A New Linear Two-State Dynamical Model for Athletic Performance Prediction in Elite-Level Soccer Players

Recent advancements in wearable technology have allowed researchers to collect high-resolution data on athletes’ workloads and performance, paving the way for more accurate mathematical models in sports science. In this paper, inspired by the modeling of heart rate during exercise, we introduce a novel linear, time-varying, two-state discrete-time dynamical model for predicting athletic performance in elite-level soccer players. Model parameters are estimated via the Differential Evolution optimization algorithm, and GPS-derived metrics such as metabolic power and equivalent distance index are incorporated. The model originally accounts for complex interactions between a performance-related state variable and a second lumped variable, whose dynamics are intertwined. This model was compared to the most effective deterministic (though uncertain) one in the literature, namely the (nonlinear) Busso model. Results, concerning two professional soccer players over a half-season period, show that the proposed model outperforms the traditional approach in estimation and predictive accuracy, with significantly higher correlation coefficients and lower estimation and prediction errors across all players. These findings suggest that integrating two-state dynamics and fine-grained GPS metrics provides a more biologically realistic framework for load monitoring in team sports. The proposed model thus represents a powerful tool for training optimization and athlete readiness assessment, with potential applications in real-time decision support systems for coaching staff. By predicting the effects of training load on future performance, it might also contribute to injury risk reduction and the prevention of maladaptive responses to excessive workload.