Notes for the 1/3/93 TCHCR
A CALL TO ARMS
When Army is included, they fall into 40th place. They are 2-3 versus
the other 43 teams. The most significant drop with Army in the fray is
Union, losing 3 spots to #43. The big winner is Denver, climbing 5 to
#20. None of the teams in the top 10 shift places.
LIKE A GOOD NEIGHBOR
I can calculate a (very) simple "connectivity" measure this year. It
is the average distance between teams. For example, the shortest
distance between Minnesota-Duluth and Alaska-Fairbanks is 3: UMD has
played North Dakota, who has played Bowling Green, who has played UAF.
Next week the distance will be 2, after Wisconsin plays UAF.
Each of the 43 teams has 42 distances. I am defining connectivity as
the average of these 43*42 numbers.
Right now, the connectivity is 2.041. Since the only remaining
tournament (Beanpot) will not give us any new connections in the
championship/consolation games, I can find what the connectivity will
be at the end of the regular season: 1.886. The drop is because there
are still some more non-conference games, plus not all league opponents
have faced each other yet. This will be slightly better than last
year's connectivity, 1.903. Plus, this season, the league play-offs in
the CCHA and WCHA may add a few more connections.
GOOD, BAD AND UGLY
Right now, BU has the best average distance at 1.7. Duluth is the
worst, 2.5.
At the end of the regular season, BC and BG will be tied for best at
1.6. BC and BG will be the only two league teams* that have played a
full member from each league. BC plays several ECAC teams, but it faced
Wisconsin and Miami in the Badger Showdown to get complete coverage.
Playing 30 league games, the Bowling Green scheduler should get an
award for still meeting up with a team from each league. In fact, BG
played 2 different ECAC teams while also confronting Maine and North
Dakota twice. Plus, they played their affiliate, Fairbanks.
(*Air Force and UAF also play at least 1 full member from each league,
but with their limited Division I schedules, they only see 11 different
D1 opponents. BG and BC each face 16.)
St. Cloud, who will not play a Division I team out of its own
conference for the second year in a row, will be the worst, 2.4.
MARIUCCI MADNESS
OK, so what happens if Minnesota faces St. Lawrence "like it is
supposed to"? The connectivity improves to 2.030 today and 1.875 at the
end of the year. This is 0.011 better. Creating a connection between the
WCHA and the ECAC would have helped a lot, but the alternative of
having SLU play FSU and UM play UIC was not disastrous.
The other tournaments turned out pretty good, connectivity-wise. I
calculated 1.871 as the absolute best possible connectivity. If the
Mariucci goes the best way, we would have been only 0.004 off of that
mark.
THE KEY SERIES
One problem that people raised last year was that they thought the
single WCHA-ECAC game (Wisconsin-Yale) was too important to the
connectivity. I think I have figured out a way to detect such key
connections. I consulted my local graph theory guru on this topic, but
he was not able to help, so I am kind of making this up as I go along.
Anyway, what I did was to take the schedule graph for the end of the
season, temporarily delete each connection 1 at a time, and
re-calculate the connectivity. The connection that caused the
connectivity measure to jump up the most when it was deleted shall be
called "the most important connection." This turns out to be the
Colorado-Air Force connection, with the North Dakota-Bowling Green one
a close second. The connectivity climbs 0.011 to 1.897 when the CC-USAF
link is cut and 0.010 when the ND-BG edge is gone.
Please note that these are CONNECTIONS and not games played that I am
evaluating. Since CC and USAF play twice, maybe I should divide 0.011
by two to get the importance of the individual games. Like I said,
I am making this up, so I'll listen to any bright ideas out there.
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