Sport score is the mathematical measure of a player’s performance in a sports game. It is used by a sports announcer to announce the score of a play or the outcome of a specific event, and by players to measure their own performance.

Scoring & tempo

Games in these sports are competitions between two teams of fixed size on flat, featureless playing surfaces with points awarded for each time a team places the ball or puck in the opponent’s goal. Each game is divided into three or four distinct scoring periods within a maximum of 48 or 60 minutes, depending on the sports (not including overtime).

Scoring tempo describes how quickly events occur in a game. This tempo is highly correlated with the average probability of scoring events in that period, with the highest correlations occurring during the first and last scoring periods, and lowest during the middle.

The tempo of within-game events is well described by a Poisson process, with a rate that is independent of the number of intervals (which vary across sports). It also predicts a simple geometric distribution for the mean time between consecutive events, with a two-point correlation between these delays that is zero at all time scales.

Lead-size variability in scoring tempo

The lead-size variation in the tempo of scoring events varies significantly over gameplay and across sports. This pattern is reminiscent of a memoryless coin flip with a bias that depends on the difference in inherent skill levels between teams. It is a common phenomenon in football and hockey, with a large lead increasing the probability of winning a scoring event, while the probability decreases with lead size in basketball. This phenomenon is consistent with a basic Bernoulli process.