College Hockey:

Bracketology: March 14, 2005

It’s time once again for what we like to call Bracketology — college hockey style. It’s a weekly look at how the NCAA tournament might look if the season ended today.

More than that, it’s a look into the thought process behind selecting and seeding the NCAA tournament teams.

This is the penultimate installment of Bracketology, and we’ll make our final picks just before the field is announced on Saturday night.

Here are the facts:

Sixteen teams are selected to participate in the national tournament.

There are four regional sites (East – Worcester, Massachusetts, Northeast – Amherst, Massachusetts, Midwest – Grand Rapids, Mich., West – Minneapolis, Minn.)

A host institution which is invited to the tournament plays in the regional for which it is the host, and cannot be moved.

Seedings will not be switched, as opposed to years past. To avoid undesirable first-round matchups, including intraconference games (see below), teams will be moved among regionals, not reseeded.

Here are the NCAA’s guidelines on the matter, per a meeting of the Championship Committee:

In setting up the tournament, the committee begins with a list of priorities to ensure a successful tournament on all fronts including competitive equity, financial success and likelihood of playoff-type atmosphere at each regional site. For the model, the following is a basic set of priorities:

The top four teams as ranked by the committee are the four No. 1 seeds and will be placed in the bracket so that if all four teams advance to the Men’s Frozen Four, the No. 1 seed will play the No. 4 seed and the No. 2 seed will play the No. 3 seed in the semifinals.

Host institutions that qualify will be placed at home.

No. 1 seeds are placed as close to home as possible in order of their ranking 1-4.

Conference matchups in first round are avoided, unless five or more teams from one conference are selected, then the integrity of the bracket will be preserved.

Once the six automatic qualifiers and 10 at-large teams are selected, the next step is to develop four groups from the committee’s ranking of 1-16. The top four teams are the No. 1 seeds. The next four are targeted as No. 2 seeds. The next four are No. 3 seeds and the last four are No. 4 seeds. These groupings will be referred to as “bands.”

Additionally, the NCAA recently clarified its selection criteria to include a bonus factor for “good” nonconference wins, which are wins against non-league opponents in the top 15 of the Ratings Percentage Index.

Given these facts, here are the top 16 of the current PairWise Rankings (PWR), regular-season conference champions (Quinnipiac, Michigan, Cornell, Boston College and Denver), and Bemidji State, the CHA champion (through all games of Sunday, March 13, 2005):

1t Colorado College
1t Denver
1t Boston College
4 Minnesota
5 Cornell
6t Harvard
6t Michigan
8 Boston University
9 North Dakota
10 New Hampshire
11t Maine
11t Wisconsin
11t Colgate
14 Dartmouth
15 Vermont
16 Ohio State
23 Bemidji State
– Quinnipiac

Step One

From the committee’s report, choose the 16 teams in the tournament.

We break ties in the PWR by looking at the individual comparisons among the tied teams, and add all of the conference leaders, based on winning percentage.

From there, we can start looking at the bubble in a more detailed fashion.

Breaking ties in the PWR using head-to-head comparisons among the tied teams, the 16 teams in the tournament, in rank order, are:

1 Colorado College
2 Denver
3 Boston College
4 Minnesota
5 Cornell
6 Harvard
7 Michigan
8 Boston University
9 North Dakota
10 New Hampshire
11 Maine
12 Wisconsin
13 Colgate
14 Dartmouth
15 Bemidji State
16 Quinnipiac

All ties were broken because of individual comparison wins.

Our biggest difference from Sunday morning is that Colgate is now in the tournament and Ohio State is out. Bowling Green getting swept by Alaska-Fairbanks — and therefore falling out of the Teams Under Consideration — really, really, really hurt both Ohio State and Michigan.

Step Two

Now it’s time to assign the seeds.

No. 1 Seeds — Colorado College, Denver, Boston College, Minnesota
No. 2 Seeds — Cornell, Harvard, Michigan, Boston University
No. 3 Seeds — North Dakota, New Hampshire, Maine, Wisconsin
No. 4 Seeds — Colgate, Dartmouth, Bemidji State, Quinnipiac

Step Three

Place the No. 1 seeds in regionals.

We place host schools first and then place the other No. 1 seeds based on proximity to the regional sites.

No. 4 Minnesota is placed in the West Regional in Minneapolis as the host school.
No. 1 Colorado College is placed in the Midwest Regional in Grand Rapids.
No. 2 Denver is placed in the East Regional in Worcester.
No. 3 Boston College is placed in the Northeast Regional in Amherst.

Step Four

Now we place the other 12 teams so as to avoid intraconference matchups if possible.

Begin by filling in each bracket by banding groups. Remember that teams are not assigned to the regional closest to their campus sites by ranking order within the banding (unless you are a host school, in which case you must be assigned to your home regional).

If this is the case, as it was last year, then the committee should seed so that the quarterfinals are seeded such that the four regional championships are played by No. 1 v. No. 8, No. 2 v. No. 7, No. 3 v. No. 6 and No. 4 v. No. 5.

So therefore:

No. 2 Seeds

No. 8 Boston University is placed in No. 2 Denver’s Regional, the East, as the host.
No. 5 Cornell is placed in No. 4 Minnesota’s Regional, the West.
No. 6 Harvard is placed in No. 3 Boston College’s Regional, the Northeast.
No. 7 Michigan is placed in No. 1 Colorado College’s Regional, the Midwest.

No. 3 Seeds

Our bracketing system has one Regional containing seeds 1, 8, 9, and 16, another with 2, 7, 10, 15, another with 3, 6, 11, 14 and another with 4, 5, 12 and 13.

In this case with the No. 2 seeds being displaced, we’re trying to get the 8-9, 7-10, 6-11, and 5-12 matchups as close as possible.

Therefore:

No. 9 North Dakota is placed in No. 8 Boston University’s Regional, the East.
No. 10 New Hampshire is placed in No. 7 Michigan’s Regional, the Midwest.
No. 11 Maine is placed in No. 6 Harvard’s Regional, the Northeast.
No. 12 Wisconsin is placed in No. 5 Cornell’s Regional, the West.

No. 4 Seeds

One more time, and this time we’re going back to taking No. 16 v. No. 1, No. 15 v. No. 2, etc.

No. 16 Quinnipiac is sent to Colorado College’s Regional, the Midwest.
No. 15 Bemidji State is sent to Denver’s Regional, the East.
No. 14 Dartmouth is sent to Boston College’s Regional, the Northeast.
No. 13 Colgate is sent to Minnesota’s Regional, the West.

The brackets as we have set them up:

West Regional:

13 Colgate vs. 4 Minnesota
12 Wisconsin vs. 5 Cornell

Midwest Regional:

16 Quinnipiac vs. 1 Colorado College
10 New Hampshire vs. 7 Michigan

East Regional:

15 Bemidji State vs. 2 Denver
9 North Dakota vs. 8 Boston University

Northeast Regional:

14 Dartmouth vs. 3 Boston College
11 Maine vs. 6 Harvard

Our first concern is avoiding intraconference matchups. We have none, so this is our bracket.

Bracketing the Frozen Four, if all four number-one seeds advance, then the top overall seed plays the No. 4 overall, and No. 2 plays No. 3. Therefore, the winners of the Midwest and West Regionals face each other in one semifinal (Colorado College and Minnesota’s brackets), while the winners of the East and Northeast Regionals (Denver and Boston College’s brackets) play the other semifinal.

But…

Bonus Time

We know there is a bonus component to the criteria, the NCAA’s tweak to the system which rewards “good” nonconference wins.

Without official word on the size of the bonuses, we take these numbers: .003 for a good road win, .002 for a good neutral win and .001 for a good home wi