Measures Of Competitive Balance Research Articles

Foundations of Preference for Competitive Balance

This article introduces an explicit model for sporting fans’ preferences which captures their desire for balanced contests, or competitive balance. Key parameters of the model naturally correspond to the strength of fan’s preference for competitive balance. Efficient contests are then characterized based on the preference for competitive balance, contrasting the resulting solutions with a widely recognized measure of competitive balance.

Dispersion and persistence in the competitive balance of North American major leagues 1960–2019

PurposeThis paper focuses on the proliferation of empirical measures of competitive balance arising from its multi-dimensionality (i.e. win dispersion versus performance persistence), and the increasing complexity and specificity of league structures. This has led to significant inconsistencies in the assessments of competitive balance, rendering it difficult to derive policy recommendations.Design/methodology/approachThe authors extend previous empirical studies of the four North American major leagues (i.e. MLB, NFL, NBA and NHL) using six competitive balance measures to (1) compare changes in competitive balance over the period 1960–2019; (2) to investigate the degree to which win dispersion and performance persistence move in the same direction; and (3) to explore the extent to which competitive balance has changed across facility construction eras and regulatory regimes.FindingsThe authors find that the assessment of competitive balance is both metric-dependent and time-dependent, reinforcing the importance of using a portfolio of measures rather than a single metric. The findings also highlight the importance of understanding the dispersion-persistence relationship.Originality/valueThe authors stress that leagues must be aware of a potential dispersion-persistence trade-off when intervening to improve competitive balance.

Measuring competitive balance in sports leagues that award bonus points, with an application to rugby union

We examine within-season competitive balance measurement in sports leagues where points allocated in each match depend on bonus points awarded as well as the win/draw/loss outcome, as in rugby union. The bilateral nature of matches imposes constraints on the range of competitive balance measures, as teams cannot win matches in which they do not play. Application of normalized competitive balance indices requires knowing the maximum value the index can attain, representing the most unequal distribution of points among teams. However, evaluation of the points distribution consistent with maximum imbalance is non-trivial when the total points allocated are not known in advance, as when bonus points are awarded. We theoretically derive the corresponding perfectly unbalanced distribution of points, characterized as a ‘Double Cascade distribution’, and provide an Excel tool to obtain it for different parameter values. We apply our results to examine variation in within-season competitive balance in the Six Nations Championship in rugby. The degree of competitive balance, as measured by a normalized concentration index, has improved since the award of bonus points in 2017, primarily because the index's maximum value increases with bonus points. However, with limited available data on the bonus-points regime, it is not possible to establish or reject a causal link, due to induced behavioural changes by teams, between the raw concentration index and bonus points. A relatively high level of imbalance still exists compared to other sports leagues, which will be an important consideration in evaluating future developments of the competition.

Historical evolution of competitive balance in the Mexican football league: a time series analysis, 1943-2015

This paper employs the Bai-Perron (BP) approach to perform a time series analysis of two measures of competitive balance (CB) in the unexplored area of the Mexican football league. A significant break point where CB experienced a substantial reduction is found. The time of the break point coincides with a modification of the league's regulations, which implemented two short tournaments instead of a single annual season to increase the revenue by doubling the final playoff games. This paper also establishes a first periodisation of the league's evolution, from its professionalisation in 1943 to 2015, on the basis of key historical events. In defence of the invariance principle, elements of collusion do not seem to have repercussions in CB. Nevertheless, the findings support the argument regarding the potential of significant regulatory changes to affect competitive equilibrium in sports contests.

A goal based index to analyze the competitive balance of a football league

Abstract Competitive balance in a football league is extremely important from the perspective of economic growth of the industry. Many researchers have earlier proposed different measures of competitive balance, which are primarily adapted from standard economic theory. However, these measures fail to capture the finer nuances of the game. In this work, we discuss a new framework which is more suitable for a football league. First, we present a mathematical proof of a theoretically optimal situation where a football league becomes perfectly balanced. Next, a goal based index for competitive balance is developed. We present relevant theoretical results and show how the proposed index can be used to formally test for the presence of imbalance. The methods are implemented on the data from the top five European leagues, and it shows that the new approach can be helpful in explaining the changes in the seasonal competitive balance of the leagues. Further, using panel data models, we show that the proposed index is more suitable to analyze the variability in total revenues of the football leagues. We also discuss how the methods can be easily extended to develop other goal-based indices under different modeling assumptions.

The multi-dimensionality of competitive balance: evidence from European football

PurposeThe purpose of this paper is to address the problem of designing league regulatory mechanisms given the multi-dimensionality of competitive balance and the proliferation of empirical measures.Design/methodology/approachA three-stage approach is adopted. Firstly, a taxonomy of empirical measures of competitive balance is proposed, identifying two fundamental dimensions – win dispersion and performance persistence. Secondly, a simple two-team model of league competitive balance is used to explore the dispersion–persistence relationship. Third, correlation and regression analysis of seven empirical measures of competitive balance for the 18 best-attended top-tier domestic football leagues in Europe over the 10 seasons, 2008–2017, are used to (1) validate the proposed categorisation of empirical measures into two dimensions; and (2) investigate the nature of the dispersion–persistence relationship across leagues.FindingsThe simple model of league competitive balance implies a strong positive dispersion–persistence relationship when persistence effects increase for big-market teams relative to those for the small-market teams. However, the empirical evidence indicates that while leagues such as the Spanish La Liga exhibit a strong positive dispersion–persistence relationship, other leagues show little or no relationship, and some leagues, particularly, the English Premier League and top-tier divisions in Belgium and Netherlands, have a strong negative dispersion–persistence relationship. The key policy implication for leagues is the importance of understanding the direction and impact of dispersion and persistence effects on the demand for league products.Originality/valueThe variability in the strength and direction of the dispersion–persistence relationship across leagues is an important result that undermines the “one-size-fits-all” approach to designing league regulatory mechanisms.

Competitive balance measures and the uncertainty of outcome hypothesis in European football

AbstractCompetitive balance is an important issue in professional sport in general and European football in particular. However, competitive balance is difficult to quantify because competitiveness is multi-dimensional and particular sports are distinctive. We aim to identify the most appropriate index for a holistic view of competitive balance in European football. We use data from eight domestic European football leagues over a time span of 60 years. The indices we consider are specifically designed to capture competitiveness at different levels of performance and in this way reflect the peculiarities of European football leagues. Our findings support the longstanding uncertainty of outcome hypothesis. A bivariate index that captures competitiveness in the top K places is shown to have the highest association with attendance. A seasonal index of champions’ domination is also found to have a large association with attendance. Finally, ranking mobility is found to have a slightly higher association with attendance than seasonal performance. These results imply that sports policy makers should use these indices to assess strategic decisions that may influence competitive balance.

The future of women's football in Asia: a look at competitive balance in top 5 domestic football leagues from 2010 to 2019

PurposeThis paper analyses competitive balance in the “big five” women's football leagues in Asia longitudinally between 2010 and 2019.Design/methodology/approachCompetitive balance has been measured using recognised measures of concentration, HICB and NHICB, alongside recognised measures of dominance, i.e., identification of top teams. A time-trend analysis has been employed to identify trends of CB in the respective leagues followed by ANOVA and relevant post-hoc tests to identify difference in concentration measures. A multiple linear regression analysis has been conducted to identify the impact of external economic factors on CB.FindingsSome significant differences were detected in the levels of concentration between leagues. There was also some variation in terms of some leagues being dominated by a fewer number of teams. However, these two measures of competitive balance (concentration and dominance) were not necessarily correlated with each other. The paper also tries to find the optimum number of teams to maintain CB in the women's football leagues in Asia, but an exact figure could not be found.Research limitations/implicationsSome significant differences were detected in the levels of concentration between leagues. There was also some variation in terms of some leagues being dominated by a fewer number of teams. However, these two measures of competitive balance (concentration and dominance) were not necessarily correlated with each other. External economic factors were found to have negative impact on CB.Originality/valueThe paper is an original research and aims to add to the growing body of CB research in world through analysis of competitive balance (ACB).

She Kicks: The State of Competitive Balance in the Top Five Women’s Football Leagues in Europe

Competitive balance remains a core component of sport economics literature and an important management consideration for league organisers. This paper analyses competitive balance in the 'top five' women's football leagues in Europe longitudinally between 1997/98 and 2018/19. Using recognised measures of league concentration and dominance, the results display a mixed picture in respect of competitive balance across the five major women's leagues in European football. The women's football industry has seen positive growth during the last ten years while competitive balance in most of the leagues examined has remained relatively stable. Some significant differences were detected in the levels of concentration between leagues. There was also some variation in terms of some leagues being dominated by a fewer number of teams. However, these two measures of competitive balance (concentration and dominance) were not necessarily correlated with each other. In a broader governance context, questions remain over the potential for further growth in the women's game as leagues are moving towards commercialisation of TV rights from 2021 to 2022.

Simulation evidence on Herfindahl-Hirschman measures of competitive balance in professional sports leagues

Measurement of the degree of competitive balance, how evenly teams are matched, is central to the analysis of professional sports leagues. A common problem with within-season competitive balance measures, however, is their sensitivity to the number of teams and the number of matches played by each team, i.e. season length. This paper uses simulation methods to examine the effects of changes in season length on the distributions of several widely used variants of the Herfindahl-Hirschman index applied to wins in a season. Accounting for both the lower and upper bounds of the index improves its robustness to variation in the numbers of teams or games played per season, but does not completely remove overestimation of imbalance associated with shorter season lengths. Overall, McGee’s balance measure significantly mitigates the dependence on the number of matches and, of the measures considered, is recommended as the most robust to variation in season length.

Measuring competitive balance in sports

AbstractIn order to make comparisons of competitive balance across sports leagues, we need to take into account how different season lengths influence observed measures of balance. We develop the first measures of competitive balance that are invariant to season length. The most commonly used measure, the ASD/ISD or Noll-Scully ratio, is biased. It artificially inflates the imbalance for leagues with long seasons (e.g., MLB) compared to those with short seasons (e.g., NFL). We provide a general model of competition that leads to unbiased variance estimates. The result is a new ordering across leagues: the NFL goes from having the most balance to being tied for the least, while MLB becomes the sport with the most balance. Our model also provides insight into competitive balance at the game level. We shift attention from team-level to game-level measures as these are more directly related to the predictability of a representative contest. Finally, we measure competitive balance at the season level. We do so by looking at the predictability of the final rankings as seen from the start of the season. Here the NBA stands out for having the most predictable results and hence the lowest full-season competitive balance.

The AFL Pick Trading Market as a Coasian Utopia

Sporting leagues have various competitive balance measures including player drafts, where teams are awarded picks based on prior performance. Teams, however, have the option to either exercise this pick or trade it as they see fit. An analysis of this trading market in the NFL stated that players obtained through traded picks contributed more to their recruiters in comparison to their counterparts. This paper retested this within the AFL and disproved this fact, establishing the Coasian notion of the efficient allocation of resources, based on some differences between the list management systems between the two leagues.

A Bias-Corrected Estimator of Competitive Balance in Sports Leagues

The ratio of the actual standard deviation (ASD) to the idealized standard deviation of win percentages (RSD) is the conventional measure of competitive balance (CB). RSD is designed to control for the effect of season length on the sample standard deviation of win percentages (ASD). Theoretically, the RSD should be greater than 1, but empirical values below 1 have been found in previous studies. This article employs a mathematical statistics approach to evaluate the statistical properties of RSD and ASD. In doing so, this study finds that RSD is constructed by an invalid normalization approach and that ASD is biased. It also presents a bias-corrected standard deviation (BCSD) as a new estimator of the standard deviation of true win probabilities. Results from the simulations confirm the following: (i) ASD is prone to underestimate CB levels when the number of games is small, (ii) the RSD values become unreasonably large when the number of games is large, and (iii) BCSD performs well with respect to mean bias and root mean squared errors. According to empirical analysis of the English Premier League (EPL) and the Korea Baseball Organization (KBO), BCSD shows that the KBO was more competitively balanced than the EPL between 2000 and 2015, while the RSD implies that the two leagues were roughly equal.

Is Egyptian soccer well-positioned for business purposes? Assessing competitive balance in the Egyptian Premier League

PurposeThe Egyptian Premier League (EPL) holds a prominent place in Egypt’s sporting culture and serves as the stage for some of Africa’s most competitive soccer clubs. However, the actual competitive balance in this league has come under scrutiny in recent years as the two historically dominant Cairo clubs, Ahly and Zamalek, continue to retain the EPL championship. A major concern is that the competitive imbalance of the EPL may actually be hampering the league’s progress and the progress of soccer in Egypt. In order to more closely assess this situation, the purpose of this paper is to use historical EPL performance data to conduct a series of competitive balance analyses on league results from 1948 to 2014. The findings revealed that competition in the league is almost nonexistent as Ahly and Zamalek continue to enjoy a number of direct and indirect financial benefits that are unrealized by their competitors. The dominance of these clubs has compromised the elements of match uncertainty and drama that are traditionally viewed as being important to the prestige and financial achievements of leagues and teams. Discussion is therefore offered for how the EPL could go about resolving some of its organizational and competitive balance issues.Design/methodology/approachThis study adopted four basic measures of competitive balance to conduct descriptive analyses on EPL data that were collected from egyptianfootball.net and the Rec Sport Soccer Statistics Foundation. These analyses began with the EPL’s inaugural season (1948-1949) and extended to the conclusion of the 2014-2015 season. During this timeframe, seven seasons were canceled due to global and political tensions and four more went unfinished. Because these seasons were excluded, the total sample size consisted of 56 seasons, each of which contained between 10 and 24 EPL teams. The data were analyzed using variations of the following competitive balance measures: the range and standard deviation of winning percentages, the ratio of the standard deviation/Noll-Scully approach, the Herfindahl-Hirschman Index, and five-club concentration ratio.FindingsThe results confirmed that the league is largely imbalanced, leading the authors to recommend systemic and structural changes that could help promote competitive balance in the league. The call for competitive balance in the EPL was bolstered by a literature review of studies that advocated for parity in professional sports leagues. In the end, the researchers recommend the EPL to improve its organizational policies and consider a revised revenue-sharing system that would allow the small-market teams to survive and thrive.Originality/valueThe EPL holds a prominent place in Egypt’s sporting culture and serves as the stage for some of Africa’s most competitive soccer clubs. The primary purpose of this study was to perform a series of competitive balance analyses on EPL results from 1948 to 2015 in an effort to better understand the various degrees of competitiveness in the league during this time.

A longitudinal and comparative analysis of competitive balance in five European football leagues

PurposeThis paper aims to provide empirical evidence on competitive balance in the “big five” European football leagues, namely, the English Premier League, French Ligue 1, German Bundesliga, Italian Serie A and Spanish La Liga.Design/methodology/approachThis paper uses recognised measures of competitive balance to measure levels of concentration (within-season competitive balance) and dominance (between-season competitive balance) in the selected leagues over 22 seasons between 1995/96 and 2016/17.FindingsFrench Ligue 1 emerged as the most balanced league in terms of both concentration and dominance measures. The analysis also points to a statistically significant decline in competitive balance in all leagues apart from Serie A (Italy).Originality/valueThe findings of this study are of concern for the league organisers. Competition intensity is a key component of a sport league, and a league that is dominated by one or a select few clubs is less attractive within the marketplace. This paper presents challenges at the league governance level for the five leagues examined.

Averting a tragedy of the commons: revenue sharing and competitive balance in the NHL

PurposeThe purpose of this paper is to measure the effect of the National Hockey League (NHL) collective bargaining agreement (CBA) of 2005 between the NHL owners and the NHL Players Association, to determine whether competitive balance in the NHL increased after the CBA.Design/methodology/approachCompetitive balance in the NHL was compared between 11 seasons before the NHL Lockout Season in 2004-2005 and 11 seasons after, with a new CBA and a new revenue sharing plan. Competitive balance was measured in multiple ways, within seasons, across multiple seasons, by the margin of victory in individual games, by the concentration of teams winning and playing in the NHL championship, in the correlation of winning percentage of a season with subsequent seasons, and the number of consecutive winning or losing seasons.FindingsThere was greater competitive balance after the Lockout Season and the new CBA than before on all of the measures of competitive balance. The NHL has found a management solution to the effective management of a common pool resource and avoided a tragedy of the commons.Practical implicationsWhile this research builds on previous work which examines the presence of competitive balance in the NHL, it encourages those engaged in labor policy to consider not only the merit of design when negotiating labor policy, but also to explore the impact of policy on organizational outcomes over time.Originality/valueThis paper combines perspectives and insights from multiple disciplines including economists’ ideas about competitive balance in a sports league, ecologists’ ideas about effective management of a common pool resource, and strategic management ideas about management solutions to a sustainability problem.

Structural Change in Competitive Balance in Big-Time College Football

Competitive balance is an important element of fan preferences in sports industries. We analyze the time series behavior of competitive balance measures over the entire histories of each of the current US. “Power 5” football conferences. Competitive balance has been remarkably stable. All series are stationary by unit root tests. None of the very few structural break points that we do find coincide with economy-wide shocks (wars and the Great Depression) or with any particular college-football-wide policy alteration. This has important implications for sports researchers and for policy in the “big-time” college football industry.

Gini playing soccer

The level of income inequality in a European country influences the competitive balance of its major soccer leagues. We test this hypothesis using cointegration techniques for seven male professional soccer leagues (the Dutch, English, French, German, Italian, Spanish and Ukrainian soccer leagues) from the 1980/1981 season to the 2011/2012 season. Controlling for the level of income inequality using variables such as real GDP per capita, trade openness and the emigration rate, we conclude that income inequality (measured by the Gini index) causes changes in the measures of competitive balance that we employ (the Hirschman–Herfindahl index and the SD) concerning the final number of points scored by the various teams.

Testing for Competitive Balance

We present two tests for the hypothesis that a league is competitively bal- anced, identifying in each case the appropriate statistic as well as its sampling distribution. We then apply these tests to Major League Baseball and the National Football League. We demonstrate how these tests can be applied to full sports leagues, or to just intradivisional play, and to both single season and multiple season outcomes.We also show how one of our statistics is related to existing measures of competitive balance, and note the possibility that that, because our statistics have known sampling distributions, that knowledge may ultimately allow them to be transformed into measures that are comparable between leagues of different sizes and season lengths.

COMPETITIVE BALANCE MEASURES IN SPORTS LEAGUES: THE EFFECTS OF VARIATION IN SEASON LENGTH

Appropriate measurement of competitive balance is central to the economic analysis of professional sports leagues. We examine the distributional properties of the ratio of standard deviations (RSD) of points percentages, the most widely used measure of competitive balance in the sports economics literature, in comparison with other standard‐deviation‐based measures. Simulation methods are used to evaluate the effects of changes in season length on the distributions of competitive balance measures for different distributions of the strengths of teams in a league. The popular RSD measure performs as expected only in cases of perfect balance; if there is imbalance in team strengths, its distribution is sensitive to changes in season length. It is therefore not recommended for comparisons of competitive balance for different sports leagues with different numbers of teams and/or games played. (JEL L83, D63, C63)