Optimizing daily fantasy sports contests through stochastic integer programming

Abstract

The possibility of becoming a millionaire attracts over 200,000 daily fantasy sports (DFS) contest entries each Sunday of the NFL season. Millions of people play fantasy sports and the companies sponsoring daily fantasy sports are worth billions of dollars. This thesis develops optimization models for daily fantasy sports with an emphasis on tiered contests. A tiered contest has many different payout values, including the highly sought after million-dollar prize. The primary contribution of this thesis is the first model to optimize the expected payout of a tiered DFS contest. The stochastic integer program, MMIP, takes into account the possibility that selected athletes will earn a distribution of fantasy points, rather than a single predetermined value. The players are assumed to have a normal distribution and thus the team’s fantasy points is a normal distribution. The standard deviation of the team’s performance is approximated through a piecewise linear function, and the probabilities of earning cumulative payouts are calculated. MMIP solves quickly and easily fits the majority of daily fantasy sports contests. Additionally, daily fantasy sports have landed in a tense political climate due to contestants hopes of winning the million-dollar prize. Through two studies that compare the performance of randomly selected fantasy teams with teams chosen by strategy, this thesis conclusively determines that daily fantasy sports are not games of chance and should not be considered gambling. Besides creating the first optimization model for DFS tiered contests, this thesis also provides methods and techniques that can be applied to other stochastic integer programs. It is the author’s hope that this thesis not only opens the door for clever ways of modeling, but also inspires sports fans and teams to think more analytically about player selection.