Time-Weighted Result-Based Strength Indicators from Head-to-Head Outcomes: An Application to Trotter (Harness) Racing

We propose a general methodology for constructing dynamic performance indicators (or strength metrics) in any sport that relies on comparative outcomes among competitors, using chronological positional data. Specifically, we develop a family of strength indicators for harness trotting races based on time-weighted, head-to-head results. Using the official Balearic trotting records (1990–2023), we construct win, draw, and confrontation matrices up to each event and apply a triweight kernel to reduce the influence of older results. From these matrices, we derive a family of five bounded, interpretable indicators on the interval $[0,1]$: an overall average win rate, a category-adjusted version, and three distance-specific versions (short, medium, and long). Indicator validation is performed via predictive validation, employing regularized logistic regression models (Elastic Net) based on indicator differences between horse pairs. Standard metrics (accuracy, calibration, discrimination, and Brier score) are used for the validation analysis. The results confirm that the indicators are coherent, stable, and interpretable, demonstrating that the generic construction procedure yields robust outcomes. We conclude that these indicators establish a solid and easily updatable foundation for developing dynamic ranking systems and practical selection/handicap procedures in trotting.