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KRACH: Division III Women
- RRWP: Round Robin Winning Percentage. What your theoretical winning percentage would be if you played every other team, one time each.
- Ratio: The Ratio of wins to losses (as opposed to Win %, which is wins divided by games).
- SOS: Strength of Schedule
- **Win Ratio is infinite
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).
(Note on the calculation: KRACH requires all teams to have a winning percentage below 1.000 for the calculation to be made. Until all teams in a gender and division have at least a loss or a tie, our calculation adds a single “fictitious tie” to all teams' results.)