Illinois Wesleyan University

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4-19-2012

Economics of Salary Dispersion in the National Basketball Economics of Salary Dispersion in the National Basketball

Association Association

Daniel Schouten

Illinois Wesleyan University

, [email protected]

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The purpose of this study is to discover the optimal amount of salary

dispersion for an NBA team and the affect that dispersion has on team wins and

revenue. The optimal amount of salary dispersion could be different for teams that

want to maximize wins and teams that want to maximize revenue. For the purpose

of this study, five different measures of salary dispersion are utilized to most

effectively understand the effects. Empirical models are constructed and OLS

regressions employed using cross-sectional data from the 2006-07 NBA season

through the 2010-11 season to understand the relationship. The empirical evidence

I. Introduction

Teams in the National Basketball Association (NBA) face important salary allocation

decisions. NBA players provide different value to their respective team and therefore are worth

different amounts of money. General managers have to determine how to allocate the total

salary given to their signed players. An important research question to consider is: What is the

best way to allocate salary amongst an NBA team? The term “best” in this situation can be

interpreted in different ways. ”Best” can be viewed as a salary distribution that maximizes wins.

Wins are obviously important to both fans and management. “Best” can also be viewed as a

salary distribution that maximizes revenue as each team is attempting to make money.

competitive imbalance. A large amount of imbalance can lead to a contraction in the number of

teams, or even the disbanding of the entire league (Rosen et al, 2000). The NBA has the biggest

competitive imbalance problem of any of the four major sports leagues when it comes to number

of wins and amount of revenue generated. At the end of the 2010-11 NBA season, two teams,

the Boston Celtics and Los Angeles Lakers, have won a combined 33 NBA Championships in

the NBA’s 65 years. In addition, differences across teams in revenue generation are enormous.

Within the last five years, there has been up to a 254% difference between the top and bottom

teams in total revenue. The competitive imbalance problem deals with a problem at the league

level, whereas the research question at hand deals with the team level disparity. They are

connected, however, because if general managers knew how salary dispersion on a team level

much more easily measured than workers in other firms because of the statistics that are

compiled with the sport.

This study aims to determine the optimal amounts of salary dispersion to maximize wins and

maximize revenue. Based on economic theory provided in the following section, I hypothesize

that the optimal amount of salary dispersion will be different for teams that have a goal of

maximizing wins and teams that have a goal of maximizing revenue. Labor demand theory,

human capital theory, and superstar theory all play a role in the following section. Based on these

economic theories, I hypothesize that the greater the dispersion the greater the number of wins

achieved. I also hypothesize that the greater the dispersion the greater the amount of revenue

generated.

dispersion in sports deals with the effect of salary dispersion on the number of wins and does not

consider revenue. The literature that deals with wins and salary dispersion is relatively new and

has mostly appeared after the Collective Bargaining Agreement (CBA) between the NBA owners

completed their roster with players offered the NBA minimum wage or close to it.

Berri and Jewell (2004) in addition to Katayama and Nuch (2011) saw this rapid change

in distribution of salaries as a chance for a natural experiment to understand how changes in

disparity impact team/firm performance. Each study defined the dispersion variable differently,

but came to the same conclusions. Both studies found the amount of salary dispersion within a

team to have no significant effect on team performance. The authors say that, for this industry at

least, the idea of tournament theory, which states that pay inequality results in higher worker

productivity, and pay compression school of thought, which states that wage equality will

enhance cooperation and therefore performance, are both inapplicable (Berri et al, 2004). The

datasets used, however, were admittedly somewhat small and both Berri and Katayama believe

there could be a significant effect if the sample size was larger (Katayama et al, 2011). Another

Stefan Kesenne (2007) discusses the multiple objectives of professional sports teams in

The Economic Theory of Professional Team Sports

many teams are focused on maximizing wins. Studies have been inconclusive in accepting or

rejecting the profit or win maximization goals. Kesenne provides a simple diagram that leads to

his underlying hypothesis that revenue maximizing teams and win maximizing teams will have a

differing amount of salary dispersion. Figure 1 shows the different amount of talent demand

levels depending on team goals. The number of talents, or superstars, is represented on the

horizontal axis and total revenue and cost is represented on the vertical axis. The variables t

, t

,

etcetera, on the horizontal axis do not specifically mean one superstar, two superstars, and so

forth. They represent different possible number of talents on a team, but not incremental

increases in talents. The farther to the right on the horizontal axis, the higher the total number of

assumption that the most successful teams have more talents, a win maximizing team would

want to hire as many talents as financially possible. Therefore, a win maximizing team will hire

t

any money (Kesenne, 2007). This analysis makes clear that the revenue maximization point and

win maximization point requires a different amount of talents and therefore a differing amount of

salary dispersion.

The effect of superstars on revenue has also been extensively studied, especially by

Sherwin Rosen (1981) and Walter Oi (2008). Rosen discusses that the settings in which

admiration, and a desire to understand how they are as good as they are that creates revenue for

their firm.

Jerry Hausman and Gregory Leonard (1997) studied the effect that NBA superstars had

on both team and league revenue during a number of seasons in the 1990’s. Some of the avenues

that superstars help produce revenues are through increases in television ratings, game

attendance, and sport paraphernalia sales. They found that a superstar positively impacts both

his team’s total revenue and other teams’ revenue (Hausman et al, 1997). This means that small

market teams would attempt to free-ride off large market teams. According to Hausman, a

suggestion to fix this free rider benefit is to impose a salary cap. A salary cap, however, could

over correct the superstar externality. The NBA has tried to correct this problem by instituting a

soft salary cap (Coon, 2011). This means that there are a few exceptions to the salary cap rule

determinant of the marginal productivity of workers. Human capital refers to the productive

capabilities of human beings as income generating components in the economy (Rosen, 2008).

According to human capital theory, the higher the productivity that is obtained through

investments in education and training, the higher amount of income a person should achieve.

Also, human capital theory suggests that the returns to investments in education and training are

directly related to the individual’s innate ability and physical endowments. Therefore, the higher

the basketball player’s skill, the higher the amount of income he should generate and the higher

According to Oi (2008), small differences in talent can be associated with large

player one to player 12. The perfect distribution line in Figure 6 represents perfect equality of

income. As a result of no teams having perfectly equal distribution of salaries, no team’s

distribution follows the perfect distribution line. The Lorenz Curve represented in Figure 6 is

respective Gini coefficient for each season.

The second measure of dispersion that is used is the standard deviation of each team’s

player salaries. This, like the Gini coefficient, is a representative measure of the dispersion that

takes all players salaries into account. As the standard deviation of salaries increases, the wage

dispersion on a team increases as well. This measure of dispersion has been used in past studies,

however, it has not been utilized for the time frame that this study is reviewing (Berri, 2004).

The effect of standard deviation on wins and revenue might be different in this study because of

recent changes in the CBA, changes in the number of superstars in the league, and evolution of

The last three measures of dispersion are all related. They are the top player salary as a

measures, have not been applied in published studies to test the effect salary dispersion has on

team wins and revenue. Despite this, they are measures that completely take into account the

representing the “best” possible dispersion level.

impact on wins even greater (Dosh, 2001). The market size variable is predicted to contain a

The next explanatory variable is a dummy variable that takes into account a team’s salary

position relative to the luxury tax level. The luxury tax level is greater than the salary cap level

and needs to be controlled for in the study. This is because teams can have payrolls that exceed

threshold. The above luxury tax dummy variable, in this sense, is a proxy for the level of a

team’s payroll and is predicted to be positively correlated with wins and revenue. If teams are

spending enough money to have a payroll that exceeds the luxury tax level, they most likely have

a number of superstars that should create more wins and revenue.

The last variables are fixed effect dummy variables for time. These are included to deal

with possible omitted variable bias. They control for things not already controlled for in the

regression that may be correlated with time. Fixed effect dummy variables are defined for each

year except for 2010-11 which is the reference year for each model. Each of the five seasons has

its own dummy variable associated with it. There is no logical predicted relationship of the time

dummy variables on wins and revenue.

Wins Model: Wins = ß

(Dispersion Measure) + ß

(Dispersion Measure

) + ß

(MRKT) +

Revenue Model: Revenue = ß

+ ß

(Dispersion Measure

) +

V. Results

is discussed.

to be seen. The effect that is represented by the linear curve will result in the optimal amount of

remain constant in each regression of the Wins Model.

Each measure of dispersion tested, the most important variables to this study, reveals that

statistically significant at the 5% level, but it is still statistically significant at the 10% level.

players but across the entire team impacts wins in a positive manner.

The other three dispersion measures (TOP1, TOP2, and TOP3) also show a positive

correlation with wins. The results become more significant and contain a larger effect with every

additional player being included in the percent of total salary. For example, using the TOP1

These measures of dispersion only take the dispersion that exists from the highest paid players

on a team compared to everyone else. The results indicate that the greater the salary dispersion of

top paid players in comparison to the lower paid players, the more wins a team will achieve. The

simulations of the effects of a one standard deviation change in the three dispersion measures

(TOP1, TOP2, and TOP3) yield interesting results. A one standard deviation increase in TOP1,

TOP2, and TOP3 is estimated to lead a team to win 1.80, 3.04, and 3.83 more games respectively

in a season.

In all the regressions, the market size control variable is the only variable to have an

Every other control variable behaves according to the presumed logic. All of the fixed

The market size had a statistically significant negative effect on the number of wins a

team achieves during the regular season for each dispersion level tested. The coefficients of

market size somewhat change depending on the measure of dispersion tested, but not by a great

In terms of the dispersion measures, there are conflicting results. Every dispersion

measure carries a positive impact on revenue, but four of the five measures of dispersion are not

statistically significant. The standard deviation measure of dispersion, however, shows a

These results, similarly to the Wins Model, do not show a specific optimal amount of

salary dispersion for a revenue maximizing team, but they do show the effects salary dispersion

has on revenue. The most common result is that salary dispersion does not significantly affect

revenues, but the model that measures dispersion by standard deviation does show that the

Every control variable behaves according to the presumed logic and contains the

predicted sign. The fixed effect variables were, once again, largely statistically insignificant.

The one difference, however, is that in each regression, the Fixed Effect 09-10 variable was

In terms of policy implications of salary dispersion and revenues, the conclusions drawn

from this study are more tentative. With salary dispersion having no direct significant effect on

revenue it is impossible to state what an NBA team should strive to do in terms of salary

due to the nature of the indirect effect versus the direct effects.

these results, it is possible that in service business environments where team performance is

important, like it is in the NBA, managers may benefit from hiring as many top notch employees

at each respective job and then complete the hiring process with lower salaried workers. This

may lead to increases in performance. This possibility suggests the need for future research that

focuses on the applicability of NBA results on the non-sports sector.

One possible way to further explore this research is to create even more definitions of

salary dispersion and test each one to see if the effect/absence of effect does change depending

on the definition of dispersion. The definitions of dispersion utilized in this study may have a

significant impact on the effect it has on both performance and revenue. In addition to this, the

appropriately.

Berri, David, and Todd Jewell. "Wage Inequality and Firm Performance: Professional

Basketball's Natural Experiment." Atlantic Economic Journal 32.2 (2004): 130-39. Web

Byrns, Ralph. "Economics Interactive." Lorenz Curve and Gini Coefficients. University of North

Carolina. Web. 30 Mar. 2012.

revenue-sharing/>.

Hausman, Jerry, and Gregory Leonard. "Superstars in the National Basketball Association:

Economic Value and Policy." Journal of Labor Economics 15.4 (1997): 586-624. JSTOR.

Web. Sept. 2011.

Katayama, Hajime, and Hudan Nuch. "A Game-Level Analysis of Salary Dispersion and Team

Performance in the National Basketball Association." Applied Economics 43.10-12

(2011): 1193-1207. EconLit. EBSCO. Web. 21 Sept. 2011.

Cheltenham, UK: Edward Elgar, 2007. Print.

Krinsky, I and A. L. Robb. 1986. “On Approximating the Statistical Properties of Elasticities.”

Oi, Walter. "Superstars, Economics of." The New Palgrave Dictionary of Economics Online.

2008. Web. Sept. 2011.

Rosen, Sherwin, and Allen Sanderson. "Labor Markets in Professional Sports." Journal of

Rosen, Sherwin. "Human Capital." The New Palgrave Dictionary of Economics Online. 2008.

Web. Sept. 2011.

Rosen, Sherwin. "The Economics of Superstars." The American Economic Review. JSTOR, Dec.

1981. Web. Sept. 2011

“The Business Of Basketball." Information for the World's Business Leaders - Forbes.com.

Forbes, 26 Jan. 2011. Web. 13 Nov. 2011.

<http://www.forbes.com/lists/2011/32/basketball-valuations_land.html>.