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

2014 ◽  
Vol 53 (1) ◽  
pp. 731-744 ◽  
Author(s):  
P. Dorian Owen ◽  
Nicholas King
Keyword(s):  
Competitive Balance ◽  
Season Length ◽  
Sports Leagues

Measuring competitive balance in sports

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Matthew Doria ◽  
Barry Nalebuff
Keyword(s):  
General Model ◽  
Competitive Balance ◽  
Season Length ◽  
Sports Leagues ◽  
Variance Estimates ◽  
Insight Into ◽  
Do So

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.

A Bias-Corrected Estimator of Competitive Balance in Sports Leagues

2018 ◽  
Vol 20 (4) ◽  
pp. 479-508 ◽  
Author(s):  
Young Hoon Lee ◽  
Yongdai Kim ◽  
Sara Kim
Keyword(s):  
Standard Deviation ◽  
Competitive Balance ◽  
Season Length ◽  
Sample Standard Deviation ◽  
Mean Squared Errors ◽  
Premier League ◽  
Conventional Measure ◽  
Sports Leagues ◽  
Korea Baseball Organization ◽  
English Premier League

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.

Competitive balance with unbalanced schedules

2019 ◽  
Vol 15 (3) ◽  
pp. 239-260 ◽  
Author(s):  
Young Hoon Lee ◽  
Yongdai Kim ◽  
Sara Kim
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Time Series Analysis ◽  
Unbiased Estimator ◽  
Statistical Approach ◽  
Empirical Studies ◽  
Competitive Balance ◽  
Season Length ◽  
Series Analysis ◽  
Winning Percentage

Abstract Many empirical studies on competitive balance (CB) use the ratio of the actual standard deviation to the idealized standard deviation of win percentages (RSD). This paper suggests that empirical studies that use RSD to compare CB among different leagues are invalid, but that RSD may be used for time-series analysis on CB in a league if there are no changes in season length. When schedules are unbalanced and/or include interleague games, the final winning percentage is a biased estimator of the true win probability. This paper takes a mathematical statistical approach to derive an unbiased estimator of within-season CB that can be applied to not only balanced but also unbalanced schedules. Simulations and empirical applications are also presented, which confirm that the debiasing strategy to obtain the unbiased estimator of within-season CB is still effective for unbalanced schedules.

Competitive Balance in Sports Leagues

2002 ◽  
Vol 3 (2) ◽  
pp. 111-121 ◽  
Author(s):  
Andrew S. Zimbalist
Keyword(s):  
Competitive Balance ◽  
Sports Leagues

The Impact of Free Agency on Competitive Balance in North American Professional Team Sports Leagues

2006 ◽  
Vol 20 (3) ◽  
pp. 345-365 ◽  
Author(s):  
Joel Maxcy ◽  
Michael Mondello
Keyword(s):  
National Football League ◽  
Team Sports ◽  
National Hockey League ◽  
Competitive Balance ◽  
Free Agency ◽  
Free Agent ◽  
Professional Team Sports ◽  
Dependent Variables ◽  
Sports Leagues ◽  
The Impact

Free agency was reintroduced to professional team sport leagues in the 1970s. Sport enthusiasts expressed concern that competitive balance would diminish as star players congregated to large market cities. However, the economic invariance principle rejects this notion, indicating that balance should remain unchanged. This article empirically examines the effects of changes in free agent rules on competitive balance over time in the National Basketball Association (NBA), National Football League (NFL), and National Hockey League (NHL). Regression analysis using within-season and between-season measures of competitive balance as dependent variables provides mixed results. The NFL and NHL provide evidence that an aspect of competitive balance has improved, but results from the NBA indicate that balance has worsened since the introduction of free agency. We conclude that the ambiguous results suggest that the effects are not independent, but instead depend on the interaction of free agent rights with other labor market and league rules.

Optimal Competitive Balance in Single-Game Ticket Sports Leagues

2010 ◽  
Vol 11 (6) ◽  
pp. 587-601 ◽  
Author(s):  
Rodney Fort ◽  
James Quirk
Keyword(s):  
Competitive Balance ◽  
Sports Leagues

scholarly journals Competitive Balance and Revenue Sharing in Sports Leagues With Utility-Maximizing Teams

2011 ◽  
Vol 12 (3) ◽  
pp. 284-308 ◽  
Author(s):  
Helmut M. Dietl ◽  
Martin Grossmann ◽  
Markus Lang
Keyword(s):  
Revenue Sharing ◽  
Competitive Balance ◽  
Sports Leagues

Individual Team Incentives and Managing Competitive Balance in Sports Leagues: An Empirical Analysis of Major League Baseball

2008 ◽  
Vol 45 (5) ◽  
pp. 535-549 ◽  
Author(s):  
Michael Lewis
Keyword(s):  
Programming Model ◽  
Major League Baseball ◽  
Revenue Sharing ◽  
Local Market ◽  
Competitive Balance ◽  
Structural Dynamic ◽  
Local Revenue ◽  
Major League ◽  
Sports Leagues ◽  
The Impact

Major League Baseball and other professional sports leagues have long been concerned with competitive imbalances caused by differences in local revenues. The fear is that in the absence of salary caps or other regulatory mechanisms, smaller-market teams will be unable to remain competitive. This research uses a structural dynamic programming model to analyze ownership's payroll investment decisions. This model estimates the relationship between optimal payrolls and local-market populations and the influence of long-term customer equity dynamics on payroll investments. In addition, the author analyzes the impact of a recent policy intervention that implemented revenue transfers from high-local-revenue markets to low-local-revenue markets. The statistical results indicate that market population has a significant impact on the value of a team's payroll investments. For example, optimal payrolls double as the population increases from 2.5 million to 7.5 million. Furthermore, rather than improving competitive balance, the adoption of revenue sharing has decreased the incentives for small-market teams to remain competitive. The author uses the estimation results to evaluate alternative approaches to managing competitive balance. Specifically, the results suggest that basing revenue-sharing payments on local-market population and (higher) attendance rates reduces payroll dispersion.

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