Using Conformal Win Probability to Predict the Winners of the Cancelled 2020 NCAA Basketball Tournaments

TL;DR

This paper develops conformal predictive distributions to estimate the likelihood of NCAA basketball teams making the tournament and winning March Madness, providing better-calibrated probabilities than traditional regression methods.

Contribution

It introduces conformal win probabilities for NCAA tournaments, offering a novel, well-calibrated approach that outperforms linear and logistic regression in predictive accuracy.

Findings

Conformal win probabilities are better calibrated than traditional methods.

The approach requires fewer distributional assumptions.

Probabilities of tournament qualification and victory are effectively estimated.

Abstract

The COVID-19 pandemic was responsible for the cancellation of both the men's and women's 2020 National Collegiate Athletic Association (NCAA) Division 1 basketball tournaments. Starting from the point at which the Division 1 tournaments and any unfinished conference tournaments were cancelled, we deliver closed-form probabilities for each team of making the Division 1 tournaments, had they not been cancelled, aided by use of conformal predictive distributions. We also deliver probabilities of a team winning March Madness, given a tournament bracket. We then compare single-game win probabilities generated with conformal predictive distributions, aptly named conformal win probabilities, to those generated through linear and logistic regression on seven years of historical college basketball data, specifically from the 2014-2015 season through the 2020-2021 season. Conformal win probabilities are shown to be better calibrated than other methods, resulting in more accurate win probability estimates, while requiring fewer distributional assumptions.