### 1. What is CHODR?

CHODR is a computer generated rating system applied to collegiate hockey. It produces an Offensive, a Defensive, and an Overall rating for each of 52 NCAA Division I Men's Ice Hockey teams based on past game results. CHODR is pronounced the same as that tasty New England clam soup.

### 2. How are the ratings determined?

CHODR places equal emphasis on offense and defense and provides an overall rating for each team based on its offense/defense ratio. A team's Offensive rating is based on the goals it has scored, with an adjustment for the quality of the defenses it has faced to score those goals. Similarily, the Defensive rating uses goals allowed and adjusts for the offensive ratings of the opponents. An adjustment is also made for home-ice advantage. An Expected Winning Pct is computed to reflect a team's outlook when playing a balanced schedule against all teams.

### 3. How does CHODR account for the quality of the opponent?

The philosophy behind the adjustment calculations is based on the principle of maximum likelihood. Since we can use the ratings to "predict" scores for individual games, we can determine ratings which best match the games which have already been played, i.e. maximize the probability of past game scores.

### 4. How can the ratings be interpreted?

(a) An offensive/defensive rating represents the goal scoring/allowing rate (average goals per game) which would be predicted against a mythical "average" team on neutral ice. A team with an Offensive rating of 6 and a Defensive rating of 2 would therefore be predicted to beat an "average" team on neutral ice by the score of 6 to 2.

(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.

### 5. Predicting future scores.

A key feature of CHODR is that it may be used to forecast future scores.
Suppose that Team A is playing at home against Team B.
The relevant formulas are :

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 Clarkson ( 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

Clarkson'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.

### 6. Assumptions:

(a) We do NOT use any information about who wins or loses a game in generating the ratings. We are intending only to rate a team's ability to score and keep the other team from scoring. This provides a direct contrast to other ratings which disregard goal scoring and depend only on won-loss-tie outcomes.

(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 which are eligible for the NCAA Division I tournament 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.

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CHODR is produced by Robin Lock with programming assistance from Abhishek Parajuli.