March 6, 2014
PAC-8 Hockey Conference adopts KRACH Ranking System for 2014-15 post season play.
KRACH Ranking Notes:
-KRACH is well vetted and utilized by NCAA (not an even amount of games), USA Hockey, USHL, EJEPL (not an even amount of games), EJHL, Minnesota High School Hockey League (not an even amount of games), etc
-Widely used to rank teams where there is an unbalanced schedule
-Only factors wins, losses, and ties
-Does not factor goals for, goals against, goal differential
-Teams can play as many PAC-8 Games as desired (up to 16 games)
-Teams are required to play at least 8 PAC-8 games
-System cannot easily be distorted by teams with strong records playing against weak opposition
-The Statistical model in which this is based has been around since 1929
KRACH — or “Ken’s Ratings for American College Hockey” — is the implementation for college hockey of a sophisticated mathematical model known as the Bradley-Terry rating system, first applied to college hockey by a statistician named Ken Butler.
This method is based on a statistical technique called logistic regression, in essence meaning that teams’ ratings are determined directly from their won-loss records against one another. A key feature of KRACH is that strength of schedule is calculated directly from the ratings themselves, meaning that KRACH, unlike many ratings (including RPI) cannot easily be distorted by teams with strong records against weak opposition.
The ratings are on an odds scale, so if Team A’s KRACH rating is three times as large as Team B’s, Team A would be expected to amass a winning percentage of .750 and Team B a winning percentage of .250 if it played each other enough times. The correct ratings are defined such that the “expected” winning percentage for a team in the games it’s already played is equal to its “actual” winning percentage.
An alternative definition of a team’s KRACH rating is as the product of its Winning Ratio (winning percentage divided by one minus winning percentage) with the weighted average of its opponents’ KRACH ratings. (The definition of the weighting factor makes this equivalent to the first definition of the KRACH ratings.) In addition to KRACH and RRWP, the table above lists each team’s Winning Percentage, Winning Ratio and Strength of Schedule (the aforementioned weighted average of their opponents’ KRACH ratings).
Link 1: http://www.mscs.dal.ca/~butler/krachexp.htm
Link 2: http://www.elynah.com/tbrw/tbrw.cgi?krach