Bayesian Biostatistical and Physiological Modeling for Optimal Triathlon Relay Team Assembly from Historical Results

We present a unified biostatistical and Bayesian physiological modeling framework for assembling optimal triathlon relay teams using historical results. The performance of athletes and disciplines is first captured through the time–distance scaling of the power law (T = aDb), where a encodes the baseline physiological capacity and b the endurance-fatigue exponent. To enhance robustness under sparse observations, we extend this with a hierarchical Bayesian model that pools information across athletes while producing posterior distributions for performance parameters. This allows uncertainty-aware projections to canonical formats (Sprint, Olympic, Half, Ironman) and probabilistic relay optimization. Our approach outputs both deterministic rosters and posterior selection probabilities, bridging statistical rigor with actionable decision support for coaches and sport scientists. The pipeline yields robust projections and actionable rosters.