How to Play Strategically in Fantasy Sports (and Win)

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 portfolio feasibility constraints. We relate this formulation to the finance literature on mean-variance optimization and in particular, the literature on outperforming stochastic benchmarks. Using this connection we show how our problems can be reduced (via some simple assumptions and approximations) to the problem of solving binary quadratic programs. One of the contributions of our work is the introduction of a Dirichlet-multinomial data generating process for modeling opponents' team selections. We estimate the parameters of this model via Dirichlet regressions. A benefit to modeling opponents' team selections is that it enables us to estimate the value of ``insider trading'' where an insider, e.g. an employee of the DFS contest organizers, gets to see information on opponents' portfolio choices before making his own team selections. We demonstrate the value of our framework by applying it to both double-up and topheavy DFS contests in the 2017-2018 NFL season.