Sport score is a quantitative measure of relative performance in competitive sports that usually involves the accumulation of points. The winning team is one that accrues a larger number of points than its opponents. Several different scoring conventions exist in the many different types of sport, with some being more complex than others. The system used in association football and hockey is relatively simple, but other basket/net sports have more complicated methods. For example, the point metric in tennis is more ambiguous than in basketball and baseball, with players/teams able to win points for various reasons, such as hitting the ball out of bounds or failing to return the shuttlecock.

Despite increasing interest in quantitative analysis and modeling of the dynamics of sports games, relatively little is known about what patterns or principles cut across different sports. Using an unusually comprehensive dataset of scoring events from nearly a dozen seasons of college (American) football, professional American football, professional hockey, and NBA games, we identify a number of common patterns in the tempo and balance of scoring. The timing of scoring events – how close together they occur in time – is well-modeled by a Poisson process with a sport-specific rate, while the balance between teams – how often they win events – follows a Bernoulli process with a bias parameter that effectively varies with lead size.

In addition, the model we construct predicts the evolution of lead sizes over gameplay with accuracy comparable to or better than several commercial odds-makers, despite knowing nothing about teams, players, or strategies. This is consistent with the assumption that scoring dynamics in all four sports follow a three-phase pattern: an early burst of events followed by a stabilization period, and finally a dramatic late surge.