March 27, 2008
What Are the Odds?
by John Whelan/CHN Staff
"What are the odds?" That's a question college hockey fans often ask themselves this time of year. What are the odds that my team will beat its first-round opponent in the NCAA, what are the odds it will win two games and make it to the Frozen Four, what are the odds it will win the whole thing?
Well, one way of answering these questions is to use KRACH, the rating system recommended by CHN for assessing the strengths of teams based on the outcomes of their games, accounting for strength of schedule. KRACH is based on a model that says a team's odds of winning a particular game is the ratio of their rating to their opponent's rating.
For example, North Dakota's KRACH rating (613.7) is about four times the rating (157.1) of Princeton, their first-round opponent. So their odds of winning that game are 4-to-1, or about an 80 percent chance. In the other Midwest Regional semifinal, Denver's rating is about twice that of Wisconsin (471.8 to 230.4), so it has about a 67 percent chance of winning in the first round.
What are the odds of North Dakota winning two games and making the Frozen Four? Well, if it wins its first game (an 80 percent chance, remember), it has a 67 percent chance of playing Denver (which, it turns out, it has a 57 percent chance of beating) and a 33 percent chance of playing Wisconsin (which it should beat 73 percent of the time). Putting it all together — 0.80 x ((0.67 x 0.56) + (0.33 x 0.73)), for those of you who majored in math or science — you come up with a 49 percent chance that the Sioux will make the Frozen Four this year.
So here they are, the odds of each team making it through each round of the NCAAs, according to KRACH:
| Seed | Team | KRACH | Odds of Winning | |||
| 1 game | 2 games | 3 games | 4 games | |||
| 1W | New Hampshire | 427.7 | 69% | 33% | 15% | 7.1% |
| 2W | Colorado College | 585.3 | 67% | 42% | 22% | 12% |
| 3W | Michigan State | 294.5 | 33% | 16% | 5.8% | 2.2% |
| 4W | Notre Dame | 192.5 | 31% | 9.2% | 2.6% | 0.77% |
| Seed | Team | KRACH | Odds of Winning | |||
| 1 game | 2 games | 3 games | 4 games | |||
| 1M | North Dakota | 613.7 | 80% | 49% | 29% | 16% |
| 2M | Denver | 471.8 | 67% | 34% | 18% | 8.4% |
| 3M | Wisconsin | 230.4 | 33% | 11% | 4.0% | 1.2% |
| 4M | Princeton | 157.1 | 20% | 6.1% | 1.7% | 0.41% |
| Seed | Team | KRACH | Odds of Winning | |||
| 1 game | 2 games | 3 games | 4 games | |||
| 1N | Miami | 558.6 | 91% | 62% | 33% | 17% |
| 2N | Boston College | 265.7 | 50% | 18% | 6.7% | 2.3% |
| 3N | Minnesota | 268.4 | 50% | 19% | 6.9% | 2.3% |
| 4N | Air Force | 55.06 | 9.0% | 1.5% | 0.17% | 0.018% |
| Seed | Team | KRACH | Odds of Winning | |||
| 1 game | 2 games | 3 games | 4 games | |||
| 1E | Michigan | 769.4 | 89% | 68% | 43% | 26% |
| 2E | St. Cloud State | 285.5 | 61% | 20% | 8.0% | 3.0% |
| 3E | Clarkson | 180.7 | 39% | 9.4% | 2.8% | 0.79% |
| 4E | Niagara | 97.14 | 11% | 3.3% | 0.62% | 0.11% |
Hey John, cool article, but your math needs a double-check.
Totalling up the last column, I see that we have a 72% chance of having a national champion emerge from this collection of 16 teams.
Not sure what the outcome is the other 28% of the time ;)
FWIW, here are the "win 4" odds I've computed:
Michigan 26.7%
North Dakota 15.4%
Miami 17.0%
New Hampshire 7.1%
Colorado College 12.2%
Denver 8.3%
St. Cloud State 3.1%
Boston College 2.3%
Michigan State 2.2%
Minnesota 2.4%
Wisconsin 1.2%
Clarkson 0.8%
Notre Dame 0.8%
Princeton 0.4%
Niagara 0.1%
Air Force 0.0%
Mar 28 2008, 1:37 pm by Dave, Madison
Ack, you're right. There was a bug in the way the some potential opponents were determined. It's been fixed now. Thanks!
Mar 29 2008, 7:22 am by John, Berlin
