Metric Dimensions of March Madness Brackets

TL;DR

This paper investigates the minimum number of brackets needed to accurately reconstruct the outcomes of a March Madness tournament, providing exact bounds applicable to various scoring systems and tournament structures.

Contribution

It establishes the exact minimum number of brackets required to determine tournament results for any March Madness-style event, regardless of scoring methods.

Findings

Derived exact minimum bracket counts for tournament reconstruction

Provided bounds for arbitrary single-elimination tournaments

Applicable to various scoring systems and tournament formats

Abstract

Say you and some friends decide to make brackets for March Madness and are told how each of your brackets scored. The question we ask is: when can you determine how the actual tournament went given your scores? We determine the exact minimum number of brackets needed to do this for any March Madness-style tournament regardless of the scoring system used, and more generally we prove effective bounds for the problem for arbitrary single-elimination tournaments.