Last Modified: 2019 July 24
Joe Schlobotnik / joe@amurgsval.org
URL for this frameset: http://www.elynah.com/tbrw/tbrw.cgi?2001/fineprint.shtml
Okay, of course life is never completely easy. First of all, a general caveat. I'm not on the selection committee, the current system of seeding the tournament is an inexact science, so even though the NCAA is working to educate the public on the process, we can never be sure what the committee will do until it's announced. But it's my hope that by thinking about these things ahead of time, we can spend the afternoon of March 18, 2001 waiting to find out whether the committee does X, Y, or maybe Z, and not be stunned to learn they've chosen Q. (Even with some preparation, I've been taken by surprise each year, but I've learned not to make too many assumptions about the one subjective area that remains: placing teams in regions.)
When calculating opponents' winning percentage for a given team, games against that team are not included. However, the opponents' opponents' percentage is simply calculated by averaging the "opponents' percentage" (as specified above), which subtracts games against the intermediate team but not those against the initial team. That is to say, if Vij is the number of times team i has beaten team j, Nij=Vij+Vji is the number of times they've played, Vi=∑jVij is the total number of wins for team i and Ni=∑jNij is the total number of games they've played, then team i's RPI is given by
0.35*Vi/Ni + 0.50 *
∑j(Nij/Ni)*(Vj-Vji)/(Nj-Nji)
+ 0.15 * ∑j (Nij/Ni)*∑k(Njk/Nj)*(Vk-Vkj)/(Nk-Nkj)
If a team with a losing record earns an automatic berth by winning its conference tournament, they are considered a TUC for all calculations.
When comparing two teams, their head-to-head games are subtracted from each team's record against Teams Under Consideration. I.e., in the comparison between team A and team B, this criterion actually compares team A's record against all TUCs except team B to team B's record against all TUCs except team A.
Since head-to-head games are not included in records vs common opponents (after all, no team plays itself), one should be careful using conference record as a starting point for record against common opponents when the two teams are in the same conference.
The observant reader will have noticed that I say PWR stands for "pairwise rating", while USCHO uses the term "pairwise ranking". The way I see it, since the PWR is the number of comparisons that a team wins, it's not actually a ranking. If there are 24 Teams Under Consideration, a team which wins comparisons with the other 23 teams has a PWR of 23, while its ranking according to the PWR would be 1.
Contrary to some opinions expressed on HOCKEY-L, I consider KRACH a superior rating system to RPI not because its harsh judgement of the MAAC teams last year agrees with some preconceived ideas of the conference's weakness, but because it is demostrably more precise and efficient at doing what RPI was designed to to in the first place. RPI is supposed to judge the strength of a team's performance by combining its winning percentage with its strength of schedule. The problem, in large part, is that the notions of "strength" are not the same. Strength, as defined by the Ratings Percentage Index, is seven parts winning percentage, ten parts opponents' winning percentage and three parts opponents' opponents' winning percentage. On the other hand, the strength-of-schedule which is part of the RPI is effectively ten parts winning percentage and only three parts opponents' winning percentage. This means that while RPI tries to correct for a team playing an unusually weak or strong schedule, it assumes that the winning percentages of that team's opponents are, on average, accurate indicators of their strengths, and does not do much to correct for them. In a case where a group of teams is predominantly playing one another, that assumption will not be valid if all the teams in the group are weaker than average. On the other hand, the Bradley-Terry method, upon which KRACH is based, requires ratings to satisfy the self-consistent set of equations, in which the rating of each team is related to their winning percentage and the ratings of their opponents. In the face of this kind of "feedback", the relative strength of two almost-but-not-quite completely "insular" groups of team will be established by whatever basis for comparison exists, such as the MAAC performance against the Independents in their first season.