Analyzing Fantasy Sport Competitions with Mixed Integer Programming

Abstract

A fantasy sport competition is an online competition in which participants act as the coach and selector of their own fantasy team of real players. These competitions are remarkably popular with currently over 5.5 million teams in the major competition of the English Premier League. A fantasy team scores points based on the statistical performances of the team’s players in their real-world sporting matches. The objective for each coach is to finish the season with the highest total number of points. During the season, coaches must manage a budget as well as trade players in and out of the team subject to a number of constraints. Due to their well-defined nature, as well as the simple objective function, these competitions lend themselves very naturally to analysis by Mixed Integer Programming (MIP). In this paper, we consider three different problems for the 2018 season of the AFL SuperCoach competition, modelling and solving each with MIP. The aim of each problem is to highlight the gap between what was achieved by real players and what was theoretically possible. The first problem is to determine all the decisions that a coach should have made to obtain the highest score possible. The second problem is to determine the lowest starting budget from which it would have been possible to win the competition. The third problem is to determine whether it would have been possible for a team that was set up at the start of the competition and completely forgotten about to win the competition.