Research Papers

Hassan Rafique, Shane Sanders

This study evaluates modern playoff and tournament designs across global sports, an important aspect of League and Tournament success. Using axiomatic theory, Bayesian modeling, and large-scale simulation, we assess tournament formats against core economic criteria—efficacy, fairness, and attractiveness—showing that the ADBC classic single-elimination final-four bracket is optimal within its class but dominated once hybrid designs, such as the Page Playoff System, are permitted. The PPS has been gaining traction in major sports leagues such as the NBA (Play-In Tournament) and top professional cricket leagues. It adds a top-bracket, double-elimination provision to a single-elimination final-four format of middling efficiency to dominate the efficiency of all single-elimination formats. Our analysis combines closed-form theoretical probability derivations with Monte Carlo simulation experiments—up to one million tournament realizations—parameterized using Bradley–Terry and Thurstone–Mosteller models of team strength. Results show that the Page Playoff System strictly increases the probability that the strongest teams win the tournament while preserving ordinal fairness, even under moderate seeding inefficiencies. These gains arise from top-bracket double-elimination concessions, which sharply reduce premature elimination of elite teams relative to optimized single-elimination formats. Applying the same simulation logic to the College Football Playoff, we find that the 2024 conference-champion bye rule induced a bimodal distortion in championship probabilities, weakening both fairness and efficacy. Simulated counterfactuals confirm that the CFP’s 2025 shift to straight seeding restores a meritocratic mapping between team strength and postseason success. This research highlights the need for robust probabilistic modeling in the design process. By conducting simulation analyses that adjust constraints, administrators can balance entertainment value, revenue, and fairness, ensuring the tournament maintains the sport's integrity while satisfying fan expectations.