(b) NEW in 2004-05: An overall rating (expected winning pct) is computed by using the offensive and defensive ratings to pedict scoring rates (see below) for games (on neutral ice) against every other Division I team and then using the Poisson probability function to find the expected probability of winning each of those games (with ties counting as one half wins). Thus the overall rating is the projected winning percentage for a team if they played a balanced schedule against all teams.
(c) We can rank teams according to their overall ratings or provide separate rankings to reflect offensive or defensive prowess. The better teams have the higher overall ratings, while the better offenses have higher offensive ratings and the better defenses have lower defensive ratings.
Team A's predicted goals = ((A's Offense*B's Defense)/Average Rating)*(Home Ice Advantage)
Team B's predicted goals = ((B's Offense*A's Defense)/Average Rating) / (Home Ice Advantage)
The Average Rating is divided into the predicted score because the average is already included in each teams rating, so it ends up getting included twice when the ratings are multiplied. The Home Ice Advantage (generally a number slightly more than 1.00) will slightly improve the home team's predicted scoring rate and work against the visiting team. No adjustment is made for a game on neutral ice.
EXAMPLE: Let's suppose that St. Lawrence University is rated as Off = 3.00, Def = 3.20 and is hosting Harvard ( Off = 3.80, Def = 2.80) where the average rating for all teams is 3.10 and the home ice adjustment is estimated at 1.04:
SLU's predicted score = ((3.00* 2.80 )/3.10) * 1.04 = 2.82
Harvard's predicted score = (( 3.80 * 3.20 )/3.10) / 1.04 = 3.77
Although it may seem awkward to predict non-integral scores, this number actually represents the expected average score for the given team if they played many games under the given conditions (same opponent and same location). Of course, in any one game, the actual result may or may not be close to this average. As we all know, upsets have been known to occur from time to time.
(b) Goals scored in overtime are ignored when generating ratings. We'd also like to eliminate empty net goals, but getting reliable data on those is problematic. Thus our ratings reflect regulation time goal scoring ability.
(c) Only games between two Division I teams are counted. No prior information is used in the rating, i.e. all teams are equal at the beginning of the season.
(d) Because of the way ratings are calculated, scoring 5 goals against a very good defensive team will help your Offensive ratings a lot more than doing the same to a team which allows many goals. Likewise, allowing 6 goals against an offensive powerhouse won't hurt your Defensive ratings as much as allowing the same number to a weak scoring team. This is how the "strength of schedule" figures into the ratings.
(e) Although we give ratings fairly early in the season, estimates based on a small number of games are not very stable and will tend to exhibit considerable variability until later in the season. Inter-league play will have a large effect on these ratings as it will in any system which accounts for strength of schedule.
More information on the multiplicative model.