As soon as the NCAA Men’s Hockey selection show ends, three questions inevitably come up:

Which is the toughest bracket?

Where are the likely upsets?

Which teams will make the Frozen Four?

And for most of us, we haven’t seen enough of the teams from the other conferences to make more than a guess about the game results. In that respect, it’s much like filling out a March Madness bracket for college hoops.

Fortunately, there’s a system that allows us to compare teams against each other and calculate each team’s expected winning percentage against any other.

The system is called **KRACH**, short for “Ken’s Ratings for American College Hockey”. KRACH rates teams based on their won-loss records against each other, and a key component is that a team’s strength of schedule is based on the ratings themselves, and as such cannot easily be distorted by teams with strong records against weak opposition.

The ratings are on an odds scale, so if Team A’s KRACH rating is three times as large as Team B’s, Team A would be expected to amass a winning percentage of .750 and Team B a winning percentage of .250 if the two teams played each other enough times. The correct ratings are defined such that the “expected” winning percentage for a team in the games it’s already played is equal to its “actual” winning percentage.

*A more complete explanation can be found here. The KRACH ratings for each team can be found here. Note that all 59 Division I tournament-eligible teams are included in the ratings, so all tournament teams can easily be compared.*

Using these ratings, let’s revisit the questions we posed above.

**Which is the toughest bracket?**

By every measure, the **West Regional** in Colorado Springs, Colorado is the toughest bracket. New Hampshire (427.7 KRACH) has the most difficult road of any #1 seed, with #4 Notre Dame (192.5) in the first round and, should they advance, the winner of #2 Colorado College (585.3) and #3 Michigan State (294.5) in the regional final. So looking at these four teams, here are each team’s chances of advancing to the Frozen Four:

#1 New Hampshire: 33.04%

#2 Colorado College: 42.05%

#3 Michigan State: 15.70%

#4 Notre Dame: 9.22%

Note that #2 seed Colorado College is the favorite to come out of the West Regional, despite being a lower seed than New Hampshire. This has nothing to do with home-ice advantage, as that factor is not included in the ratings.

*Remember, the KRACH ratings are on an odds scale, and comparing each team’s rating gives us an expected winning percentage. Anything can happen in a one game format, but these percentages give us an idea of what would happen if the games were played enough times.*

The next toughest bracket is found in the **Midwest Regional** (Madison, WI), where #1 North Dakota (613.7) will face #4 Princeton (157.1) in the opener. Should they advance to the regional final, they would meet either #2 Denver University (471.9) or #3 Wisconsin (230.4). Each team’s chance of advancing to the Frozen Four is listed below:

#1 North Dakota: 49.23%

#2 Denver: 33.53%

#3 Wisconsin: 11.11%

#4 Princeton: 6.13%

We move next to the **East Regional** (Albany, NY), where #1 Michigan (769.5) takes on #4 Niagara (97.14) while #2 St. Cloud State (285.5) battles #3 Clarkson (180.7). This bracket is slightly stronger than the Northeast Regional (found below) because Niagara is a tougher first round opponent than Air Force would have been. Here are the percentages:

#1 Michigan: 67.53%

#2 St. Cloud State: 19.84%

#3 Clarkson: 9.37%

#4 Niagara: 3.26%

And finally, the **Northeast Regional** (Worcester, MA): #1 Miami (558.7) draws #4 Air Force (55.05) in round one, while #2 Boston College (265.7) takes on #3 Minnesota (268.4). Minnesota has a slightly better chance of coming out of this bracket than Boston College, as you’ll see below:

#1 Miami: 61.59%

#2 Boston College: 18.29%

#3 Minnesota: 18.58%

#4 Air Force: 1.53%

So from the percentages above, we can see that the likely “upsets” are #3 Minnesota over #2 Boston College in the Northeast Regional semifinal and #2 Colorado College over #1 New Hampshire in the West Regional final. The #4 with the best shot of knocking off a #1 seed? Notre Dame.

And now to question 3:

**Which teams will make the Frozen Four? **

Here are each team’s chances to win a regional and advance to the Frozen Four, listed in the PairWise seed order that the committee used to fill in the bracket:

#1 Michigan: 67.53%

#2 Miami: 61.59%

#3 North Dakota: 49.23%

#4 New Hampshire: 33.04%

#5 Colorado College: 42.05%

#6 Boston College: 18.29%

#7 Denver: 33.53%

#8 St. Cloud State: 19.84%

#9 Michigan State: 15.70%

#10 Clarkson: 9.37%

#11 Minnesota: 18.58%

#12 Wisconsin: 11.11%

#13 Notre Dame: 9.22%

#14 Princeton: 6.13%

#15 Niagara: 3.26%

#16 Air Force: 1.53%

So by the numbers, look for Michigan, Miami, North Dakota, and Colorado College in the Frozen Four, but don’t be surprised to see Denver, New Hampshire, St. Cloud, or Minnesota in the mix as well. As they say: anything can happen, and probably will.

*Thank you for reading. I welcome your comments and suggestions. Check back later this week for regional tournament previews and predictions.*

Here’s the same exercise carried out for each game:

KRACH predicts NCAA Hockey 2008

(Don’t worry about the KRACH values being different, remember that it’s the ratios that matter and they’re the same; Dave used USCHO’s KRACH where 100 is normalized to a fictitious average team, whereas I used SiouxSports.com KRACH where 100 is normalized to North Dakota)