Multilayer network framework and metrics for table tennis analysis: Integrating network science, entropy, and machine learning

This study introduces two novel metrics within table tennis technical-tactical networks: technical decision-making style (TDS) and connecting technical style (CTS), inspired by the entropy concept, to quantify players' technical-tactical styles. This study proposes a multilayer technical-tactical network framework to capture interactive information and technique-to-technique confrontations between players. Additionally, we develop four new metrics—absorbing rate, releasing rate, stalemate rate, and usage rate—based on three states within table tennis matches: scoring, losing, and stalemate, to analyze inter-links within these networks. The champion table tennis player, who won gold medals in both the 2016 Rio Olympics and the 2020 Tokyo Olympics, and his opponents were analyzed in 5054 technical actions during these events. Metrics such as TDS, CTS, out-degree centrality (ODC), and in-degree centrality (IDC) within the networks were calculated. We also created datasets for TDS, CTS, ODC, and IDC and employed six machine learning algorithms for modeling. The results indicate that nodes utilizing TDS and CTS demonstrate superior predictive accuracy for game outcomes compared to those using ODC and IDC. SHAP analysis revealed the feature importance in the best-performing models for TDS and CTS, revealing non-linear relationships between the TDS and CTS values of each key node and game outcomes. The analysis of the multilayer network offers insights into the dynamic interactions between the champion player and his opponents, enhancing our understanding of the key factors influencing match victories. By integrating network science, entropy, and machine learning, this study presents a comprehensive framework and practical metrics for match analysis, with potential implications in performance analyses of other racket sports.