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It’s time once again to do what we like to call Bracketology — College Hockey Style, a weekly look at how the NCAA tournament would shake out if the season ended today, and a look into the thought process behind selecting and seeding the NCAA tournament teams.

This is the next-to-last edition of Bracketology. We’ll bringing you one more just before the field is announced, at the end of Saturday night’s championship games.

Here are the facts:

• Sixteen teams are selected to participate in the national tournament.

• There are four regional sites (Northeast — Worcester, Mass.; East — Albany, N.Y.; Midwest — Green Bay, Wis.; West — Grand Forks, N.D.)

• 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 includes a bonus factor for “good” nonconference wins. The exact amount of the bonus is kept secret, but experience in previous seasons has given us some idea as to how large it must be.

Because of this bonus factor, we won’t even talk about the PairWise Rankings (PWR) without an added bonus. We know that the bonus is at least .003 for a quality road win, .002 for a quality neutral-site win and .001 for a quality home win. So everything that we do will reference the 3-2-1 bonus as a base.

Given these facts, here are the top 16 of the current PairWise Rankings (PWR), with a 3-2-1 bonus, plus any other teams that are currently leading their conferences, but are not in the top 16, and Bemidji State, who has captured the CHA autobid (through all games of March 12, 2006):

1 Minnesota
2 Wisconsin
3 Miami
4t Michigan State
4t Boston University
6 Cornell
7t Harvard
7t North Dakota
9 Michigan
10 Colorado College
11 New Hampshire
12 Maine
13t Boston College
13t Nebraska-Omaha
15t Dartmouth
15t Denver
17 Dartmouth
19 Holy Cross
30 Bemidji State

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 in Holy Cross and Bemidji State.

Now let’s break the ties.

Michigan State wins the comparison with Boston University, Harvard with North Dakota and Boston College with Nebraska-Omaha.

Now choose your teams in the tournament. First we take the autobids, a total of six teams. Because we do not know who will receive the automatic bids, except for Bemidji State, we are going to make a huge assumption here — that the number-one seed in each tournament will win the tournament. We all know that this might not happen, but it’s the best guess at the moment. These six teams are:

AHA — Holy Cross
CHA — Bemidji State
CCHA — Miami
ECACHL — Dartmouth
HEA — Boston University
WCHA — Minnesota

We also take the next 10 teams, in rank order. The 16 teams in the tournament, in rank order, are therefore:

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

Step Two

Now it’s time to assign the seeds.

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

Step Three

We place the No. 1 seeds based on proximity to the regional sites.

No. 1 Minnesota is placed in the West Regional in Grand Forks.
No. 2 Wisconsin is then placed in the Midwest Regional in Green Bay.
No. 3 Miami is placed in the East Regional in Albany.
No. 4 Michigan State is placed in the Northeast Regional in Worcester.

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. 5 Boston University, the host school, is placed in No. 4 Michigan State’s Regional, the Northeast Regional.
No. 8 North Dakota, the host school, is placed in No. 1 Minnesota’s Regional, the West Regional.
No. 6 Cornell is placed in No. 3 Miami’s Regional, the East Regional.
No. 7 Harvard is placed in No. 2 Wisconsin’s Regional, the Midwest Regional.

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.

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

No. 4 Seeds

One more time, taking No. 16 v. No. 1, No. 15 v. No. 2, etc.

No. 16 Bemidji State is sent to Minnesota’s Regional, the West Regional.
No. 15 Holy Cross is sent to Wisconsin’s Regional, the Midwest Regional.
No. 14 Dartmouth is sent to Miami’s Regional, the East Regional.
No. 13 Boston College is sent to Michigan State’s Regional, the Northeast Regional.

The brackets as we have set them up:

West Regional:

Bemidji State vs. Minnesota
Michigan vs. North Dakota

Midwest Regional:

Holy Cross vs. Wisconsin
Colorado College vs. Harvard

Northeast Regional:

Boston College vs. Michigan State
Maine vs. Boston University

East Regional:

Dartmouth vs. Miami
New Hampshire vs. Cornell

Our first concern is avoiding intraconference matchups. We have one — Maine vs. Boston University.

So we have to switch out Maine. We can’t do this with New Hampshire, so the next highest seed is Colorado College. So we just shuffle. Colorado College can only play Boston University in this grouping, so we move Colorado College to play BU, then give the highest seed the lowest seed.

In this case, that would mean a Cornell-Maine matchup and a Harvard-New Hampshire matchup.

West Regional:

Bemidji State vs. Minnesota
Michigan vs. North Dakota

Midwest Regional:

Holy Cross vs. Wisconsin
New Hampshire vs. Harvard

Northeast Regional:

Boston College vs. Michigan State
Colorado College vs. Boston University

East Regional:

Dartmouth vs. Miami
Maine vs. Cornell

And we have our bracket for this week.

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 East Regionals face each other in one semifinal (Wisconsin and Miami’s brackets), while the winners of the Northeast and West Regionals (Michigan State and Minnesota’s brackets) play the other semifinal.

Bonus Time

We know there is a bonus component to the criteria, the NCAA’s tweak to the system which rewards “good” nonconference wins. We’ve determined that it is at least .003 for a good road win, .002 for a good neutral win and .001 for a good home win.

We also know that it’s not as high as .005 for a good road win, .003 for a good neutral win and .001 for a good home win.

So let’s find a medium here. Let’s take .004 for a good road win, .0025 for a good neutral win and .001 for a good home win.

Does anything change?

It does indeed.

1 Minnesota
2 Wisconsin
3t Michigan State
3t Boston University
5t Cornell
5t Miami
7t Harvard
7t North Dakota
9 Colorado College
10 Michigan
11 New Hampshire
12 Maine
13t Boston College
13t Nebraska-Omaha
15 Dartmouth
16t Denver
16t Northern Michigan
18t Holy Cross
30 Bemidji State

A lot of movement at the top, with Miami falling all the way down out of a No. 1 seed.

Let’s bracket it up.

West Regional:

Bemidji State vs. Minnesota
Michigan vs. North Dakota

Midwest Regional:

Holy Cross vs. Wisconsin
Colorado College vs. Harvard

Northeast Regional:

Dartmouth vs. Boston University
Maine vs. Cornell

East Regional:

Boston College vs. Michigan State
New Hampshire vs. Miami

And there you have it. We had one intraconference matchup we had to get rid of, and that was North Dakota-Colorado College, so we just swapped CC with Michigan.

Then we bracket the Frozen Four where the winners of the West and Northeast Regionals play each other and the winners of the Midwest and East Regionals play each other.

The final Bracketology and the final predictions are coming next on Saturday night.