A game-level analysis of salary dispersion and team performance in the national basketball association

Abstract

Using game-level panel data on the National Basketball Association (NBA), we examine the causal effect of within-team salary dispersion on team performance. We exploit three measures of salary dispersion and examine the effect at three levels: whether the outcome of the game is influenced by salary dispersion among (1) players participating in the current game (active players), (2) players who played more than half of their team's games in a season (regular and occasional players) and (3) the entire player population. Regardless of the measures used, we find that salary dispersion does not influence team performance.

Acknowledgements

We are grateful to the editor and two anonymous referees for helpful comments. The views expressed in this article are those of the authors and do not necessarily reflect the views of the Productivity Commission or the Australian Government.

Notes

¹ The inquiry started originally in the context of firms. Empirical studies on firm performance include Main et al. (1993), Ericksson (1999), Winter-Ebmer and Zweimüller (1999), Lallemand et al. (2004) and Heyman (2005).

² The dependent variable representing relative performance is not unique to game-level studies. A team's season winning percentage, the dependent variable commonly used in season-level studies, is considered to measure the relative performance of the team. In Berri and Jewell (2004) where the dependent variable is the change in winning percentages from the previous season to the current season, the authors state, ‘it is noted that the proposed dependent variable measures the change in the relative strength of the team’ (p. 135, emphasis added).

³ Zak et al. (1979) maintain that ‘the essence of sports competition is to gauge one's performance relative to others’. (p. 382, emphasis added).

⁴ Each covariate can be interpreted as the composition of a positive input for one team and a negative input from another team.

⁵ In the season-level analysis by Berri and Jewell (2004), (the change in) the level of salary dispersion relative to the league average is used as a salary dispersion measure. When estimating production efficiency of NBA teams, Hofler and Payne (1997) use (the log of) the ratios of the variables associated with a given team relative to its opponents.

⁶ Jones et al. (1999) found that salary differences in the NHL are primarily determined by productivity differences. Torgler and Schmidt (2007) found that salary and individual performance are significantly associated in the German soccer league Bundesliga.

⁷ In this study we could construct two other types of coefficients of variation: (1) the coefficient of variation using only players who played more than half of their team's games and (2) the coefficient of variation using team rosters that include all players who had participated in at least one game during the season. These two measures are left for future research.

⁸ More precisely, Berri and Jewell (2004) constructed a salary dispersion measure from the Herfindahl index. In the recognition that a team's winning percentage represents the relative strength of the team, Berri and Jewell (2004) constructed the variable that represents the number of SDs above or below the league average Herfindahl index a team's salary dispersion is located.

⁹ Little information is provided in Frick et al. (2003) regarding how the data should be treated to account for traded players or players with low levels of participation. We thus assume that the variable (i.e. the Gini coefficient) is constructed using team rosters that include all players who had participated in a game during a season, with the exception of players who had played for more than one team in the season. Players who switched teams mid-season were only included on the roster of team for which they had played the most games.

¹⁰ We do not control for team size which is used in Frick et al. (2003). However, team size is implicitly controlled for in this study, as minute-adjusted ‘average’ salary is used, not total team salary bill.

¹¹ Arellano and Bover (1995) suggest additional moment conditions under stronger assumptions. Although this study attempts to exploit those moment conditions, exclusion restrictions are rejected at the 10% levels in most cases.

¹² All the estimation in this study is done using a STATA module ‘xtabond2’ written by Roodman (2006).

¹³ Although she has no official affiliation with the NBA or any of its teams, various economic researchers recognize Patricia Bender as a credible source of data. NBA statistics gathered by her have been used by various econometric studies including Berri and Jewell (2004), Rosenbaum (2003) and Groothuis et al. (2005).

¹⁴ Salaries provided by Patricia Bender were often the amounts paid by team management to players as calculated ex post. Thus, many figures posted by Bender show the partial salaries that teams were required to pay for players who were subject to early release.

¹⁵ First established in 1983, the salary cap is a guaranteed percentage of NBA revenues to be paid as player salaries. The initial cap set in 1983 was 53% of team revenues. The collective bargaining agreement of 1999 set the cap at 48.04% of basketball related income, and in 2005 it was set at 49.5%.

¹⁶ We are grateful to an anonymous referee for suggesting this possibility.

¹⁷ These results are available on request.

¹⁸ We also estimate the model where avesal _it is replaced with the minute-unadjusted average salary. The coefficient on disper _it has never become significant even at the 10% level, regardless of the dispersion measures.

¹⁹ We are thankful to anonymous referees for pointing this out.

²⁰ We thank an anonymous referee for this insight.