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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 is 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 (through all games of March 5, 2006):

1 Minnesota
2 Wisconsin
3 Miami
4t Boston University
4t Michigan State
6 Colorado College
7 Nebraska-Omaha
8t Harvard
8t North Dakota
10 Cornell
11t Maine
11t Denver
13t Michigan
13t New Hampshire
15 Ferris State
16 Boston College
17 Dartmouth
21t Holy Cross
— Niagara

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

Adding in Niagara in the PairWise, we now get a Top 16, plus teams that won the regular-season titles in their conferences, giving us:

1 Minnesota
2 Wisconsin
3 Miami
4t Boston University
4t Michigan State
6 Colorado College
7 Nebraska-Omaha
8t Harvard
8t North Dakota
10 Cornell
11t Maine
11t Denver
13t Michigan
13t New Hampshire
15 Ferris State
16 Boston College
17 Dartmouth
21t Holy Cross
— Niagara

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 Niagara.

Now let’s break the ties.

Boston University wins the comparison with Michigan State. Likewise Maine wins against Denver and Michigan wins against New Hampshire.

Now choose the teams in the tournament. First we take the autobids, a total of six teams. Because we do not know who will win the tournaments, we are going to make an assumption — that the number-one seed in each tournament will win it. Obviously, this might not happen, but it’s the best guess at the moment. These six teams are:

AHA – Niagara
CHA – Holy Cross
CCHA – Miami
ECACHL – Dartmouth
HEA – Boston University
WCHA – Minnesota

Then we take the next 10 teams, in rank order, that are not autobids. Therefore, 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 Nebraska-Omaha
8 Harvard
9 North Dakota
10 Cornell
11 Maine
12 Denver
13 Michigan
14 Dartmouth
15 Holy Cross
16 Niagara

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, Nebraska-Omaha, Harvard
No. 3 Seeds – North Dakota, Cornell, Maine, Denver
No. 4 Seeds – Michigan, Dartmouth, Holy Cross, Niagara

Step Three

We place No. 1 seeds based on proximity to the regional sites. 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 Nebraska-Omaha 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. 9 North Dakota is placed in No. 8 Harvard’s Regional, the West Regional.
No. 10 Cornell is placed in No. 7 Nebraska-Omaha’s Regional, the Midwest Regional.
No. 11 Maine is placed in No. 6 Colorado College’s Regional, the East Regional.
No. 12 Denver 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 Niagara 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 Michigan is sent to Boston University’s Regional, the Northeast Regional.

The brackets as we have set them up:

West Regional:

Niagara vs. Minnesota
North Dakota vs. Harvard

Midwest Regional:

Holy Cross vs. Wisconsin
Cornell vs. Nebraska-Omaha

Northeast Regional:

Michigan vs. Boston University
Denver vs. Michigan State

East Regional:

Dartmouth vs. Miami
Maine vs. Colorado College

Our first concern is avoiding intraconference matchups. We have none.

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.

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.