An Extension of the Pythagorean Expectation for Association Football
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Howard H Hamilton
This publication presents a formulation of an extension to the Pythagorean expectation for association football and other sports in which a draw result is a nontrivial event. Instead of estimating win percentage as in baseball, the extended Pythagorean estimates points won per game. A least-squares algorithm is used to fit offensive and defensive goal distributions to a three-parameter Weibull distribution, of which the parameter of interest is the Pythagorean exponent. Further analysis reveals that the league Pythagorean exponent remains stable across multiple leagues in the same calendar year and within a single league over multiple seasons, which gives support to the notion of a “universal” Pythagorean exponent. Application of the extended Pythagorean to results of domestic soccer leagues in Europe, Asia, and the Americas shows excellent agreement between goal statistics and league records for a majority of teams, and it indicates the teams that strongly overperform or underperform with respect to their expected performance.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
Artikel in diesem Heft
- Conference Paper
- Uncovering Europe's Best Goalscorers from the 2009-2010 Season
- Dynamic Effort, Sustainability, Myopia, and 110% Effort
- The Intra-Match Home Advantage in Australian Rules Football
- The Relationship between Leader Experience and Team Performance in Cross-Sectional and Longitudinal Designs
- Stratified Odds Ratios for Evaluating NBA Players Based on their Plus/Minus Statistics
- Dependence Relationships between On Field Performance, Wins, and Payroll in Major League Baseball
- Optimal Dynamic Clustering Through Relegation and Promotion: How to Design a Competitive Sports League
- Perception ? Reality: Analyzing Specific Allegations of NBA Referee Bias
- NFL Prediction using Committees of Artificial Neural Networks
- An Alternative to the NFL Draft Pick Value Chart Based upon Player Performance
- Monte Carlo Simulation for High School Football Playoff Seed Projection
- Defining the Performance Coefficient in Golf: A Case Study at the 2009 Masters
- Reconsideration of the Best Batting Order in Baseball: Is the Order to Maximize the Expected Number of Runs Really the Best?
- Never Too Late to Win
- An Extension of the Pythagorean Expectation for Association Football
- Pitcher Accuracy Through Catcher Spotting: Assessing Rater Reliability
- Valuing Nostalgia: The Case of the Topps 1957 Baseball Cards
Artikel in diesem Heft
- Conference Paper
- Uncovering Europe's Best Goalscorers from the 2009-2010 Season
- Dynamic Effort, Sustainability, Myopia, and 110% Effort
- The Intra-Match Home Advantage in Australian Rules Football
- The Relationship between Leader Experience and Team Performance in Cross-Sectional and Longitudinal Designs
- Stratified Odds Ratios for Evaluating NBA Players Based on their Plus/Minus Statistics
- Dependence Relationships between On Field Performance, Wins, and Payroll in Major League Baseball
- Optimal Dynamic Clustering Through Relegation and Promotion: How to Design a Competitive Sports League
- Perception ? Reality: Analyzing Specific Allegations of NBA Referee Bias
- NFL Prediction using Committees of Artificial Neural Networks
- An Alternative to the NFL Draft Pick Value Chart Based upon Player Performance
- Monte Carlo Simulation for High School Football Playoff Seed Projection
- Defining the Performance Coefficient in Golf: A Case Study at the 2009 Masters
- Reconsideration of the Best Batting Order in Baseball: Is the Order to Maximize the Expected Number of Runs Really the Best?
- Never Too Late to Win
- An Extension of the Pythagorean Expectation for Association Football
- Pitcher Accuracy Through Catcher Spotting: Assessing Rater Reliability
- Valuing Nostalgia: The Case of the Topps 1957 Baseball Cards
