Predicting the NCAA basketball tournament using isotonic least squares pairwise comparison model

Each year, millions of people fill out a bracket to predict the outcome of the popular NCAA men's college basketball tournament, known as March Madness. In this paperwe present a new methodology for team ranking and use it to predict the NCAA basketball tournament.We evaluate our model in Kaggle'sMarchMachine LearningMania competition, inwhich contestantswere required to predict the results of all possible games in the tournament. Our model combines two methods: The least squares pairwise comparison model and isotonic regression. We use existing team rankings (such as seeds, Sagarin and Pomeroy ratings) and look for a monotonic, non-linear relationship between the ranks' differences and the probability to win a game. We use the isotonic property to get new rankings that are consistent with both the observed outcomes of past tournaments and previous knowledge about the order of the teams. In the 2016 and 2017 competitions, submissions based on our methodology consistently placed in the top 5% out of over 800 other submissions. Using simulations, we show that the suggested model is usually better than commonly used linear and logistic models that use the same variables.