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Entropy Analysis of Soccer Dynamics.

António M Lopes1, J A Tenreiro Machado2

  • 1UISPA-LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal.

Entropy (Basel, Switzerland)
|December 3, 2020
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Summary
This summary is machine-generated.

This study uses information theory and fractional calculus to analyze national soccer league dynamics. Complex systems analysis reveals team performance patterns through goal data, visualized in 3D maps.

Keywords:
Jensen–Shannon divergencecomplex systemsentropyfractional calculusmultidimensional scalingmutual information

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Area of Science:

  • Complex Systems Science
  • Information Theory
  • Fractional Calculus
  • Sports Analytics

Background:

  • Soccer leagues exhibit complex dynamics influenced by team performance.
  • Traditional analysis may not fully capture the intricate state changes within a league season.
  • Understanding these dynamics can offer insights into competitive balance and performance trends.

Purpose of the Study:

  • To apply information-theoretic and fractional calculus tools to model soccer league dynamics.
  • To analyze the state of a soccer league, represented by team goals scored.
  • To visualize and interpret the complex system behavior of a league season.

Main Methods:

  • Treating a soccer league season as a complex system (CS) with states observed at discrete time instants (rounds).
  • Utilizing entropy, mutual information, and Jensen-Shannon divergence to process the CS state (goals scored).
  • Employing multidimensional scaling to generate 3-D maps for visualizing CS behavior and round-to-round changes.

Main Results:

  • The study successfully visualizes the complex dynamics of a national soccer league season.
  • 3-D maps generated by multidimensional scaling provide an interpretable representation of league states.
  • The relative positioning of points (rounds) on the maps allows for direct interpretation of system evolution.

Conclusions:

  • Information-theoretic and fractional calculus tools are effective for analyzing the dynamics of complex systems like soccer leagues.
  • The visualization method offers a novel approach to understanding competitive balance and performance trajectories within a sports league.
  • This framework can be extended to analyze other competitive systems or complex data with discrete states.