Data-driven budget optimization for team sports

Budget optimization in team sports is critical for achieving competitive success while maintaining financial sustainability. This paper examines budget optimization in professional basketball and proposes a data-driven framework for roster construction under financial constraints, contributing to the sparse literature on optimization methods applied to European club sports. The case study investigates how to construct a maximally competitive EuroLeague basketball team, measured by aggregate PIR, within a fixed €7 million budget constraint. The proposed framework integrates Mixed-Integer Linear Programming, machine learning models, and Monte Carlo simulation to evaluate roster quality and estimate team performance across 1000 simulated seasons. Team performance is assessed using the Performance Index Rating (PIR), the official EuroLeague player evaluation metric, and match outcome probabilities derived from a Logistic Regression model trained on three seasons of historical data. Simulation results suggest that budget-optimized rosters may achieve championship probabilities of approximately 8%–9% (95% CI: 7%–11%), despite significantly lower budgets than established clubs. These are indicative estimates and have not been externally validated. The framework offers decision support for budget-constrained teams, though its applicability is subject to limitations including salary data uncertainty, the normality assumption in simulation, and the exclusion of dynamic factors such as injuries and player development.