Using Multilevel Models to Compare Performance Prediction and Characterization Abilities Between Power-Law and Critical-Speed Models in Middle- and Long-Distance Running.

Abstract

Purpose: Speed-duration relationships are widely used to predict performances and characterize athletes. The critical-speed (CS) and power-law (PL) models share the spotlight for practitioners. Therefore, the present study compares performance prediction accuracy and characterization abilities between PL and CS models using a multilevel model (MLM) for middle- and long-distance runners.

Methods: Data from 184,755 performances by 52,847 athletes from France, Great Britain, Italy, Poland, and Switzerland across 6 events (400-10,000 m running) were computed. MLMs were developed based on the hierarchical structure of the data. Prediction accuracy was evaluated using mean absolute error and mean absolute relative error (MARE) for time and speed. Athletes were characterized by model-derived parameters: speed (S), endurance (E), anaerobic capacity (D'), and CS.

Results: The PL MLM (MAREtime = 1.32% and MAREspeed = 1.32%) outperformed the CS MLM (MAREtime = 6.87% and MAREspeed = 9.1%) on prediction accuracy. Long-distance specialists expressed higher E and CS values, whereas middle-distance runners showed higher S values. The 1500- to 5000-m specialists relied on higher D'. Gender differences highlighted lower S, D', and CS for female athletes but comparable E values to male athletes. International-level athletes demonstrated maximized S, E, and CS in accordance with their specialization.

Conclusions: MLMs enhance understanding of speed-duration relationships across clusters, gender, and performance levels. Model-derived parameters provide valuable insights for athlete profiling. Finally, the PL MLM is a reliable prediction tool.