View Full Version : The affects of a Soft cap/LT an interesting article atleast to me

07-27-2011, 03:19 PM
So I am not going to post the entire article as it is too long to do so but I highlighted some interesting points made. I realize some are the main points made by posters here already but I thought the statistical analysis was pretty good although I can be easily fooled.

The NBA soft cap and luxury tax (http://thurj.org/social-science/2011/04/2304/)
How it increases talent disparity

John Gobok Ď12
Harvard University, Department of Economics

This paper evaluates the impact of the National Basketball Association (NBA)ís soft salary cap and luxury tax system. First, analysis of standard deviation of team winning percentages from 1976 to 2010 shows that league parity worsened in general, but imposition of the cap in 1984 temporarily improved parity. Second, a regression of a teamís winning percentage on payroll deviation from the league median, while controlling for tax regime and team-fixed effects, shows that a positive relationship between a teamís payroll and performance exists. Third, there is a positive, significant relationship between a large-market teamís performance and the presence of the luxury tax. After the imposition of the tax, it is observed that the talent disparity between the middle- and large-market teams has increased. This counterproductive effect of the tax is explained by the discontinuity of the cost function at the tax threshold, effectively levying a higher implicit marginal tax on middle-market teams. By studying the mechanism of the Earned Income Tax Credit, the NBA can adopt a phase-out system for income subsidies, and incorporate the MLBís gradation of tax rates into its own system.

Relationship between winning percentage and payroll

This paper assumes that paying higher leads to better teams. This assumption is tested in this regression of winning percentage, win, on payDev, defined as the ratio between a teamís payroll and the median payroll of the league in that particular year. The data used is from 1986 to 2010, excluding 1987 and 1989 due to insufficient information. The dummies regime, taxMid, and taxBig are added to the regression to see the impact of the presence of the luxury tax on win, and the interaction variables are there to measure the taxís impact on middle- and big-market teams (assuming market size is proportional to their payrolls). Team-fixed effects are also added to control for team-specific characteristics. Relevant results are displayed in Table 1.

From Table 1, the coefficient of payDev is 0.174, which is significant at the 5% level. Assuming all else constant (including controlling for the regime and the team), a unit increase in payDev (increase in a teamís payroll equivalent to the league median) increases that teamís winning percentage by 0.174 or adds about an extra 14 wins. In a league where a win of 0.50 can almost certainly guarantee a playoff spot, this is significant. Hence, these regression results support the assertion that there is a positive correlation between a teamís payroll and talent.

From Table 2, it can be deduced that most of the teams that are negatively affected by the team-specific characteristics are usually small-market teams. The Phoenix Suns, 15<SUP>th</SUP> out of 30 in terms of market size, is dropped in the regression and used as the point of reference for the coefficients. The negative coefficients are interpreted as the drop in a teamís winning percentage solely due to the teamís inherent characteristics.

For example, Indiana has a coefficient of -0.130, which means that its winning percentage, keeping all other things constant, decreases by 0.130 simply because it is the Indiana Pacers. Out of the eight teams with significant negative team coefficients, six of them belong to the bottom half of the league in terms of market size. This is intuitive since smaller market teams like Indiana, Charlotte and Utah earn less local revenue which could be used to hire better coaching staff, secure state-of-the-art facilities, and fund expert scouts. Furthermore, bigger markets can be a draw to superstar players; this was the main reason why Lebron James entertained leaving Cleveland for cellar-dwellers New York, New Jersey and Chicago during the summer of 2010 (OíConnor 2010). Hence, these intuitions and the regression results support the notion that smaller market teams are inherently disadvantaged in terms of competing in the league.

Counter-productive Luxury Tax Model

For the purpose of analyzing the taxís effects on different types of teams, teams are classified under three categories A, B, and C. Group A comprises teams that are already over the tax threshold (between 1986-2000 when the tax did not exist, tax threshold is assumed to be 61% of BRI). Group B comprises teams under the tax threshold but over the soft cap (teams with payrolls between 57-61% of BRI). Group C comprises teams under the cap.
To see the initial impact of the tax on team payroll, a model of predicted team payroll is constructed for the period before the tax implementation. In this regression model, current team payDev is regressed on the previous yearís payDev and win, while also including a teamís group classification from the previous year assuming that market size is positively correlated with payroll (llow, lmiddle, lhigh). This model used data from 1996 to 2000, a period when the league size and composition remained. After obtaining the model, 2001 team payDev are predicted and compared to the teamsí actual 2001 payDev. Figure 2 plots this difference between the predicted and actual pay deviations against the teamís 2000 payDev, which is assumed to be indicative of market size. The graph shows how the tax affected the payroll decisions of teams of different market sizes.
From the Figure 2 plot, the difference for teams with 2000 payDev greater than one is mostly positive, indicating that the predicted payDev was higher than the actual payDev; hence, the tax moved the large-market teamsí payrolls closer to the league median. For teams with 2000 payDev less than one, the difference is mostly negative, indicating that the tax increased their payDev and moved it closer to the league median. As a result, the spread between the payrolls of the highest- and lowest-paying teams has narrowed with the tax. Such a movement towards the median for both extreme groups shows how the tax decreased the league payroll deviations, which was the original intention of the tax.
http://thurj.org/wp-content/uploads/2011/04/THURJ4-1-Gobok-f2-300x166.png (http://thurj.org/wp-content/uploads/2011/04/THURJ4-1-Gobok-f2.png) Figure 2. Impact of tax on teams with different previous year payroll

However, from the graph of ratio of actual and ideal standard deviations (Figure 1), league competitive imbalance seemed to increase a few years after the tax implementation. As such, evaluating the impact of the tax warrants examining its long-term impact on the teams. Critiquing the first system of the NBA Luxury Tax, Kaplan (2004) asserted how the system was misguided as it worked against its stated goals of promoting competitiveness. In a sample case that outlined implicit marginal tax rates for teams in the respective groups A, B, C, he showed how Group B teams are implicitly taxed the highest, which puts them at a disadvantage against Group A teams. This paper utilizes the same approach of analyzing the impact on the three groups under the new system, and also adds empirical analysis of the teamsí winning percentages to support the claim that Group B teams are indeed disadvantaged even with the modified version of the tax regime under the 2005 CBA.
To investigate the long-term impact of the tax on Groups A, B, and C, the median winning percentage is calculated for each group from 1986 to 2010. Due to the small population size of teams under Group C, analysis is focused on the difference between the medians of Groups A and B for each year. This difference in medians is assumed to reflect the talent gap between Groups A and B. Figure 3 illustrates the median winning percentages for each group as well as the difference between median values of Groups A and B between 1986-2010.
In Figure 3, the spread between median team winning percentages of Groups A and B decreased right after the imposition of the luxury tax in 2001, with the difference drastically dropping to about 0.1 from 0.55. This resonates with the finding in Figure 2, where the team salaries moved closer to the league median immediately after tax imposition. As such, the introduction of the tax decreased both payroll deviations and talent disparity in the league. The regime change could have compelled the teams to rethink their payroll decisions, making high-spending teams averse to spending more.

However, this initial effect is short-lived, as indicated by the post-2001 upward trending line of the difference between medians in Figure 3. People tend to overreact to regime changes, and after a few years the highest spending teams could have reverted to their old ways since marginal benefit of spending more (more wins and advertisements) is higher than the marginal cost (even after incorporating tax).

The increasing talent disparity between Groups A and B can be attributed to how the current luxury tax system causes teams that cross the threshold to fall off a ďcliff.Ē On one hand, crossing the tax threshold forces them to pay a dollar-for-dollar tax for any amount in excess. Furthermore, it also disqualifies them from receiving tax payouts, which can be substantial for a small- and middle-market team. In this context, implicit marginal tax rate is defined as the combination of the luxury tax payments and the effective loss of tax payout eligibility. Table 3 lists the total tax revenues and the payouts to each non tax-paying team during the latest CBA.

http://thurj.org/wp-content/uploads/2011/04/THURJ4-1-Gobok-t3-300x113.png (http://thurj.org/wp-content/uploads/2011/04/THURJ4-1-Gobok-t3.png) Table 3. Yearly luxury tax revenues and payouts (2006-2010)

When determining the optimal payroll amount, teams face a similar problem to what workers face with the presence of welfare benefits and a progressive tax regime. In the real world case for workers, the middle-income earners face a higher implicit marginal tax rate than the highest income earners due to the middle incomersí loss of eligibility to social insurance programs. This is analogous to the NBA luxury tax model, where teams just at the threshold face a considerably higher implicit marginal tax compared to teams already above the threshold since crossing the threshold implicitly taxes them extra by making them ineligible for tax payouts. Figure 4 illustrates the discontinuity in the cost function that a team in Group B faces.

http://thurj.org/wp-content/uploads/2011/04/THURJ4-1-Gobok-f4-300x166.png (http://thurj.org/wp-content/uploads/2011/04/THURJ4-1-Gobok-f4.png) Figure 4. Graph of team cost function vs. talent (under current tax regime)


The challenge of creating a more competitively balanced league has always been a perennial one facing market designers. The NBA initially adopted a soft salary cap, which only aided the building of dynasties in the 1990s. It then introduced a taxation and redistribution mechanism in the form of a luxury tax in the hope of reigning in the spending of the large-market teams and subsidizing the small-market teams. However, empirical results have shown that the tax has positively impacted the winning percentages of the highest spending teams, suggesting a widening of talent disparity between the high and middle spenders. This counterproductive effect of the tax is explained by the discontinuity of the cost function at the tax threshold, effectively levying a higher implicit marginal tax on middle-market teams.


07-27-2011, 04:39 PM
This is only related because it's about the lockout, but felt like it'd be a decent fit here since I can't seem to find a sort of catch-all lockout thread.

Larry Coon just did a long and VERY informative chat over at Hoopsworld (http://www.hoopsworld.com/Chat.asp?CHAT_TOPICS_ID=1766).