Daily fantasy sports (DFS) is a multibillion-dollar industry with millions of annual users and widespread appeal among sports fans across a broad range of popular sports. Building on recent work, 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 mean-variance optimization and the outperformance 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 submodularity properties of the objective function and by some new results on parimutuel betting. 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 both insider trading and collusion. We demonstrate the value of our framework by applying it to DFS contests during the 2017 National Football League season.