Inter-arrival Times of Goals in Ice Hockey

Previous studies have attempted to model goal scoring in sports such as ice hockey as simple Poisson processes. Others (Thomas, 2006) have shown that events within the game of ice hockey are better modelled as a Semi-Markov process determined by puck possession and location. I demonstrate that a similarly defined Semi-Markov process model is well-suited to describe the times between goals scored in NHL hockey, and use this to demonstrate that the scoring of a goal has the effect of shortening the remainder of the game by roughly 20 seconds. This is used to improve previous estimates of the value of a goal scored, calculated as a difference in win probabilities at specific time points during the game.