The College Hockey Offensive/Defensive
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.
What about the Overall Rating?
New in 2004-5: If we know the expected scoring rates for any game, we can use the Poisson probability function to compute an expected probability that Team A beats Team B (just sum up the joint probabilities for all game scores with that outcome) and find the expected probability that Team A ties Team B. To get a measure of overall ability, we compute an Expected Winning Pct by finding the average P(win)+1/2P(Tie) based on the current ratings assuming a team were to play a balanced schedule (on neutral ice) against all Division I teams.