Application and evaluation of PCA-CA composite model for technical effectiveness in table tennis matches

This study aims to scientifically evaluate the competitive performance of table tennis athletes in matches, examine the reliability and practical value of the "New Four-Phase Index Statistical Method" in statistical analysis of technical and tactical indicators, and establish a new evaluation system for technical and tactical indicators. A total of 40 significant international men's table tennis matches were selected for analysis. The video analysis method was employed to calculate the scoring rates and utilization rates of the eight sub-observational indicators within the "New Four-Phase Index." Subsequently, a table tennis technical effectiveness indicator system was established. Principal component analysis (PCA) was applied in conjunction with cluster analysis (CA) to comprehensively evaluate the competitive strength of each table tennis match and to select matches with similar strengths. The technical effectiveness data of the "New Four-Phase Index" were suitable for principal component model analysis (KMO > 0.5, P < 0.01). Following the principle that eigenvalues greater than or equal to 1 should be retained in principal component analysis, four principal components were extracted, reflecting 75.343% of the original variable information. Additionally, the overall rankings derived from the principal components analysis of the 40 matches were generally consistent with the match results. However, there were instances of imbalance between the total score and the match outcome. Cluster analysis categorized the 40 matches into three comprehensive competitive strength classes: "fluctuating competitive level," "consistent competitive level," and "weaker competitive level." Variance analysis revealed statistically significant differences among these three categories (P < 0.05). The PCA-CA comprehensive analysis model provided strong validation for the empirical research of competitive performance in table tennis matches. It effectively reflects the comprehensive competitive level of athletes in each match, offering valuable guidance to coaches for understanding their athletes' competitive states and formulating appropriate match strategies.