Sports score is a point-based system in many popular sports, such as American football and hockey. The goal of each sport is to obtain a certain number of points in a fixed amount of time, and the winning team is awarded the most points.

The scoring of sports games is a complex task that has been the subject of considerable interest in recent years, but relatively little is known about what common patterns cut across different sports. Here, we explore this question in a series of empirical studies based on a comprehensive data set of scoring events from nearly a dozen consecutive seasons of college and professional (American) football, hockey, and basketball.

Scoring tempo: when scoring events occur

We show that the timing of scoring events in each sport is well-described by a Poisson process with a sport-specific rate. Moreover, the correlation function between inter-arrival times (C(n)C(n)) is almost zero for all values of n. This indicates a memoryless game, in which the timing of scoring events early in a game has little or no impact on the timing of later ones.

Lead-size dynamics: how often a team wins an event

We find that the evolution of lead sizes over the course of a game in CFB, NFL and NHL games largely follows a well-established Bernoulli model, with a parameter that effectively varies with the size of the lead. In contrast, NBA games are significantly less predictable.