The Madness of Multiple Entries in March Madness

TL;DR

This paper investigates multi-entry strategies for March Madness betting pools, developing algorithms to maximize expected scores and demonstrating a heuristic that significantly improves winning chances in real-world scenarios.

Contribution

The paper introduces an exact dynamic programming approach and a novel heuristic for optimizing multi-entry betting strategies in single-elimination tournaments.

Findings

The heuristic outperforms previous methods in experiments.

The best 100-entry solution has a 2.2% chance of winning a $1 million prize.

Structural properties of the problem inform effective solution techniques.

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.