Picking Winners in Daily Fantasy Sports Using Integer Programming
Abstract
We consider the problem of selecting a portfolio of entries of fixed cardinality for contests with topheavy payoff structures, i.e. most of the winnings go to the topranked entries. This framework is general and can be used to model a variety of problems, such as movie studios selecting movies to produce, venture capital firms picking startup companies to invest in, or individuals selecting lineups for daily fantasy sports contests, which is the example we focus on here. We model the portfolio selection task as a combinatorial optimization problem with a submodular objective function, which is given by the probability of at least one entry winning. We then show that this probability can be approximated using only pairwise marginal probabilities of the entries winning when there is a certain structure on their joint distribution. We consider a model where the entries are jointly Gaussian random variables and present a closed form approximation to the objective function. Building on this, we then consider a scenario where the entries are given by sums of constrained resources and present an integer programming formulation to construct the entries. Our formulation uses principles based on our theoretical analysis to construct entries: we maximize the expected score of an entry subject to a lower bound on its variance and an upper bound on its correlation with previously constructed entries. To demonstrate the effectiveness of our integer programming approach, we apply it to daily fantasy sports contests that have topheavy payoff structures. We find that our approach performs well in practice. Using our integer programming approach, we are able to rank in the topten multiple times in hockey and baseball contests with thousands of competing entries. Our approach can easily be extended to other problems with constrained resources and a topheavy payoff structure.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 DOI:
 10.48550/arXiv.1604.01455
 arXiv:
 arXiv:1604.01455
 Bibcode:
 2016arXiv160401455H
 Keywords:

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