How Do Sports Score?

A score in sports is a quantitative measure of success in the competition. It may be an abstract quantity, such as a point, or a more natural measure of time or distance. In most sports, the objective is to achieve a higher score than one’s opponents.

Modern sports generate large quantities of detailed data describing not only competition outcomes but also individual events and team characteristics. While such data has enabled many quantitative analyses of individual sports, relatively little work has asked whether any fundamental patterns or principles cut across different sports.

Using a comprehensive dataset from college and professional football, hockey, and basketball, we identify several common features of scoring dynamics. Scoring tempo – when scoring events occur – follows a common Poisson process with a sport-specific rate, while scoring balance – how often each team wins an event – follows a Bernoulli process with a parameter that effectively varies with the size of the lead. We use these insights to construct a generative model of gameplay that reproduces observed evolutions of lead sizes and accurately predicts game outcomes, even when the model knows nothing about teams or players.

Post hoc Hochberg GT 2 comparisons reveal that soccer athletes perform better than basketball athletes on tasks of SRT and PS, while baseball and softball outperform basketball (P .001). The differences are not due to gender or sport, but rather appear to be related to life events. This suggests that introducing kids to different sports is not only a fun way to spend their summer, but also an excellent opportunity to improve their math skills in the context of more complex scoring systems.