Sport score is a quantitative indicator of the relative performance of competitors in a sporting discipline. The goal of most sports with scoring is to obtain a higher score than one’s opponents, usually by attaining a specified number of points within an agreed-upon time limit.

The multitude of different scoring systems found across the wide range of sports makes it challenging to quantify and understand their dynamics. While there is growing interest in quantifying and modeling the scoring dynamics of individual sports, relatively little work has been done to investigate what patterns or principles, if any, cut across different sporting disciplines.

In this paper, we analyze scoring data from college and professional football, professional hockey, and professional basketball to identify common patterns in their dynamics. We find that scoring tempo, or when scoring events occur, closely follows a Poisson process, with a sport-specific rate. We also find that scoring balance, or the probability that a team wins an event, is well-described by a Bernoulli process, with a bias parameter that effectively varies with the size of the lead.

Our findings suggest that there are underlying dynamics common to all these sports, despite the enormous variation in their equipment and rules. We also examine the safety of the sports, based on overall injury and concussion rates, emergency room injury data, and other academic research/literature. Boys and girls tennis and soccer emerged as the safest sports, while football and boys basketball scored near the bottom in both categories.