Competitive balance measures in us professional sport: an empirical comparison

The methodology will begin by investigating the philosophical background of the study and will outline its ontological position in section 3.2 and its epistemological position in section 3.3.

It will then introduce two main generalised null hypotheses in section 3.4. One will be that the initiatives used by the governing bodies to attempt to improve CB have had no effect. The other will be that all the measures used by academics to measure CB give the same results when compared using the same data. In the results chapter these hypotheses will be expanded to cover all four sports considered and therefore multiple individual hypotheses will be tested. Section 3.4 will briefly introduce the regression equations used but the full set will not be introduced until section 3.9.

Section 3.5 will review the data used in this study and will outline the assumptions made. It will also show a table summarising key information such as when league expansions occurred, when strikes occurred and when the relevant league initiatives were in place.

Section 3.6 will examine the data and clean it as much as possible, focussing on data that would otherwise distort the results such as data from strike seasons. It will explain in detail why strike seasons have been removed rather than modelled.

Section 3.7 will review the ethical considerations of the study and describe why there weren’t any ethical issues.

Section 3.8 will formally define the five measures of CB being examined by this study and present the mathematical formulae for their calculation.

Section 3.9 will introduce the regression technique to be used to determine whether the initiatives used by leagues to increase CB have been successful. It will review regression in general before fully specifying the equations for this study. It will also look at how the study will compare the regression equations for the different measures of CB to see whether they all show the same results.

The ontological position of this paper is Realist. Quine (1948) defines realism as “the Platonic doctrine that universals or abstract entities have being independently of the mind; the mind may discover them but cannot create them.”

In this study the North American sports leagues are the entities being examined and exist independently of the researcher.

The Realist ontology implies that causes can be understood as constant conjunctions of events. This study uses quantitative methods to understand the causes of changes in behaviour in the North American sports leagues and in doing so is consistent with its ontological position.

The basis for this paper is empirical data drawn from the North American sports leagues. Mathematical methods are being used to test the hypothesis that league initiatives affect CB. Mathematical methods are also being used to test whether there are differences between different measures of CB.

O’Neill (1952) explains Hypothetico-Deductivism as “a set of explanatory hypotheses are put forward; from these conclusions are deduced, and finally empirical data are sought which will show whether or not these conclusions are true”.

This is the approach of this paper and its Epistemological position is therefore Hypothetico-Deductivist.

The research questions of this study are:

• 
  Do the initiatives used by North American sports leagues to increase Competitive Balance work?
  
• 
  Do the different measures of Competitive Balance show the same results when calculated on the same sports data?
  

CB_a = β_1a + β_2aX_2t + β_3aX_3t + β_4aX_4t + ε_at

CB_b = β_1b + β_2bX_2t + β_3bX_3t + β_4bX_4t + ε_bt

CB_c = β_1c + β_2cX_2t + β_3cX_3t + β_4cX_4t + ε_ct

CB_d = β_1d + β_2dX_2t + β_3dX_3t + β_4dX_4t + ε_dt

CB_e = β_1e + β_2eX_2t + β_3eX_3t + β_4eX_4t + ε_et

The five different models represent the five different measures of CB (labelled a to e for the purposes of the equations) being examined by this study.

A fuller description of regression will be given in section 3.9. This study will test the null hypothesis that β_n=0 in the above equations for n>1, namely that the explanatory variables (the initiatives undertaken by the leagues) have no effect on CB. This will be tested against the alternative hypothesis that β_n≠0.

To answer the second research question the models will be compared and the null hypotheses that β_na = β_nb , β_na = β_nc … for all combinations of a to e will be tested. This will investigate whether the coefficients for each league initiative are the same across the different CB models.

3.5 Data

The data for this study comes from the four main professional North American sports leagues. The sports are American Football, Baseball, Basketball and Ice Hockey and the leagues are the National Football League (NFL), Major League Baseball (MLB), National Basketball Association (NBA) and National Hockey League (NHL) respectively.

Table 1 shows the current league structure for each league along with the data being considered in this study and the justification for the selection. It also shows which explanatory variables are being considered in the regression models.

League	Current Structure	Data Used / Justification	Explanatory Variables used in Regression
NFL	Two conferences each consisting of 16 teams split into 4 divisions. Each team plays 16 regular season games, 6 against teams from their own division, 6 against teams from their own conference and 4 against teams from the other conference. There are then playoffs at the end of the season for the best teams culminating in the Superbowl.	Data from 1970 onwards. The NFL merged with the AFL in that season and doubled the number of teams in the league, significantly changing the structure as well.	Free Agency plan A. Free Agency plan B. Existence of a low salary cap. Existence of a high salary cap. Existence of a balanced schedule. The presence of a new team as a result of expansion. The presence of a “young” team as a result of a recent expansion.
MLB	Two conferences, one with 16 teams, the other with 14. Each team plays 162 regular season games with playoffs for the best teams culminating in the World Series.	Data from 1961 onwards. The 162 game format was adopted in 1961.	Existence of a luxury tax. Existence of revenue sharing. The presence of a new team as a result of expansion. The presence of a “young” team as a result of a recent expansion.
NBA	Two conferences each with 15 teams split into three divisions of 5 each. Each team plays 82 regular season games with playoffs for the best teams culminating in the NBA Finals.	Data from 1962 onwards. The NBA started playing a minimum of 80 games in the regular season in 1962.	Existence of a low salary cap. Existence of a medium salary cap. Existence of a high salary cap. The presence of a new team as a result of expansion. The presence of a “young” team as a result of a recent expansion.
NHL	Two conferences each with 15 teams split into three divisions of 5 each. Each team plays 82 regular season games with playoffs for the best teams culminating in the Stanley Cup Finals.	Data from 1967 onwards. In 1967 six new teams joined the league in a large expansion and the NHL started playing more than 70 games per season.	Existence of a salary cap. The presence of a new team as a result of expansion. The presence of a “young” team as a result of a recent expansion.

Table 1 – Overview of North American sports leagues.

To clarify the justifications for the data used it was felt that the structure of the league should be as consistent as possible allowing for the fact that there have been expansions over the last 50 years. In each case the point that saw the most significant expansion or change in league structure was identified and used as the starting point for the data. The impact of other subsequent expansions was then accounted for by introducing a dummy variable into the regression models for the season when the expansion took place. A further variable, “Young Team”, was introduced into the regression models. This was to model the existence of a team that had joined the league through an expansion either the previous season or two seasons ago. The expansion and young team explanatory variables were included despite neither being an initiative designed to improve CB because it is believed that they may have a significant adverse influence.

The tables in section 3.5 show the evolution of the four major North American sports leagues. They highlight the expansions seen, the initiatives implemented by the league to try to improve CB and the strikes seen in the league. The strikes were caused by a variety of labour disputes and resulted in different numbers of games being lost. In some cases they also resulted in the reorganisation of the league season and a change in season structure. It is because all the strikes were different and had different effects that they have been removed from this study with the exception of two very short strikes in MLB. An alternative approach would have been to include these seasons and model the effects via the introduction of dummy variables for the strike seasons. However, each one would have had to have its own dummy variable and there would have only been one data point with a non-zero value for that dummy variable.

The data gathered was the win percentages and games played for all teams in the four major sports leagues for the seasons described above. This data was gathered from the following website:

http://www.rodneyfort.com/Rods_Sports_Economics/Data.html

It has been assumed that this data is accurate.

The information about the league expansions, league initiatives and strikes has been taken from a variety of sources. This is summarised in table 6: