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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.

We’ll be bringing you a new one every week until we make our final picks before the field is announced in March.

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 currently leading their conferences, but are not in the top 16 (through all games of March 1, 2006):

1 Minnesota
2 Wisconsin
3 Miami
4 Boston University
5 Michigan State
6 Colorado College
7t Cornell
7t Harvard
9t Nebraska-Omaha
9t North Dakota
9t Maine
9t Michigan
13 Boston College
14t New Hampshire
14t Denver
16t Dartmouth
16t Northern Michigan
27t Sacred Heart
— Alabama-Huntsville

Let’s take something into account at this point in time. Alabama-Hunstville is currently not a TUC, but if given the CHA autobid, it will be a TUC. So let’s take that into account and make UAH a TUC.

Adding UAH into the PairWise, we now get a Top 16, plus teams that are currently leading their conferences, as follows:

1 Minnesota
2 Wisconsin
3 Miami
4 Boston University
5 Michigan State
6 Colorado College
7 Cornell
8 Harvard
9 Nebraska-Omaha
10t North Dakota
10t Maine
10t Michigan
13 Boston College
14t New Hampshire
14t Denver
16t Dartmouth
16t Northern Michigan
27t Sacred Heart
— Alabama-Huntsville

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. North Dakota wins comparisons with Maine and Michigan, while Maine wins its head-to-head comparison with Michigan.

Now we choose the teams in the tournament. First we take the autobids, a total of six teams:

AHA – Sacred Heart
CHA – Alabama-Huntsville
CCHA – Miami
ECACHL – Dartmouth
HEA – Boston College
WCHA – Minnesota

We also take the top 10 teams, based on rank order in the PairWise, that are not autobids, and rank the whole group using the PairWise.

So the 16 teams in the tournament, in rank order, are:

1 Minnesota
2 Wisconsin
3 Miami
4 Boston University
5 Michigan State
6 Colorado College
7 Cornell
8 Harvard
9 Nebraska-Omaha
10 North Dakota
11 Maine
12 Michigan
13 Boston College
14 Dartmouth
15 Sacred Heart
16 Alabama-Huntsville

Notice that this is just the top 13 from our previous list, plus autobids Dartmouth, Sacred Heart and UAH.

Step Two

Now it’s time to assign the seeds.

No. 1 Seeds – Minnesota, Wisconsin, Miami, Boston University
No. 2 Seeds – Michigan State, Colorado College, Cornell, Harvard
No. 3 Seeds – Nebraska-Omaha, North Dakota, Maine, Michigan
No. 4 Seeds – Boston College, Dartmouth, Sacred Heart, Alabama-Huntsville

Step Three

We place No. 1 seeds based on proximity to the regional sites. But we place Boston University first, as it is a host school.

No. 4 Boston University is placed in the Northeast Regional in Worcester.
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.

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

We have to place North Dakota first, since it is a host school.

No. 10 North Dakota is placed in No. 8 Harvard’s Regional, the West Regional.
No. 9 Nebraska-Omaha is placed in No. 7 Cornell’s Regional, the Midwest Regional.
No. 11 Maine is placed in No. 6 Colorado College’s Regional, the East Regional.
No. 12 Michigan is placed in No. 5 Michigan State’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 Alabama-Huntsville is sent to Minnesota’s Regional, the West Regional.
No. 15 Sacred Heart is sent to Wisconsin’s Regional, the Midwest Regional.
No. 14 Dartmouth is sent to Miami’s Regional, the East Regional.
No. 13 Boston University is sent to Boston University’s Regional, the Northeast Regional.

The brackets as we have set them up:

West Regional:

Alabama-Huntsville vs. Minnesota
North Dakota vs. Harvard

Midwest Regional:

Sacred Heart vs. Wisconsin
Nebraska-Omaha vs. Cornell

Northeast Regional:

Boston College vs. Boston University
Michigan vs. Michigan State

East Regional:

Dartmouth vs. Miami
Maine vs. Colorado College

Our first concern is avoiding intraconference matchups. We have two, both in the Northeast Regional. Therefore, we move both the bottom seeds and exchange them with the East Regional. This gives us:

West Regional:

Alabama-Huntsville vs. Minnesota
North Dakota vs. Harvard

Midwest Regional:

Sacred Heart vs. Wisconsin
Nebraska-Omaha vs. Cornell

Northeast Regional:

Dartmouth vs. Boston University
Maine vs. Michigan State

East Regional:

Boston College vs. Miami
Michigan vs. Colorado College

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 (Boston University and Minnesota’s brackets) play the other semifinal.

Now many people have asked me why Minnesota, as the number one seed, is sent to Grand Forks in my projection. Yes, Minneapolis is 314 miles from Grand Forks and 279 from Green Bay, but I have my reasons.

Here is my official reason — Grand Forks and Green Bay are pretty much equidistant from Minneapolis. Grand Forks and Green Bay are not equidistant from Madison. Therefore, for that reason and for attendance reasons, I will always put Wisconsin in Green Bay and Minnesota in Grand Forks.

But let’s ask another question — is it fair for Minnesota to get sent to Grand Forks to possibly play North Dakota in the second round of the tournament?

Of course it’s fair. Colorado College was sent to Yost Arena. Minnesota hosted last year’s West Regional. That’s just the way it is — that’s the system. So is it fair? If you ask me, yes.

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 not. So our bracket remains the same.