Daily Fantasy Sports (DFS) is a multi-billion dollar industry with millions of annual users and widespread appeal among sports fans across a broad range of popular sports. Building on the recent work of Hunter, Vielma and Zaman (2016), we provide a coherent framework for constructing DFS portfolios where we explicitly model the behavior of other DFS players. We formulate an optimization problem that accurately describes the DFS problem for a risk-neutral decision-maker in both double-up and top-heavy payoff settings. Our formulation maximizes the expected reward subject to feasibility constraints and we relate this formulation to the literature on mean-variance optimization and the out-performance of stochastic benchmarks. Using this connection, we show how the problem can be reduced to the problem of solving a series of binary quadratic programs. We also propose an algorithm for solving the problem where the decision-maker can submit multiple entries to the DFS contest. This algorithm is motivated by some new results for parimutuel betting which can be viewed as a special case of a DFS contest. One of the contributions of our work is the introduction of a Dirichlet-multinomial data generating process for modeling opponents’ team selections and we estimate the parameters of this model via Dirichlet regressions. A further benefit to modeling opponents’ team selections is that it enables us to estimate the value in a DFS setting of (i) insider trading and (ii) collusion whereby a number of DFS players combine to construct a single portfolio of entries to a given contest. We demonstrate the value of our framework by applying it to both double-up and top-heavy DFS contests during the 2017 NFL season.
Martin Haugh is an Associate Professor of Analytics and Operations Research at Imperial College, London. Before joining Imperial in 2017 he spent over 10 years in the IEOR department at Columbia University and 4 years working as a quant in the hedge-fund industry. His research interests include finance/risk management, data science and dynamic programming/stochastic control. He earned his PhD in Operations Research from MIT in 2001.