This study introduces a graphical methodology to the analysis of competitive balance in sports, which is prospective in nature and captures more subtleties than commonly-used retrospective measures. Thus, this study examines the evolution of competitive balance in Major League Soccer from 2004 to 2015, including the potential role played by certain league policies. For this purpose, we use prospective measures, based on probabilities that are extracted from betting odds (ex-ante) and on retrospective indicators (ex-post). The results differ slightly when analyzing competitive balance and predicting attendance. However, the graphical measures provide additional practical information about the characteristics of competitive balance.
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The insight that descriptive statistics are not necessarily indicative of the whole sample is hardly new. For instance, Anscombe (1973) illustrates this issue with the use of four datasets that have the same descriptive statistics but appear very different when they are plotted. The author described the article as an effort to contradict the belief that numerical outcomes are more informative than graphs.
We note the difference between expected competitive balance and perceived competitive balance. The former refers to fans’ predictions about the final outcome of a game (based on teams’ potential), which indicates that uncertainty of an outcome and competitive balance levels. In contrast, the latter refers to how much fans care about competitive balance (and the effect that this has on the demand). The literature on perceived competitive balance (PCB) mainly uses survey data. Please see Nalbantis et al. (2017) and Pawlowski (2013) as examples of this line of research.
As an example, consider a match with closing odds listed as: home win (1.70); draw (3.25); and away win (4.12). The over-round is 14%, which results in the implicit probabilities of: home win = 0.52; draw = 0.27; and away win = 0.21.
The number of games varies somewhat in MLS over the analyzed period. In order to analyze competitive balance over time, we adjust for the total number of possible points in a season. The maximum number of points achievable by teams is standardized to 100 to facilitate inter-season comparisons.
Like most other North American professional sports leagues, MLS runs a post-season tournament to determine the yearly champion. Post-season games are not included in our analysis.
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The authors are grateful to Ph.D. Leonor Gallardo for her former contribution to this paper, which is a revised version of the undergraduate thesis of Carlos Gomez-Gonzalez. Moreover, the authors would like to thank the reviewers for their thoughtful comments and, especially the editor for the effort to improve the paper. This contribution benefited from the financial support of the government of Castilla-La Mancha (Project PPII-2014-004-A) and the funds for international visiting scholars stays at the University of Castilla-La Mancha (2017).
The analysis of the probabilities of the winning average of teams over time is another measure of long-run competitive balance. Figure 5 shows the evolution of Western Conference and Eastern Conference teams in MLS during the 2004 through 2015 in terms of the average probability of winning games based on betting odds. This measure serves a dual purpose: (1) to analyze visually the role of specific teams in the long-run competitive balance and (2) to track the changes in the expected performance of teams over time.
To interpret the graph, note that the more similar are the average probabilities among teams, the greater is the competitive balance. Moreover, crossings and variations in the positioning of teams over the years show variability and, consequently, stronger long-run competitive balance levels. For example, we observe that the conferences’ expected winners change in both conferences over time. This figure is a graphical and prospective version of the top ranking teams that has been used in previous competitive balance studies (Goossens 2006).
This measure provides a more specific follow-up of teams that can be compared to one another with respect to the implementation of strategies, such as the hiring of players. For example, Fig. 5 highlights the evolution of Toronto (gray line in Eastern Conference) and Vancouver (gray line in Western Conference). Both teams have some similarities. They are expansion teams that come from cities that are outside the US, entered the league with low expected performance, and finally show a positive tendency. However, the main difference is that Vancouver managed to increase its expectations above the average much more rapidly than did Toronto. Similar to this measure, the density functions have the potential to isolate the evolution of specific clubs over time in the estimated distribution.
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Gomez-Gonzalez, C., del Corral, J., Jewell, R. et al. A Prospective Analysis of Competitive Balance Levels in Major League Soccer. Rev Ind Organ 54, 175–190 (2019). https://doi.org/10.1007/s11151-018-9667-3
- Betting odds
- Competitive balance