One of the advantages of the KRACH rating system is that it lets you
not only say whether one teams is better than another, but quantify
that difference, in terms of a probability that one or the other would
win a head-to-head game.  I've gone through the NCAA tournament and
worked out the probability for each team of advancing to the regional
finals, Frozen Four[TM], championship game, or national title, given
their potential opponents.  Here they are:

                             ____O d d s   o f   w i n n i n g____
Seed ___Team___      KRACH   1 game  2 games   3 games    4 games

1W Minnesota         787.43  97.58%  59.19%    27.91%     14.40%
2W Ferris State      494.43  48.43%  19.35%     6.998%     2.826%
3W North Dakota      526.57  51.57%  21.37%     8.033%     3.363%
4W Mercyhurst        19.530   2.42%   0.08917%  0.002072%  0.0000566%

1M Colorado College  1105.1  95.14%  60.48%    37.79%     22.57%
2M Maine             698.83  55.60%  22.99%    11.83%      5.758%
3M Michigan          558.04  44.40%  16.13%     7.403%     3.202%
4M Wayne State       56.395   4.855%  0.3994%   0.03224%   0.002403%

1E Cornell           1022.7  68.03%  43.7%     26.49%     14.78%
2E Boston College    706.33  66.82%  31.28%    16.2%       7.576%
3E Ohio State        350.68  33.18%  10.24%     3.607%     1.106%
4E MSU-Mankato       480.58  31.97%  14.78%     6.281%     2.361%

1N New Hampshire     892.32  69.76%  43.34%    23.74%     12.46%
2N Boston University 664.66  64.43%  31.5%     15.01%      6.799%
3N Harvard           366.94  35.57%  12.47%     4.222%     1.335%
4N St. Cloud State   386.76  30.24%  12.69%     4.443%     1.454%

Credits: the KRACH ratings are based on the results of the entire
season from US College Hockey Online, and the program to calculate the
KRACH and the probabilities was written by me and run on USCHO's
server.  Ken Butler first developed KRACH, which is an application to
college hockey of a method independently discovered by Zermelo and by
Bradley and Terry.

Lots of observations can be made, but the most interesting is probably
to compare Cornell's and Minnesota's odds of reaching each round.
Minnesota has a better shot to make the Frozen Four[TM] despite a
lower KRACH, because their odds of beating their weaker first-round
opponent are higher, but Cornell has a slightly better chance of
winning the whole tournament.  Discuss.
                                          John Whelan, Cornell '91
                                                 [log in to unmask]
                                     http://www.amurgsval.org/joe/

Enjoy the latest Hockey Geek tools at slack.net/hockey