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Mathematical Models to Measure the Variability of Nodes and Networks in Team Sports
Fernando Martins1,2,3, Ricardo Gomes1,3,4, Vasco Lopes5
1Instituto Politécnico de Coimbra, ESEC, UNICID-ASSERT, 3030-329 Coimbra, Portugal.
Entropy (Basel, Switzerland)
|August 27, 2021
Summary
This study introduces new mathematical models for team sports analysis, combining information and probability theory for robust network analysis. These models enhance understanding of player interactions and team passing capacity.
Area of Science:
- Sports Science
- Network Analysis
- Information Theory
Background:
- Pattern analysis is key in team sports performance, often using information theory.
- Bayesian methods are applied, but their link with information theory is evolving.
Purpose of the Study:
- To present novel mathematical concepts integrating information and probability theory for team sports network analysis.
- To offer a more robust method for analyzing interaction variability in team sports.
Main Methods:
- Utilizing transition matrices from Markov chains and adjacency matrices of networks with 'n' nodes.
- Developing new models for individual and collective variability rates and indexes.
- Assessing overall passing capacity within a sports network.
Main Results:
- The models provide robust analysis of interaction variability in team sports.
- Quantified individual and collective rates and indexes of total variability.
- Demonstrated the application of these models using data from the UEFA 2020/2021 Champions League Final.
Conclusions:
- The proposed mathematical framework offers a robust approach to network analysis in team sports.
- These methods enhance the understanding of player and team dynamics and passing capacity.
- The study provides a foundation for advanced performance analysis in team sports.
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