March Madness and the Office Pool

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.

A logistic regression/Markov chain model for NCAA basketball

“…As Breiter and Carlin [4] and Kaplan and Garstka [13] pointed out, picking the highest-ranked available team might not always be the best strategy. Their models require estimates of team-vs.-team win probabilities in order to find a pool strategy.…”

“…Carlin [7], Breiter and Carlin [4], and Kaplan and Garstka [13] use a simple method for determining team-vs.-team win probabilities. Given an estimated point difference x between the two teams (i.e., given that team i is expected to score x more points than team j in a head-to-head matchup) and a standard error σ of the difference in score, they estimate the probability of i beating j as p ij = Φ(x/σ).…”

“…Kaplan and Garstka [13] describe a dynamic programming model which, given estimated probabilities of each team beating each other team head-to-head in a tournment game and given point values for each game in the pool, suggests a prediction strategy that can be used to maximize one's pool score. Breiter and Carlin [4] obtain similar (though slower) results via a brute force algorithm.…”

“…Caudill and Godwin [9] use a heterogeneouslyskewed logit model for the same purpose. Kaplan and Garstka [13] propose methods for estimating win probabilities from scoring rates, Sagarin ratings, and Las Vegas point spreads.…”

Tournaments and piece rates revisited: a theoretical and experimental study of output-dependent prize tournaments

“…Empirical studies on tournament compensation systems often rely on sports data (e.g., Ehrenberg and Bognanno, 1990;Becker and Huselid, 1992;Bothner et al, 2007;Kaplan and Garstka, 2001) and increasingly on field studies from the organizational practice (Knoeber and Thurman, 1994;Bandiera et al, 2005;Matsumura and Shin, 2006;CasasArce and Martínez-Jerez, 2009;Backes-Gellner and Pull, 2013). The first experimental evidence on tournaments was provided by Bull et al (1987), to be followed by a wide range of studies relying on laboratory data (e.g., Irlenbusch, 2008, Freeman andGelber, 2010 etc.…”