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The Payoff to Consistency in Performance
1
Christian Deutscher,
2
Oliver Gürtler,
3
Joachim Prinz,
4
and Daniel Weimar
5
Please cite as follows:
Deutscher, C., Gürtler, O., Prinz, J., & Weimar, D. (2017). The payoff to consistency in
performance. Economic Inquiry, 55(2), 1091-1103.
Abstract: This study investigates whether firms are willing to pay higher
wages to workers who demonstrate consistent performance than to those
whose performance is more volatile. A formal model reflects a production
technology view, assuming the law of diminishing marginal product. This
model suggests that a more consistent worker produces higher expected out-
put and therefore receives a higher wage. The test of the model uses data from
the National Basketball Association. The empirical data support the model:
Players whose performances were more consistent than the performances of
other players received higher wages on average.
Keywords: wage determinants, consistency in performance, National Bas-
ketball Association
JEL-Codes: D41, J31, M52, Z20
1
We thank the anonymous reviewer for very helpful comments.
2
Department of Sport Science, Bielefeld University, Universitätsstraße 25, 33615 Bie-
lefeld, Germany. Tel. +49(0)521 / 106006. E-mail: christian.deutscher@uni-biele-
feld.de.
3
Faculty of Management, Economics and Social Sciences, University of Cologne, Al-
bertus-Magnus-Platz, 50923 Cologne, Germany, Tel. +49(0)221 / 4701450, E-mail:
oliver.guertler@uni-koeln.de.
4
Department of Managerial Economics, University of Duisburg-Essen, Lotharstrasse
53, 47057 Duisburg, Germany. Tel. +49(0)203 / 3794544. E-mail: joa-
chim.prinz@uni-due.de.
5
Department of Managerial Economics, University of Duisburg-Essen, Lotharstrasse
53, 47057 Duisburg, Germany Tel. +49(0)203 / 3793598. E-mail: daniel.weimar@uni-
due.de.
2
1. Introduction
When a firm hires a worker, the firm pays the worker a salary to demand some service in
return. Some workers provide consistent performance; others exhibit performance that is
inconsistent, such that it is high on some days but relatively low on others. When workers
vary in the consistency of their performance, an obvious question arises, regarding
whether firms offer higher wages to workers who promise consistent performance, com-
pared with those with greater performance volatility. In other words, is there a deduction
for risk, as modern portfolio theory would predict (Markowitz, 1952)?
Substantial literature addresses the effect of a worker’s expected performance on
his or her wages. Usually, the worker’s level of education serves as the proxy for her or
his expected ability and talent, which then should increase expectations of the worker’s
likely performance. Studies accordingly reveal that workers with a higher level of educa-
tion receive higher wages on average (e.g., Mincer, 1974; Waldman, 2013a). The human
capital theory originated by Becker (1964) is largely based on this observation: Workers
are willing to invest in their human capital and acquire skills only if they expect this
investment to later be rewarded with a higher wage. Job-market signaling theory suggests
these investments to be wasteful at times without enhancing workers’ productivity (e.g.,
Spence, 1973). The intuition is simple: If workers of relatively high ability can acquire
some job-market signal such as a certain level of education at lower cost than workers of
low ability, they may have an incentive to do so just to reveal their superior ability.
6
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While education represents possibly the most important job-market signal, other job-market signals
such as promotions exist. Starting with the paper by Waldman (1984), there is by now a large literature
on promotion signaling (e.g., Bernhardt, 1995; Zábojník and Bernhardt, 2001; Owan, 2004; Ghosh and
Waldman, 2010; Cassidy et al., 2012; DeVaro and Waldman, 2012; Zábojník, 2012; Waldman, 2013b;
and Gürtler and Gürtler, 2015). Waldman (2014) presents a synthesis of the education-signaling and the
promotion-signaling approach.
3
The effect of performance consistency on wages has received little research atten-
tion though. Such an analysis is difficult, due to the lack of readily available, suitable
data. Studies investigating the determinants of worker wages tend to rely only on the
worker’s level of education to proxy for expected productivity, but this level of education
is relatively constant and cannot signal the likely consistency of a worker’s performance.
Whereas previous performance seemingly could help anticipate the rate of consistency,
this performance is often unobservable.
With the current study, we seek to explicate the effects of performance consistency
on workers’ wages.
7
The analysis consists of both a theoretical and an empirical part. In
the theoretical model, we assume that a firm organizes production in a team and needs to
fill one position in that team. To do so, it hires a worker whose ability is subject to fluc-
tuations. The output that the team produces for the firm depends on all workers’ abilities
and thus is subject to fluctuations as well. A worker’s wage is an increasing function of
the value of the team’s expected output. A final assumption is that the law of diminishing
marginal product holds, such that a positive deviation of the worker’s ability from the
mean by x units increases output less than a negative deviation of ability from the mean
by x units decreases it. Inconsistency in performance therefore reduces expected output,
so the firm is willing to offer a higher wage to more consistent workers. The model de-
livers some other results as well. For example, a worker’s wage increases with her or his
expected ability.
7
Lazear (1998) and Bollinger and Hotchkiss (2003) refer to a worker as risky when it is unclear which
level of performance the firm can expect from that worker at the moment the worker enters the labor
market. After the firm has observed the worker for some time and gathered information about the
worker’s characteristics (Jovanovic, 1979), the firm knows exactly what to expect. In the current model,
we consider workers who already have entered the labor market and about whom substantial perfor-
mance information is already available. Even then, a worker’s performance may be subject to fluctua-
tions, and we call a worker inconsistent in this case, that is, if the worker performs quite well on one
day but poorly on another.
4
In the empirical part, we use data from the National Basketball Association (NBA)
to test the model predictions. Data sets that include the information required to address
our research question are rare; in particular, information about the volatility of workers’
performance is hard to derive. Professional sport settings can overcome these measure-
ment problems, because information about salaries, individual characteristics, and con-
tinual performance measures are common and readily available (Kahn, 2000; Rosen and
Sanderson, 2001). Our data include information from the 2007/08 to 2010/11 NBA sea-
sons and contain game-by-game statistics for 259 different players and 22,520 individual
performance observations. To measure performance consistency, we use the standard de-
viations of scoring and non-scoring activities. This empirical study strongly supports the
findings from the theoretical model: Players with better performance measures earn
higher wages on average. In addition, we observe a negative correlation between volatility
in the performance measures and a player’s wage. Therefore, the risk-expected return
profiles appear to play an important role in hiring decisions, and firms (i.e., NBA teams)
reward consistent performance with higher wage payments.
This study also relates to literature on the determinants of professional basketball
players’ remuneration (e.g. Kahn and Sherer, 1988; Koch and Vander Hill, 1988; Wal-
lace, 1988; Brown et al., 1991; Jenkins, 1996; Dey, 1997; Hamilton, 1997; Bodvarsson
and Brastow, 1998; Gius and Johnson, 1998; Eschker et al., 2004; Hill, 2004; Prinz,
2005). Prior studies unanimously agree that NBA player wages are a function of a player’s
ability/potential (measured by his draft position, years of experience, or previous perfor-
mance) and “fan appeal” (measured by the number of All-Star appearances). Perhaps sur-
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prisingly though, to our knowledge, only one empirical work addresses performance con-
sistency.
8
Bodvarsson and Brastow (1998) propose a model of worker remuneration, in
which worker monitoring is costly. They assume that the corresponding monitoring costs
are higher for less consistent workers, so these workers receive a lower wage. Bodvarsson
and Brastow test their model predictions by analyzing a subgroup of NBA players in the
early 1990s. Their empirical results indicate that employers prefer consistency by their
employees for some performance criteria. However, the league also has undergone drastic
changes since that time. The average payroll, around $12.5 million annually in the 1990s,
has grown exponentially to reach around $70 million per year in our observation period.
In addition, the growing importance of statistical analysis has led to implementations of
analytics capabilities by all teams. Similar to findings about salary discrimination, the
results from two decades ago cannot be taken for granted when it comes to consistency
(Hill, 2004). Furthermore, by observing consecutive seasons, we can control for player
characteristics and use quantile regression to reveal the impact of consistency across dif-
ferent segments of the league’s salary distribution.
The remainder of this paper is organized as follows: In the next section, we present
a theoretical model to investigate general determinants of workers’ wages and the contri-
butions of consistency. We then derive three main hypotheses. Section 3 contains the
empirical analysis we used to test our main hypotheses. Finally, we discuss the results
and provide an outlook for further research in Section 4.
8
Using subjective rather than objective performance measures, Deutscher and Büschemann (2016) study
the effect of performance consistency on soccer players’ estimated market values. They find a negative
correlation between performance consistency and market values.
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2. The model
Consider a firm that organizes work in teams of n members and that so far has hired n-1
workers and thus decides to hire another worker i. The workers produce output for the
firm, the value (or price) of one unit of output is given by . The amount of output
that the workers produce depends on workers’ abilities
and is given
by , with
satisfying and for all
.
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implies that workers of higher ability produce more output and
means that the law of diminishing marginal product applies. The latter
assumption of diminishing marginal products is central to our analysis, and we very much
believe that this assumption is fulfilled in professional basketball. The main argument is
that basketball is a team sport. If one of the players excels, this player still depends on his
teammates and typically cannot win the game single-handedly. If the other players show
only an average performance, the exceling player’s impact on the game will thus be lim-
ited.
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In contrast, if one of the players performs extremely poorly, e.g., by repeatedly
missing shots and failing to defend his opponent, it will be extremely difficult for this
player’s team to win the game. This means that it is well conceivable that a player loses
a game single-handedly (unless the player is replaced by a substitute; see the discussion
at the end of this section).
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In the specification of the production function, we focus on ability and abstract from effort. In profes-
sional basketball (and, particularly, in the NBA), explicit performance incentives in the form of bonuses
are relatively rare and negligible compared to the fixed salary. Instead, players have strong incentives
to exert effort because of their career concerns (Holmström, 1982) and therefore typically compete at
the highest intensity, especially in the final year of a contract, fittingly referred to as ‘contract year’. All
the results to be derived in this section could be reinterpreted to capture both ability and effort. In par-
ticular, can simply be understood as some combination of ability and effort.
10
Take LeBron James as an example. During his first stint with the Cleveland Cavaliers organization, he
showed outstanding performances. Still, lacking substantial support from his teammates, he did not
manage to lead his team to the championship.
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For all j, ability is a random variable, distributed according to the cumulative distribu-
tion function , whose realization is unknown to both the firm and the worker. The
interpretation of this assumption in the setting of professional basketball is the following:
the variable y should be thought of as the team’s performance in a given game. The team
manager should have a good idea of the performance he can expect from each of the
players (since performance and statistics are publicly observable; Kahn, 2000). In a given
game, however, players sometimes fail to live up to these expectations, while at other
times they exceed all expectations. We therefore assume that a worker’s expected ability
is known to all market participants, whereas the exact realization (that is, the worker’s
actual performance in a given game) depends on random factors and is unobservable prior
to the game.
The wage that worker i receives from the firm is denoted by and is an increasing func-
tion of the value of the team’s expected output, pE[y], i.e. , with
. An implicit assumption behind this wage formula is that there is (at least) some com-
petition for workers’ services. The value of the team’s expected output can be thought of
as the rent that the team produces. That workers’ wages are increasing functions of the
value of expected output, require that workers receive part of the rent. In a monopsonistic
labor market (i.e. in the case of a single firm), however, the firm would keep the entire
rent, and workers would just receive a fixed wage equal to their reservation value. Clearly,
in professional basketball, there is competition for players’ services, underscoring our
choice of wage formula. In the NBA team owners and players share basketball related
revenues as determined by the collective bargaining agreement.
8
We begin by investigating the effect of the value of one unit of output () and the
worker’s expected ability on the worker’s compensation, keeping all other variables con-
stant. To study the latter effect, we replace by , and we analyze how the worker’s
compensation changes with variations in the constant .
Proposition 1: The worker’s wage is increasing both in (value of the team’s output)
and in the worker’s expected ability.
Proof: The worker’s wage equals We obtain
and
The higher the value of the team’s output or the more the worker contributes to the firm’s
output, the more willing the firm is to pay a higher wage to hire that worker. Proposition
1 formalizes this result.
Because our research question focuses on whether the firm rewards consistency
in performance (i.e., output production), we introduce a measure of consistency.
Definition 1: For any ability distributions and , is a mean-preserving spread
of if and only if with some random variable , such that
for all .
Definition 2: Worker ib is more consistent than worker ia if is a mean-preserving
spread of .
A simple proof establishes the following result:
Proposition 2: If worker ib is more consistent than worker ia, he or she receives a higher
wage, i.e. .
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Proof: Let be a mean-preserving spread of . For a given
we define and notice that 0. Then we
can write,
where the inequality follows from Jensen’s inequality, given the strict concavity of .
Proposition 2 demonstrates that the firm values consistency in performance and is
willing to pay a higher wage to a more consistent worker than to a less consistent one.
This result is intuitive. If one worker is less consistent than another, his or her ability
realization is more likely to be very high, but also is more likely to be very low. Because
of the law of diminishing marginal product, the increase in output when the worker’s
ability is above the mean level is less than the parallel decrease in output when the
worker’s ability is below the mean (by the same amount). A team with a less consistent
worker thus produces lower expected output, and the worker receives a lower wage.
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From Propositions 1 and 2, we derive three hypotheses:
Hypothesis 1: The higher the value of the team’s performance, the higher is the worker’s
wage.
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Notice that this result does not depend on the sign of the cross partial derivatives of the production
function. In particular, the result holds if the cross partial derivatives are positive, meaning that the
production technology is characterized by complementarities.
10
Hypothesis 2: The higher the worker’s expected ability, the higher is the wage.
Hypothesis 3: The more consistent a worker’s performance, the higher is the wage.
Regarding the third hypothesis, the particular structure of the basketball labor mar-
ket gives rise to three comments. First, we assume the firm to be risk neutral, which is in
line with past sports economic studies (Dietl et al., 2008; Scully, 1994, 1995; Robinson
et al., 2012; Szymanski, 2003). We believe that this is a very reasonable assumption for
the NBA. The typical argument is that relatively wealthy people find it easy to diversify
their income, meaning that these people are well ensured against income losses and can
therefore be thought of as being (close to) risk neutral. The NBA team owners are indeed
wealthy people, with fourteen of the thirty owners having fortunes exceeding $1 billion.
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If instead the firm were risk averse, our results might be strengthened, such that a more
consistent worker would receive a higher wage relative to a less consistent one, both be-
cause the employer (NBA team owner) expects him to be more productive and because
hiring this player is less risky for the firm than hiring a less consistent one. One may also
come up with arguments for why a team owner may be thought of as risk loving. For
instance, the worst possible consequence of performing poorly is that the team may miss
the playoffs (since there is no relegation in the NBA), whereas the team may win the
championship in the case of great performance. This means that the gain from outstanding
performance may outweigh the loss from very poor performance, implying a greater ten-
dency to take risks.
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This would of course counteract the effects from our model.
12
http://www.forbes.com/pictures/edik45flemf/the-nbas-billionaire-owners/
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However, other arguments exist for why, e.g., compared to soccer, the reward for very good perfor-
mance is lower in the NBA, thereby implying a lower tendency to take risks. For instance, in NBA
basketball particularly good season performance is not rewarded by qualification for external competi-
tion. In European soccer, international competition secures major financial rewards.
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Second, if an NBA player has a bad day, he can be replaced by another player, such
that a decrease in one player’s performance may be offset by an increase in another
player’s performance. Because underperforming players can be substituted for (i.e.,
benched), the adverse effects of inconsistency may not be as severe as our model suggests.
Third, our proposed model is static, but a basketball player’s consistency gets re-
vealed over the course of the season, so that dynamic aspects of consistency should have
influences as well. Managerial reasons highlight the advantageousness of variability in
performance over time. Most importantly, basketball teams face both strong and weak
opponents, so coaches or team managers want players to play extremely well against good
teams but might accept reduced effort when playing bad teams. This argument requires
that players are able to adjust their performance in response to opponents’ strength.
3. Empirical analysis
3.1 Data
For an empirical test of our hypotheses, we compiled a comprehensive database about
average player performance, volatility in players’ performance, and salary compensation
in the NBA. This league provides a good setting for studying the effect of consistent
performance on salary, because players’ pay levels are available to the public, and their
performance measures are published as well. We drew individual player statistics from
the official website of the NBA; the player salaries came from the USA Today newspaper
website.
Our data set includes individual game-by-game statistics for all non-rookies who
appeared on a roster in the NBA anytime between the 2007/2008 and the 2010/2011 sea-
sons and who signed a new contract during this period. Hence, and according to Robst et
12
al. (2011), we focus on free agents only. This delimitation is important for several reasons.
First, players new to the league are mostly signed to contracts predetermined by the reg-
ulations of the collective bargaining agreement between the teams and the players’ union.
The salary levels thus relate directly to the position at which a player was selected during
the draft. Therefore, we need to exclude players under rookie contracts, whose remuner-
ation is not the result of an individualized bargaining process. Second, we gathered salary
data in the first year of the contract and performance indicators from the season immedi-
ately prior to that signing. Since most of the contracts are multi-year duration we would
otherwise misidentify performance as a driver for running contracts that were determined
years ago. We also excluded players for whom salary information was unavailable and
required that all players in our data set played in at least 41 games, equivalent to half of
the regular season. During the period considered the NBA was not subject to any lockouts
or shortened seasons, resulting in a constant number of teams (30) and games per team
per season (82). Thus the data set covers 259 different players and 330 player-year obser-
vations. To calculate performance volatility for each individual player, we used single
game performance statistics, which led to more than 22,520 performance logs for the
relevant period.
The natural logarithm of the player’s annual salary (LnSalary) serves as the depend-
ent variable for the analysis (Mincer, 1974). In the NBA, salaries are basically guaranteed
and rarely subject to individual performance-related bonuses. The individual player sala-
ries averaged $4,488,456, ranging from $202,134 to $25,244,493 per season; these values
did not change significantly across the seasons we observed. The salary distributions for
all four seasons we study are in Figure 1.
- Insert Figure 1 here -
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3.2 Empirical proxies for salary determinants
3.2.1. Measuring a player’s value to the team
Ticket and merchandise sales account for revenues to each respective team. Conse-
quently, fan appeal can add to the value of a player (Hausman and Leonard, 1997) and
even increase attendance for teams hosting an opponent that includes a superstar (Berri
and Schmidt, 2006). As a display of the league’s most popular players, the NBA All-Star
Game serves as a showcase in the middle of the season; the participating starters for both
teams are selected by the fans via ballots in the arenas and online. Therefore, to measure
popularity, we analyze the number of All-Star Game appearances prior to the signing of
a contract and their impact on player salary (All Star), assuming diminishing returns (All
Star²).
In contrast to studies of the 80`s and early 90`s identifying racial salary discrimi-
nation in the NBA, recent studies reveal that wage discrimination vanished over the past
decades (Groothuis and Hill, 2013; Kahn, 1991, 2000; Prinz et al., 2012; Robst et al.,
2011).
14
Beyond discrimination, there might also be some sort of physical and psycho-
logical advantage depending from ancestry and culture (Kahane, Longley & Simmons,
2013). Despite these recent findings nothing is known on the mutual dependence of race
and consistency in performance. To avoid a potential omitted variable bias, we control
for racial ancestry by grouping players into African ancestry (Black=1) and European
ancestry (Black=0).
15
14
The study of Yang and Lin (2012) indeed shows a significant positive effect for U.S. non-white players.
However, the authors did not control for free agency, assuming that every player would have had rene-
gotiated contracts after each and every season.
15
Due to a very small number of e.g. Hispanics (7), we did no further subordination.
14
3.2.2. Measuring a player’s expected performance
Over time, players should improve their abilities by learning how to succeed on the court.
We therefore expect players’ performance to increase over time and include the number
of seasons played in the NBA prior to the respective season in our regression, to reflect
their experience (Exp). However, physical ability also declines with age (Fair, 1994), so
we expect marginal returns to experience to decrease over time and include the variable
Exp² in the regression (Mincer, 1974). For the measure of individual expected talent, we
use the position at which each player was selected during the annual amateur draft (Wal-
lace, 1988; Gius and Johnson, 1998; Hill, 2004; Prinz et al., 2012). Each club selects
twice, in reverse order of their previous season’s winning record, for a total of 60 players
who are selected during the draft (DRAFT).
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Lower draft numbers indicate higher ex-
pected talent, in that they have been selected earlier during the annual recruiting event.
Talent is not expected to be distributed linearly among players eligible to be drafted. Be-
cause differences in talent likely decline for later selections in the draft, we control for
this non-linear effect (Draft²) (Koch and Vander Hill, 1988; Prinz, 2005).
A player’s expected performance also should depend on how well that player has
performed in the past. For this measure, we distinguish between scoring performance and
non-scoring performance. Scoring performance reflects accomplishments on offense;
non-scoring performance accounts for less “glamorous” statistics. Both are measured as
performance per minute, resulting in a points per minute indicator of offensive perfor-
mance (Scoring). Non-scoring performance is calculated as the sum of outputs not di-
rectly connected to offensive success, namely, rebounds, assists, blocks, and steals, again
16
There are 30 teams in the NBA, and each team has two picks, so the highest possible draft number is
60. Players who are not selected during a draft but appeared in our sample were coded as draft number
99. Using alternative codes did not produce different results.
15
measured on a per minute basis (Non-Scoring). On the basis of both our theoretical model
and previous research (Berri et al., 2007), we expect both performance measures to in-
crease player salaries.
3.2.3. Measuring a player’s performance consistency
Our main explanatory variables reflect performance consistency. To determine a
measure of consistency, we must conduct a game-by-game analysis. For this purpose, we
computed the standard deviation (SD) of each of our performance measures, Scoring (SD
Scoring) and Non-Scoring (SD Non-Scoring), individually for every player and season as
a proxy for variance in performance (Weimar and Wicker, 2015). The standard deviation
of Scoring is not correlated with average scoring performance, whereas Non-Scoring vol-
atility correlates positively with average Non-Scoring performance. Superstars, defined
as players who have appeared in at least one all-star game (Berri and Schmidt, 2006),
perform significantly more consistently than non-superstars in both Scoring and Non-
Scoring.
A potential drawback of these data is that external factors influencing a player’s
consistency, such as injuries, personal problems, or mental factors, are neglected. Unfor-
tunately, such information is not (or is only incompletely) available to us, whether be-
cause these data are not recorded or because players choose not to reveal injuries or per-
sonal problems. We therefore assume such external factors are randomly distributed
among players and assume no problems of omitted variable bias.
16
3.3 Descriptive statistics and empirical model
- Insert Table 1 here –
In addition to performance and volatility statistics, we account for unobserved player- and
team-related heterogeneity by including dummy variables for a player’s position, season
of observation, and team at the time of observation. The ability to play a certain position
might affect players’ salaries, because different positions require more or less substituta-
ble skills (Berri et al., 2005). Therefore, we control for point guard, shooting guard, small
forward, power forward, and center positions. Season dummies account for the discon-
tinuous salary history in the league, and team dummies reflect prevailing differences in
the teams’ financial power. To control for team-specific disturbance terms in the ordinary
least square (OLS) models, we clustered the standard errors at the team level. Table 1
contains the descriptive statistics for all 330 observations (259 unique players, sample
period: 2007/08–2010/11) in the sample.
- Insert Table 2 here –
In Table 2, all correlation coefficients among the independent variables are well
below 0.8. The maximum variance inflation factor among the explanatory variables
(squared values) is 3.32. Most important, the correlation coefficient between our two con-
sistency variables (SD Scoring and SD Non-Scoring) is 0.47 and thus well below 0.8
(dangerous correlation). Accordingly, we are confident that multicollinearity among the
regressors is not an issue and does not bias the subsequent regression models (Kennedy,
1998).
- Insert Table 3 here –
With Table 3, we provide an overview of the best and worst paid players during
2008–2011, which helps deepen understanding of the consistency variables. On average,
17
“bench warmers” are less consistent in both their scoring and non-scoring performance.
The mean standard deviations for the scoring/non-scoring measures of the ten lowest paid
players in our analysis are 0.26/0.18, whereas the corresponding values for the ten best
paid players are 0.17 and 0.11.
To estimate salaries in the NBA and test the hypotheses derived from our theoret-
ical model, we assume the following model to determine salary for player i in season t:
It is beyond dispute that performance and salaries relate, but the precise nature of this
relation is uncertain. Guided by our theoretical model and existing literature, we include
multiple control variables to account for salary determinants.
Furthermore, because of the panel character of our data, we apply random effects
models together with conventional OLS models. The random effects model accounts for
player-specific heterogeneity (Mátyás and Sevestre, 1996). Our talent indicator Draft is
time invariant, so we abstain from applying a fixed effects model to measure the effect of
talent. Given the potential for reverse causality between the dependent and independent
variables, especially between pay and performance indicators, we introduced a one-sea-
son time lag (Dobson and Goddard, 1998; Granger, 1969; Hall et al. 2002; Torgler and
Schmidt, 2007). The salary information thus came from season t, whereas the indicators
of performance were drawn from the previous season t – 1.
18
In addition to the overall significance of a potential effect of performance con-
sistency on wages, managers might be interested in the magnitude of this effect. Standard
inference statistics do not offer any indicator of magnitude relative to other explanatory
variables, but dominance analyses can be applied to generate information about the indi-
vidual contributions of each variable to the overall variance explained (Budescu, 1993).
We are interested in the general influence of consistency, so general dominance statistics
(Johnson, 2000) are preferred as the procedure “sum to the R² of the full model (contain-
ing all predictors), so they allow for a decomposition of the overall R² across the individ-
ual predictors” (Azen and Traxel, 2009, p. 329). Accordingly, we estimate dominance
statistics for every model.
As depicted in Figure 1, the distribution of salaries in the NBA is clearly skewed
to the right, motivating a more fine-grained analysis that uses quantile regression
(Koenker and Bassett 1978; Koenker and Hallock 2001). The particular advantage of
quantile regression analysis is that it specifies salary returns to characteristics and perfor-
mance measures for different ranges of the salary distribution (Koenker, 2005), exposing
possible differences over the quantiles. In contrast, OLS estimates constrain the marginal
effects of the covariates to be the same at the mean and elsewhere. Especially in sport
contexts though, the average salary exceeds the median, due to the excess kurtosis in the
distribution. Marginal effects at the median are not necessarily identical to those at the
mean or anywhere else in the distribution. The presence of salary outliers may cause mar-
ginal effects of covariates, especially performance consistency, to differ over the distri-
bution. Therefore, we applied an unconditional quantile regression analysis (Firpo et al.,
2009).
19
3.4 Regression results and discussion
The results for two alternative specifications are in Table 4. In contrast with the assump-
tion of unobserved heterogeneity among players, a Breusch-Pagan (1980) test indicates
preference for a pooled OLS model (p = 0.1536). This effect might be caused by the
strong unbalanced panel structure (259 groups out of 330 observations). Nevertheless, we
also report random effect coefficients, as a robustness check.
- Insert Table 4 here/ Insert Table 5 here –
The impacts of our control variables on salary are approximately as we predicted.
In line with Hypothesis 1, the number of All-Star Game appearances positively influ-
ences player salary; the diminishing returns also are supported by our data. However, this
effect is significant only at the 10% level. The results of the dominance analysis further
indicate that this cumulative effect explains only 3.79% of the total R2 of the OLS model,
which makes it less important than other predictors.
Similarly, the estimation results strongly support Hypothesis 2. In line with our
previous argumentation, both scoring and non-scoring performance per minute positively
affect player remuneration, and the coefficients are highly significant in both estimations.
Players who score an additional 0.01 points per minute generate a wage bonus of 3.29%.
Considering non-scoring performance, every 0.01 increase in our measure increases an
athlete’s salary by 3.68%. Consequently, players receive higher salaries when their aver-
age performance in the preceding season, on offense or defense, improves. Although the
coefficients of both Exp and Draft have the predicted signs, the effect is not statistically
significant. According to the relative weight predictions, scoring is the most important
factor, explaining 19.41% of the overall variance in the OLS model. Non-scoring perfor-
mance emerges as the third most important variable, explaining 7.38% of the variance.
20
To test Hypothesis 3, we turn to the impact of performance volatility on remuner-
ation. As an initial effort to measure performance consistency empirically, we include the
standard deviation in scoring and non-scoring performance in our basic salary analysis.
According to the theoretical model in Section 2, we expect salaries to rise with greater
consistency (decreasing standard deviation). Controlling for average performance and in
line with our model, the OLS estimations support the expectation that performance con-
sistency induces monetary rewards. Negative coefficients power the idea that salaries sig-
nificantly decline as the standard deviation in performance increases for both scoring and
non-scoring. Specifically, every additional standard deviation in SD Scoring (0.06) leads
to an 11.97% (-1.995/1006) decrease in salary. Players for whom SD Non-Scoring is
one standard deviation (0.04) less earn 27.07% (-6.766/1004) more than their less con-
sistent competitors. The dominance analyses similarly reveal the importance of SD Non-
Scoring, which explains 11.32% of the R2. The relative weights instead indicate a smaller
effect of SD Scoring, with an explained variance of 4.66%. Moreover, the results of the
random effects estimations reveal no significant effect of scoring consistency, which
might reflect two main causes. First, the strong unbalanced structure of our panel might
lead to an overestimation of relatively bad players, who are more likely to negotiate new
contracts more than once every four years. Second, the right-skewed distribution of the
salary data could bias the OLS results. To adjust for the right-skewed distribution and
better substantiate the effects of SD Scoring and SD Non-Scoring, we therefore reesti-
mated the OLS model by applying an unconditional quantile regression analysis (Table
6). The estimation results reveal that average performance in both scoring and non-scor-
ing are equally important and highly significant in the upper quantiles. The estimations
also reveal highly significant effects of SD Non-Scoring in the lower quantiles, but no
21
significant effects are detected for consistency related to scoring activities. Thus, less
consistent non-scoring performance is punished by reduced compensation, whereas con-
sistency in scoring activities does not seem to matter as much. Still, we note that the
number of observations is relatively low in each of the quantiles, which could potentially
explain the observation of only few significant effects in the quantile regressions. The
variable Black controlling for racial wage discrimination showed no significant impact
on wage determination, which is in line with recent findings on wage discrimination in
the NBA (Groothuis and Hill, 2013; Prinz et al., 2012; Robst et al., 2011).
17
We also ran
some regressions where we included interaction terms between the variable
Black and our consistency measures (these results are not reported in our tables, but avail-
able upon request). The interaction terms between the variable Black and our consistency
measures were insignificant.
18
- Insert Table 6 here –
In summary, the evidence presented in these tables indicates a high impact of over-
all performance on player remuneration. In addition to achieving this expected result, our
analysis demonstrates empirically that consistency in performance seems crucial to wage
determinations in the NBA. However, differences in the effect of performance con-
sistency arise, depending on the underlying performance statistics. Consistency in non-
scoring performance significantly affects remuneration, but the estimations indicate that
the results for consistency in scoring are less clear-cut.
17
With regard to Yang and Lin (2012), we alternatively tested nationality by including a dummy for for-
eign players. In contrast to the findings of Yang and Lin (2012), foreign players were found to earn
significantly more than U.S. players (at the five percent level). Most important, the coefficients and p-
values of the consistency related variables only changed slightly.
18
Unsurprisingly, given the potential correlation between the consistency variables and the interaction
terms, standard errors were much higher in those alternative regressions with the result that some of
the consistency variables in the estimations also became insignificant.
22
4. Conclusion
The aim of this study has been to investigate the effect of consistency in an employee’s
performance on salary. This research question is of general managerial interest, but stud-
ies have been hindered by the lack of data available about performance consistency in
traditional business environments. To overcome this drawback, we analyze performance
and salary data from a professional sport setting (NBA), using different regression meth-
ods.
The most important predictors are scoring and non-scoring performance. In addi-
tion, the empirical results indicate that consistency in non-scoring performance by pro-
fessional basketball players is financially rewarded, whereas the results for consistency
in scoring performance depend on the econometric specification. That is, it appears that
consistent performance in some tasks is rewarded more strongly than in others. Further
research should expand the panel matrix to explore the impact of consistency in different
tasks in more detail. With game-by-game information over the course of four seasons,
our study offers a theoretical motivation and empirical support for the notion that general
managers reward both high expected performance and performance consistency.
These results shed new light on evaluations of professional athletes’ performance
consistency and also suggest different research paths. In particular, our study ignores the
importance of individual performance (consistency) for team success. From a managerial
standpoint, the composition of a team might demand the inclusion of very inconsistent
workers (players) in the production process. Assuming that performance is easily observ-
able, this composition would allow the manager to replace workers who are temporary
performing badly. In professional basketball games, coaches may substitute arbitrarily,
which might allow them to include players who display greater volatility on their rosters.
23
We also did not address opponent quality or within-game dynamics that might affect the
strategic composition of the teams on the floor (Grund and Gürtler, 2005). Additional
research should take such factors into account.
The significant effect of performance consistency we find makes it surprising that
consistency statistics for players are not more widely available (e.g., on the Internet).
Reflecting a moneyball effect (Lewis 2003), this gap could be interpreted as a signal of
market inefficiency, especially for players. As the moneyball proposition did, the findings
of this study seemingly could influence individual players’ behavior: Athletes might fo-
cus their training more on achieving consistent performance (Berri et al., 2014).
The factors discussed in this investigation pertain specifically to basketball or, more
generally, to team sports, but some arguments suggest the potential for transferring these
results to other industries. First, team production functions exist in virtually any industry,
because workers in any work environment are not entirely independent from one another.
The outcome of any firm with more than one employee constitutes a form of team pro-
duction (Alchian and Demsetz 1972). Second, NBA players and their teams follow a
wage/win maximization function, just as any other employee and firm would (Hoehn and
Szymansky 1999). Third, players and teams enter into classical principal–agent encoun-
ters, marked by agency costs and ex ante and ex post uncertainties (Holmström 1979;
Jensen and Meckling, 1976). Having said this, arguments also exist for why the basketball
market and other labor markets differ. For instance, in contrast to classical labor markets,
principals (teams) mostly initiate separations instead of agents (players) themselves (Bor-
land and Lye, 1996). Moreover, team managers (principals), who are primarily in charge
of negotiations, often earn less than their best paid players (agents), which is unlikely to
be the case in “classical” principal-agent situations. Furthermore, players face higher risks
24
by future uncertainty related to injuries and shortened career duration (Dietl et al., 2008;
Frick, 2007). Summing up, differences between the basketball industry and other indus-
tries of course exist. The same, however, can probably be said of almost every industry,
as every labor market/industry is idiosyncratic in some way (Kalleberg and Sorensen,
1979; Kalleberg et al., 1981). Therefore, there are at least some reasons to believe that
NBA teams and players are likely to behave similarly to the way organizations and work-
ers outside the sports industry do, especially considering that “many basic elements of
supply and demand are very clearly seen in sports” (Rosen and Sanderson, 2001, p. 48).
We find that consistency is partially rewarded in professional basketball; we believe this
finding likely holds in other working environments too. However, further research should
focus on finding a valid consistency measurement in a more traditional firm environment
to support an investigation into the extent to which our findings generalize to firm behav-
ior outside sports.
25
Figure 1
Density estimation of players’ salary per season
0
5.000e-08 1.000e-07 1.500e-07 2.000e-07
kdensity
0 5000000 10000000 15000000 20000000 25000000
2008 2009
2010 2011
Salary
26
Table 1
Descriptive statistics (n=330)
Variable
Explanation
Mean
SD
Min
Max
Salary
Annual salary
4,488,456
4,150,459
202,134
25,244,493
LnSalary
Natural log of player salary
14.91
0.94
12.22
17.04
Experience
Number of seasons in the NBA
5.85
3.75
0.00
17.00
Draft
Position selected at the draft
33.53
31.84
1.00
99.00
All Star
Appearances in All-Star Games
0.59
1.88
0.00
15.00
Black
African ancestry
0.79
0.41
0.00
1.00
Scoring
Points scored per minute
0.38
0.12
0.12
0.76
Non-Scoring
Non scoring per minute
0.30
0.08
0.15
0.56
SDScoring
Standard dev. in Scoring
0.21
0.06
0.11
0.43
SDNon-Scoring
Standard dev. in Non-Scoring
0.14
0.04
0.07
0.30
27
Table 2
Correlation table of metric variables (n=330)
1: Sa
2: Ex
3: Dr
4: Al
5: Sc
6: No
7: SD
8: SD
1: Salary
1.00
2: Experience
0.09
1.00
3: Draft
-0.34
-0.32
1.00
4: All Star
0.35
0.48
-0.23
1.00
5: Scoring
0.62
-0.06
-0.32
0.32
1.00
6: Non-Scoring
0.34
0.14
-0.14
0.14
0.00
1.00
7: SD Scoring
-0.27
-0.26
0.17
-0.17
0.03
-0.27
1.00
8: SD Non-Scoring
-0.37
-0.12
0.29
-0.20
-0.46
0.27
0.47
1.00
28
Table 3
Consistency of the ten best and the ten worst paid players
Name
Salary
Scoring
Non-
Scoring
SD
Scoring
SD Non-
Scoring
Bryant
25244493
0.75
0.33
0.18
0.11
Arenas
19269307
0.42
0.31
0.21
0.13
Gasol
18714150
0.51
0.42
0.17
0.12
Nowitzki
17278618
0.67
0.32
0.17
0.10
Stoudemire
16486611
0.67
0.33
0.20
0.11
Johnson
16324500
0.56
0.28
0.17
0.11
Durant
15506632
0.71
0.30
0.14
0.08
Randolph
15200000
0.55
0.43
0.15
0.10
James
14500000
0.76
0.47
0.18
0.10
Bosh
14500000
0.66
0.41
0.19
0.13
Mean
17302431
0.63
0.36
0.17
0.11
Carney
633158
0.37
0.26
0.28
0.15
Jones
622531
0.30
0.23
0.23
0.12
Croshere
612134
0.38
0.32
0.29
0.22
Hart
546416
0.22
0.32
0.40
0.24
Williams
321652
0.30
0.18
0.20
0.15
Elson
305792
0.22
0.30
0.17
0.27
McRoberts
300000
0.33
0.40
0.18
0.16
Udoka
264232
0.26
0.31
0.43
0.25
Stackhouse
222712
0.42
0.23
0.18
0.10
Pavlovic
202134
0.30
0.23
0.25
0.17
Mean
403076
0.31
0.28
0.26
0.18
29
Table 4
NBA salary regression, 2007/08–2010/2011
DV: LNSalary
OLS
RE
Experience
0.047 (1.34)
0.050 (1.21)
Experience²
-0.005 (-1.94)*
-0.005 (-1.68)*
Draft
-0.004 (-0.95)
-0.004 (-0.69)
Draft²
0.000 (0.56)
0.000 (0.35)
All Star
0.131 (1.95)*
0.114 (1.95)*
All Star²
-0.011 (-1.9)*
-0.010 (-1.85)*
Black
-0.079 (-0.86)
-0.065 (-0.65)
Scoring
3.288 (4.78)***
3.291 (6.97)***
Non-Scoring
3.630 (5.34)***
3.758 (5.23)***
SD Scoring
-2.074 (-2.5)**
-1.560 (-1.65)*
SD Non-Scoring
-6.672 (-3.46)***
-6.604 (-4.42)***
Constant
14.340 (30.048)***
14.128 (29.29)
Team Fixed Effects
Yes
Yes
Position Fixed Effects
Yes
Yes
Season Fixed Effects
Yes
Yes
R²/ R between
0.61
0.63
Observations
330
330
Notes: The t-values are presented in parentheses next to the coefficient estimates ***, **, and *
denote 10%, 5%, and 1% statistical significance levels, respectively.
30
Table 5
Dominance analysis
OLS
RE
Relative Weights*
Rank
Relative Weights**
Rank
Set 1: Experience + Exp²
0.018
9
0.021
9
Set 2: Draft + Draft²
0.045
6
0.050
5
Set 3: All Star + All Star²
0.038
7
0.035
6
Set 4: Black
0.002
11
0.001
11
Set 5: Scoring
0.194
1
0.192
1
Set 6: Non-Scoring
0.073
3
0.091
3
Set 7: SD Scoring
0.047
4
0.062
4
Set 8: SD Non-Scoring
0.113
2
0.114
2
Set 9: Team FE
0.045
5
0.034
7
Set 10: Position FE
0.019
8
0.023
8
Set 11: Season FE
0.015
10
0.013
10
Sum
0.610
0.634
Notes: * contribution to the overall R²; ** contribution to the R²-between.
31
Table 6
Impact of consistent performance on LNSalary (unconditional quantile regressions)
Variable
0.1
0.25
0.5
0.75
0.9
Experience
0.084 (1.62)
-0.061 (-0.88)
-0.011 (-0.16)
0.104 (1.68)*
0.103 (1.80)*
Experience²
-0.004 (-0.94)
0.008 (1.55)
-0.004 (-0.83)
-0.009 (-2.21)**
-0.010 (-2.4)**
Draft
0.004 (0.67)
0.009 (1.05)
-0.009 (-0.98)
-0.017 (-1.99)**
-0.011 (-1.21)
Draft²
0.000 (-0.44)
0.000 (-1.1)
0.000 (0.38)
0 .000(1.74)*
0.000 (1.42)
All Star
-0.039 (-0.83)
-0.082 (-1.26)
0.080 (0.8)
0.238 (2.32)**
0.557 (4.03)***
All Star²
0.003 (0.93)
-0.001 (-0.26)
-0.009 (-1.06)
-0.019 (-2.62)***
-0.042 (-3.62)***
Black
-0.018 (-0.15)
-0.109 (-0.66)
-0.243 (-1.41)
-0.099 (-0.64)
0.123 (0.86)
Scoring
0.958 (1.42)
2.519 (3.37)***
3.783 (4.33)***
4.613 (5.53)***
4.451 (5.69)***
Non-Scoring
0.831 (0.85)
2.909 (2.54)**
4.895 (4.01)***
5.29 (4.29)***
4.231 (2.99)***
SD Scoring
-1.429 (-0.98)
-1.594 (-1.04)
-2.772 (-1.74)*
-1.936 (-1.31)
-1.089 (-0.78)
SD Non-Scoring
-5.318 (-2.35)**
-10.786 (-4.06)***
-9.905 (-3.44)***
-3.367 (-1.48)
-6.604 (-4.42)***
Constant
14.209 (22.30)
14.395 (19.78)
15.597 (18.13)
12.083 (17.23)
12.993 (16.61)***
Team Fixed Effects
Yes
Yes
Yes
Yes
Yes
Position Fixed Effects
Yes
Yes
Yes
Yes
Yes
Season Fixed Effects
Yes
Yes
Yes
Yes
Yes
R²
0.26
0.35
0.46
0.51
0.51
Notes: The t-statistics are presented in parentheses next to the coefficient estimates ***, **, and * denote 10%, 5%, and 1% statistical significance lev-
els, respectively.
32
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