the length of the contract, and also the end date of the contract for each player in the
NBA. The database contains data from the 2001-02 season through the 2008-09
season.
34
I plan to use contract data from the 2008-09 season to determine the players who
will be included in my sample. The USAToday database contains data for 463 players
who were signed to an NBA contract by any of the 30 different teams at some point
during the season; I will keep the ones under multi-year contracts for my empirical study.
In this case, multi-year is defined as two or more seasons.
One shortcoming of these data is that they do not differentiate between the
guaranteed portion of the contract and any incentives that might be included. However,
incentives are usually a small portion of the total contract, if they are included at all, so
the results should not be greatly affected.
35
34
If only one year is given to designate a season, it will be the year in which the season began. For
example, the 2008-09 season would be referred to as the 2008 season.
After eliminating players
under contract for only one season, the dataset was narrowed to 397 players.
Furthermore, players who were currently in their first NBA contract will not be included
35
Players signed to shorter term contracts, specifically one-year deals, may be inherently different from
those players who sign multi-year contracts. These differences may lead to complications in analysis, and
difficulties in drawing conclusions. For example, many players signed to one-year contracts do not play in
many games, or if they do, receive far fewer minutes. As such, they may have a disproportionally large
impact on the results of regressions in which they are included.
28
in the dataset, as shirking behavior cannot be checked for without the existence of pre-
contract, NBA statistics.
36
After cross-checking the list with data from various sources
and eliminating players with incomplete or inconsistent records, I finally arrived at a list
of 231 players with contract characteristics that are ideal for this study.
37
The top panel of Table 1 reports contract data summary statistics for the 231
players with multi-year contracts. The mean contract length is 4.409 years, with a
standard deviation of 1.436 years. The longest contract in the dataset was for 7 years,
and the highest total value was a 7-year, $136 million deal for Kobe Bryant with the Los
Angeles Lakers. The average annual salary for an NBA player was $7.76 million, with
standard deviation of approximately $4.88 million.
Table 1: Summary statistics
Observations Mean Standard Deviation Minimum Maximum
Contract data
Ex ante season
231
2005.17
1.68
2001
2010
Ex post season
231
2006.17
1.68
2002
2011
Contract end season 231 2009.58 1.29 2007 2013
Contract length 231 4.41 1.44 2 7
Total value (millions)
231
$37.00
$27.56
$2.00
$136.40
Annual salary (millions)
231
$7.76
$4.88
$1.00
$20.67
Player data
Age
1864
25.61
3.55
18
36
Experience 1864 5.09 3.17 1 17
∆GP
1864
0.41
20.33
-77
80
MP48 1864 8.24 4.57 -48 49.15
Player performance statistics have all been acquired from www.basketball-
reference.com, a Sports Reference LLC site that keeps an extensive database of NBA
36
Generally this subset of players is composed of players still in their rookie contracts, international players,
or players called up from the NBDL (National Basketball Developmental League). It is important that
players were active in the NBA prior to their current contract, as statistics cannot be accurately compared
across leagues (NCAA, European leagues, NBDL, etc.).
37
I had also planned on estimating my model using players under contract for three or more years, in case a
two-year contract cycle was not long enough to provide the necessary incentive for shirking behavior.
After running both datasets and finding nearly identical results, I decided to use the full dataset of players
with multi-year contracts exclusively.
29
statistics. Statistics for each individual player over the course of his career are organized
by season, in a per-game format. Combining these with the USAToday data, I have a
panel including the performance and contract data for every season of each of the 231
players’ careers. The panel is sorted by player and season, so each individual observation
will be referred to as a player-season, and will include performance statistics and contract
cycle data for that player, in that season. The lower panel of Table 1 reports some of the
relevant summary statistics for individual player characteristics and productivity. In total,
there are 1864 player-season observations, so the average player in the dataset has been
in the NBA for approximately 8 seasons.
V. Empirical Specification
My base regression is similar to the one described in Stiroh (2007) in that it has
the same objective of testing for both ex ante and ex post strategic behavior in the NBA
labor market. Testing for the possibility of increased effort in the contract year provides
an advantage over the model used in Berri and Krautmann (2006), which only tested for
ex post shirking behavior, since Stiroh found that ex ante strategic behavior had a larger
effect on player productivity. The change in games played variable from the Berri and
Krautmann (2006) model will be added as a proxy for injury, which was unaccounted for
in the Stiroh (2007) model. Unfortunately, this proxy is unable to distinguish between
games missed for injury and games missed for other reasons, such as league and team
suspensions, personal matters, or coaching decisions. However, suspensions are rare in
the NBA, and games played as a result of coaching decisions may largely be controlled
for by the individual player fixed effect, meaning that the effects of changes in the
30
number of games played result primarily from injury patterns. I also plan to use several
new variables unaddressed by either of the previous studies on this topic. As stated
before, experience and age can mean quite different things in the context of the NBA, so
separate controls are needed, and since I expect the effects of age and experience to be
nonlinear, second order terms are included for each. The base form of the regression that
I plan to estimate is the following fixed effects model:
38
tijtiGPEXPEXP
AGEAGEPOSTANTE0ti
GPEXPEXP
AGEAGEPOSTANTEP
,
2
2
2
2,
εαααβββ
βββββ
++++∆+++
++++=
The α’s correspond to fixed effects controlling for unobserved individual ability, and
dummy variables for season and team respectively.
39
The dependent variable used in my base regression, MP48, will be similar to the
PROD
A fixed effects model was chosen
to account for any unobserved differences in ability between individual players. For
example, it could be the case that unobserved player ability is correlated with contract
length, meaning that players of varying ability levels in our sample would exhibit
systematic differences in their contract characteristics. Such systematic variation could
interfere with our capacity to attribute changes in player effort level solely to varying
incentives throughout the contract cycle.
MP
38
Here, the dependent variable P represents the measure of productivity chosen for each individual model.
developed by Berri, with the adjustments mentioned in Section III. The
productivity measure will be adjusted to reflect a per-minute rate of productivity, as
players often switch teams when they sign new contracts; changing teams also changes
players’ roles and their playing time, which could potentially interfere with the effects
39
Fixed effects and random effects models were both estimated, with a Hausman test showing that the
random effects model was not consistent. All following models will be estimated using fixed effects.
31
that we hope to measure. The per-minute productivity will then be multiplied by 48,
reflecting the marginal product that each player would contribute to his team over the
course of a full 48-minute game. Figure 1 shows a histogram of the distribution of MP48
values for all player-seasons:
40
Figure 1: MP48 Distribution
Using this playing-time-adjusted measure of marginal productivity, I hope to provide a
clearer answer to the question of whether or not long-term guaranteed contracts in the
NBA provide incentives for players to vary their effort levels strategically over the course
of the contract cycle.
A major advancement of this paper with respect to the existing literature is the
inclusion of age and experience as separate inputs in estimating player productivity. As
40
As the distribution of MP48 values looks roughly normal, I see no reason to take logs or otherwise scale
or normalize the values before running the regression.
32
stated before, high correlation between the two presents a problem of multicollinearity.
41
The breakthrough comes in devising a way to measure player experience that does not
rely heavily on the passage of time. For each player-season observation, instead of using
the number of seasons played in the NBA, I record the total number of minutes played up
until that point in the player’s career. By dividing first by the number of minutes in a
game (48) and then by the number of games in a full season (82), I arrive at the
equivalent number of full seasons of experience if each player had played every minute
of every game.
42
Since I expect the overall shapes of the graphs of productivity versus age and
experience to be downward-opening parabolas, the coefficients on AGE and EXP should
be positive while the coefficients on the corresponding squared terms should be negative.
For values within our dataset range of 1 to 17, I expect that performance should be
monotonically increasing with respect to experience. For age, I expect to see a maximum
in performance somewhere within our age range of 18 to 36, representing the age at
Using this full season equivalent definition of experience has several
benefits. It not only breaks down the correlation between age and experience, but also
measures the experience gained by a player actually playing in the NBA, not just the
amount of time that the player has spent employed by an NBA team. It is more intuitive
to assume that players benefit from varying amounts of experience as a function of the
number of minutes that they play, rather than believing that all players accumulate similar
gains each season, regardless of playing time.
41
Most players in the NBA enter the league at around the same age, and experience is typically measured
by simply counting the number of seasons that the player has been in the league. Clearly, age and
experience by this measure increase hand in hand, leading to a correlation between the two of ρ = 0.874.
42
In a simple example, if Player X had played a total of 7872 minutes over a 6 season career, EXP would
be recorded as 2, since 7872 = 2*82*48. Although he has been in the NBA for a total of 6 seasons, by my
measure of experience, Player X has played the equivalent of 2 full seasons.
33
which players tend to reach their physical peak. Finally, for the ∆GP variable, I expect
the coefficient to be positive, as an increase in games played should correspond to greater
health, a condition under which we expect the player to be more productive.
43
The driving hypotheses behind this paper are that the coefficients on the ANTE
and POST variables will be positive and negative respectively. Such results would
confirm that NBA players do indeed demonstrate increased productivity in the contract
season and decreased productivity after signing a long-term contract. Before estimating
any regressions, I ran a few simple summary statistics on the dependent variable (MP48)
to determine if these hypotheses were reasonable. Table 2 below contains these statistics,
sorted by player position:
44
Table 2: MP48 by Player Position
Ex Ante MP48 Ex Post MP48 All Other Seasons
Position
Mean
SD
Mean
SD
Mean
SD
C
12.877
3.326
12.252
4.174
12.216
4.508
F
10.337
2.909
9.725
3.079
9.389
3.247
F-C
12.872
2.980
12.039
3.090
11.431
5.435
G
5.353
2.330
4.863
2.436
4.692
2.711
G-F
6.985 2.110 5.920 3.872 6.349 2.716
As we can see, in all cases, the mean marginal productivity is higher in the ex ante season
than in the ex post season, while both ex ante and ex post averages are higher than the
averages in all other seasons, except in the case of G-F.
45
43
If the change in games played is negative, then since the coefficient is positive, we will see a decrease in
predicted productivity, which follows our intuition.
This leads us to believe that,
after controlling for experience, age, and other independent variables, we may find
evidence supporting the existence of strategic behavior in the NBA. The results in this
table seem to strengthen my belief that contract year increases in performance may be
44
SD columns list standard deviations.
45
The category All Other Seasons refers to any season that is not an ex post or ex ante season.
34
more prevalent than shirking behavior. One potential concern is the obvious systematic
differences in productivity between players who play different positions. Although
player position will be controlled for in the fixed effects model, it is possible that such a
large difference in productivities across positions is a sign that MP48 does not accurately
capture different players’ contributions towards their team’s success.
Table 3: Fixed Effects Models with Different Controls
Using MP48 as Dependent Variable
Standard errors in parentheses
*** p<0.001, ** p<0.01, * p<0.05
Table 3 above reports the results of my base regression, along with the results for
several other regressions with different sets of controls. Starting with the base regression
in column (1) of the table, the results seem to support the hypothesis that players increase
performance in the ex ante season, although there is no evidence that they decrease
(1)
(2)
(3)
(4)
(5)
Variables
Age and
experience
Age only
No season or
team controls
Season only
Team only
Ante
0.684***
0.685***
0.666***
0.649**
0.677***
(0.202)
(0.202)
(0.195)
(0.201)
(0.195)
Post
-0.049
-0.044
-0.071
-0.049
-0.076
(0.203)
(0.203)
(0.200)
(0.202)
(0.202)
∆GP
0.020***
0.020***
0.019***
0.020***
0.019***
(0.003)
(0.003)
(0.003)
(0.003)
(0.003)
Age
0.787*
1.089***
1.055**
0.876*
1.005**
(0.395)
(0.303)
(0.348)
(0.383)
(0.359)
Age
-0.018**
2
-0.022***
-0.018**
-0.019**
-0.018**
(0.006)
(0.005)
(0.006)
(0.006)
(0.006)
Exp
0.303
0.288
0.292
0.282
(0.269)
(0.261)
(0.265)
(0.265)
Exp
-0.024
2
-0.024
-0.023
-0.024
(0.020)
(0.019)
(0.019)
(0.020)
Season controls
Yes
Yes
No
Yes
No
Team controls
Yes
Yes
No
No
Yes
Constant
-0.152
-4.386
-6.980
-1.338
-6.579
(7.144)
(6.089)
(4.910)
(6.947)
(5.112)
Observations
1864
1864
1864
1864
1864
Number of players
231
231
231
231
231
R-squared
0.107
0.106
0.070
0.077
0.099
Adj. R-squared
-0.051
-0.051
-0.066
-0.067
-0.051
35
productivity in the following season. Examining the variables of primary interest, we can
see that the coefficient on the ANTE variable has a positive coefficient and is statistically
significant at the 0.1% level. This confirms our hypothesis that players hoping to sign a
new contract will tend to outperform, exerting maximum effort in order to lock in the
highest possible salary. The evidence for ex post shirking behavior is not nearly as strong:
We do find a negative coefficient on the POST variable in each case, as expected, but the
magnitude of the effect is not close to being statistically significant.
These findings agreed with those of Berri and Krautmann, and might be explained
by the confounding effects described in the theoretical framework. In theory, the ex post
shirking effects might be overcome by two confounding variables acting in the opposite
direction. First, teams attempt to sign players that they believe have the potential to
continue performing at a high level, or even to improve, which would lead to an increase
in productivity after the new contract is signed. Secondly, each player also has an
economic incentive to perform well after signing a new contract. Unless the player
knows that the current contract will be the last of his career, he must remember that his
present productivity can affect his reputation and future valuation. Both of these
confounding effects would work against the shirking hypothesis, so perhaps the
incentives to shirk are balanced out by effective player valuation by NBA teams and
players’ awareness that present production may dictate future compensation.
Looking at the other independent variables in the base regression, we see that the
calculated ΔGP, AGE, and AGE
2
variables are also statistically significant. The
coefficient on ΔGP is positive, as we expected; players are likely to be more productive
when they spend less time injured and on the bench.
36
In order to understand the effects of age and experience on productivity, I start
with the results of column (2), which are based on a model in which only age is used to
account for the combined effects of age and experience.
46
By including AGE and AGE
2
,
I expected the graph of productivity versus age to be an inverted parabola, reaching a
maximum within the domain of the sample.
47
Qualitatively, this maximum should
correspond to the age at which a combination of the player’s athleticism, knowledge of
the game, experience in the NBA, and overall physical condition allow him to reach his
peak productivity. Figure 2 graphs productivity against age for this model, which does
not include experience as a separate variable:
Figure 2: Productivity vs. Age
48
The effect of age on productivity peaks around 24.6 years, which is a reasonable
estimate of when most NBA athletes reach their physical prime. After this point, the
marginal decrease in productivity as a result of declining athletic abilities or wear and
46
This model, with only age, is similar to both Stiroh (2007) and Berri and Krautmann (2006) in that the
effects of age and experience are explained by variation in only one of the two highly correlated variables.
Unlike either of the previous studies, however, I allowed for the possibility of a nonlinear relationship
between age and experience and productivity.
47
Players in the sample ranged from ages 18 through 36.
48
The gain in productivity with respect to age follows the graph y = 1.089*x – 0.022*x
2
. The domain of
the graph includes values of experience in the interval [15,40]. This graph represents the model which
includes only age and not experience.
37
tear from the daily grind of practicing and playing a professional sport begins to outweigh
the positive but decreasing marginal returns from the accumulation of experience.
Although this simpler model seems to capture the combined effects of age
and experience fairly accurately, one of the goals that drove the specification of my base
regression was to create a new model of player productivity in which the entangled
effects of age and experience on productivity could be identified and separated. By
measuring experience with the equivalent number of seasons played by each player rather
than the total number of seasons the player has been in the NBA, I can include both age
and experience in my base model, which allows for more specific insight into their
individual effects on productivity. Figure 3 at the top of the following page graphs
productivity against age in the base regression, which also includes experience as an
input of productivity.
Again, the results closely match our theoretical expectations. According to the
model, productivity as a function of age increases until it peaks around 22.21 years, and
then decreases at an increasing rate as the player continues to age. Comparing this result
to the previous model, which only includes age, it is quite believable that the average
player actually reaches his maximum athleticism or physical prime around 22 rather than
25, as the effect of age on productivity is now isolated from productivity gains due to
increases in experience.
49
49
When age is used to account for the effects of both age and experience, the increases in experience that
begin upon the player entering the NBA have a monotonically increasing effect on production, so it is not
until the player is older that the negative effect of aging begins to overcome the positive effect of gaining
experience. In the base model, age captures the pure physical effect of aging, so as soon as the player
begins to lose physical ability, it is reflected through decreasing productivity with respect to age.
38
Figure 3: Productivity vs. Age
50
Figure 4: Productivity vs. Experience
51
The effect of experience on productivity in the base regression is displayed in
Figure 4 above. Since the players in the sample have equivalent levels of experience,
ranging from 0 to 11 seasons, it is clear that productivity is not monotonically increasing
in experience as postulated earlier. However, it may be that there are again two factors at
50
The gain in productivity with respect to age follows the graph y = 0.787*x – 0.018*x
2
. The domain of
the graph includes values of age in the interval [15,40].
51
The gain in productivity with respect to experience follows the graph y = 0.303*x – 0.024*x
2
. The
domain of the graph includes values of experience in the interval [0,11].
39
work here. On the one hand, there is the positive effect that experience has on players
both mentally and psychologically, which could in fact continuously increase with
experience.
52
In models (3) through (5), I remove one or both of the team and season controls,
finding that the removal of these controls from the model has no significant effect on the
results. For all subsequent models, both season and team controls are included.
Furthermore, note that the coefficients and standard errors on the ANTE and POST
variables are almost exactly the same in the base regression and the regression using only
age to account for the combined effects of age and experience. As neither model seems
to have an advantage in consistency or efficiency, I use the base regression for the
remainder of the paper, since it is supported by the theoretical framework and can offer
more specific insight into the factors affecting productivity.
At the same time, every additional minute of experience comes with a cost.
Eventually, the player’s body will start to feel the day-to-day attrition of playing
professional basketball, as well as the accumulated effects of injuries sustained, both
major and minor. This process is separate from that of the natural aging process, as it is
directly related to the amount of time that the player has spent on the basketball court. At
the quantity of equivalent seasons when the negative effects of physical deterioration
begin to overcome the diminishing mental and psychological returns of increasing
experience, productivity as a function of experience peaks. In the base model, this peak
occurs when the player has played the equivalent of approximately 6.38 full seasons in
the NBA, or about 523 complete games.
52
As players play more cumulative minutes in the NBA, one would assume that they gain a greater
understanding of basketball and familiarity of the league, allowing them to make better decisions, handle
additional pressure, and more capably evaluate their opponents, all of which would likely lead to increases
in productivity.
40
Table 4: Fixed Effects Models with Post Interactions
Using MP48 as Dependent Variable
(1)
(2)
(3)
(4)
Variables
Base
Post x Length
Post x Age
Post x Length x
Age
Ante
0.684***
0.683***
0.682***
0.684***
(0.202)
(0.202)
(0.202)
(0.202)
Post
-0.049
0.209
-0.521
0.256
(0.203)
(0.664)
(1.696)
(0.675)
ΔGP
0.020***
0.020***
0.020***
0.020***
(0.003)
(0.003)
(0.003)
(0.003)
Age
0.787*
0.791*
0.806*
0.784*
(0.395)
(0.395)
(0.401)
(0.395)
Age
-0.018**
2
-0.018**
-0.018**
-0.018**
(0.006)
(0.006)
(0.006)
(0.006)
Exp
0.303
0.312
0.302
0.314
(0.269)
(0.270)
(0.269)
(0.270)
Exp
-0.024
2
-0.024
-0.024
-0.024
(0.020)
(0.020)
(0.020)
(0.020)
Post x Length
-0.057
(0.140)
Post x Age
0.018
(0.062)
Post x Length x Age
-0.003
(0.005)
Season controls
Yes
Yes
Yes
Yes
Team controls
Yes
Yes
Yes
Yes
Constant
-0.152
-0.165
-0.377
-0.076
(7.144)
(7.146)
(7.191)
(7.148)
Observations
1864
1864
1864
1864
Number of player
231
231
231
231
R-squared
0.107
0.107
0.107
0.107
Adj. R-squared
-0.051
-0.052
-0.052
-0.052
Standard errors in parentheses
*** p<0.001, ** p<0.01, * p<0.05
In models (2) through (4) of Table 4 above, I add independent variables for the ex
post variable interacted with contract length, player age, and both contract length and age,
respectively. The underlying intuition is that for longer and longer contracts, a player in
his ex post season has less and less to worry about in terms of signing a subsequent
contract. This should provide further incentive for him to decrease his effort. Similarly,
41
for age, an older player would expect to be spending less time in the NBA in the future
than a younger player, all else equal, so increasing age would also increase the incentive
to shirk. In all three cases, the coefficients on the interaction terms were within the
margin of error, so the results show no evidence that either contract length or player age
has an effect on the propensity of a player to shirk in the ex post season.
After running my base regression using marginal productivity per 48 minutes as
my dependent variable, I decided to conduct a sensitivity test by substituting several
different measures as my dependent variable. Using the independent variables of my
base regression, I tried to predict successively marginal productivity, the NBA measure
of efficiency, points, total rebounds, assists, field goals attempted, and free throws
attempted.
53
In models (2) and (3), where comprehensive productivity measures of marginal
productivity per game and NBA efficiency per 48 minutes are used, the coefficients on
ANTE are positive and significant at the 1% level.
Table 5 on the following page reports the results.
54
However, unlike the base regression
with marginal productivity per 48 minutes as the dependent variable, the coefficient on
POST is positive as well, though not significantly different from zero. Models (4)
through (8), which used individual statistics as the dependent variables, found varying
results. Evidence for contract year strategic behavior was found to be significant at the
1% level for PTS48 and at the 10% level for TRB48, FGA48, and FTA48.
5556
53
This was the marginal productivity unadjusted for minutes played, as MP48 was already used in the base
regression. Each of the other variables, NBA efficiency, points, total rebounds, FGA, and FTA, was
adjusted to a per-48 minutes basis.
The
coefficient on ANTE is slightly negative for AST48, though not statistically significant.
54
MP = marginal productivity per game; NBA48 = NBA efficiency per 48 minutes.
55
PTS48 = points per 48 minutes. The other individual statistics are denoted similarly.
56
FGA and FTA were hypothesized to be good proxies for player effort, as a player would seemingly have
more direct control over how many shots he takes than over how many rebounds he is able to get.
42
There is no statistical evidence of ex post shirking behavior in any of the estimated
regressions. Since similar results are obtained using several different measures of player
productivity, this sensitivity test increases my confidence in the robustness of my model.
Table 5: Fixed Effects Models of the Base Regression
Using Different Productivity Measures as Dependent Variable
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Variables
MP48
MP
NBA48
PTS48
TRB48
AST48
FGA48
FTA48
Ante
0.68***
0.46***
1.07***
0.77***
0.20*
-0.01
0.31*
0.19*
(0.20)
(0.11)
(0.28)
(0.22)
(0.10)
(0.07)
(0.16)
(0.10)
Post
-0.05
0.09
0.10
0.07
-0.02
0.08
0.09
0.07
(0.20)
(0.11)
(0.28)
(0.22)
(0.10)
(0.07)
(0.16)
(0.10)
ΔGP
0.02***
0.01***
0.03***
0.00
0.00
0.00
-0.01***
-0.00
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
Age
0.79**
0.59***
1.79***
1.45***
0.17
0.19
0.88***
0.38*
(0.39)
(0.22)
(0.55)
(0.43)
(0.20)
(0.14)
(0.31)
(0.20)
Age
-0.02***
2
-0.02***
-0.05***
-0.05***
-0.01**
-0.01***
-0.03***
-0.02***
(0.01)
(0.00)
(0.01)
(0.01)
(0.00)
(0.00)
(0.00)
(0.00)
Exp
0.30
1.62***
2.39***
3.79***
-0.25*
0.59***
2.24***
1.41***
(0.27)
(0.15)
(0.37)
(0.29)
(0.13)
(0.10)
(0.21)
(0.14)
Exp
-0.02
2
-0.11***
-0.13***
-0.21***
0.02*
-0.03***
-0.13***
-0.06***
(0.02)
(0.01)
(0.03)
(0.02)
(0.01)
(0.01)
(0.02)
(0.01)
Constant
-0.15
2.26
5.28
3.84
9.38***
2.37
6.14
2.40
(7.14)
(3.95)
(9.88)
(7.77)
(3.56)
(2.62)
(5.68)
(3.68)
Observations
1864
1864
1864
1864
1864
1864
1864
1864
Number of player
231
231
231
231
231
231
231
231
R-squared
0.11
0.32
0.18
0.29
0.07
0.13
0.25
0.22
Adj. R-squared
-0.05
0.20
0.03
0.16
-0.10
-0.02
0.12
0.08
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
An early concern that I had was with the weak predictive power offered by the
fixed effects model. Comparing my low R-squared and adjusted R-squared values with
adjusted R-squared values in the 0.7-0.8 range using the weighted OLS method of Stiroh
(2007), I was initially wary of my results and concerned with both my methodology and
my panel data. I conducted several checks to make sure that each was valid. Estimating
the model used by Stiroh on my dataset, after adding dummies to capture individual
effects, I was also able to reproduce similar adjusted R-squared values, convincing me
that my dataset was not invalid or incomplete in any obvious way. Checking my results
43
with Berri and Krautmann (2006), I found that they had reported similar R-squared
values. Econometrically, it makes sense that a weighted OLS model would better predict
individual player productivities than a fixed effects model, as each player will be
associated with a unique constant value that sets an appropriate base level of production
for that individual. However, with a set of panel data, I choose to use the fixed effects
model, rather than random effects or a pooled OLS model, as it is consistent and efficient
under the condition that time-invariant individual effects are correlated with the
independent variables.
VI. Conclusions
The existing literature on strategic behavior in the context of the National
Basketball Association showed inconsistent results using different empirical approaches.
By drawing upon and building on work done by Stiroh (2007) and Berri and Krautmann
(2006), my research provides greater insight on the theory behind models of player
productivity. Additionally, my results also present further evidence to substantiate the
claim that players do indeed vary their effort levels in response to changing incentives
over the course of their contract cycle, much as economic theory predicts.
Specifically, my model—which held up for a variety of measures of player
productivity—provides relatively robust evidence that ex ante strategic behavior, or the
contract year phenomenon, is quite real. Following the model’s underlying theory,
players currently in a contract year have an incentive to increase their productivity
because they know that the value of their next long-term contract will be determined in
part by their performance in the current season. Thus, they will expend more effort now,
44
in order to lock in a higher guaranteed salary in the future. On the other hand, no
evidence was found to support the shirking hypothesis, corroborating the findings of
Berri and Krautmann (2006). Ex post performance declines either do not exist or are
masked by a variety of confounding factors. For example, there may be a selection effect
working in the opposite direction as shirking behavior if teams are succeeding in their
goal of identifying players who have the most potential for continued improvement.
A possible extension of this study involves examining the players on individual
NBA teams as separate subgroups, and attempting to draw a link between the success of a
franchise and the types of players that it signs, relative to the norm. For example, if
players on the Knicks show greater variation in their performance level over the contract
cycle relative to the league average, are the Knicks more likely or less likely to have a
winning team? If a team has many players who are much more productive in their
contract year than in other seasons of their contract cycle, it would probably have a
negative impact on team success, as these players tend to exert maximum effort only
when faced with the proper incentives.
My findings have the potential to benefit NBA teams in their player evaluation
process, as it allows them to more accurately determine contract cycle effects on player
performance. For example, when trying to decide whether to sign a player to a new
contract who is currently in his contract year, my model of player productivity could
offer insight into how much of the player’s productivity is explained by his being in a
contract year, and how much is a function of his individual characteristics. The inclusion
of both age and experience as inputs in estimating production should allow for greater
accuracy in predicting future productivity, especially of players who do not follow the
45
typical path to the NBA. These players might not exhibit the usual correlation between
age and experience, so modeling the two as separate effects will be much more accurate
in these cases. With greater success in player evaluation, teams would be able to save
money that they previously would have spent on unworthy players, and parity and
competitiveness in the NBA would likely increase. Additionally, teams might apply this
research on a player-by-player basis to determine which players would benefit most from
the motivation of performance incentives. Guided by the theories of player productivity
variation formulated in this paper and working under the inevitable financial constraints
imposed by the league salary cap, an NBA team could maximize its aggregate
productivity, and thus its overall success, by limiting the contractual incentives for
players to engage in strategic behavior.
46
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