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Shannon Entropy and Herfindahl-Hirschman Index as Team's Performance and Competitive Balance Indicators in Cyclist
1School of Business, University of Leicester, Brookfield, Leicester LE2 1RQ, UK.
Entropy (Basel, Switzerland)
|June 28, 2023
Summary
This study introduces Shannon entropy and the Herfindahl-Hirschman index to measure team sporting value and competitive balance in professional cycling races. Focusing on finishing riders provides a more objective assessment of team performance.
Area of Science:
- Sports Science
- Statistical Mechanics
- Network Science
Background:
- Limited research exists on applying entropy concepts to sports competitions.
- Quantifying team sporting value and competitive balance in multi-stage races presents challenges.
- Objective performance metrics are crucial for analyzing team dynamics in professional sports.
Purpose of the Study:
- To apply Shannon intrinsic entropy (S) as a measure of team sporting value.
- To utilize the Herfindahl-Hirschman index (HHi) for assessing team competitive balance in cycling.
- To establish a more objective method for evaluating team performance in multi-stage races.
Main Methods:
- Employed Shannon intrinsic entropy (S) and Herfindahl-Hirschman index (HHi).
- Analyzed data from the 2022 Tour de France and 2023 Tour of Oman.
- Utilized classical and novel ranking indices based on the best three finishing riders' times and places.
Main Results:
- The constraint 'only finishing riders count' yields a more objective team performance measure.
- Graphical analysis revealed Feller-Pareto distributions, suggesting self-organized processes in team performance.
- Demonstrated distinct team performance levels within the analyzed cycling races.
Conclusions:
- Objective scientific measures can be effectively applied to sport team competitions.
- The proposed entropy and HHi-based approach offers a robust method for evaluating team value and balance.
- The findings suggest potential for probabilistic forecasting in professional cycling.
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