MULTIPLICATIVE MODEL FOR CHODR

The College Hockey Offensive/Defensive Ratings are based on a multiplicative maximum likelihood model..

What's a multiplicative model?

We assume that a team's scoring rate in a particular game depends on its offensive ability, the quality of the defense it faces, and a home ice factor. Under the multiplicative CHODR model, these factors will interact as products. So the predicted scoring rate,l AB, for Team A playing Team B on neutral ice would be

where AVG represents the average rating (scoring rate) for all teams. If Team A was playing this game at home, we would multiply the predicted scoring rate by a home ice advantage H, assumed to be constant for all teams. If Team B was the home team, we would divide Team A's predicted scoring rate by the same amount H.

How do we compute the ratings under the new system?

We assume that the scoring in any game follows a Poisson distribution, with the scoring rates determined by the formula above. Thus if Team A has a scoring rate of l , the probability that they score exactly k goals would be given by

Offensive ratings, Defensive ratings, and the Home Ice Adjustment are then chosen to maximize the probabilities of all previous game scores (hence the ratings are maximum likelihood estimates of a team's ability). .

How does this affect how we interpret the ratings?

We can interpret an offensive rating as the expected scoring rate against the hypothetical "average" team and a defensive rating as the expected goals allowed. The Home Ice Advantage can now be viewed as a percentage, i.e. H=1.04 would mean about a 4% increase in scoring rate for the home team and corresponding decrease for the visitor.