Combating Uncertainty with Context: Optimal Lineup Construction in Daily Fantasy Baseball

Abstract

Over the past several years Daily Fantasy Sports have emerged as a huge industry, with participants being able to compete against one other for money on a daily basis. Here we investigate how to construct an optimal lineup in Daily Fantasy Baseball specifically, using the FanDuel scoring system and lineup restrictions. The daily timescale poses the challenge of increased variability in player performance, but also allows us to add more context to our predictions by leveraging game-day information. We develop two prediction models, one for hitter point totals and one for pitcher point totals. In both cases a Generalized Boosted Model performed best with Root Mean Squared Errors of 3.014 and 5.37 respectively. We then use these predictions as an input into an Integer Program that solves for the lineup with the highest expected point total subject to the salary cap and the other constraints FanDuel imposes. This two-step process of prediction and optimization resulted in an average actual lineup point total (as opposed to the value of the objective function which is expected points) of 42.60, which was 5.53 points higher than a ’naive’ prediction approach that only used a player’s average Points per Game and ignored game-day factors. Furthermore this point total falls above the 70th percentile of historical point totals in Head-to-Head and 50/50 contests suggesting our approach should win the majority of the time. We then modify our optimization approach to account for the role of lineup variance in the context of different contest types drawing on concepts from Portfolio Optimization such as the efficient frontier and the Capital Market Line. As part of this process we quantify the covariance between player point totals. We see that in Head-to-Head contest one should choose the lineup with the highest expected point total with no regard for lineup variance. In 50/50 contests one should limit lineup variance to an extent due to the flat payout structure that does not reward extreme point totals. For tournaments one needs to pick a lineup with higher variance in order to have a chance at reaching the high point totals that are necessary to win among the thousands of entries. Finally, future work is discussed.