Modern sports produce large amounts of detailed data describing not only competition outcomes, but also the dynamical behavior of teams and individual players throughout gameplay. Although a great deal of work has been done quantifying and modeling these dynamics in individual sports, relatively little is known about what patterns or principles cut across different types of sports. Here we use a comprehensive data set of scoring events from college and professional football, hockey, and basketball to identify common patterns in scoring dynamics. Specifically, we find that scoring tempo – when events occur in the game clock – is well-described by a Poisson process with a sport-specific rate, and that scoring balance – how often one team wins an event – follows a common Bernoulli process, with a parameter that effectively varies with lead size.

We combine these insights into a generative model of gameplay, which accurately reproduces the observed evolution of leads and makes predictions of future score with accuracy comparable to or better than commercial odds-makers. The model explains a number of phenomena, including the observation that short intervals tend to be followed by other short intervals (and long by long), and the fact that the likelihood of winning a scoring event decreases as the lead becomes larger.

We also show that this approach provides strong criterion validity, with the SPORTS score (which assesses patients’ ability to return to their prior level of recreational activity) predicting a patient’s likelihood to be back to their preferred sporting activities by a year after surgery.