Advanced feature engineering in Acute:Chronic Workload Ratio (ACWR) calculation for injury forecasting in elite soccer.

Controlling training monotony and monitoring external workload using the Acute:Chronic Workload Ratio (ACWR) is a common practice among elite soccer teams to prevent non-contact injuries. However, recent research has questioned whether ACWR offers sufficient predictive power for injury prevention in elite competition settings. In this paper, we propose a novel feature engineering framework for training load management, inspired by bilinear modeling and signal processing principles. Our method represents external workload variables, derived from GPS data, as discrete time series, which are then integrated into a temporal matrix termed the Footballer Workload Footprint (FWF). We introduce calculus-based techniques-applying integral and differential operations-to derive two representations from the FWF matrix: a cumulative workload matrix ([Formula: see text]) generalizing Acute Workload (AW), and a temporal variation matrix ([Formula: see text]) generalizing Chronic Workload (CW) and formulating the ACWR. Our approach makes traditional workload metrics suitable for modern machine learning. Using real-world data from an elite soccer team competing in LaLiga (Spain's top division) and UEFA tournaments, we conducted exploratory and confirmatory analyses comparing multivariate models trained on FWF-derived features against those using traditional ACWR calculations. The FWF-based models consistently outperformed baseline methods across key performance metrics-including the Area Under the ROC Curve (ROC-AUC), Precision-Recall AUC (PR-AUC), Geometric Mean (G-Mean), and Accuracy-while reducing Type I and Type II errors. Tested on temporally independent holdout data, our top model performed robustly across all metrics with 95% confidence intervals. Permutation tests revealed a significant association between FWF matrices and injury risk, supporting the empirical validity of our approach. Additionally, we introduce an interpretability framework based on heatmap visualizations of the FWF's cumulative and temporal variations, enhancing explainability. These findings indicate that our approach offers a robust, interpretable, and generalizable framework for sports science and medical professionals involved in injury prevention and training load monitoring.