Luck and the Law: Quantifying Chance in Fantasy Sports and Other Contests

Abstract

One of the consequences of this recent rapid growth is increased scrutiny surrounding the legal aspects of the games, which typically hinge on the relative roles of skill and chance in the outcome of a competition. While there are many ethical and legal arguments that enter into the debate, the answer to the skill versus chance question is grounded in mathematics. Motivated by this ongoing dialogue we analyze data from daily fantasy competitions played on FanDuel during the 2013 and 2014 seasons and propose a new metric to quantify the relative roles of skill and chance in games and other activities. This metric is applied to FanDuel data and to simulated seasons that are generated using Monte Carlo methods; results from real and simulated data are compared to an analytic approximation which estimates the impact of skill in contests in which players participate in a large number of games. We then apply this metric to professional sports, fantasy sports, cyclocross racing, coin flipping, and mutual fund data to determine the relative placement of all of these activities on a skill-luck spectrum.