Competitive balance measures in us professional sport: an empirical comparison

Jon Garrett

August 2011

Abstract

The need for competitive balance in major sports leagues has been well researched and documented. It is generally accepted that for a league to maintain high levels of spectator interest it is better if it is uncertain who is going to win each game and ultimately who is going to win the league championship. Leagues have consequently undertaken actions to attempt to improve this balance.

Having accepted that competitive balance is desirable it becomes necessary to be able to measure such a quantity with the objectives of proving that it is being maintained and that the league initiatives are working. Several methods for undertaking this measurement have been used in the literature.

This study will focus on two areas: whether the league initiatives are working and whether the methods used to measure this are consistent. It will conclude with a recommendation for the development of a more consistent method of analysis of competitive balance.

List of Diagrams

Commonly Used Abbreviations

1 – Introduction

1. 
   – Research Questions
   
2. 
   – Research Objectives
   
   1. 
      – Research Objectives Relating to Question 1
      
   2. 
      – Research Objectives Relating to Question 2
      

2. 
   – Literature Review
   

1. 
   – Introduction
   
2. 
   – The Importance of Uncertainty of Outcome
   
3. 
   – Competitive Balance
   
4. 
   – Initiatives used to try to improve Competitive Balance
   
   1. 
      – Labour Market Initiatives
      
      1. 
         – Salary Caps
         
      2. 
         – Luxury Tax
         
      3. 
         – The Draft System
         
      4. 
         – Free Agency
         
   2. 
      – Non Labour Market Initiatives
      
      1. 
         – Revenue Sharing
         
      2. 
         – Schedule Strength
         
5. 
   – Measures of Competitive Balance
   
   1. 
      – Standard Deviation
      
   2. 
      – Gini Coefficient
      
   3. 
      – Herfindahl Hirschmann Index
      
6. 
   – Conclusion
   

3. 
   – Methodology
   

1. 
   – Introduction
   
2. 
   – Ontology
   
3. 
   – Epistemology
   
4. 
   – Hypotheses
   
5. 
   – Data
   
6. 
   – Data Reliability / Validity
   
   1. 
      – Summary of Data Included
      
7. 
   – Ethical Considerations
   
8. 
   – Competitive Balance Measures
   
   1. 
      – Standard Deviation
      
   2. 
      – Normalised Standard Deviation
      
   3. 
      – Gini Coefficient
      
   4. 
      – Herfindahl Hirschmann Index
      
   5. 
      – Five Club Concentration Ratio
      
9. 
   – Regression
   
10. 
    – Conclusion
    

4. 
   – Results
   

1. 
   – Introduction
   
2. 
   – Data Manipulation
   
3. 
   – Descriptive Statistics
   
   1. 
      Baseball
      
   2. 
      Basketball
      
   3. 
      American Football
      
   4. 
      Ice Hockey
      
4. 
   – Regression Models
   
   1. 
      – MLB(Baseball)
      
   2. 
      – NBA(Basketball)
      
   3. 
      – NFL(American Football)
      
   4. 
      – NHL(Ice Hockey)
      
5. 
   – Overall Summary of Results
   
6. 
   – Limitations
   
7. 
   – Future Research
   
   1. 
      – Theoretical Maxima and Minima
      
   2. 
      – Worked Example (Basketball)
      
8. 
   – Conclusion
   
   1. 
      – League Initiatives
      
   2. 
      – Comparison of Measures
      

5. 
   – Conclusion
   

1. 
   – Introduction
   
2. 
   – Summary of Analysis
   
3. 
   – Main Conclusion
   

6. 
   – References
   
   1. 
      
      

1 – p30 - Pictorial Representation of Gini Calculation

2 – p38 - Baseball Data Graph and Competitive Balance Measures

3 – p40 - Basketball Data Graph and Competitive Balance Measures

4 – p41 - American Football Data Graph and Competitive Balance Measures

5 – p42 - Ice Hockey Data Graph and Competitive Balance Measures

6 – p52 - Values of the Competitive Balance Measures for Basketball

7 – p53 - Relationship between HHI and Number of teams in the NBA

8 – p57 - Measures for Basketball after adjustment

Tables

1 – p24 - Overview of North American sports leagues

2 – p25 - Significant events in the development of the NFL

3 – p26 - Significant events in the development of MLB

4 – p26 - Significant events in the development of the NBA

5 – p27 - Significant events in the development of the NHL

6 – p28 - Sources of information for league expansions and initiatives

7 – p29 - Summary of data

8 – p30 - Summary of the five measures of Competitive Balance used in this study

9 – p43 - Dependent variables used in Baseball models

10 – p43 - Explanatory Variables used in Baseball models

11 – p45 - Statistical analysis of Baseball models

12 – p45, p60 - Baseball models

13 – p47 - Dependent variables used in Basketball models

14 – p47 - Explanatory Variables used in Basketball models

15 – p47 - Statistical analysis of Basketball models

16 – p48 - Dependent variables used in American Football models

17 – p48 - Explanatory Variables used in American Football models

18 – p49 - Statistical analysis of American Football models

19 – p50 - Dependent variables used in Ice Hockey models

20 – p50 - Explanatory Variables used in Ice Hockey models

21 – p50 - Statistical analysis of Ice Hockey models

22 – p51, p61 - Statistically significant variables for each sport

Commonly Used Abbreviations

General

CB – Competitive Balance

SD – Standard Deviation

NSD – Normalised Standard Deviation

GC – Gini Coefficient

HHI – Herfindahl Hirschmann Index

FCCR – Five Club Concentration Ratio

MLB – Major League Baseball

NBA – National Basketball Association

NFL – National Football League

NHL – National Hockey League

1 Introduction

The National Football League (NFL) prides itself on being the most exciting and competitive league in North American sports. Many initiatives have been introduced to attempt to keep it as such while the league has also undertaken a period of expansion due to increased TV coverage of sports in general.

There has been much talk about the New England Patriots’ perfect season when they won all their regular season games in 2007 and the Detroit Lions’ imperfect season when they lost all their regular season games in 2008. Byrne (2009) described recent events in the NFL, including a week of games that were the most one-sided since 1970. His article outlined why he believed parity was dead. It analysed league statistics and recent championship winners and concluded that NFL executives should be afraid as the same teams were consistently the best in the league. He attributed this to differences between teams in management quality which he concluded had become more important since the league had levelled the financial playing field in terms of player salaries.

It was this article along with my own recent personal opinions and love of the sport that led me to ask whether this was actually true and whether in fact the NFL was in danger of becoming predictable. This study was initially shaped to determine whether such a change in parity had actually taken place.

On further inspection it became obvious that determining whether there was a change in the NFL was not sufficient in case there was an outside influence such as the economic climate. It was necessary to undertake the same analysis for the other major sports in North America to see whether the same pattern (if there was one in the NFL) was being observed elsewhere. All the major sports leagues have undertaken initiatives to attempt to increase competitive balance and it was decided to review these to determine their success or otherwise.

Competitive Balance (CB) is very difficult to define explicitly. Chapter 2 will review the development of the concept in the literature but for now this study notes the definition offered by Ajilore & Hendrickson (2005) of “an individual teams’ competitiveness” and acknowledges that their paper was looking at individual teams rather than the league as a whole. However, a small extension allows this study to offer as good a definition as it has found in the literature namely:

“CB is the ability of all teams contained within a league to compete with each other over a period of time with a reasonable chance of success”.

The period of time referred to in the definition is most likely to be a single season but the definition doesn’t rule out the possibility of looking at longer periods. Success may be defined in many ways including qualifying for playoff competitions or winning championships.

Whilst one focus of this study is whether the initiatives taken have been successful in improving CB it is necessary to recognise that other factors could potentially affect it. As previously stated the NFL has undergone a period of expansion since its merger with the American Football League between 1966 and 1970. Each time it expanded a new franchise was formed, with new players and coaches. While the NFL attempted to ensure this team was instantly competitive by running a special draft system a number of these teams struggled to win games in their early seasons. The Tampa Bay Buccaneers, an expansion team in 1976, lost their first 26 games. Similar expansions have taken place in all other major North American sports. This study will also take account of such league expansions in any statistical modelling.

Much has been written about measuring CB in sports leagues and this will be reviewed in more detail in chapter 2. However, it is not clear from the literature which method is best. There are many statistical measures used by different authors, seemingly without full justification or understanding of the characteristics of the measure. This raises the question of whether the different measures show the same trends or whether there are differences between them. There is a gap in the CB literature relating to an empirical study of these measures using the same sports data. This study will therefore use common data to investigate whether it is necessary to understand which measure is being used or whether all will produce the same results.

The two research questions of this study are:

1. 
   Do the initiatives used by North American sports leagues to increase Competitive Balance work?
   
2. 
   Do the different measures of Competitive Balance show the same results when calculated on the same sports data?
   

Each of the two research questions has its own set of research objectives.

• 
  Identify the initiatives used by each sports league
  
• 
  Identify when each initiative was used
  
• 
  Gather data that allows CB to be measured over a period of time
  
• 
  Produce statistical models that prove or disprove the effectiveness of the league initiatives
  

• 
  Identify the different measures of CB
  
• 
  Gather data that allows CB to be measured over a period of time
  
• 
  Produce values for each of the different measures of CB
  
• 
  Compare and contrast using statistical methods
  

This chapter will review the literature relating to CB in sports. Section 2.2 will review why uncertainty of outcome in sporting events is important. Section 2.3 will extend from uncertainty of outcome and review the development of the wider concept of CB. Section 2.4 will look at some of the initiatives used, particularly in North American sport, to try to increase CB. As discussed in chapter 1 this study will attempt to assess whether they have been successful. Section 2.5 will review some of the measures of CB. As also discussed in chapter 1 this study will also compare these measures of CB and will highlight any differences between them.

Uncertainty of outcome is important for sports leagues because it is argued that fans will be much more likely to watch a sporting event if the result is uncertain than if it is easy to predict. Rottenberg (1956) examined the labour market for Baseball players, concluding that there was a need for change from the rules governing player contracts at that time which allowed certain teams to dominate the league on a regular basis. He proposed a number of options including revenue sharing, a maximum player wage and a redistribution of the franchises so that each had an equal population catchment area. Each was designed to ensure that the same resources were available to all franchises, the conclusion being that if that was the case the games would be more exciting as they would be between equal teams.

Neale (1964) examined the case of Joe Louis and Max Schmelling and explained that Louis, the World Heavyweight Boxing champion, needed Schmelling, a strong contender, in order to ensure the fights were popular with the public. With no-one to fight Louis would not have made any money. Neale (1964) extended this analysis to Baseball and compared the New York Yankees to Joe Louis, stating that the Yankees needed strong teams to play against in order for Baseball to flourish. Neale (1964) also introduced the term “League standing effect”, stating that the closer the league standings are the higher the revenues from attendance.

2.3 Competitive Balance

The term CB has been defined in chapter 1 as:

“The ability of all teams contained within a league to compete with each other over a period of time with a reasonable chance of success”.

This is a broader definition than uncertainty of outcome which relates to single competitive matches. CB looks at the league as whole and also covers changes over a period of time. If the entire league standings are repeated year after year and the same teams repeatedly win the championships regardless of whether the games are close the league is clearly not in balance. It is not clear however how much balance their needs to be in a league. This was summed up by Zimbalist (2002) who stated that “Competitive Balance is a good thing to have, but nobody is able to discover how much Competitive Balance a person or league needs”.

The professional leagues in North America have introduced initiatives to attempt to improve CB. Many relate to the labour markets and are detailed in section 2.4.1. Others are not related to the labour aspect of the sport and are detailed in section 2.4.2.

The Labour market initiatives are based on the idea that if teams have the same labour resources available to them they will be of a similar playing standard and therefore CB will be improved.

Leagues have set salary caps in two main ways. Firstly, leagues have imposed total salary caps that can be paid to the teams’ players. These are usually set based on the league revenues and are the same for all teams in the league. Secondly, some leagues have imposed salary caps for individuals, both maximum and minimum.

The first is most commonly used and is designed to ensure that each team has the same resources available to it in terms of player ability.

Lee (2010) looked at the potential effects of the collective bargaining agreement of 1993 in the NFL, covering changes in free agency and salary caps as a whole, concluding that the measures taken did indeed serve to increase parity on an interseasonal basis. Larsen et al (2006) also looked at the NFL in detail, covering the seasons 1970-2002 and examined salary caps and free agency among other factors such as new stadia, players strikes and concentrations of player talent and concluded that all affect CB.

Instead of salary caps as described in section 2.4.1.1 Baseball has used a system called Luxury Tax. This sets a salary cap for each team but teams are not prevented from exceeding it. Instead if they choose to do so they are fined (taxed) a significant amount of money, usually a percentage of how much they have exceeded the cap by. Most teams have chosen to comply with the salary caps but notably the New York Yankees have regularly exceeded the caps and paid Luxury Tax.

Leagues have long used the college draft as a way of attempting to improve CB. The NFL started in 1935 while the other major sports leagues all started before 1965. Each season the new college graduates are drafted into the leagues by the professional teams. The order that the professional teams choose the college players is determined by their finishing positions the previous season. The team that finished with the worst record is given the first choice and in theory should therefore be able to choose the best player. This should then help to improve the balance of the league. In practice teams often make deals with each other, sometimes trading one high pick for several lower ones in order to strengthen in a number of areas while foregoing a potential superstar. Regardless, the draft system is designed to help the weaker teams improve.

There are some differences between the mechanics of the drafts used in the different sports but they are not relevant to this study as we shall not be using the draft as an explanatory variable due to the fact that all sports have had drafts in place for the entirety of our sample periods.

2.4.1.4 Free Agency

A free agent is a player whose contract has expired and who is therefore able to join another team. In North American sports teams were able to use a clause in the players contract called the reserve clause, enabling them to automatically renew the contract without the player having the right to terminate it, even when it expired.

This changed in the NFL in 1989 with the introduction of Plan B free agency. This allowed a team to protect 37 players such that they were still unable to sign for another team without their current team having the first option. This was ruled to violate anti-trust laws and abandoned in 1992. Plan A followed immediately which developed the concept to give more rights to players who have been with a team for a longer period of time. In the NFL players who have been with a team for at least 6 seasons and whose contract has expired are termed “Unrestricted Free Agents” and are free to negotiate with any other team. Players who have been with a team for at least 3 seasons are termed “Restricted Free Agents” and are free to negotiate with any other club but their existing club has the right to match any new offer and retain their services.

Free Agency has relaxed the rules regarding players moving from one team to another. In an open market with no restriction on salaries this would have an adverse effect on CB as the teams with the most resources would buy the better players when their contracts expired.

Maxcy & Mondell (2006) looked at Free Agency in depth with mixed results. Their study suggested that CB had been improved by Free Agency in the NFL and NHL but not in the NBA. We shall revisit this analysis in this study.

2.4.2 Non Labour Market Initiatives

The other initiatives used to try to improve CB focus on areas unrelated to the labour market.

The significant rise in broadcasting revenues generated by the sports leagues meant that the league had large sums of money at its disposal. Leagues chose to split this revenue equally between the teams regardless of the size of the team, its fan base or the number of fixtures broadcast. This ensured that even teams from small cities had the financial resources to compete.

The nature of the league structure in all North American sports is such that teams play a large proportion of their games against other teams from their own division. By definition the team that finished last in the division in the previous season will be playing games against higher ranked teams than the team that finished first in the previous season. To compensate some leagues altered the remaining games played outside the division so that those teams who finished last play each other and those that won their divisions also play each other. In that way each team plays the same number of teams of each strength and in theory the schedule is balanced. This innovation is only possible with a league that has a symmetrical structure and has only been adopted by the NFL.

When measuring the CB of a particular league it is possible to use a number of different methods. This section will review the relevant literature and will highlight the strengths and weaknesses as identified by other authors. The measures chosen for use in this study will be formally defined in chapter 3.

The Standard Deviation of win percentages (SD) has been extensively used to measure the CB within a league. Scully (1989) used this when examining Baseball in detail and Quirk and Fort (1997) used it across the major sports in North America. Comparisons between leagues are easy to perform and the concept of the SD of a set of data is simple.

Humphreys (2002) examined the use of SD in detail and concluded that it has shortcomings when looking at a number of consecutive seasons. Humphreys constructed an artificial example of two sets of seasons where one set had the same team winning every time and the other had a mix of teams winning. The traditional approach showed no difference between the two in terms of CB but there was much less CB in the set of seasons where the same team was winning every time than in the set where the winners were different.

Humphreys (2002) developed a measure called Competitive Balance Ratio which looked at the SD within seasons and the SD between seasons and calculated the ratio of the two. This has some appeal as it seems to look at a number of consecutive seasons as well as considering the balance within seasons. However, this author believes that the numerator and denominator used in the calculation are measuring different entities and as such should be kept separate and analysed as such. This study will tackle the question of whether the different measures behave differently.

Schmidt (2001) used a different measure, the Gini Coefficient (GC), when analysing Baseball. The GC describes how far a given league is from a perfectly balanced league by constructing the Lorenz curves. A perfectly balanced league is one in which each team wins exactly 50% of its matches. The Lorenz curves are constructed by ranking the teams in order of their win percentages and producing a cumulative wins variable and plotting it against the number of teams. This is fully defined in chapter 3.

GCs can produce values between 0 and 1. However, the upper boundary of 1 can only be achieved if all teams win or lose all of their games. Clearly in a league where all teams play all other teams this is impossible. There is therefore an upper bound which is much lower than the theoretical value of 1. This is not an issue when using the GC to compare CB across seasons within the same league but becomes one when looking at CB in broader terms or comparing measures.

2.5.3 Herfindahl Hirschmann Index

Another measure that has been commonly used to measure CB is the Herfindahl Hirschmann Index (HHI). Named after economists Orris Herfindahl and Albert Hirschmann it has been used in industry to measure how competitive a particular market is. The principle is to compare the market share of the largest firms to the size of the market, typically using the top 50 firms. The higher this market share the less competitive the market. This approach has been adapted to sports leagues and has been used in two ways. Michie & Oughton (2004) looked at the performance of the top five teams compared to the league as a whole in the English Premier Football league. They also calculated the percentage of points won by each team and calculated a sum of squares for that using all teams. Michie & Oughton (2004) concluded that these measures were sensitive to changes in league size, something this study will confirm and offer a solution for.

Section 2.2 looked at why uncertainty in sport is important drawing on articles by Rottenberg (1956) and Neale (1964) and concluded that spectators are more likely to watch a sporting event where the result is uncertain than one where the result is a foregone conclusion.

Section 2.3 extended this to introduce the term CB as a wider description covering the relationship between all teams within the league. It also acknowledged that CB may be defined over a longer period of time than a single season.

Having established that it is believed that CB is a desirable attribute for a league section 2.4 reviewed a number of initiatives taken by leagues to increase CB. This identified two major groups, namely Labour Market related Initiatives and Non Labour Market related Initiatives. These were reviewed in detail. As part of this study we shall attempt to discover whether they have been successful.

Section 2.5 reviewed the different measures that have been used to measure CB and highlighted some of their perceived advantages and disadvantages. What is not clear is whether all the measures give the same results. This study will calculate and compare these measures using the same data. It will then highlight, and attempt to explain, any differences.