Ice hockey scoring follows a similar structure to football (soccer) in that its goals are continuous, scored in integers and the event is dynamic with a time decay factor for win and goal probabilities. A simple method to estimate the number of expected goals left in a game would be to take the market’s expectation at the start of the match and decay that figure according to how much time is left in the match. For example, if you were to try and work out how many goals to expect in the last 45 minutes of a football match, you could simply half the expected goals over 90 minutes, as determined by the total goal line at the start of the match, for a close approximation. Obviously, you are ignoring additional data gained in-play and not accounting for any effect the score differential or playing conditions would have on this figure, but it would still be a reasonably accurate guide. Hence, the probabilities of number of goals scored or team win decay over time.This is also true for Ice Hockey but is not applicable to cricket or tennis and is less useful in sports like basketball and american football where ‘possessions remaining’ moderated by relative scores is a better candidate for the decay factor.
Ice hockey is also similar to soccer in that team goals can be modelled using a Poisson distribution (see our guide to building a simple football model). However, one of the most significant differences between modelling football and ice hockey is how the goals scored by one team influence the expected goals of the other team. We know that there is a small but significant bivariate effect in football, meaning that the number of goals scored by one team, and the resulting goal differential, influences the number of expected goals scored by the second team. The chart below shows the score differential in 2019 for the top three English leagues from the perspective of the home team. The distribution approximates a normal distribution with a skew towards the positive integers due to home advantage.
However, the nature of ice hockey and specifically the tendency for teams to pull goalies if they are down by a small number of goals with a few minutes left, results in a much more significant bivariate effect in which the probability of normal-time one goal losses is drastically reduced versus expectations.This is displayed in the chart below which plots the frequency of winning margins in the current NHL season from the perspective of the home team.
Therefore, one of the biggest challenges with modelling ice hockey, especially in-running, is taking into account the influence that the score differential has on the remaining expected goals in the game and the win margin between the two teams.