### Abstract

The paper examines the relationship between state income tax rates and the success of National Basketball Association (NBA) franchises. The model indicates that state income tax policy has an influence on team performance. The higher the rate for the top marginal tax bracket, the greater the negative bias on team performance. Team performance is dependent on the successful acquisition of quality resources which include players, coaches, and team management. The results infer that NBA franchises located in high tax states impose a burden on the ability of team ownership to attract the best resources in order to achieve success. The relationship could have broader implications on professional sports and their Collective Bargaining Agreements.

**Key words:** National Basketball Association (NBA), Professional Sports, Collective Bargaining Agreement (CBA), Salary Cap, Bias, Free Agency, State Income Tax Policy

### Introduction

The National Basketball Association (NBA) is a sports entertainment enterprise with yearly revenues surpassing $4 billion (5). The majority of these revenues are derived from ticket sales, merchandising and television revenues. The distribution of these revenues between franchises and players has been negotiated and is governed by the Collective Bargaining Agreement (CBA). The current version of the CBA was implemented before the 1984-85 season and was most recently re-negotiated prior to the 2005 season. The current CBA contract expires following the 2010-2011 NBA season, but league owners have the option to extend the agreement through the 2011-2012 NBA season (5).

A large component of the CBA is the provision of a salary cap. The salary cap dictates a fixed percentage of league revenues which are to be paid to players in terms of salaries and benefits. NBA teams are presented with a yearly salary cap number to be used as player compensation. This amount can only be exceeded utilizing certain exceptions as further defined by the CBA.

One justification for the salary cap is the concept that it is designed to benefit middle and small market teams. It is argued that larger market teams have significantly more ability to profit from ticket, merchandising and television revenues. This advantage could be used to enlist top talent by paying salaries far exceeding those of smaller markets. In using superior financial resources to lure and retain better talent (players, coaches and management), it is feared that larger market teams could dominate the league over a prolonged period.

The salary cap system, it is argued, should allow every NBA franchise an equal opportunity in acquiring and obtaining comparable resources. While not a perfect system, the CBA should work to distribute resources (player skill, coaching talent and management expertise) more evenly throughout the league. While the CBA only governs player salaries, the even distribution of quality players throughout the league should also dissuade quality coaches and management from concentrating and distribute them throughout the league.

League ownership believes that an equal chance of team success should promote larger game attendance and provide for a healthier competitive balance in the league. However, these goals have repeatedly been disputed in research (7, 3, 9) which have found increased disparity of play after the imposition of revenue sharing amongst teams and other results inconsistent with stated goals. This paper will extend this research by examining potential causes of the breakdown between the intended goals of the CBA and its results.

In assessing NBA franchise success, the incentive structure facing potential resources (players, coaches, management) should be examined. The different tax environment of NBA franchises is a potential variable which could disrupt league parity. It is argued in this paper that resources are influenced by the financial incentives created by varying state income tax rates applied to the differing NBA franchises based on location. The implications of these findings could have impacts on future CBA negotiations.

### Methodolgy

The study examines the potential for state tax income tax policy to influence NBA team success. The model employs data for eleven years (2000 through 2010) of previous NBA seasons. Also included are the rates (in percentage terms) for the individual states top marginal tax brackets for these eleven years.

The basketball data was assembled using information from a sports database website (6). The income tax bracket data was derived using information from the tax foundation website (10). For ease of computation and data gathering, only the top marginal tax bracket was used. As NBA salaries escalate, the importance of lower tax brackets becomes nominal.

The data from the Canadian-based team was removed. The examination is on the impact of income taxes on player decisions, which in the United States will be uniform at the federal level and vary only at the state level. Canadian players face differing income tax systems at both the federal and state/province level. Rather than trying to incorporate or properly account for these significant differences, the Canadian observations were removed.

A team’s success for a year is influenced by the players it has on the team from prior seasons. A proxy for the ability of players from prior seasons is created, which is the winning percentage for the team from prior years. Three years of winning percentages were lagged to account for anomalies in play in any one given year. While this proxy has shortcomings, it should provide a good baseline of team ability.

When a NBA team struggles to achieve success, the coaching position is often assessed. Coaching turnover in the NBA is prevalent and its impact on team performance must be considered. Teams will react differently to coaching change. Team ownership chooses a coach in the hopes that the new coach will develop player skills and enact schemes of play which will positively impact performance. For some teams, new coaching techniques might take some time to integrate into their play. For this reason, a lagged coaching change variable is created to account for this learning period.

A method for adding players is through the NBA draft. A variable is created to control for player acquisition through the player draft. A lagged variable is also created to account for maturation of these drafted players.

The use of financial incentives to pool resources in larger markets, has been somewhat muted by the CBA and the salary cap. However, larger metropolitan areas can provide amenities and lifestyle options not found in many smaller markets, which may still bias resources towards these markets. Additionally, salaries for coaches and management are not governed by the CBA and thus a larger market team could use financial resources to attract higher quality talent. To account for the potential residual bias in regard to market size, a control variable is created. The data incorporated is the 2000 Census Metropolitan Area found on the U.S. Census website (11).

NBA franchises attempt to achieve success by attracting the high-quality resources. These resources include players, both the addition and retention of high skilled free agents, coaches, and management personnel. While the significance of changes has been examined, particularly with regard to coaching and drafting of players, the issue of quality has not been addressed. The tax environment of each franchise may influence the potential of the team to attract the highest quality resources in order to achieve success. The tax environment of the team will bias the best resources (players, coaches, and management alike) towards certain franchises and away from others creating a performance bias. The decision process of these resources is contemplated the year prior to a given season. For this reason, the state income tax is lagged by a year.

The top marginal tax rate and metropolitan population for each team in 2010 is provided in Table 1. Tax information is time dependent and may vary in each year of the study. Also, in some instances teams switched host cities and states, such as the Sonics moving in 2008 from Seattle to Oklahoma. In these instances, not only would the tax information change, but so would the metropolitan population data. This type of movement increases data variation and helps to provide a more robust analysis. Descriptive statistics for all non-binary variables in the study are found in Table 2.

Using larger data sets can account for player injury. Player injury is frequent in the NBA and can have a substantial impact on team performance. By utilizing a large number of years, it can assume that player injury is random. Player injury is a risk every team takes when committing a large contract to a free agent. It is assumed that the risk of injury is normally distributed among the teams over a large sample.

The following equation is used to estimate the winning percentage of the team for the current season.

(Equation 1)

The dependent variable, WinPcti, t, represents the winning percentage of “i” team in the current “t” year. Yearly influences are captured through the use of a binary year variable Yeart, with the variable for 2005 dropped to prevent linear dependency. The regressor WinPcti,(t-1) is the winning percentage of the “i” team from one year prior. The variables WinPct(t-2) and WinPct(t-3), represent the winning percentage of the “i” team lagged two and three years respectively.

Coaching change is accommodated in the model through the Coachi,t variable. This is a binary variable and is positive if a new coach for the “i” team is in place at the start of current “t” year or if a coaching change is made during the year. To account for the potential of the learning period, this variable is further lagged one period and represented by the Coachi,(t-1) variable.

A NBA team can improve by changing its roster through the player draft.

The selection order of the NBA draft is the inverse of how the teams finished the season in terms of winning percentage. The draft is structured so that the worst teams, determined by winning percentage, have the best opportunity (in a lottery format) for high selections. In order to assess the influence of drafted players, a team is awarded points for the first pick in the first round of the NBA draft. Only the best pick was awarded points in the rare instance of a team having multiple first round picks. The first pick is awarded 30 points, scaled down one point for each pick down to the last pick of the first round which was awarded 1 point. The trading of draft picks is not considered as it is assumed the teams would require equal compensation for the traded draft pick.

The picking order of teams in the draft is scaled linearly. However, changes in player ability throughout the draft are likely non-linear. To account for the non-linear scaling of talent, draft points are squared to emphasis the ability of earlier picks to immediately influence team performance. The variable DraftSqri,t represents the value of the draft pick for team “i” going into the current “t” year. As these players mature and develop their skills, an additional lag variable DraftSqri,(t-1) is employed to capture these effects. The variable captures the lag effects for one period.

The variable MetroSizei represents the population of the metro or surrounding area to each NBA franchise. The variable is team dependent “i”, but is time invariant. The variable will detect larger market bias in the data.

Finally, the variable StateIncTaxi,(t-1) is the top marginal tax bracket for the state in which the “i” team competes lagged one period from the current “t” year. The variable will capture the effect of taxes on performance.

It is important to note that the dependent variable in “Equation 1” is integer-valued with a discrete distribution. To address this concern, it is possible to assume that the score differential Y is a manifestation of an underlying continuous variable Z. Where Y is determined by rounding Z to the nearest integer, and to assume Z follows the model (12):

(Equation 2)

Previous studies have indicated that for most purposes “Equation 1” provides an adequate approximation to the model determined by “Equation 2” (1). As a result, “Equation 1” can be estimated using ordinary least squares (OLS).


The estimation results are presented in Table 3. The binary year variables are all shown to be insignificant, thus discounting the influence of yearly variation.

The prior two years’ season performances are an accurate predictor of a team’s level of play in the current season. The positive and significant coefficients two years lagged winning percentage implies commonality in team play over multiple seasons. The result also implies that it is difficult to altering a team success and may require several years of rebuilding a losing franchise. The third year being significant and negative suggests the cyclical nature of team success in a league governed by a salary cap restrictions and draft ordering process focused on parity.

The coaching variable is highly significant and negative. Rather than guiding a team towards success, a change in coaching personnel is associated with a negative response in team performance. There also does not appear to a learning curve with respect coaching change, as the lagged coaching variable is insignificant. Not only does the team suffer negatively in the short term from coaching change, the team does not improve in the longer term even after allowing time for the team to absorb the new coach’s playing philosophy.

The draft variables are shown to be insignificant. At least in the short term, drafted players do not have an impact on team performance in terms of winning percentage. The time required to develop these players may exceed the two years accounted for in this model. While accepting the potential for non-linear skill distribution of drafted players marginally increased the viability of the draft variable, it never appeared statistically significance.

Market size is shown not to bias team success. NBA franchises in larger markets are shown to be unable to significantly leverage their market size into acquiring superior skilled resources (players, coaches, and management) as reflected by team success.

Finally, of particular note is the significant and negative relationship between team success and state income tax policy. Teams which play in states with higher top marginal tax rates have less success and a lower winning percentage. The prolonged disparity in winning percentage is argued as an inherent bias of better resources avoiding teams in locations of high taxes. Teams in high tax states could have a more difficult time obtaining comparable talent compared to NBA franchises in low tax states.

### Conclusions

The study examined the potential incentive that state income taxes have on the ability of NBA teams to lure top talent and gain a competitive advantage. The results provide several insights which can be incorporated in the operation of the league and the collective bargaining agreements (CBA).

The results indicate commonality in team success over multiple periods. If a team wishes to alter its winning percentage, the data suggests that one season is insufficient to achieve this goal. Progress is only witnesses as a gradual process over several seasons.

The results also indicate that the window of opportunity for an established team having success is approximately two years before parity efforts begin to take affect and the team’s winning percentage begins to revert to the norm. Team management must understand that the opportunities for a successful team are fleeting and urgency is required for decisions during this period to maximize winning potential.

Once a decision is made to reconstitute a team, it is difficult to accomplish this task quickly. Fans are inherently impatient, which often manifests itself in team management making hasty decisions with regard to coaching. Coaching change is shown to have a negative impact on team performance. The data suggests that rebuilding progress can only be witnessed gradually.

The impact of the NBA draft is shown to have a negligible immediate impact term team performance in the short term. The benefits of the draft do not materialize in the model, even when considering the potential of a non-linear distribution of skill level in the draft. Also of negligible importance on team success is market size. The argument that larger markets can attract superior players due to lifestyle benefits and superior coaches/management through financial considerations is unsubstantiated by the data.

Finally, it is determined that a state’s top marginal tax bracket in which a particular team plays has a negative influence on the team’s success. The data suggests that NBA teams in states with high income taxes are negatively biased when attempting to lure superior talent in terms of player ability, coaching talent or management skill. The state tax influence on team success is indirect, suggesting that subsequent research can be done to detect the direct method of transmission of this influence through players, coaches, management, or some combination. Further research can also be conducted to determine if other professional sports exhibit a similar negative relationship between state tax policy and team success.

### Application In Sports

The Collective Bargaining Agreement (CBA) was recently renegotiated in the NBA. If owners and players in professional sports are interested in promoting league parity, thus ensuring an equal chance of team success and fan excitement, perhaps they should consider a scaled salary cap to benefit teams in high-taxed markets. A tax adjustment index could be applied to the salary cap thus ensuring equal opportunity to acquire equal resources and minimizing the negative bias.

### Tables

#### Table 1
State Income Tax Rate (Highest Marginal Bracket)

Team State Top Marginal Tax Bracket Market Size (2000 Census)
Metropolitan Areas (in millions)
Blazers OR 11.00% 2.265223
Clippers CA 10.55% 16.373645
Kings CA 10.55% 1.796857
Lakers CA 10.55% 16.373645
Warriors CA 10.55% 7.039362
Knicks NY 8.97% 21.199865
Nets NJ 8.97% 21.199865
Wizards Washington, DC 8.50% 7.608070
Wolves MN 7.85% 2.968806
Bobcats NC 7.75% 1.499293
Bucks WI 7.75% 1.689572
Cavs OH 5.9325% 2.945831
Grizzlies TN 6.00% 1.135614
Hawks GA 6.00% 4.112198
NO-Hornets LA 6.00% 1.337726
Sonics OK 5.50% 1.083346
Celtics MA 5.30% 5.819100
Jazz UT 5.00% 1.333914
Nuggets CO 4.63% 2.581506
Suns AZ 4.54% 3.251876
Pistons MI 4.35% 5.456428
Pacers IN 3.40% 1.607486
76ers PA 3.07% 6.188463
Bulls IL 3.00% 9.157540
Heat FL 0.00% 3.876380
Magic FL 0.00% 1.644561
Mavs TX 0.00% 5.221801
Rockets TX 0.00% 4.669571
Spurs TX 0.00% 1.592383

Tax data from [Tax Foundation Website](http://www.taxfoundation.org)

Population data from [U.S. Census](http://www.factfinder.census.gov)

#### Table 2
Descriptive Statistics

Variable Observations Mean Standard Deviation Min Max
Winning Pct 312 0.5030 0.1503 0.15 0.82
Tax Rate 312 0.0539 0.0342 0.00 0.11
Draft Position 312 13.3494 10.2441 0.00 30.00
Metro Size (in millions) 312 5.7900 5.7315 1.08 21.20

#### Table 3
Basketball Team Winning Percentage Estimation

Variable Coefficient Standard Error
Variable Coefficient Standard Error
Constant 0.2464
2001 -0.0175 0.0310
2002 -0.0162 0.0309
2003 -0.0290 0.0309
2004 -0.0050 0.0310
2006 -0.0105 0.0303
2007 -0.0379 0.0306
2008 -0.0279 0.0308
2009 -0.0094 0.0304
2010 -0.0195 0.0300
Win Pct Lagged 1 Year (WinPct(t-1)) 0.5656 0.0942***
Win Pct Lagged 2 Year (WinPct(t-2)) 0.1586 0.0963*
Win Pct Lagged 3 Year (WinPct(t-3)) -0.1148 0.0587**
Coach (Coachi,t) -0.0808 0.0155***
Coach Lagged 1 Year (Coachi,(t-1)) -0.0066 0.0160
Draft Squared (DraftSqri,t) 0.00005 0.00004
Draft Squared Lagged 1 Year (DraftSqri,(t-1)) 0.00006 0.00004
Metro Size (MetroSizei) -0.0011 0.0012
State Income Tax Lagged 1 Year (StateIncTaxi,(t-1)) -0.4167 0.2167**
Observation 281
R-squared 0.4612
F(18,262), Prob>F 12.46 0.0000***

* Significant at the 10% level
** Significant at the 5% level
*** Significant at the 1% level

### References

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4. Kendall, T.D. (October, 2003). Spillovers, Complementarities, and Sorting in Labor Markets with an Application to Professional Sports. Southern Economic Journal. 70 (2), 389-402.
5. NBA data website: www.insidehoops.com.
6. NBA data website: www.basketballreference.com.
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8. Scully, Gerald W. (March, 2004). Player Salary Share and the Distribution of Player Earnings. Managerial and Decision Economics. 25 (2), Sports Economics, 77-86.
9. Szymanski, S. and Kesenne, S. (March, 2004). Competitive Balance and Gate Revenue Sharing in Team Sports. The Journal of Industrial Economics. 52 (1), 165-177.
10. Marginal Tax Data: www.taxfoundation.org.
11. United States Census Data: <http://www.factfinder.census.gov>.
12. Zimmer, Timothy and Kuethe, Todd. (2008). Major Conference Bias and the NCAA Men’s Basketball Tournament. Economics Bulletin. 12 (17), 1-6.
13. Zodrow, G., and Mieszkowski, P. (1986). Pigou, tiebout, property taxation, and the underprovision of local public goods. Journal of Urban Economics. 19, 356-370.

### Corresponding Author

Timothy E. Zimmer, Ph.D.
6718 W. Stonegate Dr.
Zionsville, IN 46077

### Author Bio

Tim Zimmer is an adjunct professor of economics at Butler University.

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