Heterogeneous skewness in binary choice models: Predicting outcomes in the men's NCAA basketball tournament

Abstract

Several authors have recently explored the estimation of binary choice models based on asymmetric error structures. One such family of skewed models is based on the exponential generalized beta type 2 (EGB2). One model in this family is the skewed logit. Recently, McDonald (1996, 2000) extended the work on the EGB2 family of skewed models to permit heterogeneity in the scale parameter. The aim of this paper is to extend the skewed logit model to allow for heterogeneity in the skewness parameter. By this we mean that, in the model developed, here the skewness parameter is permitted to vary from observation to observation by making it a function of exogenous variables. To demonstrate the usefulness of our model, we examine the issue of the predictive ability of sports seedings. We find that we are able to obtain better probability predictions using the skewed logit model with heterogeneous skewness than can be obtained with logit, probit, or skewed logit.

Tournament Seeding Efficiency and Home Court Advantage: College Basketball’s National Invitation Tournament

“…4, No. 3;2015The Schwertman et al (1996 result is also supported by Caudill and Godwin (2002), who examine NCAAT contests over the 1985-1998 period. These authors attempt to improve upon previous work by using a skewed logit model in order to account for heterogeneous skewness in order to improve the accuracy of the probability predictions.…”

“…Note 12. The coefficient for SeedDiff found in this study is 1.5 times larger than that from Caudill and Godwin (2002). The probit-logit coefficient transformation described in Gujarati (2012) can be used to facilitate a comparison of our results to those from Mixon and Withers (2005).…”

“…These authors attempt to improve upon previous work by using a skewed logit model in order to account for heterogeneous skewness in order to improve the accuracy of the probability predictions. 9 Caudill and Godwin (2002) find the greater the seeding differential the higher the probability that the higher-seeded team wins a given NCAAT contest, and also that the higher the seed value of the highest seed in an NCAAT game, the greater the probability that the higher seed wins. More recently, the first of the two Caudill-Godwin findings is verified by Mixon and Withers (2005), who examine NCAAT outcomes over the 1985-2004 period using linear probability and simple logit models.…”

Comparing Team Selection and Seeding for the 2011 NCAA Men's Basketball Tournament

“…The tournaments often sprout office pools and are frequently referred to as "March Madness". Furthermore, the men's tournament has been the subject of several statistical analyses, see for example, Carlin (1996), Caudill and Godwin (2002), Schwertman et al (1991), Schwertman et al (1996), Smith and Schwertman (1999) or West (2008). The focus of these papers is to predict team's success in the tournament based on their seed position or other measures of team strength.…”

A logistic regression/Markov chain model for NCAA basketball

“…Caudill [8] uses a maximum score estimator model that is also based on seedings and also tries to maximize the number of correct predictions. 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.…”