How Does a Sport Score?

A competitive sport in which the winner is determined by accumulating more points than the opponent within a fixed time limit. Many sports use different methods to calculate a score, such as the common system of scoring in football, or the way in which boxing and mixed martial arts (MMA) award points for blows given or success in a round.

Despite growing interest in quantitative analysis and modeling of competition in general and sports in particular, relatively little is known about what patterns or principles cut across different sports. In this article, we explore some of these questions using a comprehensive database of scoring events from college and professional football, hockey, and basketball. This database is unusual both in its scope – every league game over 9-10 seasons of play – and in its depth – timing and attribution information on all points scored within each game.

We find that the scoring tempo of these four sports is well-described by a Poisson process with a sport-specific rate, and that the scoring balance between teams – how often one team wins an event – closely follows a Bernoulli process with a bias parameter that effectively varies with lead size. We also show that, for all sports except baseball, the probability of scoring again while in the lead rapidly increases with lead size, a pattern consistent with differential latent team skill.

While these findings suggest that some aspects of scoring dynamics are similar across sports, the differences in rules, player abilities, and strategies of the various sports make it difficult to generalize these conclusions. In future work, we plan to explore these variations in more detail, with the goal of developing models of the underlying dynamical processes.