Competitive balance measures in us professional sport: an empirical comparison
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- Dependent Explanatory Coefficient t-Statistic
- Sport Measure Significant Variables
- 5 Conclusions
- Measure Model
- 6 References
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Table 19 – Dependent Variables used in Ice Hockey Models
Table 20 – Explanatory Variables used in Ice Hockey Models
Table 21 – Statistical Analysis of Ice Hockey Models In all five models the coefficients for Expansion Team and Salary Cap are negative suggesting that they improve CB while the coefficient for Young Team is positive suggesting that it has an adverse effect on CB. For the SD, NSD and GC models the Young Team variable is statistically significant. For HHI and FCCR it is not but the Salary Cap is.
Table 22 – Statistically Significant variables for each Sport Table 22 shows a summary of the variables that were found to be statistically significant in the regression models. It appears that a league expansion or the presence of a young team reduces CB for Baseball while revenue sharing improves CB. Basketball is reviewed in more detail below as there appears to be a contradiction as to the impact of salary caps. There are no variables that are significant for American Football. For Ice Hockey the presence of a young team reduces CB while the presence of a salary cap improves it. 
Diagram 6 – Values of the measures for Basketball Diagram 6 shows the calculated values for each of the five measures used for CB and plots against the season. The NSD measure is shown on the secondary axis. This clearly highlights that we have two types of measure. The first type are SD, NSD and GC. They all behave similarly across time. The HHI and FCCR measures behave completely differently but follow similar patterns to each other. 
Diagram 7 – Relationship between HHI and Number of teams in the NBA Diagram 7 shows the relationship between the number of clubs in the league and the HHI measure. Clearly there is a strong inverse correlation suggesting that the number of clubs in the league is far more important to this measure (and also the FCCR because they behave the same way) than to the other measures of CB. It is this that explains the strange results seen for Basketball where the analysis suggests that the Salary Caps have a positive effect on CB if looking at HHI and FCCR but a negative effect if looking at the other measures. The salary caps have only been present since 1984 since when the number of teams has remained fairly constant and high. The inverse correlation between teams and the HHI means that the HHI measure is much lower during this period of time and therefore when modelled the salary cap variables appear to have a positive effect on CB. 4.6 Limitations The Basketball example clearly shows that comparisons of CB measures are difficult. The number of teams in the league causes problems, particularly if this changes significantly over a period of time. Any future research that wishes to look at more than one CB measure should understand this effect very clearly and if possible, remove it. This example also shows how difficult it is to assess whether initiatives taken by the leagues have been successful or not. If a data period is used where the number of teams changes significantly the HHI and FCCR give completely different results to the other measures, particularly when the initiatives taken by the leagues happen at one end of the data sample. To understand whether an initiative has been successful requires a lot of further careful work. One option is to limit the sample data period to a period where there has been a constant number of teams in the league. However, the nature of the leagues has been to expand so this would result in a very short sample period and would compromise the statistical significance of the method. Section 4.7 will tackle this briefly and offer another idea about how to proceed. This idea will need considerable development but could form the basis of future research. The analysis could be repeated for other sports leagues should authors wish although there are few where the league has actively tried to improve CB. Additional and more complex variables that could potentially affect CB could be modelled. Given the findings relating to the number of teams in the league this should certainly be one that is modelled unless the approach suggested in section 4.7 is used.
Since league expansion has been shown to reduce CB for MLB and NBA but not for NFL and NHL a future piece of research worth undertaking would be to determine why. Comparisons between expansion drafts and other mechanics could be made and detailed analysis of the performance of the expansion teams could be undertaken. The objective would be to make recommendations for changes to the process used by the MLB and NBA to allow the expansion teams to be competitive from their first seasons. As discussed in section 4.6 this section will also examine a potential method for future research that will allow comparisons between measures of CB. This method will also allow the effects of league initiatives to be assessed with improved reliability. The proposed method is based on calculating the maximum and minimum possible values for the current measures on a season by season basis, the actual measure, and then creating a percentage measure that shows how far between the theoretical minima and maxima the measure is. 4.7.1 Theoretical Maxima and Minima The theoretical minimum for a measure for a given season is determined by the situation where the league is completely balanced. There are two possibilities for this. The first is to consider that each team wins exactly 50% of its games and therefore all teams finish with the same win percentage. The second is to assume that each individual game is decided by a random coin toss and then to calculate the expected end of season win percentages based on a large number of simulated seasons. Both accurately describe a league in perfect CB. Further study may undertake both options and report on which appears favourable. In the worked example in section 4.7.2 the first option is used. The minimum values are calculated from all teams finishing the season with exactly the same win percentage (50%). The theoretical maximum for a given measure is determined where the league completely unbalanced. There are again two possibilities but here one is impossible to achieve. The first is where half the teams win all their games and half of the teams lose all their games. This is impossible to achieve given league structures and schedules and should be disregarded. The second option is to create a ranking of teams and then to simulate all games subject to that ranking such that a team higher in the ranking automatically beats a team lower in the ranking. This gives a distribution for win percentages that is possible and matches the definition of the league being unbalanced. Denote the maximum and minimum values as: Measuremax and Measuremin The measure is then calculated as normal but the percentage measure is calculated as follows: Percentage Measure = This will remove bias created by influences such as the number of teams in the league and will create measures that are easy to understand. The league will be described as being x% unbalanced according to the given measure. These measures can then be used to assess the impact of league interventions as outside influences have been removed.
The full analysis including re-running the statistical models to assess the impact of the league initiatives is outside the scope of this study. However, the five measures were recalculated as described above for NBA data. Diagram 8 shows these over the full data period used in this study. It clearly shows that all five now have very similar patterns and therefore behave in the same way. Comparison with diagram 6 would suggest that SD, NSD and GC have remained with similar patterns whereas the HHI and FCCR have changed suggesting they were the ones that were not robust. 
Diagram 8 – Measures for Basketball after adjustment Diagram 8 suggests that the high salary cap has probably improved CB. It also seems that the peaks tend to coincide with the presence of a young team in the league. Formal analysis through regression modelling would prove or disprove these observations.
Table 22 in section 4.5 summarises the findings of the analysis. This analysis has concluded that:
These conclusions are subject to the conditions that have been explored in section 4.6 and should be treated very cautiously. It would be better to repeat the analysis using the method outlined in section 4.7 before drawing conclusions about the league interventions and their effectiveness. However, section 4.7 has suggested that the SD, NSD and GC measures are robust and therefore the results obtained from those models may be more reliable. 4.8.2 Comparison of Measures Through the analysis we have seen that the measures behave differently, even on the same data. There are two types of measure. The first looks at the distribution of the win percentages. These are the SD, NSD and the GC. They are more robust to the influence of the number of teams in the league than the other measures, HHI and FCCR. The HHI and FCCR are heavily correlated with the number of variables in the league by their definitions and give significantly different results. This has been most clearly revealed by the analysis of the Basketball data shown in detail in section 4.6. 5 Conclusions 5.1 Introduction This chapter will conclude the study and will draw together the conclusions from each of the previous chapters. Section 5.2 will present a brief summary of the analysis performed in chapter 4 and section 5.3 will then present the main conclusions drawn from the analysis, relating them back to the original research questions. 5.2 Summary of Analysis The analysis chapter began by looking at the basic data for each sport. Diagrams 2-5 displayed the values of each measure of CB over the data period chosen and also when each of the dummy variables took a value of “1” and therefore when the explanatory variables such as league initiatives or expansions took place. Section 4.4 then presented the regression analysis for each sport. This included the full models for Baseball as shown in Table 12 – reprinted below.
Table 12 – Baseball Models Key:
ET – Expansion Team YT – Young Team LT – Luxury Tax RS – Revenue Sharing The * denotes statistically significant at the 5% level It showed that for three of the measures of CB the Expansion and Young variables are statistically significant and show that they reduce CB. It also showed that for the other two measures of CB, namely the HHI and FCCB the Expansion and Young variables are not statistically significant. Instead the Revenue Sharing variable is statistically significant and increases CB. This analysis was repeated for the other sports and Table 22, reprinted below, summarised the significant variables.
Table 22 – Statistically Significant variables for each Sport The Basketball results in particular highlighted the issue that the Explanatory variables relating to salary caps appeared to behave differently depending on which measure of CB was being used. Further analysis of these results for Basketball revealed that the measures HHI and FCCR are heavily correlated with a variable not being used in the models, namely the number of teams in the league. Diagram 7 showed this clearly for the HHI measure. Having identified an anomaly and explained it through further analysis chapter 4 concluded by offering a solution. It developed refined measures that would remove the issue of number of teams and demonstrated that this method resulted in all measures of CB behaving in a similar way.
The two research questions were:
The analysis performed by this study suggests that very few initiatives used by North American sports leagues actually increase CB. Only the revenue sharing for Baseball and the salary caps for Basketball and Ice Hockey are shown statistically to increase CB. No initiatives used by the NFL were shown to increase CB for American Football. This study also concludes that expansion of the MLB and NHL has the effect of decreasing CB and does so for at least three seasons. This was not seen for the NFL or the NBA. The most important conclusion of this study is that different measures of CB show different results even when calculated on the same data. This brings into question the conclusions drawn about whether the league initiatives have worked or not and states that it is imperative that any analyst wishing to examine CB needs to understand fully which measure they are using and its characteristics and limitations, particularly with regard to the changes in the number of teams in the league over their sample time period. It is also essential that the analyst examines all other variables that could affect CB or the measures. Removing influences such as the number of teams in the league should be a precursor to performing any analysis relating to CB in sports. 6 References Ajilore, O. and Hendrickson, J. (2005) The Impact of the Luxury Tax on Competitive Balance in Major League Baseball. International Association of Sports Economists & North American Association of Sports Economists, Working Paper 0727 Byrne, K.J. (2009) Six Signs Parity is Dead in NFL. Sports illustrated, Posted online October 29th 2009 Downward, P. and Dawson, A. (2000) The Economics of Professional Team Sports, Routledge, London, Ch. 5 p75-85 Hair Jr, J.F., Anderson, R.E., Tatham, R.L. and Black, W.C. (1995) Multivariate Data Analysis fourth edition, Prentice Hall, New Jersey, Ch. 3 p78-165 Humphreys, B. R (2002) Alterative Measures of Competitive Balance in Sports Leagues. Journal of Sports Economics, 3, 133-148
Maxcy, J. and Mondello, M. (2006) The Impact of Free Agency on Competitive Balance in North American Professional Team Sports Leagues, Journal of Sport Management 2006,20, 345-365 Michie, J. and Oughton, C. (2004) Competitive Balance in Football: Trends and Effects, Football Governance Research Centre, Research Paper 2004 No. 2
Schmidt, M.B (2001) Competition in Major League Baseball: The Impact of Expansion. Applied Economics Letters,8, 21–26 Scully, G. W (1989) The business of Major League Baseball. Chicago: University of Chicago Press Zimbalist, A.S. (2002) Competitive Balance in Sports Leagues: An Introduction. Journal of Sports Economics, 3(2), 111-121 Directory: 2013 2013 -> Annual InStructional unit plan 2013 -> The Ministry of Education and Science of Ukraine 2013 -> #1 a lifesafer of virginia inc 2013 -> Name(s): your name here team or Group #(if applicable): Professor’s name 2013 -> Alcott Local School Council (lcs) Meeting Minutes 2013 -> Table Of Contents introduction 2 2013 -> Supplemental demographic information 2013 -> 【Education&Working Experience】 Download 362.34 Kb. Share with your friends:
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