  Statistical applications in sports have long centered on how to best separate
signal (e.g. team talent) from random noise. However, most of this work has
concentrated on a single sport, and the development of meaningful cross-sport
comparisons has been impeded by the difficulty of translating luck from one
sport to another. In this manuscript, we develop Bayesian state-space models
using betting market data that can be uniformly applied across sporting
organizations to better understand the role of randomness in game outcomes.
These models can be used to extract estimates of team strength, the
between-season, within-season, and game-to-game variability of team strengths,
as well each team's home advantage. We implement our approach across a decade
of play in each of the National Football League (NFL), National Hockey League
(NHL), National Basketball Association (NBA), and Major League Baseball (MLB),
finding that the NBA demonstrates both the largest dispersion in talent and the
largest home advantage, while the NHL and MLB stand out for their relative
randomness in game outcomes. We conclude by proposing new metrics for judging
competitiveness across sports leagues, both within the regular season and using
traditional postseason tournament formats. Although we focus on sports, we
discuss a number of other situations in which our generalizable models might be
usefully applied.
