Productivity Spillovers in Team Production:
Evidence from Professional Basketball
∗
Peter Arcidiacono Josh Kinsler Joseph Price
Duke University University of Georgia Brigham Young University
& NBER & NBER
August 24, 2015
Abstract
Workers contribute to team production through their own productivity and through their
effect on the productivity of other team members. We develop and estimate a model where
workers are heterogeneous both in their own productivity and in their ability to facilitate the
productivity of others. We use data from professional basketball to measure the importance
of peers in productivity because we have clear measures of output, and members of a worker’s
group change on a regular basis. Our empirical results highlight that productivity spillovers play
an important role in team production, and accounting for them leads to changes in the overall
assessment of a worker’s contribution. We also use the parameters from our model to show that
the match between workers and teams is important and quantify the gains to specific trades of
workers to alternative teams. Finally, we find that worker compensation is largely determined by
own productivity with little weight given to the productivity spillovers a worker creates, despite
their importance to team production. The use of our empirical model in other settings could
lead to improved matching between workers and teams within a firm, and compensation that is
more in-line with the overall contribution that workers make to team production.
∗
We thank Patrick Coate, Fabian Lange, Lars Lefgren, Craig Palsson, Michael Ransom, and seminar participants
at Iowa State, McGill, Boston College, Brigham Young University, and the University of Georgia for helpful comments.
1
1 Introduction
The classic economic model predicts that workers will be paid the value of their marginal product of
labor. Estimating this marginal product may be complicated by team environments in which workers
contribute to team production directly but also indirectly through their effect on the productivity
of other team members. If firms are able to identify workers who boost peer productivity, they can
leverage complementarities in team production through team and task assignments. Workers who
bring out the best in others will likely be assigned to tasks essential for firm production.
Mas and Moretti (2009) provide an excellent example of spillovers in team production by looking
at the placement of cashiers in a supermarket. Placing the most productive cashiers in full view of
the other cashiers resulted in the other cashiers working faster. However, Mas and Moretti provide
one of the few examples where actual productivity is observed. Other examples include Hamilton,
Nickerson, and Owan (2003), who examine worker interactions in the garment industry, and a set
of papers analyzing productivity in the academy, Azoulay, Zivin, and Wang (2010) and Waldinger
(2010, 2012).
1
The assumption made in this literature–as well as the abundant literature on peer effects in
education–is that the individuals who are most productive themselves are also the ones who will
make others most productive. This assumption may not be true in many contexts. For example,
there are professors who choose to focus exclusively on their own research, providing little in terms
of public goods while other professors who are particularly adept at helping their colleagues in
their research and may do so even at the expense of their own research. Similarly, a brilliant but
introverted student may not be as helpful to the learning of the other students as the perhaps
not-so-brilliant student who asks good questions in class.
We may expect workers to be compensated for both their productivities and their abilities to
make others more productive. However, peer effects, particularly heterogeneous peer effects, are
notoriously difficult to measure, in part because of the data requirements. But the advent of “Big
Data”, as well as the accompanying means of estimating models with large state spaces, may result in
measures of productivity spillovers becoming more readily available. For example, patent scientists
and financial advisors are both occupations for which there is rich data on individual output and
information about network structure within the firm. These are both settings where a firm could
identify workers who improve the productivity of their peers through interaction and advice.
1
Field experiments have also been used to examine peer effects in the workplace. See the papers by Bandiera,
Baranakay, and Rasul (2009, 2010) as well as Falk and Ichino (2006).
2
In this paper, we develop and estimate a model of team production where individuals are hetero-
geneous in their own productivity as well as in their ability to help others be productive. We then
relate our measures to compensation, focusing in particular on the extent to which the ability to
make others more productive is rewarded in the marketplace. We focus on an industry, professional
basketball, where the ability to help others is clearly an important part of team production. Sports
data provide an excellent opportunity to study team production because the members of a team
can be clearly identified, there are frequent changes in the players that compose a particular team,
and compensation data is available.
Two papers using sports data highlight the heterogeneity in how spillovers may operate. Gould
and Winter (2009) use data on baseball players to analyze how batter performance is related to the
performance of other batters on the team. This paper fits perfectly with the idea that the most
productive players have the largest positive peer effects: batting in front of a high-performing player
results in receiving better pitches because the pitcher will not want to risk a walk prior to facing
the high-performing player. Guryan, Kroft, and Notowidigdo (2009) examine how the productivity
of one’s golf partners affects own performance, finding no significant effects from being paired with
better golfers. Even though there is no team production in golf, it may be that individual spillovers
are multidimensional in the sense that they work through multiple player attributes. Certain players
may be very productive but are surly or disobey common golf etiquette, both of which may serve
to distract their partners. The authors allow for this additional flexibility, but find no evidence of
heterogenous spillovers.
Using possession-level data from games played in the National Basketball Association (NBA),
we demonstrate that productivity spillovers play an important role in team production. We find
that a standard deviation increase in the spillover effect of one player improves team success by 63%
as much as a standard deviation increase in the direct productivity of that player. Estimates of the
model also allow us to form player rankings based on the overall contribution to team production.
We compare these rankings to estimates of team production when spillovers are ignored. Players
who are generally perceived by the public as selfish see their rankings fall once we account for
productivity spillovers.
We also use our model to highlight how the value of a particular player can vary depending on the
composition of his teammates. Most firms have various teams within their organization and have the
ability to reassign workers across teams. Since individual productivity and productivity spillovers
play a complementary role, the overall contribution of a player will depend on the composition of the
3
other players already on the team.
2
We find that the assignment that produces the greatest increase
in team productivity is often an assignment that does not maximize the direct productivity of the
player. This suggests a tension that firms need to balance between team and player productivity,
especially in firms where individual productivity has a large effect on compensation.
Given the large role spillovers play in team production in this industry, we would expect signifi-
cant returns in the labor market to the ability to help others. This is not the case. Returns to own
productivity are substantially higher than returns to the ability to help others, well beyond their
differences in their contribution to team production. Part of the reason for this may be the difficulty
in measuring the ability to help others. As in the academy, direct productivity is easily observed
in ways that facilitating the productivity of others is not. To the extent that own productivity and
facilitating the productivity of others is endogenous, the lack of returns to the latter may result in
inefficient effort allocations among workers.
2 Data
To estimate a model of player performance, we use publicly available NBA play-by-play data covering
all games during the 2006-2009 regular seasons gathered from espn.com. For those readers unfamiliar
with the basic rules of basketball we have included a brief description in Appendix A. The raw play-
by-play data provides a detailed account of all the decisive actions in a game, such as shots, turnovers,
fouls, rebounds, and substitutions. Plays are team specific, meaning that there is a separate log
for the home team and the away team. Associated with each play are the player(s) involved, the
time the play occurred, and the current score of the game. While our model of player productivity
is estimated using only the play-by-play data, we augment it with additional biographical and
statistical information about each player gathered from various websites which we discuss later in
this section. As described in Appendix B, we took a number of steps to clean the data. These
included establishing which players were on the court, acquiring the outcomes of possessions, and
matching the names of the players to data on their observed characteristics such as position and
experience.
Table 1 describes our estimation sample in further detail. We use data from 905,378 possessions
and 656 unique players active in the NBA from 2006-2009. On average, each player is part of
13,801 possessions, split evenly between offense and defense. The average number of possessions for
2
Similarly, Ichniowki, Shaw, and Prennushi (1997) find that the returns to innovative work practices (e.g. teams,
incentive pay, etc.) are complementary in the steel finishing industry.
4
each player-team-season combination is 4,507. The corresponding 25th and 75th percentile values
are 1,130 and 7,470. The final four rows of Table 1 describe the typical outcomes for a possession.
Slightly more than 50% of the time the offensive team scores, and, conditional on scoring, the offense
scores on average 2.1 points.
To supplement the play-by-play data, we merge in biographical and statistical information about
each player. Our primary source for this information is basketball-reference.com. The website
contains basic player information such as date of birth, height, position, and college attended and
a full set of statistics for each season the player is active. We also gathered information on salaries
and contract years from prosportstransactions.com and storytellerscontracts.com. We also obtained
additional measures of player performance from basketballvalue.com and 82games.com.
3 Model and Estimation
In this section we present a model of team production, discuss identification, and describe our
estimation strategy. The innovation of the model is that the ability of an individual to influence
the productivity of others is not directly tied to own productivity. We tailor the model to the
NBA context, though it would be simple to expand the framework to other types of production.
3
The number of parameters to be estimated is quite large and would be computationally prohibitive
using straight maximum likelihood. Consequently, we take an iterative approach as in Arcidiacono,
Foster, Goodpaster, and Kinsler (2012).
4
3.1 Model setup
Our unit of analysis is an offensive possession during an NBA game. There are five offensive and
five defensive players on the court during every possession. For a given possession n, denote the
set of players on the court as P
n
, where P
n
includes the offensive players on the court O
n
and the
defensive players on the court D
n
. For notational ease we abstract from the fact that possessions
are typically observed within games, which themselves are observed within seasons. Additionally we
abstract from the concept of team, even though the potential sets of offensive and defensive players
will be determined by team rosters. A possession can end in one of six ways, no score or one of the
3
For example, in Mas and Moretti (2009) checkout cashiers are assumed to influence other cashiers through their
own productivity. However, it would be straightforward to allow for completely separate effects.
4
See Burke and Sass (2013) for an application of this method in education and Cornelissen, Dustmann, and
Schonberg (2013) for an application in the labor market.
5
