Ranking Systems for College hockey

© 1999-2001, Joe Schlobotnik (archives)

URL for this frameset: http://slack.net/~whelan/tbrw/tbrw.cgi?2001/rankings.shtml

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

See also

• Last year's rankings
• The NCAA Selection Procedure
• You Are The Committee, an interactive run through the selection process (also available in a versatile self-service hypothetical interface)
• US College Hockey Online's explanation of the PWR and tournament selection FAQ
• The current PWR and RPI as calculated by USCHO.
• Ken Butler's KRACH ratings
• A Proposed Modification to the NCAA Selection Criteria

KRACH vs RPI

The NCAA assigns at-large bids and seeds for its Division I Men's Ice Hockey Tournament based primarily on the system of pairwise comparisons, an important component of which is the Ratings Percentage Index. However, as was demonstrated by the case of MAAC regular season champions Quinnipiac the past few seasons, the RPI can overestimate the strength of a team's schedule if their opponents also played predominantly weak schedules. A rating system which seems, both in theory and in practice, to be immune to this defect, while only considering the factors used in producing the RPI (won-lost-tied records between pairs of teams, without regard to factors such as score or home-ice advantage) is the Bradley-Terry or KRACH rating system. The table below lists the 58 tournament-eligible Division I teams by their KRACH ratings (The RRWP column lists the expected winning percentage a team would have, according to the Bradley-Terry ratings, if they played each other team in the country an equal number of times), along with their ratings and rankings according to RPI. The "Strength" column under RPI gives the combination (10/13 winning percentage and 3/13 opponents winning percentage) which is the effective measure of the strength of an opponent in the RPI calculations. (So it is a measure, not of the strength of a team's schedule, but of the contribution of that team to the strength of a schedule they appear on.) Note that this is more heavily weighted towards winning percentage than is RPI itself.

Impact of Strength of Schedule

Although it is not usually defined this way, the KRACH rating can be thought of as a product of two factors, one quantifying a team's won-lost-tied record, the other its strength of schedule. The first factor is simply the ratio of points for (twice wins plus ties) to points against (twice losses plus ties); the "strength of schedule" factor is a weighted average of the KRACH ratings of a team's opponents. (This sounds circular at first, but under normal circumstances, there is a unique ranking which satisfies these conditions for all teams. In fact, this self-referential definition is what gives KRACH the power to ferret out the strength of teams in the presence of mostly isolated schedules.) The RPI can also be split into contributions from won-lost-tied record and strength of schedule. In this case, the two are added, 7 parts winning percentage to 13 parts strength of schedule. The strength of schedule is made up of 10 parts opponents' winning percentage and 3 parts opponents' opponents' winning percentage. (It is the average "strength" of a team's opponents, where "strength" is closely related to the last column in the table above.)

The following table lists each team's strength of schedule according to the two measures and breaks down the KRACH and RPI ratings into their contributions from W-L-T record and strength of schedule.

Pairwise Comparisons

The RPI is one of five selection criteria used by the NCAA to evaluate teams with non-losing records against tournament-eligible competition, known as Teams Under Consideration (TUC), performing pairwise comparisons among them. For each team, the table below lists the number of comparisons they win with other TUCs (PWR), their RPI, and the teams with which they win comparisons. Each entry in the table corresponding to a comparison is a link to a breakdown of the criteria in that comparison. Additionally, each team's name in the table is a link to a list of the games contributing to their RPI as well as to their record vs TUCs and in the last 16 games.

Bradley-Terry Modified Pairwise Comparisons

In addition to the potential use of KRACH or RRWP as a replacement for RPI, the other criteria in the NCAA's pairwise comparison system can also be improved with the use of Bradley-Terry methods. A modification to the pairwise comparison system has been proposed which replaces RPI as a criterion and tiebreaker with RRWP, and replaces the three criteria which compare the two teams' winning percentages in subsets of their games (record vs TUCs, in the last 16 games and against common opponents) with a comparison of the Bradley-Terry ratings they would need in order to compile the observed set of results in those games. Modifying the criteria in this way corrects for possible differences in the strength of the opposition being considered; if two teams have for example played the same set of TUCs the same number of times, comparing these effective Bradley-Terry ratings will produce the same results as comparing the won-lost-tied records against TUCs.

The table below lists the results of these modified pairwise comparisons, analogously to the table above. Once again, each comparison result is linked to a breakdown of which team won which criterion in the modified system, and each team's name is a link to the breakdown of the team's overall KRACH rating plus the criterion-specific ones for "vs TUCs" and "Last 16".