For those who may not have seen CHODR before, or those who would
like another look, here's some explanation of the rating.  (This
week's ratings were included in a separate post)
 
 
      CHODR - The College Hockey Offensive / Defensive Ratings
                       (pronounced "chowder")
 
1. What is CHODR?
 
CHODR assigns an Offensive, a Defensive, and an Overall rating to
each of the 44 Division I Men's Ice Hockey teams.
 
 
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
combination.  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. The philosophy
behind the adjustment calculations is similar to the least squares
optimization that was used by Keith Instone's TCHCR.  The Overall
rating is just the difference between a team's Offensive and
Defensive ratings.  A more technical explanation of the math is
available for those who are interested.
 
 
3. 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.  An 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) A positive/negative Overall rating indicates that a team has
more/less overall scoring potential than the "average" team.
 
(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.
 
 
4. Comparing individual teams.
 
One nice feature of this system is that it allows comparisons between
teams on an easily understood numeric basis.  Basically, the
difference in overall ratings between two teams represents the
predicted average goal differential if they were to play lots of
games on neutral ice.
 
Example:  Colorado College (2.89 Overall) vs. Boston University
(1.89 Overall) would predict an average goal differential of about
2.89 - 1.89 = 1.00 or an even goal in Colorado College's favor.
 
 
5. Predicting future scores.
 
Another bonus of CHODR is that it may be used to forecast future
scores.  The relevant formula is
 
   Team A's predicted goals = A's Offensive Rating
                            + B's Defensive Rating
                            - Average Offensive/Defensive Rating
                          +/- Home Ice Advantage
 
   Team B's predicted goals = B's Offensive Rating
                            + A's Defensive Rating
                            - Average Offensive/Defensive Rating
                          +/- Home Ice Advantage
 
The Average Rating is subtracted from each team's predicted score
because the average is already included in each teams rating, so it
ends up getting included twice when the ratings are summed.  The Home
Ice Advantage value gets added to the home team's predicted score and
subtracted from the away team's predicted score.  No adjustment is
made for a game on neutral ice.  The Home Ice Advantage value
(currently +/- 0.171 goals) is based on the amount by which home
teams hove outscored their oppposition to the current point in the
season.
 
EXAMPLE:  Let's try BU ( Off = 5.39, Def = 3.50 ) at
                 Maine ( Off = 3.95, Def = 2.49 ):
 
     BU's predicted score = ( 5.39 + 2.49 ) - 3.81 - 0.171 = 3.90
  Maine's predicted score = ( 3.95 + 3.50 ) - 3.81 + 0.171 = 3.81
 
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. Notes:
 
(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 disregared goal
differentials.
 
(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 usually not possible.  Thus our ratings reflect the
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 Vermont (Defensive = 2.33) will help your Offensive ratings a
lot more than doing the same to Army (Defensive = 5.90).  Likewise,
allowing 6 goals against Michigan (Offensive = 5.60) won't hurt your
Defensive ratings as much as allowing the same number to Mass-Amherst
(Offensive = 2.02).  This is how the "strength of schedule" figures
into the ratings.
 
(e) The estimated ratings are based on a fairly small number of games
so far and will tend to exhibit some 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.
 
 
Questions, comments, and/or suggestions about CHODR are of course
welcomed and encouraged.
 
Timothy J. Danehy
Robin Lock                        [log in to unmask]