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It seems that one cannot find many papers relating entropy to sport competitions. Thus, in this paper, I use (i) the Shannon intrinsic entropy (S) as an indicator of "teams sporting value" (or "competition performance") and (ii) the Herfindahl-Hirschman index (HHi) as a "teams competitive balance" indicator, in the case of (professional) cyclist multi-stage races. The 2022 Tour de France and 2023 Tour of Oman are used for numerical illustrations and discussion. The numerical values are obtained from classical and and new ranking indices which measure the teams "final time", on one hand, and "final place", on the other hand, based on the "best three" riders in each stage, but also the corresponding times and places throughout the race, for these finishing riders. The analysis data demonstrate that the constraint, "only the finishing riders count", makes much sense for obtaining a more objective measure of "team value" and team performance", at the end of a multi-stage race. A graphical analysis allows us to distinguish various team levels, each exhibiting a Feller-Pareto distribution, thereby indicating self-organized processes. In so doing, one hopefully better relates objective scientific measures to sport team competitions. Moreover, this analysis proposes some paths to elaborate on forecasting through standard probability concepts. [ABSTRACT FROM AUTHOR]

This is the first article to empirically examine what drives TV audience demand for the UEFA Champions League (UCL) in major European markets. It then asks: How well does the tournament structure meet the preferences of TV viewers? The article analyses the UCL from 2013/14–2018/19, considering TV viewing figures for all televised games from the group stages through to the finals in six nations – France, Germany, Italy, the Netherlands, Spain and the UK. It then analyses match data in the UCL since its most recent tournament restructure in 2003/04, along with Ballon d'Or results and UEFA Club Coefficient rankings, to assess the efficiency of the current tournament structure. Uncertainty of outcome is not significantly associated with the size of TV audiences for the UCL, but both the presence of star players and team quality are. However, analysis of match data reveals that the current structure of the UCL does not maximise the number of star players or top clubs that progress to the latter stages of the tournament. These findings enable UEFA and other sport competition organisers to make evidence-informed decisions about how to structure competitions, while balancing the needs of multiple stakeholders. They also contribute to the small but growing body of empirical work that seeks to identify the key drivers of TV demand for sport – increasingly the dominant form of revenue for many sport organisations. [ABSTRACT FROM AUTHOR]

Copyright of Cultura, Ciencia y Deporte is the property of Cultura, Ciencia y Deporte and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Competitive balance is a key variable in the analysis of sports competitions. There are several indexes that measure competitive balance but, either they are not a mathematical metric or they do not have the unit interval as a range. Therefore, these indexes do not indicate the magnitude of the differences, and the measurements cannot be interpreted as percentages. We characterize the space of all admissible configurations of the results of a competition. Then, we construct a new index, based on the concept of distance, whose range is the unit interval, and define it as a function in a metric space. So, it solves issues linked to the limited cardinality of most existing indexes, and we can answer this question: What is the meaning of the differences between the levels of competitive balance? We applied this index to the major European soccer leagues over the last twenty seasons. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This article examines competitive balance at the Summer Olympic Games between 1992 and 2016 by measuring the distribution of gold medals, medals and medal points amongst nations, for overall and male and female competitions. The key findings are overall; there has been no improvement in competitive balance since the 1992 Olympics. There is some evidence that competitive balance has improved in male competitions, as shown by decreased HHIN, CV and CR4 values. The analysis of female competitions suggests that competitive balance has remained largely unchanged. However, the CV Gold indicator provides evidence of a significant decline in competitive balance. The findings facilitate a more evidence-based evaluation of existing policy measures and strategies, and their refinement where appropriate. Policy suggestions are proffered for the International Olympic Committee (IOC) and various International Federations (IFs), and non-major nations to promote a more balanced development and competition particularly for women. [ABSTRACT FROM AUTHOR]

Competitive balance within interscholastic athletics in the United States is governed by state athletic associations. The policies derived by these associations vary by state and are meant to ensure high school athletic teams have an equitable chance of athletic success, especially in post-season tournament competition. Two specific policy types, recruiting and transfer restrictions, are often designed to safeguard against schools targeting specific athletes, or students choosing schools based on athletic motives. These policies are particularly challenging to create and enforce when private schools are involved, as private schools admit students differently than public schools and because private schools tend to have disproportionately high levels of athletic success. Consequently, legal cases challenging recruiting and transfer policies often include private high schools where violations of fundamental rights are alleged. A thorough review of such cases revealed that state athletic associations are generally supported by the courts to create and enforce recruiting and transfer limitations. [ABSTRACT FROM AUTHOR]

Purpose -- The 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/approach -- This 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. Findings -- The 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/value -- The 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. [ABSTRACT FROM AUTHOR]

In this paper we analyze the argument—which has been used by both the National Labor Relations Board and the National Collegiate Athletic Association—that unionization and/or player pay will hurt competitive balance in college sports. We present a theoretical analysis of universities that recruit athletes and examine the assumptions that are needed for player compensation to decrease competitive balance. We also empirically illustrate the differences in balance between professional and college sports. Given the theoretical and empirical analysis, we argue that unionization and/or player pay is unlikely to hurt competitive balance. [ABSTRACT FROM AUTHOR]

We present evidence on the impact of revenue sharing and salary caps on both short and long-run competitive balance based on a form of unique natural experiment--the abolition of Rugby Union's ban on professionalism and the different responses of the English (EPR) and French (T14) leagues to its removal. The EPR has operated revenue sharing and a binding salary cap for most of the professional era, but the T14 only introduced a non-binding salary cap much more recently. We use a dataset of net winning margins from 9,438 matches in both leagues over 27 seasons from 1987/88 to 2015/16 to measure short-run competitive balance. Our results indicate that short run competitive balance in both leagues declined following the move to professionalism, but subsequently improved in the EPR following the introduction of revenue-sharing and a binding salary cap. Play offs also improved short-run balance, as did reductions in the number of teams. We also find some evidence that long-run balance improved in the EPR at least initially following the move to professionalism and absent a binding salary cap professionalism reduced long-run balance in the T14. [ABSTRACT FROM AUTHOR]

The aim of this article is to investigate the determinants of television audience for English Premier League (EPL) football matches during the 2013–2014 season (n = 154). The model is adapted from Buraimo and Simmons (2015) who concluded that star quality was an important determinant of television audiences for the EPL over the 2000–2008 period, whereas uncertainty of outcome and championship, Europe and relegation contention were not. Their measures for contention are replaced by indicators based on Scelles et al.’s (2013b, 2016) competitive intensity. Results show a significant positive impact of star quality but also championship and Champions League intensity and no significant impact of Europa League, potential Europa League and relegation intensity. Based on these results, the article suggests that the EPL should encourage both star quality and competitive balance so that all teams can be competitive in terms of the title or qualification for the UEFA Champions League. Given the differences in revenue generation between English teams, the best way to achieve both star quality and competitive balance would be through the introduction of a European Super League. However, this conclusion based on television audience contradicts that of Scelles et al. (2016) based on stadium attendance. [ABSTRACT FROM PUBLISHER]

Team Tennis competitions produce aggregate scores for teams, and thus team rankings, based on head-to-head matchups of individual team members. Similar scoring rules can be used to rank any two groups that must be compared on the basis of paired elements. We explore such rules in terms of their strategic and social choice characteristics, with particular emphasis on the role of cycles. We first show that cycles play an important role in promoting competitive balance, and show that cycles allow for a maximum range of competitive balance within a league of competing teams. We also illustrate the impact that strategic behavior can have on the unpredictability of competition outcomes, and show for a general class of team tennis scoring rules that a rule is strategy-proof if and only if it is acyclic (dictatorial) and manipulable otherwise. Given the benefits of cycles and their relationship with manipulability, a league valuing competitive balance may invite such social choice violations when choosing a scoring rule. [ABSTRACT FROM AUTHOR]

Despite the prominence and relevance of the uncertainty-of-outcome hypothesis (UOH) for professional sports worldwide, decades of empirical research have not been successful in establishing clear evidence for the importance of outcome uncertainty for stadium attendance and TV audience. In this regard, some recent papers were developed drawing upon a body of behavioral economic thoughts that might help to better understand the divergence between the UOH, competitive balance, and consumer choices. Since this literature has so far focused on different facets of behavioral economics, it is the objective of this paper to summarize and review the existing literature, discuss possible policy implications that can be derived from behavioral thinking in this context, and point out further research avenues. [ABSTRACT FROM AUTHOR]

Rottenberg’s uncertainty of outcome hypothesis is about preferences that can vary across fans and sports. We provide the first evidence of the empirical power of the hypothesis in the Korean Professional Baseball League (KPBL). In a panel data set, team-level aggregation over years shows that fans of this league attend in ways consistent with the hypothesis at the level of game uncertainty and consecutive season uncertainty, but only the first is statistically significant. KPBL fans appear to just be looking for a good game. This is consistent with the nearly complete concentration of post-season participation among a very few teams outside of the major population centre in Seoul and a lack of local team identification among KPBL fans. Our work adds to the diversity of league structures in the competitive balance literature since talent levels in KPBL are the result of parent company advertising choices rather than geographic identification. There are research questions and a policy implication. [ABSTRACT FROM AUTHOR]

Competitive balance is a matter of great interest among sports fans, researchers, and stakeholders. As a result, several competing metrics have been put forth by researchers. Most commonly, these measures examine variation in wins or championships ex-post. In contrast, this study uses ex-ante championship probabilities from the futures betting market to measure competitive balance in the NBA, NFL, NHL, and MLB. Uncertainty of outcome is a component of fan interest, and at this point, the literature has used betting markets to examine uncertainty for individual games. This study proposes a measure for uncertainty in the outcome of a team's season. [ABSTRACT FROM AUTHOR]

Purpose -- The purpose of this paper is to examine the competitive balance of the UEFA Champions League group stages. There are numerous financial and commercial benefits to clubs that participate in this competition. The current paper examines whether the seeding system operated by UEFA is hindering some lower ranked teams from qualification and, thus, the associated benefits. Design/methodology/approach -- Data were collected for all UEFA Champions League group stages betweenl999/2000 and 2013/2014. Data analysis techniques included Herfindahl-Hirschman Index to examine competitive balance and one-way ANOVAs to examine the impact of the current seeding system on club performance. Findings -- The findings suggest that there are flaws in the ranking and seeding system used by UEFA, as results show that the competition is competitively imbalanced at the group stage. Additionally, clubs that are continually placed in the highest seeding pot historically tend to accumulate more points and finish in a higher position in the group, thereby giving them a better opportunity to progress further in the competition. Research limitations/implications -- The study has implications for both the clubs competing in the Champions League, who will be affected by the seeding system, and UEFA themselves when considering the sporting integrity of their flagship competition. Originality/value -- To the authors' knowledge, this is the first paper of its kind to examine competitive balance in this competition, and the paper contributes new knowledge that extends the research undertaken in the field previously. [ABSTRACT FROM AUTHOR]

Copyright of Sport, Ethics & Philosophy is the property of Routledge and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Basketball is a sport that has a very long tradition in the territory of ex-Yugoslavia. The breakdown of the country led to a decrease in quality of basketball in the newly created countries. The unsteadiness of quality of the teams in national leagues resulted in formation of the Regional Adriatic Basketball League (ABA) in 2001. The main goal of this research was to measure the competitive balance in ABA, Spanish (ACB) and National Basketball Association League (NBA). The competitive balance was calculated by using Ratio of Standard Deviation index (RSD) and Herfindahl-Hirschman Index (HHI).The results of RSD showed that the most equable was ABA league, then came ACB league, while the most unequable was NBA league. The calculating of HHI index gave a different result. NBA is the most equable, then comes ABA league, and the last one is ACB league, which is the most unequable according to this parameter. ABA league has less quality than ACB and NBA league, but the results show that it is competitively the most balanced league. According to the RSD rates, NBA league is the most unequable. The main reason for that is a huge number of teams taking part in the league, which causes the unequable distribution of quality players. According to HHI, NBA is the most equable. Reason for that are different mechanisms whose goal is to reach and maintain the competitive balance. [ABSTRACT FROM AUTHOR]

In this article, we investigate whether the Australian Football League intervention policies coincided with a more even-playing field in the league, as captured by individual match margins. We find that only two out of the eight major policies implemented over the last hundred years are correlated with lower margin. [ABSTRACT FROM AUTHOR]

The NHL has realigned its conferences and divisions, and starting with the 2013-2014 season the Eastern Conference features 16 teams and the Western Conference features 14. Yet because there are eight playoff spots available in both conferences, teams in the West have a 57% probability of making the playoffs, compared to just 50% for teams in the East. As a result we should expect that, on average, the last team to make the playoffs in the West will have a worse record than the last playoff team in the East. We call the difference in points earned by the 8th seed in each conference the 'conference gap.' The purpose of this paper is to estimate the expected size of the conference gap under the new alignment. Using tens of thousands of simulated seasons, we demonstrate that the conference gap will be, on average, 2.74 points, meaning that Eastern Conference teams hoping to make the playoffs will have to win 1-2 games more than Western Conference playoff-hopefuls. We also show the 9th place team in the Eastern Conference has a better record than the 8th place Western team twice as often as the 9th best Western team has a better record than the East's 8th best. Our findings inform questions about competitive balance and equity in the NHL. [ABSTRACT FROM AUTHOR]

Competitive balance is a key issue for any professional sport league substantiated by its effect on demand for league games or other associated products. This work focuses on the measurement of between-seasons competitive balance, the longest time-wise dimension, which captures the relative quality of teams across seasons. The review of the existing indices examines their applicability in the context of European football. Given that domestic championships are multi-prized tournaments, as opposed to the more common North American unitary structure with a single prize, a set of specially designed indices that capture the complex structure of European football are introduced. An empirical investigation, using data from the English Premier League, further elucidates the main features of all appropriate indices by exploring their value and trend. It may be inferred that between-seasons competitive balance in England worsens through seasons mainly due to the very low ranking mobility of the top teams through seasons. [ABSTRACT FROM AUTHOR]

Beginning with the seminal work on the economics of sports (Rottenberg, 1956), concern over competitive balance has been a recurring theme. However, only brief and qualitative mention is given to issues of competitive balance in professional boxing (Sanderson and Siegfried, 2003; Tenorio, 2006), and the topic is only broached tangentially for amateur boxing in a study of home-field advantage in the Summer Olympic Games (Balmer, Nevill and Williams, 2003). Analyzing competitive balance in Olympic Boxing over its history and relative to major team sports, this study marks the first comprehensive quantitative analysis of competitive balance in amateur boxing. [ABSTRACT FROM AUTHOR]

Recent papers have enriched the conventional modeling of teams’ behavior through a game theoretic background at the competition level (introducing a contest success function). We take a step forward and consider contest on the talent market as well. Each team takes into account the fact that the price to be paid recruiting talent is a function that depends on both its own demand and the demands from the rival teams. For the two-team model, we show that the removal of the assumption that teams are price takers implies that the invariance proposition only survives if the price-function for talent is linear increasing. The extension to the n-team model shows that this result no longer holds; in fact, revenue sharing improves the competitive balance. More generally, an improvement in competitive balance is the most likely if one rules out the possibility of a very convex price-function. In addition revenue sharing can reduce the economic inefficiency of teams’ behavior, and so profits may increase. [ABSTRACT FROM AUTHOR]

This paper outlines a simple model of professional sports contests that can provide a number of useful insights into the operations of professional sports leagues. The model incorporates a concern for competitive balance on the part of fans and has the advantage that a number of league market structures can be analyzed using standard industrial organization techniques. The model can also be used to determine the effect of a number of league rules including revenue sharing, payroll caps, and luxury taxes on the respective demands for talented players. In addition, it can be shown that the model of professional sports contests developed here has a useful parallel with a standard model of differentiated products. [ABSTRACT FROM AUTHOR]

Several authors have recently suggested that an expanding labor pool has led to improvement in professional sports leagues' competitive balance. The basic premise is that a rise in team player options leads to less variability in player performance and therefore increased competition. The present work examines the initial step (i.e., the relationship between the in flux of foreign-born players and various measures of talent compression). The results suggest that the geographic diversity of today's baseball players has reduced variability in individual player performance. [ABSTRACT FROM AUTHOR]

A new interseasonal measure of competitive balance in a sports league is presented. It is based on a Markov model of a team's probability of qualifying for postseason play given the performance of the team in the previous season. Transitional probabilities are estimated for Major League Baseball teams before and after the 1994 players' strike. The results indicate that there has been a significant deterioration in competitive balance for the seasons following the strike. Probability density functions for the prestrike and poststrike eras are also presented. [ABSTRACT FROM AUTHOR]

There are situations in which a monopoly solution cannot be reached. In these cases, which situation represents the maximum concentration (minimum competitive balance)? It is a relevant question, given that in sports economics, measuring the competitive balance of a league is done through normalized indices. These indices require that the maximum level of concentration be known. Until now, the distribution of results that generates the maximum level of concentration has been identified in the literature as Complete cascade distribution. However, if the scoring system used does not fulfil the stability condition, which implies that the total number of points of a championship is constant, it can be demonstrated that the Complete cascade distribution does not generate the maximum level of concentration. This is the case, for example, with major European football leagues. In this article, we constructed a perfectly unbalanced distribution, which we called a Truncated cascade distribution. This distribution generates the maximum concentration level. Therefore, if we do not use Truncated cascade distribution, there is an overestimation of the concentration measured with normalized indices. Then, the calculated competitive balance will be wrong, that is, underestimated. We provided a spreadsheet for identifying this distribution. [ABSTRACT FROM AUTHOR]

Mathematical analysis of rankings is essential for a wide range of scientific, public, and industrial applications (e.g., group decision-making, organizational methods, R&D sponsorship, recommender systems, voter systems, sports competitions, grant proposals rankings, web searchers, Internet streaming-on-demand media providers, etc.). Recently, some methods for incomplete aggregate rankings (rankings in which not all the elements are ranked) with ties, based on the classic Kendall's tau coefficient, have been presented. We are interested in ordinal rankings (that is, we can order the elements to be the first, the second, etc.) allowing ties between the elements (e.g., two elements may be in the first position). We extend a previous coefficient for comparing a series of complete rankings with ties to two new coefficients for comparing a series of incomplete rankings with ties. We make use of the newest definitions of Kendall's tau extensions. We also offer a theoretical result to interpret these coefficients in terms of the type of interactions that the elements of two consecutive rankings may show (e.g., they preserve their positions, cross their positions, and they are tied in one ranking but untied in the other ranking, etc.). We give some small examples to illustrate all the newly presented parameters and coefficients. We also apply our coefficients to compare some series of Spotify charts, both Top 200 and Viral 50, showing the applicability and utility of the proposed measures. [ABSTRACT FROM AUTHOR]