Sport score is a quantitative measure of the performance of an athlete in a particular sporting discipline. Most sports use points-based scoring, where events in the competition raise or lower the score of a team or individual. Points can be measured in abstract quantities defined for the sport, such as a distance or height, or more natural measures, like time.

Scoring in different sports differs from one another, and many of the same games are not grouped together due to their differences in scoring systems. This means that understanding the patterns of game scoring dynamics across sports is important for analyzing and modeling them.

We use a large data set of scoring events in college and professional (American) football, hockey, and basketball to identify some common patterns in the tempo and balance of scoring in these four sports. We find that the tempo of scoring events closely follows a common Poisson process, with a sport-specific rate, while the balance of winning events follows a common Bernoulli process, with a parameter that effectively varies with the size of a team’s lead.

In addition, we observe unexpected patterns in the probability of winning a scoring event within a given game. In particular, NBA games exhibit an unusual ’restoring force’ pattern, in which the probability of winning a scoring event decreases with the size of a team’s score lead. NFL and CFB games, however, do not exhibit this effect. Our results suggest that the restoring force of latent team skill contributes significantly to the variance of scoring balance in these four sports.