2004-2005 ECAC Bradley-Terry Ratings

© 1999-2004, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2005/ecac.rrwp.shtml

Game results taken from US College Hockey Online's Division I composite schedule

Our ECAC standings page ranks the teams by winning percentage rather than by the traditional hockey method of total points (two for a win and one for a tie). While this corrects for the different numbers of games that teams may have played, it doesn't consider the fact that teams may have accumulated their conference records to date against stronger or weaker competition. The following table lists the ECAC record to date for each team, broken down by opponent, followed by a projection of how they are be expected to fare in their remaining games and finally the projected final record over the entire 22-game balanced schedule. All records are given as points for (i.e., twice the number of wins plus the number of ties) versus points against (ties plus twice losses).

Including games of 2005 March 19
# Team So Far Projected
PF-PA CrHaCgVtDaBnSLUnCkPnRPYa "Future" "Final"
1 Cornell38-62-23-13-12-24-04-04-04-04-04-04-00.0-0.038.0-6.0
2 Harvard32-122-20-43-12-23-12-24-04-04-04-04-00.0-0.032.0-12.0
3 Colgate31-131-34-02-22-24-02-24-01-34-04-03-10.0-0.031.0-13.0
4 Vermont29-151-31-32-22-22-24-04-01-34-04-04-00.0-0.029.0-15.0
5 Dartmouth28-162-22-22-22-24-04-02-22-20-44-04-00.0-0.028.0-16.0
6 Brown20-240-41-30-42-20-42-24-04-02-21-34-00.0-0.020.0-24.0
7 St. Lawrence19-250-42-22-20-40-42-22-24-03-12-22-20.0-0.019.0-25.0
8 Union17-270-40-40-40-42-20-42-22-23-14-04-00.0-0.017.0-27.0
9 Clarkson16-280-40-43-13-12-20-40-42-24-00-42-20.0-0.016.0-28.0
10 Princeton14-300-40-40-40-44-02-21-31-30-44-02-20.0-0.014.0-30.0
11 RPI13-310-40-40-40-40-43-12-20-44-00-44-00.0-0.013.0-31.0
12 Yale7-370-40-41-30-40-40-42-20-42-22-20-40.0-0.07.0-37.0

The projections are calculated using the Bradley-Terry method (which is also used to produce the KRACH ratings for all of college hockey). Each team has a rating, and the points in a head-to-head game are expected to be divided proportional to the ratings. (E.g., if Team A's rating is three times that of Team B, they are expected to accumulate a winning percentage of .750 in games between the two.) The correct ratings are those which reproduce the actual winning percentage to date for each team, and are shown in the following table along with the Head-to-Head Winning Probability (HHWP) between each pair of teams and the projected Round-Robin Winning Percentage (RRWP) each team would be expected to obtain by playing every other team an equal number of times.

Including games of 2005 March 19
# Team Rating Head-to-Head Winning Probability (HHWP) RRWP Winning
1 Cornell698.4.701.726.769.788.896.905.921.929.942.948.976.864 .864
2 Harvard297.6.299.530.586.613.785.802.833.847.874.886.944.727 .727
3 Colgate264.0.274.470.557.584.764.782.816.831.860.873.938.705 .705
4 Vermont209.8.231.414.443.528.720.741.779.797.830.845.923.659 .659
5 Dartmouth187.9.212.387.416.472.698.719.759.778.814.830.915.636 .636
6 Brown81. .455
7 St. Lawrence73. .432
8 Union59. .386
9 Clarkson53. .364
10 Princeton43. .318
11 RPI38. .295
12 Yale17. .159

There are some situations where the ratio of ratings between a pair of teams needs to be 0 or infinity to produce the observed results, or where any ratio would produce the correct results. To allow for this, the teams have been divided into different "groups" (each of which is labelled by the abbreviation of its highest-rated member), with the comparison of two teams' ratings only being meaningful if the teams are in the same group. When a team's HHWP against a team from a different group is needed, it is defined as follows:

At the end of the season, when every team has played a balanced schedule, each team's RRWP will be identical to their actual winning percentage, although the individual HHWPs will of course not agree with their actual records against each team.

See Also

Last Modified: 2012 March 25

Joe Schlobotnik / joe@amurgsval.org

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