Since people have been asking, I've recalculated the odds each of the
four Frozen Four teams have of winning their semifinal and of winning
the championship, as determined by their KRACH ratings, and by their
KASA ratings, both calculated from all results so fat, including last
weekend's regional games. (Since no one is on home ice for the Frozen
Four, the only difference in the calculations is that KRACH and KASA
have rated teams slightly differently due to the impact of home ice on
their strength of schedule to date.) Here are the results, followed
by an explanation of how we could calculate these probabilities by
hand.
(Note that you shouldn't really compare the KRACH and KASA ratings of a
particular team directly; what actually matters is the ratio of two
teams' ratings in either system. For example, it looks like KASA
rates Cornell lower than KRACH, but in a balanced round-robin against
every other team in Division I, KRACH predicts a winning percentage
(RRWP) of .8720 while KASA predicts .8740.)
| __Odds to win__ | __Odds to win__
Seed ___Team___ | KRACH 1 game 2 games | KASA 1 game 2 games
--------------------+-------------------------+------------------------
1(1E) Cornell | 1234.1 55.57% 34.91% | 1224.0 56.23% 36.06%
4(1N) New Hampshire | 986.79 44.43% 25.54% | 952.63 43.77% 25.47%
--------------------+-------------------------+------------------------
2(3M) Michigan | 667.47 45.91% 17.18% | 641.03 46.93% 17.33%
3(1W) Minnesota | 786.44 54.09% 22.36% | 725.00 53.07% 21.14%
(The seeds are determined by the bracketing; the East Regional
champion is the #1 seed, the Midwest #2, etc, due to the PWR rankings
of the #1 seeds in the four regionals.)
Now, how to calculate these probabilities by hand. Cornell's
probability of beating UNH in the semis is
1234.1/(1234.1+986.79) = 55.57%
In the other semi, Michigan's chance to beat Minnesota is
667.47/(667.47+786.44) = 45.91%
and Minnesota's chance to beat Michigan is
786.44/(667.47+786.44) = 54.09%
That means Cornell, if they win the semis, will have a 45.91% chance
of playing Michigan, a game they have a
1234.1/(1234.1+667.47) = 64.90%
chance of winning, and a 54.09% chance of playing Minnesota, a game
which they have a
1234.1/(1234.1+786.44) = 61.08%
chance of winning. Putting it all together, this makes their odds of
winning the whole thing
55.56% x ( 45.91% x 64.90% + 54.09% x 61.08% ) = 34.91%
which is what we have in the table. The calculations for the other
four teams can be done the same way.
John Whelan, Cornell '91
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http://www.amurgsval.org/joe/
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