NCAA Hockey Rankings
What do these rankings mean? The simplest ranking is a team's record - its winning percentage where a tie counts as half a win and half a loss.
Each team's record counts as 25% of its Rankings Percentage Index (RPI). The team's opponents' winning percentage counts 21%, and its opponents' opponents' winning percentage the other 54%.
The RPI is one of the components of the Pairwise Rankings (PWR) along with record against teams under consideration, record against common opponents and head-to-head record. The NCAA uses the PWR to determine which teams will participate in the NCAA tournament. Only teams with RPIs in the top 25 are considered for PWR.
KRACH - the Bradley-Terry System applied to college hockey - is the most mathematically sound way to rank teams. Team A's KRACH divided by Team B's KRACH gives the odds that Team A will defeat Team B. (See also http://www.mscs.dal.ca/~butler/krachexp.htm.)
Once the KRACH ratings are known, it is possible to calculate a Krach PWR. This differs from the standard PWR in three ways. First, KRACH replaces RPI as the first component. Accordingly, the criterion for a team to be under consideration becomes having a KRACH in the top 25. Lastly, the TUC and COP components are "Krachified." (See also http://slack.net/~whelan/tbrw/2000/kpairwise.shtml.)
KASA stands for KRACH Adjusted for Site Advantage. It is an extended Bradley-Terry method that takes home-ice advantage into account.
HEAL differs from the other methods by taking into account not only how many games a team has won, but which opponents they have beaten; RHEAL is a recursive version of HEAL. (See also http://maine.edu/HEAL/.)
E-ratings, developed by Eugene Potemkin, provide yet another ranking system. (See also http://rsport.narod.ru/wwrr/theory/erating.htm and http://www.mratings.com/theory/erating.htm.)
CHODR is unique in that it takes into account the actual score of each game as well as home-ice advantage. The product of Team A's offensive rating and Team B's defensive rating estimates the number of goals Team A will score on Team B. CHODR was developed by Robin Lock at St. Lawrence University. (See also http://it.stlawu.edu/~chodr/.)
CCHP is similar to CHODR, but is uses an additive model instead of CHODR's multiplicative model. CCHP was developed by Eric Carlson at the University of Alaska-Fairbanks. (See also http://www.uafhockey.com/hexplain.html.)