EXPRESS: Simplifying the Madness of Multiple Entries in March Madness

Multi-entry betting pools for single-elimination tournaments create a portfolio-design problem: a participant may submit several brackets whose scores are highly dependent, while payouts are typically concentrated on the best-performing entry. Motivated by March Madness pools, we study the problem of selecting a portfolio of brackets that maximizes the expected maximum score (EMS) across entries. This objective captures the top-heavy nature of such contests without requiring a model of opponents' bracket choices, which is difficult to estimate reliably in a tournament played only once per year. We first establish computational and structural properties of the EMS objective. Exact EMS evaluation is #P-hard in general, although it is polynomial-time computable for any fixed number of entries with an exponent that grows with the portfolio size. For two entries, EMS decomposes into single-entry expected-score terms and an expected absolute score-gap term, making explicit the trade-off between selecting individually strong brackets and diversifying across outcomes. These insights motivate two sample average approximation algorithms: an entry-by-entry method based on marginal EMS contributions and a round-by-round method that exploits the geometrically increasing scoring weights in March Madness by emphasizing late-round diversification. Computational experiments using historical tournament data show that the round-by-round method scales reliably and outperforms direct SAA and an entropy-based benchmark for larger portfolios. In a real high-stakes DraftKings pool from the 2023 tournament, our 100-entry portfolio would have achieved a 2.54% probability of attaining a maximum-scoring entry, with higher expected profit than the portfolios submitted by several elite professional bettors.