Last Modified: 2019 July 24
Joe Schlobotnik / joe@amurgsval.org
URL for this frameset: http://elynah.com/tbrw/tbrw.cgi?1999/pairwise.shtml
See also
In this enlightened age, the NCAA Division I hockey tournament is seeded largely by statistical analysis. So in principle college hockey fans should be able to predict on their own how the tournament will be seeded in advance. Problem is, the selection process has been changing slightly every year, and in the past it was difficult to find out the current rules in advance. This changed in March 1997, when the tournament pairings were announced and Selection Committee chair Joe Marsh provided a detailed explanation of how it was done to Adam Wodon of US College Hockey Online, a web site devoted to college hockey. The NCAA Division I Men's Ice Hockey Committee decided to retain the same selection criteria for the following season, and then announced some slight changes for this year. Thus, with the occasional inquiry to the NCAA for fine-tuning, we are able to say with some confidence how things will be done these days.
First of all, from the NCAA's point of view, only official games played between established programs with 20 games against Division I teams on their schedule count towards the selection process. This season, those teams are
Two of the eight MAAC teams--Sacred Heart and American International--as well as Division I independent Nebraska-Omaha, are ineligible for the tournament, and games against them will not be used in the selection process. (the fine print)
The underlying principle behind the current selection process is the pairwise comparison. One team is compared to another team based on five criteria:
A team wins one point towards the comparison for each of the first four criteria, and one point for each head-to-head game in which they defeated the other team in the comparison. Whichever team gets more points wins the comparison, and if it's a tie, the team with the higher RPI wins.
Every Team Under Consideration is compared to every other TUC in this way. The total number of such comparisons won is called the Pairwise Rating (PWR--the fine print). (USCHO has a page with the current PWR, and there is also a weekly summary of all the pairwise comparisons on the Unofficial Northeastern Hockey Site.) This number can be used to rank the TUCs, and in the past it was believed that the teams were seeded in the order of these Pairwise Rankings, but that is not precisely how it's done. The PWR is used to get a rough sense of which teams are in contention for which spots, but then those teams are placed according to the pairwise comparisons among or between them. For example, if you're battling it out for the twelfth and final spot in the postseason, it doesn't matter how you compare with the fifth-rated team. Thus a two-way tie is impossible, since one team will always win the pairwise comparison. If three teams end up in an unresolvable tie (rock-scissors-paper), we go to the RPI to resolve the deadlock.
The NCAA News report on this summer's Division I Men's Ice Hockey Committee meeting contained the following paragraph
In addition to revising one of its selection criteria, the committee noted that it reserves the right to evaluate each team based on the relative strength of their respective conference using the overall conference ratings percentage index (RPI) in determining competitive equity.
This is presumably in response to the appearance on the scene of six MAAC teams, which play enough Division I contests to qualify for the tournament, but play no games against teams from any of the four major conferences. With only second-order interactions (via four of the five Division I independents) between the MAAC and the big four, small-number statistics might cause a MAAC team to do well enough in the pairwise comparisons to make the tournament if special steps were not taken. (Of course, the RPI may also be susceptible to this pitfall, but perhaps, being based on more games than any other criterion, it is more robust. I would have gone with common opponents myself.)
To get an idea of the relative strength of the MAAC vs the other four conferences, here's how they stack up by average RPI (as of today) and their performances against the four eligible Division I Independents:
| Conference | Avg RPI | vs Indies | vs Army | vs Niagara | vs Air Force | vs MSU-Mankato | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| PF-PA | Pct | PF-PA | Pct | PF-PA | Pct | PF-PA | Pct | PF-PA | Pct | ||
| Hockey East | .523 | 14-2 | .875 | 12-0 | 1.000 | 0-2 | .000 | 2-0 | 1.000 | 0-0 | .--- |
| WCHA | .503 | 32-10 | .762 | 0-0 | .--- | 0-0 | .--- | 10-0 | 1.000 | 22-10 | .688 |
| CCHA | .503 | 5-5 | .500 | 0-0 | .--- | 2-4 | .333 | 0-0 | .--- | 3-1 | .750 |
| ECAC | .495 | 28-10 | .737 | 10-0 | 1.000 | 10-10 | .500 | 2-0 | 1.000 | 6-0 | 1.000 |
| MAAC | .454 | 8-22 | .267 | 5-5 | .500 | 0-4 | .000 | 3-5 | .375 | 0-8 | .000 |
The NCAA tournament consists of twelve teams, divided for the first round and a half into two regionals, East and West. In each regional, two teams receive first-round byes while the other four play on the first night. On the second night of the regional, the two bye teams play the two first-round winners, with the two survivors from each regional then advancing to the national semifinals the following weekend. The selection and seeding process can be divided into the following steps:
The regular season (the fine print) and tournament champions in each of the four major conferences (WCHA, CCHA, ECAC and Hockey East) receive automatic berths, which accounts for between four and eight of the twelve teams. (The MAAC does not receive any automatic bids.) The remaining four to eight at-large teams are selected according to the pairwise method. There is the one stipulation that each major conference must have at least two representatives in the tourney.
Any team which wins both the regular season title in its league and its conference tournament receives an automatic first-round bye; since there are two conferences in each region and two byes in each regional, this will fill between zero and two of those slots in a given region. The other bye(s), if any, are given to the best team(s) in the appropriate region(s) according to a pairwise analysis.
There are now four remaining spots in each regional to fill with the other eight teams. If those eight teams are evenly divided, four from each region, the two better teams in each region play in their respective regionals, while the two lower teams are "shipped out" to play in the opposite region. If there is an imbalance, the bottom team(s) from the over-represented region are placed into the other region before the swap. (snotty aside) However, the host schools (Wisconsin in the West and Boston University in the East this year) must be kept in their own regions. (the fine print) Also, see "Fine Tuning".
Once the four non-bye teams in each regional are determined, they are placed in the three to six positions according to their pairwise comparisons. The four and five seeds will play in the first round, with the winner to face the one seed, while the three and six seeds will meet for the right to play the two seed.
At this point, we have a setup for the tournament according to the numbers, but there could be other problems with it. For instance, all four first-round contests could be rematches of the conference title games, or the teams with the biggest fan bases could be playing outside of their regions. These are both considered undesirable by the NCAA, so the committee can shuffle things a bit, either by altering the seedings within a region, or choosing to send different teams to the opposite regionals. First-round intra-conference matchups are positively verboten, and potential second-round games between teams in the same conference should be avoided, especially if the teams met in their conference playoffs. If two teams are swapped within a region to eliminate a second-round matchup, the other two teams will be swapped as well to retain the first-round pairings, if that doesn't cause more problems. Also, teams can be shifted to different regions to increase attendance.
This is the one part of the selection procedure which is really a judgement call on the committee's part, and thus the most unpredictable. Ordering teams within a regional is basically deterministic, but when deciding which non-bye teams go in which regional, the committee is supposed to consider
How much weight they give to each is completely unspecified, although attendance seems to be very important, while conference considerations are not a big priority in populating the regionals. The best way to guess what they'll do is to look at historical precedent.
Here's how the procedure was actually applied to seed the 1998 tournament, and here's a summary of how it's gone for the last three years. Here's my final If the Season Ended Today column, which attempted to predict the makeup of the 1999 tournament.
To get an interactive feel for the process, you can use my tournament selection script, which is now set up to use the current results (updated each day at 2am from the USCHO Division I Composite Schedule). It also incorporates the changes in the process between this year and last: