A sport score is a record of a team’s total points in a competition. Many sports have unique scoring methods. In most cases, winning a game requires reaching a fixed number of points sooner than the opponent. These points can be awarded based on specific rules, such as field goals in soccer or free throws in basketball, or more abstract quantities such as distance or duration.

Modern sports produce huge volumes of detailed data describing not only competition outcomes but also the details of gameplay, such as ball possessions, timeouts, player fouls and court positions. The large size and high granularity of these datasets enable quantitative analyses of individual sports [1-12].

However, little work has explored whether there are general principles that cut across different types of sporting competitions. In particular, what can be learned about the dynamics of scoring from a quantitative analysis of the timing and balance of scoring events in different types of sports?

In this article, we explore these questions in a comparative analysis of the scoring dynamics of college (CFB), professional football (NFL), professional hockey (NHL) and professional basketball (NBA). The findings suggest that despite their wide variation in the details of gameplay, these four sports share common patterns in the timing of scoring events and the balance of these events.

For example, the tempo of scoring is remarkably well-described by a Poisson process that produces a scoring event at a sport-specific rate every second on the clock. This rate is depressed at the beginning of each scoring period and then increases dramatically in the final seconds of a period. Similarly, the balance of these events is characterized by a Bernoulli process with a bias parameter that varies effectively over gameplay and reflects differences in latent team skill.