Question 2

Outline two measures that can be used to estimate competitive balance within professional team sports.

Apply one of these measures to a professional team sport of your choice (in a country of your choice). Collect data (i.e. team performance information) for your chosen sport, for approximately the last 50 years.

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Examine and assess how competitiveness has varied over time and establish the extent (if any) to which this can be related to structural changes to the sport (such as league format changes, intervention policies etc).

Question 2

(i) Competitive Balance measure 1: Ratio of Standard Deviations (RSD)

where and

G = no of games played, N = number of teams in the league, wp = win percentage, wpikt is the win percentage of team i, in league k, for season t.

is the mean win percent and is a positive constant. For a sport such as basketball, where a team can only win or lose games, this will equal 0.5.

is the standard deviation of wins in a perfectly balanced league i.e. each team is of equal strength and has an equal probability of winning. This number declines as the number of games (G) played in the league increases.

is the standard deviation of wins in the actual league

represents the ratio of standard deviations. This compares the performance of an actual league when compared to that of the ideal league. A perfectly balanced league would correspond to RSD = 1 where . Competitive balance worsens when RSD increases, as the dispersion of winning percentage of the actual league grows relative to that of the ideal league.

RSD has been used extensively throughout the literature, first developed by Noll (1988) and Scully (1989) it has been employed by Quirk and Fort (1997), Berri et al. (2005), Fort and Lee (2007) amongst others.

The major shortcoming of the metric as detailed by Humphreys (2002) is that it does not capture relative standings of teams within a division. Thus, there might be two leagues with identical RSDs, but with one league where one team exhibits long run domination by consistently winning the league and one where this does not occur.

To complement this measure, a dynamic season to season measure such as that developed by Buzzacchi et al. (2003), would better be able to assess long run domination over time.

Competitive Balance measure 2: Dynamic measure developed by Buzzacchi et al. (2003). The model for a closed league (no promotion/relegation) is derived as follows.

In a perfectly competitive league, the probability a team will finish in any position of a league for one season is, where n is the number of teams.

Therefore the probability a team will place in the top k places of the league is

The probability a team will have placed at least once in the top k positions after T seasons is given by

Thus the expected number of teams who will have placed at least once in the top k positions after T seasons is

Similarly, the expected number of teams who have won the title (come 1st) at least once after T Seasons is

This increases at a decreasing rate over time. From 1 when T = 1, to n when T tends to infinity. Intuitively, we would expect a greater number of teams to have finished top at least once to increase as the number of seasons contested increases.

To compare the relative competitiveness of leagues, a Gini-style index is constructed as follows


– number of seasons considered

and are respectively the number of teams placing in the top k positions in a perfectly balanced league and an actual league over a period of T seasons.

The higher the value of G, the less competitive a league becomes. for a perfectly competitive league, where and for a perfectly unbalanced league where .

(ii) Examine and assess how competitiveness has varied over time and establish the extent to which this is due to structural changes, such as league format changes etc.


The National Basketball Association (NBA) is the professional basketball league of North America, and currently comprises 30 teams, of which 29 are in America and 1 is in Canada. The season prior to the playoffs comprises 82 games. The league has been in operation since 1946.

Basketball has historically been the least competitive of all major sports, when compared using the RSD metric, with a standard deviation of winning percentage on average more than twice the idealised level. (Berri et al., 2005). To combat this, two major intervention policies have been imposed in the NBA to improve competitive balance and also to limit team expenditure on player salary: a salary cap in the 1984/85 season and luxury tax in the 2001/02 season. The NBA were able to enact these policies without fear of loss of talent, due to the NBA enjoying monopoly power on the employment of basketball labour, following its merger with the American Basketball Association (ABA) in 1976.


The data used are season data from the 1967/68 season to the 2008/09 season, which gives 42 observations, courtesy of Rodney Fort’s website. I chose 1967/68 as the breakpoint for my dataset as this is the first 82 game season, thus holding the variable G constant in the RSD calculations. The number of teams do increase substantially however, from 12 in 1967/68 to the current level of 30.

Competitive Balance Measures

By the 1983 Collective Bargaining Agreement, player salaries had reached 75% of league revenue (Vrooman, 2009), to combat this, the Salary Cap was first introduced into the 1984/85 season following negotiations between the NBA and the National Basketball Players Association (NBPA). This set a cap that total player salaries could be no more than 53% of league revenues. This translated into a cap of $3.6m per team.

The salary cap in its current form is very much a soft cap. There are many exceptions that allow a team to exceed its salary cap for the year, most notable of which is the “Larry Bird Exception”. This allows teams to re-sign their own free agents after 3 years experience at the club upto the player’s maximum salary. Teams exceeding the luxury tax threshold (61% of basketball related income) however, are forced to pay a 100% tax on every dollar they exceed this amount. This amount is then distributed equally to all the non tax paying teams. This threshold is seen to be emerging as a de facto hard salary cap making the soft salary cap an irrelevance (Vrooman, 2009).

Fort and Quirk (1995) predicted that under a two club model, the competitive balance of the NBA should have improved following the imposition of the salary cap as outlined in the 1983 Collective Bargaining Agreement. However they noted the problem of enforcement that a salary cap brings, as the equilibrium position becomes Pareto sub-optimal, and strong-drawing teams have an incentive to break the cap, and hire more talent. This could well account for the large number of exceptions allowed under the current salary cap framework.

Looking at Figure 1, which maps RSD over time it is clear that following the imposition of the two intervention policies, there was no clear shift towards competitiveness, if anything following the Salary Cap, competitive balance got worse. Table 2 clearly shows the two worst 5 year periods for competitiveness immediately followed the Salary Cap being enacted (1987/88 – 1991/92 and 1992/93 – 1996/97). The season with the most competitiveness was the 1976/77 season, following the ABA merger, but prior to any intervention policies being enacted.

The enacting of true free agency in 1988 also has no discernable impact on competitive balance, as predicted by theory (Fort and Lee, 2007). Similarly, the many league expansions that have occurred in the NBA’s history have not made a sustained impact towards greater competitive balance. This could be explained by the new teams joining the league being of weaker standard, to those of existing teams.

Most striking of all I feel, is that the RSD for the start point of the data series (1967/68 season, 2.9485), is almost identical to that for the end point (2008/09 season, 3.065), suggesting that 42 years later, competitive balance has not improved whatsoever.

Policy Implications

Using regression analysis of the RSD metric and break-point detection techniques, Fort and Lee (2007) identified two breakpoints, 1972 and 1997, where competitive balance had increased, but neither of these corresponded to a significant rule change within the NBA. Fort and Lee also identified an underlying positive time trend for RSD suggesting that there is in fact a trend of worsening competitive balance, a finding confirmed by my more rudimentary trend line analysis.

Berri et al (2005) suggest that the underlying cause for the persistence of competitive imbalance in the NBA is the “short supply of tall people”. This is built on the theory there exists a “biomechanical limit” of athletic talent and as the population of talent for a sport expands, more players of the sport will be closer to this limit, and competitive balance will increase.

However being tall is a significant asset in the NBA, due to the nature of the contest, and one “cannot teach height”. In the 2003/04 season nearly 30 per cent of the league participants were six feet ten or taller, this compared to an average male height of between five feet nine and five feet ten in the United States. This minimum height requirement significantly reduces the pool of available individuals who would be competitive in the NBA. This large dispersion of talent between players likely accounts for the continued wide dispersion of win percentages.

This analysis suggests therefore that any league intervention policies in the NBA are doomed to fail, unless they involve widening the participating rate of basketball globally amongst those tall enough to be competitive. There is some evidence of this occurring, most notably Yao Ming, a seven foot six NBA player from China.


Berri, D. et al (2005). “The Short Supply of Tall People: Competitive Imbalance and the National Basketball Association.” Journal of Economic Issues, 39, 1029-41

Buzzachi et al. (2003). “Equality of Opportunity and Equality of Outcome: Open Leagues, Closed Leagues and Competitive Balance.” Journal of Industry, Competition and Trade, 3 (3), 167-186

Fort, R. and Lee, Y.H. (2007) “Structural Change, Competitive Balance and the Rest of the Major Leagues.” Economic Enquiry, 45 (3), 519-532

Fort, R. and Quirk, J, (1995). “Cross-subsidization, Incentives, and Outcomes in Professional Team Sports Leagues.” Journal of Economic Literature, 33, 1265-99

Humphreys, B.R. (2002). “Alternative Measures of Competitive Balance in Sports Leagues.” Journal of Sports Economics, 3, 133-48

Noll, R. G. (1988). “Professional Basketball.” Stanford University Studies in Industrial Economics Paper No. 144

Quirk, J and Fort, R. (1997). Pay dirt: The business of professional team sports. Princetone, NJ: Princeton University Press

Scully, G. W. (1989). The Business of Major League Baseball. Chicago, IL: University of Chicago Press

Vrooman, J. (2009). “Theory of the Perfect Game: Competitive balance in Monopoly Sports Leagues.” Review of Industrial Organisation, 34 (1), 5-44 – [Data Accessed on 17/03/2010]


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