The Madness of Multiple Entries in March Madness

TL;DR

This work tackles the challenge of maximizing the expected score of the best entry (EMS) in multi-entry March Madness betting pools with top-heavy payouts. It introduces an exact dynamic programming method to compute EMS for a fixed entry set and develops scalable simulation-based estimation, enabling practical evaluation on real-world data. Through structural analysis (submodularity, diversification) and multiple optimization algorithms (SAA, SIP, PROP, PROP+), the study demonstrates that problem-specific heuristics, especially PROP+, consistently outperform alternatives, achieving notable EMS gains and real-world win probabilities (e.g., 2.2% in a DraftKings pool). The findings illuminate how diversification and round-aware strategies can substantially improve odds of success in high-stakes, single-elimination tournaments, offering actionable guidance for bettors and a framework for future computational refinements.

Abstract

This paper explores multi-entry strategies for betting pools related to single-elimination tournaments. In such betting pools, participants select winners of games, and their respective score is a weighted sum of the number of correct selections. Most betting pools have a top-heavy payoff structure, so the paper focuses on strategies that maximize the expected score of the best-performing entry. There is no known closed-formula expression for the estimation of this metric, so the paper investigates the challenges associated with the estimation and the optimization of multi-entry solutions. We present an exact dynamic programming approach for calculating the maximum expected score of any given fixed solution, which is exponential in the number of entries. We explore the structural properties of the problem to develop several solution techniques. In particular, by extracting insights from the solutions produced by one of our algorithms, we design a simple yet effective problem-specific heuristic that was the best-performing technique in our experiments, which were based on real-world data extracted from recent March Madness tournaments. In particular, our results show that the best 100-entry solution identified by our heuristic had a 2.2% likelihood of winning a $1 million prize in a real-world betting pool.

Figures (23)

• Figure 1: 2023 NCAA Men's Tournament Bracket
• Figure 2: Sport Betting Legalization Status as of November 7, 2023
• Figure 3: Example Four-Team Bracket Structure and Feasible Bracket Outcomes
• Figure 4: Probability of Winning vs Selection Distribution of G-SAA by Round
• Figure 5: Width of the 95% CI for 2-entry and 100-entry Solutions for Different Sample Sizes

Theorems & Definitions (18)

• Theorem 1
• Proposition 1
• Remark 1
• Remark 2
• Remark 3
• Theorem 2
• Proposition 2
• Proposition 3
• proof : Proof of Proposition \ref{['prop:submodular']}:
• proof : Proof of Proposition \ref{['prop:det_lb']}: