March Madness and the Office Pool

TLDR

March Madness is the annual U.S. men’s college basketball tournament, and across the country many office pools aim to predict as many game winners as possible to maximize points. The study investigates how to compute the mean and variance of correctly predicted wins (or total points) in office pools and to determine optimal predictions. The authors derive formulas for single‑elimination tournaments, apply them to random and Markov models, and use these to identify optimal predictions based on various probability models.

Abstract

March brings March Madness, the annual conclusion to the U.S. men's college basketball season with two single elimination basketball tournaments showcasing the best college teams in the country. Almost as mad is the plethora of office pools across the country where the object is to pick a priori as many game winners as possible in the tournament. More generally, the object in an office pool is to maximize total pool points, where different points are awarded for different correct winning predictions. We consider the structure of single elimination tournaments, and show how to efficiently calculate the mean and the variance of the number of correctly predicted wins (or more generally the total points earned in an office pool) for a given slate of predicted winners. We apply these results to both random and Markov tournaments. We then show how to determine optimal office pool predictions that maximize the expected number of points earned in the pool. Considering various Markov probability models for predicting game winners based on regular season performance, professional sports rankings, and Las Vegas betting odds, we compare our predictions with what actually happened in past NCAA and NIT tournaments. These models perform similarly, achieving overall prediction accuracies of about 58%, but do not surpass the simple strategy of picking the seeds when the goal is to pick as many game winners as possible. For a more sophisticated point structure, however, our models do outperform the strategy of picking the seeds.