Ludometrics: Luck, and How to Measure It

Game theory is the study of tractable games which may be used to model more complex systems. Board games, video games and sports, however, are intractable by design, so "ludological" theories about these games as complex phenomena should be grounded in empiricism. A first "ludometric" concern is the empirical measurement of the amount of luck in various games. We argue against a narrow view of luck which includes only factors outside any player's control, and advocate for a holistic definition of luck as complementary to the variation in effective skill within a population of players. We introduce two metrics for luck in a game for a given population - one information theoretical, and one Bayesian, and discuss the estimation of these metrics using sparse, high-dimensional regression techniques. Finally, we apply these techniques to compare the amount of luck between various professional sports, between Chess and Go, and between two hobby board games: Race for the Galaxy and Seasons.