With the NCAA Frozen Four returning to St. Paul in April, it’s not too early to look at a potential tournament field and which teams might be playing for a trip to Xcel Energy Center.

And there’s an interesting scenario that could play out. It’s still early — things can and will change — but how fun would it be to have an NCAA West Regional in Sioux Falls that included St. Cloud State, North Dakota and the Gophers among its four teams?

If the tournament field was selected today, that just might happen. But, of course, the field isn’t being selected today and there’s still a lot of hockey to be played.

To arrive at that Huskies, Fighting Hawks and Gophers trio in Sioux Falls for the first NCAA tournament games ever in South Dakota, let’s see how the NCAA selection committee picks its 16-team field.

First, the tournament champions of the six Division I conferences — Atlantic Hockey, Big Ten, ECAC, Hockey East, NCHC and WCHA — earn automatic bids. Then, the rest of the field — 10 teams — is filled by using a statistical formula that is essentially the same as U.S. College Hockey Online’s PairWise Rankings.

There are four regionals in the single-elimination tournament, and this year’s sites are Sioux Falls (West Regional, with North Dakota as host); Allentown, Pa. (Midwest, with Penn State as host); Bridgeport, Conn. (East, with Yale as host); and Worcester, Mass. (Northeast, with Holy Cross as host). The host teams, if they make the tournament field, will play in their corresponding regional.

Through Sunday’s games, the PairWise Rankings were:

1. St. Cloud State

2. Notre Dame

3. Clarkson

4. Cornell

5. Ohio State

6. Denver

7. Minnesota State Mankato

8. North Dakota

9. Minnesota

10. Western Michigan

11. Providence

12. Penn State

13. Northeastern

14. Nebraska Omaha

15. Minnesota Duluth

16. Miami (Ohio)

There also were two conference leaders who were outside the top 16:

20. Boston College

26. Canisius

Some early(!) predictions

I’ll project all the conference leaders as tournament champions, so that puts Boston College and Canisius in the field, bumping out at-large candidates Minnesota Duluth and Miami (Ohio).

The No. 1 seeds would be St. Cloud State, Notre Dame, Clarkson and Cornell.

The No. 2 seeds would be Ohio State, Denver, MSU Mankato and North Dakota.

The No. 3 seeds would be Minnesota, Western Michigan, Providence and Penn State.

The No. 4 seeds would be Northeastern, Nebraska Omaha, Boston College and Canisius.

Now it’s time to assign the No. 1 seeds (first through fourth in the PairWise) to the regionals. Here’s what I have, with the No. 1 overall seed playing as close to home as possible:

West (Sioux Falls): St. Cloud State (No. 1 overall)

Midwest (Allentown): Notre Dame (No. 2)

Northeast (Worcester): Clarkson (No. 3)

East (Bridgeport): Cornell (No. 4)

In assigning teams to regions, the committee wants quarterfinal matchups to potentially be No. 1 vs. No. 8, No. 2 vs. No. 7, No. 3 vs. No. 6, and No. 4 vs. No. 5. Also, it wants one regional to have seeds 1, 8, 9 and 16; another to have 2, 7, 10 and 15; a third to have 3, 6, 11 and 14; and the fourth to have 4, 5, 12 and 13. All those add up to 34, to achieve balance. However, the committee will avoid first-round matchups of teams from the same conference, which could make the regionals not perfectly balanced. Host teams in regionals also could throw of the balance.

In using those guidelines, here are the No. 2 seeds:

West: North Dakota (No. 8, must be placed here as host)

Midwest: MSU Mankato (No. 7)

Northeast: Denver (No. 6)

East: Ohio State (No. 5)

Here are the No. 3 seeds:

West: Gophers (No. 9)

Midwest: Penn State (No. 12, must be placed here as host)

Northeast: Providence (No. 11)

East: Western Michigan (No. 10)

And here are the No. 4 seeds:

West: Canisius (No. 16)

Midwest: Boston College (No. 15)

Northeast: Nebraska Omaha (No. 14)

East: Northeastern (No. 13).

We have no matchups between teams from the same conference in the first round, so no changes are needed in that regard. The committee could move around some No. 4 seeds for attendance purposes, but I’ll stay with the following bracket:

West Regional (March 23-24, Sioux Falls)

No. 1 St. Cloud State vs. No. 16 Canisius

No. 8 North Dakota vs. No. 9 Gophers

Midwest Regional (March 24-25, Allentown, Pa.)

No. 2 Notre Dame vs. No. 15 Boston College

No. 7 MSU Mankato vs. No. 12 Penn State

Northeast Regional (March 24-25, Worcester, Mass.)

No. 3 Clarkson vs. No. 14 Nebraska Omaha

No. 6 Denver vs. No. 11 Providence

East Regional (March 23-24, Bridgeport, Conn.)

No. 4 Cornell vs. No. 13 Northeastern

No. 5 Ohio State vs. No. 10 Western Michigan

Again, games to be played will change things, but the potential matchups are interesting.

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Randy Johnson covers college sports for the Star Tribune. Follow him on Twitter at @RJStrib.