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Wed, 10 Mar 1993 01:03:59 EST
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First off, let's take care of some unfinished business by quickly
recapping how CHODR did the past couple of weeks.  We forgot to recap the
week that ended on February 28, which was a good week for the system as it
correctly picked 33 games and missed only 9.  This past week (ending on
March 7) wasn't as good as the system went 22-14 on predicting winners.
 
Secondly, there have been a few recent inquiries as to how the CHODR
predictions are calculated.  The predictions come directly from the
ratings, as determined by the following formulas as given in the original
CHODR introduction:
 
>   Team A's predicted goals = A's Offensive Rating
>                            + B's Defensive Rating
>                            - Average Offensive/Defensive Rating
>                          +/- Home Ice Advantage
>
>   Team B's predicted goals = B's Offensive Rating
>                            + A's Defensive Rating
>                            - Average Offensive/Defensive Rating
>                          +/- Home Ice Advantage
>
>The Average Rating is subtracted from each team's predicted score
>because the average is already included in each teams rating, so it
>ends up getting included twice when the ratings are summed.  The Home
>Ice Advantage value gets added to the home team's predicted score and
>subtracted from the away team's predicted score.  No adjustment is
>made for a game on neutral ice.  The Home Ice Advantage value used in
>the system is +/- 0.375 goals per game, since home teams have, on
>average, outscored their opposition by about 0.75 goals per game in
>Division I in recent years.
 
If you missed the full CHODR introduction and would like to have it sent
to you, please respond by private mail.
 
Note: the predictions below will be slightly different than those based
on the CHODR ratings published earlier because the results of the two ECAC
preliminary round games are included here.
 
 
And now for this week's predictions, and, as promised, something new to go
with them - probabilities.  We've listed the predictions in the normal
fashion for those who just want "the latest line" but a summary for each
series is included below.  The summary includes information such as the
chance of a win for each team in each game, along with overall chances of
winning the series.  There is alot of information that you may find fun
and interesting.  First, a bit of mathematical explanation for those who
are curious.
 
The predicted scores produced by CHODR are not meant to be an exact
estimate of the outcome for any one game.  What the predicted scores
reflect is an estimate of the average score if a very large number of
games were played between the two teams.  Of course, the score in any one
game could be quite differerent from the average, or expected score,
otherwise we wouldn't bother to play.  However, we would expect that the
most common scores are those close to the average score, and that as we
move further away from the average, those scores become less and less
likely.
 
The Poisson Random Variable Distribution is the method we use to model
this scenario.  This distribution is used to model variables which take on
integral values such as 0, 1, 2, 3, etc...  (looks like possible values
for hockey scores, doesn't it?).  Given a single paramater which is the
expected value (not necessarily an integer), i.e. the predicted score, it
provides the probabilities that the value is 0, is 1, is 2, and so on.
The distribution has the property that the sum of P(N)*N, where N is all
the integers, will be the original expected value.  Therefore, although
the value for any one trial may not be the expected value (how can a team
score 4.3 goals?), the average value for a large number of trials will
match the expected value in this distribution.
 
So there you go - we know the probability that Team A will score 0, 1, 2,
etc.. goals based on their expected value and we can do the same for their
opponent Team B.  To compute the probability that Team A will win we
simply take all the possible combinations of the two such that Team A
scores more goals than Team B.  We can do the same for B and whatever is
left over is the chance we go to overtime.  Here we are concerned not with
how many goals are scored, but who scores first so we look at the rate at
which each team scores.  We use a similar mechanism known as an Exponential
Random Variable, which models the time until some expected event takes place
(i.e. the game winning goal), based on the rate at which the events occur
(from the predicted score).
 
With me so far?  The rest is easy, once we have the probabilities of a win
for each team in a game, accounting for the appropriate overtime scenario
(none, 5-minute, sudden-death), we can compute all our interesting numbers
as appropriate for the playoff format in each league (summarized below)
using standard probability theory.
 
While that is by no means a complete explanation of all the math involved,
it does cover the basics.  Questions are of course welcome, but please
send private mail to BOTH of us and NOT the list.
 
First, a quick summary of the upcoming action.  Not surprisingly, the home
teams (higher seeds) are favored in every game.
 
 
ECAC:
Two games with no OT.  If series tied, third game with sudden death OT.
 
#10 Princeton           1.89 at #1 HARVARD             4.89
 #9 Colgate             2.30 at #2 RPI                 5.25
 #6 St Lawrence         2.78 at #3 CLARKSON            4.87
 #5 Yale                3.97 at #4 BROWN               5.25
 
 
Hockey East:
Two games with 5 min OT.  If series tied, sudden death after 2nd game.
 
 #8 Northeastern        1.98 at #1 MAINE               7.57
 #7 Boston College      2.15 at #2 BOSTON UNIVERSITY   5.85
 #6 Merrimack           2.99 at #3 NEW HAMPSHIRE       5.41
 #5 Providence          3.40 at #4 UMASS-LOWELL        4.36
 
 
CCHA:
Best of three games, each to completion (sudden death OT).
 
#12 Ohio State          1.47 at #1 MIAMI               6.73
#11 Notre Dame          1.14 at #2 MICHIGAN            6.72
#10 Illinois-Chicago    1.95 at #3 LAKE SUPERIOR       5.49
 #9 Kent                2.90 at #4 MICHIGAN STATE      5.08
 #8 Bowling Green       3.55 at #5 WESTERN MICHIGAN    4.51
 #7 Alaska-Fairbanks    3.65 at #6 FERRIS STATE        4.00
 
 
WCHA:
Best of three games, each to completion (sudden death OT).
 
#10 Alaska-Anchorage    1.77 at #1 MINNESOTA-DULUTH    5.24
 #9 Colorado College    2.78 at #2 WISCONSIN           5.91
 #8 North Dakota        3.03 at #3 MINNESOTA           4.74
 #7 St Cloud            2.89 at #4 MICHIGAN TECH       4.16
 #6 Denver              3.31 at #5 NORTHERN MICHIGAN   4.68
 
 
Now the summaries (with probabilities) for each series.  If you're going
to the games (of course you are), print out a copy of the series summary
to bring along.  It will give you something to talk about in between
periods.  Hopefully it's self-explanatory.
 
 
In the ECAC:
 
First two games are played Friday, March 12 and Saturday, March 13 with no
overtime.  If series is tied (split or two ties), a third game is played
Sunday, March 14.  If tied at the end of regulation, this game will be
played in sudden death overtime until someone wins.  Therefore, for the
first two games see the "In Regulation" column for each teams chances.
The overall chances apply only in the third game.
 
 
#10 Princeton            1.89 at
 #1 Harvard              4.89                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Princeton          wins:    10.5%      8.2%     2.3% (27.9%)
   Chance Harvard            wins:    89.5%     83.5%     5.9% (72.1%)
   Chance of a tie:                              8.2%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              6:08
   -------------------------------------------------------------------
   Chance Princeton             wins in two games:     2.0%
   Chance Harvard               wins in two games:    83.5%
   Chance of a third game:                            14.4%
   -------------------------------------------------------------------
   Chance Princeton             wins series:           3.6%
   Chance Harvard               wins series:          96.4%
   -------------------------------------------------------------------
   If Princeton          wins game #1:
      Chance Princeton          wins series:          25.3%
      Chance Harvard            wins series:          74.7%
   If Harvard            wins game #1:
      Chance Princeton          wins series:           0.9%
      Chance Harvard            wins series:          99.1%
   -------------------------------------------------------------------
 
 
 #9 Colgate              2.30 at
 #2 RPI                  5.25                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Colgate            wins:    12.4%      9.8%     2.6% (30.4%)
   Chance RPI                wins:    87.6%     81.7%     5.9% (69.6%)
   Chance of a tie:                              8.4%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:31
   -------------------------------------------------------------------
   Chance Colgate               wins in two games:     2.6%
   Chance RPI                   wins in two games:    80.6%
   Chance of a third game:                            16.8%
   -------------------------------------------------------------------
   Chance Colgate               wins series:           4.7%
   Chance RPI                   wins series:          95.3%
   -------------------------------------------------------------------
   If Colgate            wins game #1:
      Chance Colgate            wins series:          28.4%
      Chance RPI                wins series:          71.6%
   If RPI                wins game #1:
      Chance Colgate            wins series:           1.2%
      Chance RPI                wins series:          98.8%
   -------------------------------------------------------------------
 
 
 #6 St Lawrence          2.78 at
 #3 Clarkson             4.87                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance St Lawrence        wins:    21.2%     17.1%     4.1% (36.4%)
   Chance Clarkson           wins:    78.8%     71.7%     7.1% (63.6%)
   Chance of a tie:                             11.2%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:26
   -------------------------------------------------------------------
   Chance St Lawrence           wins in two games:     6.7%
   Chance Clarkson              wins in two games:    67.5%
   Chance of a third game:                            25.8%
   -------------------------------------------------------------------
   Chance St Lawrence           wins series:          12.2%
   Chance Clarkson              wins series:          87.8%
   -------------------------------------------------------------------
   If St Lawrence        wins game #1:
      Chance St Lawrence        wins series:          43.5%
      Chance Clarkson           wins series:          56.5%
   If Clarkson           wins game #1:
      Chance St Lawrence        wins series:           3.6%
      Chance Clarkson           wins series:          96.4%
   -------------------------------------------------------------------
 
 
 #5 Yale                 3.97 at
 #4 Brown                5.25                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Yale               wins:    33.0%     27.7%     5.3% (43.1%)
   Chance Brown              wins:    67.0%     60.0%     7.0% (56.9%)
   Chance of a tie:                             12.3%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              4:31
   -------------------------------------------------------------------
   Chance Yale                  wins in two games:    14.5%
   Chance Brown                 wins in two games:    50.7%
   Chance of a third game:                            34.8%
   -------------------------------------------------------------------
   Chance Yale                  wins series:          26.0%
   Chance Brown                 wins series:          74.0%
   -------------------------------------------------------------------
   If Yale               wins game #1:
      Chance Yale               wins series:          59.8%
      Chance Brown              wins series:          40.2%
   If Brown              wins game #1:
      Chance Yale               wins series:           9.2%
      Chance Brown              wins series:          90.8%
   -------------------------------------------------------------------
 
 
In Hockey East:
 
Two games are played Friday, March 12 and Saturday, March 13 with five
minute overtimes if needed.  If series is tied (split or two ties), sudden
death overtime will be played following the second game.  Overall
probabilites are based on five minute overtimes.  A separate line details
possibilities for the sudden death overtime if needed.
 
 
 #8 Northeastern         1.98 at
 #1 Maine                7.57                     In        5 Minute
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Northeastern       wins:     2.1%      1.9%     0.3% (11.4%)
   Chance Maine              wins:    96.8%     95.7%     1.0% (43.5%)
   Chance of a tie:                    1.1%      2.4%     1.1% (45.1%)
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              4:21
   -------------------------------------------------------------------
   If series is tied after two games, sudden death overtime is played:
   Chance Northeastern          wins:                 20.7%
   Chance Maine                 wins:                 79.3%
   -------------------------------------------------------------------
   Chance Northeastern          wins in two games:     0.1%
   Chance Maine                 wins in two games:    95.8%
   Chance of sudden death overtime:                    4.1%
   -------------------------------------------------------------------
   Chance Northeastern          wins series:           1.0%
   Chance Maine                 wins series:          99.0%
   -------------------------------------------------------------------
   If Northeastern       wins game #1:
      Chance Northeastern       wins series:          23.3%
      Chance Maine              wins series:          76.7%
   If Maine              wins game #1:
      Chance Northeastern       wins series:           0.4%
      Chance Maine              wins series:          99.6%
   -------------------------------------------------------------------
 
 
 #7 Boston College       2.15 at
 #2 Boston University    5.85                     In        5 Minute
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Boston College     wins:     7.0%      6.2%     0.8% (13.1%)
   Chance Boston University  wins:    89.8%     87.6%     2.2% (35.6%)
   Chance of a tie:                    3.2%      6.2%     3.2% (51.3%)
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:12
   -------------------------------------------------------------------
   If series is tied after two games, sudden death overtime is played:
   Chance Boston College        wins:                 26.9%
   Chance Boston University     wins:                 73.1%
   -------------------------------------------------------------------
   Chance Boston College        wins in two games:     0.9%
   Chance Boston University     wins in two games:    86.3%
   Chance of sudden death overtime:                   12.7%
   -------------------------------------------------------------------
   Chance Boston College        wins series:           4.4%
   Chance Boston University     wins series:          95.6%
   -------------------------------------------------------------------
   If Boston College     wins game #1:
      Chance Boston College     wins series:          34.4%
      Chance Boston University  wins series:          65.6%
   If Boston University  wins game #1:
      Chance Boston College     wins series:           1.9%
      Chance Boston University  wins series:          98.1%
   -------------------------------------------------------------------
 
 
 #6 Merrimack            2.99 at
 #3 New Hampshire        5.41                     In        5 Minute
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Merrimack          wins:    17.1%     15.3%     1.8% (17.9%)
   Chance New Hampshire      wins:    77.9%     74.7%     3.2% (32.4%)
   Chance of a tie:                    5.0%     10.0%     5.0% (49.6%)
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              4:57
   -------------------------------------------------------------------
   If series is tied after two games, sudden death overtime is played:
   Chance Merrimack             wins:                 35.6%
   Chance New Hampshire         wins:                 64.4%
   -------------------------------------------------------------------
   Chance Merrimack             wins in two games:     4.6%
   Chance New Hampshire         wins in two games:    68.5%
   Chance of sudden death overtime:                   26.9%
   -------------------------------------------------------------------
   Chance Merrimack             wins series:          14.2%
   Chance New Hampshire         wins series:          85.8%
   -------------------------------------------------------------------
   If Merrimack          wins game #1:
      Chance Merrimack          wins series:          49.8%
      Chance New Hampshire      wins series:          50.2%
   If New Hampshire      wins game #1:
      Chance Merrimack          wins series:           6.1%
      Chance New Hampshire      wins series:          93.9%
   -------------------------------------------------------------------
 
 
 #5 Providence           3.40 at
 #4 UMass-Lowell         4.36                     In        5 Minute
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Providence         wins:    32.6%     29.7%     2.9% (20.8%)
   Chance UMass-Lowell       wins:    60.2%     56.5%     3.7% (26.8%)
   Chance of a tie:                    7.2%     13.8%     7.2% (52.4%)
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:22
   -------------------------------------------------------------------
   If series is tied after two games, sudden death overtime is played:
   Chance Providence            wins:                 43.8%
   Chance UMass-Lowell          wins:                 56.2%
   -------------------------------------------------------------------
   Chance Providence            wins in two games:    15.3%
   Chance UMass-Lowell          wins in two games:    44.9%
   Chance of sudden death overtime:                   39.8%
   -------------------------------------------------------------------
   Chance Providence            wins series:          32.8%
   Chance UMass-Lowell          wins series:          67.2%
   -------------------------------------------------------------------
   If Providence         wins game #1:
      Chance Providence         wins series:          66.2%
      Chance UMass-Lowell       wins series:          33.8%
   If UMass-Lowell       wins game #1:
      Chance Providence         wins series:          14.3%
      Chance UMass-Lowell       wins series:          85.7%
   -------------------------------------------------------------------
 
 
In the CCHA:
 
Best of three series is played on Friday, March 12, Saturday, March 13,
and Sunday, March 14 if necessary.  If tied after regulation, each game is
played in sudden death overtime to completion, until someone wins.  This
is the same format as the WCHA.
 
 
#12 Ohio State           1.47 at
 #1 Miami                6.73                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Ohio State         wins:     2.0%      1.6%     0.4% (17.9%)
   Chance Miami              wins:    98.0%     96.0%     2.0% (82.1%)
   Chance of a tie:                              2.4%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:05
   -------------------------------------------------------------------
   Chance Ohio State            wins in two games:     0.0%
   Chance Miami                 wins in two games:    96.1%
   Chance of a third game:                             3.9%
   -------------------------------------------------------------------
   Chance Ohio State            wins series:           0.1%
   Chance Miami                 wins series:          99.9%
   -------------------------------------------------------------------
   If Ohio State         wins game #1:
      Chance Ohio State         wins series:           3.9%
      Chance Miami              wins series:          96.1%
   If Miami              wins game #1:
      Chance Ohio State         wins series:           0.0%
      Chance Miami              wins series:         100.0%
   -------------------------------------------------------------------
 
 
#11 Notre Dame           1.14 at
 #2 Michigan             6.72                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Notre Dame         wins:     1.1%      0.9%     0.2% (14.5%)
   Chance Michigan           wins:    98.9%     97.4%     1.5% (85.5%)
   Chance of a tie:                              1.7%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:17
   -------------------------------------------------------------------
   Chance Notre Dame            wins in two games:     0.0%
   Chance Michigan              wins in two games:    97.7%
   Chance of a third game:                             2.3%
   -------------------------------------------------------------------
   Chance Notre Dame            wins series:           0.0%
   Chance Michigan              wins series:         100.0%
   -------------------------------------------------------------------
   If Notre Dame         wins game #1:
      Chance Notre Dame         wins series:           2.3%
      Chance Michigan           wins series:          97.7%
   If Michigan           wins game #1:
      Chance Notre Dame         wins series:           0.0%
      Chance Michigan           wins series:         100.0%
   -------------------------------------------------------------------
 
 
#10 Illinois-Chicago     1.95 at
 #3 Lake Superior        5.49                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Illinois-Chicago   wins:     8.0%      6.2%     1.7% (26.3%)
   Chance Lake Superior      wins:    92.0%     87.2%     4.8% (73.7%)
   Chance of a tie:                              6.5%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:35
   -------------------------------------------------------------------
   Chance Illinois-Chicago      wins in two games:     0.6%
   Chance Lake Superior         wins in two games:    84.7%
   Chance of a third game:                            14.6%
   -------------------------------------------------------------------
   Chance Illinois-Chicago      wins series:           1.8%
   Chance Lake Superior         wins series:          98.2%
   -------------------------------------------------------------------
   If Illinois-Chicago   wins game #1:
      Chance Illinois-Chicago   wins series:          15.3%
      Chance Lake Superior      wins series:          84.7%
   If Lake Superior      wins game #1:
      Chance Illinois-Chicago   wins series:           0.6%
      Chance Lake Superior      wins series:          99.4%
   -------------------------------------------------------------------
 
 
 #9 Kent                 2.90 at
 #4 Michigan State       5.08                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Kent               wins:    20.7%     16.8%     3.9% (36.3%)
   Chance Michigan State     wins:    79.3%     72.4%     6.9% (63.7%)
   Chance of a tie:                             10.8%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:13
   -------------------------------------------------------------------
   Chance Kent                  wins in two games:     4.3%
   Chance Michigan State        wins in two games:    62.9%
   Chance of a third game:                            32.8%
   -------------------------------------------------------------------
   Chance Kent                  wins series:          11.1%
   Chance Michigan State        wins series:          88.9%
   -------------------------------------------------------------------
   If Kent               wins game #1:
      Chance Kent               wins series:          37.1%
      Chance Michigan State     wins series:          62.9%
   If Michigan State     wins game #1:
      Chance Kent               wins series:           4.3%
      Chance Michigan State     wins series:          95.7%
   -------------------------------------------------------------------
 
 
 #8 Bowling Green        3.55 at
 #5 Western Michigan     4.51                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Bowling Green      wins:    36.1%     30.1%     6.0% (44.0%)
   Chance Western Michigan   wins:    63.9%     56.3%     7.6% (56.0%)
   Chance of a tie:                             13.5%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:10
   -------------------------------------------------------------------
   Chance Bowling Green         wins in two games:    13.0%
   Chance Western Michigan      wins in two games:    40.8%
   Chance of a third game:                            46.1%
   -------------------------------------------------------------------
   Chance Bowling Green         wins series:          29.7%
   Chance Western Michigan      wins series:          70.3%
   -------------------------------------------------------------------
   If Bowling Green      wins game #1:
      Chance Bowling Green      wins series:          59.2%
      Chance Western Michigan   wins series:          40.8%
   If Western Michigan   wins game #1:
      Chance Bowling Green      wins series:          13.0%
      Chance Western Michigan   wins series:          87.0%
   -------------------------------------------------------------------
 
 
 #7 Alaska-Fairbanks     3.65 at
 #6 Ferris State         4.00                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Alaska-Fairbanks   wins:    44.7%     37.8%     7.0% (47.7%)
   Chance Ferris State       wins:    55.3%     47.7%     7.6% (52.3%)
   Chance of a tie:                             14.6%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:26
   -------------------------------------------------------------------
   Chance Alaska-Fairbanks      wins in two games:    20.0%
   Chance Ferris State          wins in two games:    30.6%
   Chance of a third game:                            49.4%
   -------------------------------------------------------------------
   Chance Alaska-Fairbanks      wins series:          42.1%
   Chance Ferris State          wins series:          57.9%
   -------------------------------------------------------------------
   If Alaska-Fairbanks   wins game #1:
      Chance Alaska-Fairbanks   wins series:          69.4%
      Chance Ferris State       wins series:          30.6%
   If Ferris State       wins game #1:
      Chance Alaska-Fairbanks   wins series:          20.0%
      Chance Ferris State       wins series:          80.0%
   -------------------------------------------------------------------
 
 
In the WCHA:
 
Best of three series is played on Friday, March 12, Saturday, March 13,
and Sunday, March 14 if necessary.  If tied after regulation, each game is
played in sudden death overtime to completion, until someone wins.  This
is the same format as the CCHA.
 
 
#10 Alaska-Anchorage     1.77 at
 #1 Minnesota-Duluth     5.24                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Alaska-Anchorage   wins:     7.6%      5.9%     1.7% (25.3%)
   Chance Minnesota-Duluth   wins:    92.4%     87.5%     4.9% (74.7%)
   Chance of a tie:                              6.6%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:56
   -------------------------------------------------------------------
   Chance Alaska-Anchorage      wins in two games:     0.6%
   Chance Minnesota-Duluth      wins in two games:    85.4%
   Chance of a third game:                            14.0%
   -------------------------------------------------------------------
   Chance Alaska-Anchorage      wins series:           1.6%
   Chance Minnesota-Duluth      wins series:          98.4%
   -------------------------------------------------------------------
   If Alaska-Anchorage   wins game #1:
      Chance Alaska-Anchorage   wins series:          14.6%
      Chance Minnesota-Duluth   wins series:          85.4%
   If Minnesota-Duluth   wins game #1:
      Chance Alaska-Anchorage   wins series:           0.6%
      Chance Minnesota-Duluth   wins series:          99.4%
   -------------------------------------------------------------------
 
 
 #9 Colorado College     2.78 at
 #2 Wisconsin            5.91                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Colorado College   wins:    12.9%     10.4%     2.5% (32.0%)
   Chance Wisconsin          wins:    87.1%     81.7%     5.4% (68.0%)
   Chance of a tie:                              7.9%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              4:47
   -------------------------------------------------------------------
   Chance Colorado College      wins in two games:     1.7%
   Chance Wisconsin             wins in two games:    75.8%
   Chance of a third game:                            22.5%
   -------------------------------------------------------------------
   Chance Colorado College      wins series:           4.6%
   Chance Wisconsin             wins series:          95.4%
   -------------------------------------------------------------------
   If Colorado College   wins game #1:
      Chance Colorado College   wins series:          24.2%
      Chance Wisconsin          wins series:          75.8%
   If Wisconsin          wins game #1:
      Chance Colorado College   wins series:           1.7%
      Chance Wisconsin          wins series:          98.3%
   -------------------------------------------------------------------
 
 
 #8 North Dakota         3.03 at
 #3 Minnesota            4.74                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance North Dakota       wins:    25.9%     21.1%     4.8% (39.0%)
   Chance Minnesota          wins:    74.1%     66.7%     7.4% (61.0%)
   Chance of a tie:                             12.2%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:21
   -------------------------------------------------------------------
   Chance North Dakota          wins in two games:     6.7%
   Chance Minnesota             wins in two games:    55.0%
   Chance of a third game:                            38.3%
   -------------------------------------------------------------------
   Chance North Dakota          wins series:          16.6%
   Chance Minnesota             wins series:          83.4%
   -------------------------------------------------------------------
   If North Dakota       wins game #1:
      Chance North Dakota       wins series:          45.0%
      Chance Minnesota          wins series:          55.0%
   If Minnesota          wins game #1:
      Chance North Dakota       wins series:           6.7%
      Chance Minnesota          wins series:          93.3%
   -------------------------------------------------------------------
 
 
 #7 St Cloud             2.89 at
 #4 Michigan Tech        4.16                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance St Cloud           wins:    30.7%     25.0%     5.7% (41.0%)
   Chance Michigan Tech      wins:    69.3%     61.2%     8.1% (59.0%)
   Chance of a tie:                             13.8%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:54
   -------------------------------------------------------------------
   Chance St Cloud              wins in two games:     9.4%
   Chance Michigan Tech         wins in two games:    48.0%
   Chance of a third game:                            42.6%
   -------------------------------------------------------------------
   Chance St Cloud              wins series:          22.5%
   Chance Michigan Tech         wins series:          77.5%
   -------------------------------------------------------------------
   If St Cloud           wins game #1:
      Chance St Cloud           wins series:          52.0%
      Chance Michigan Tech      wins series:          48.0%
   If Michigan Tech      wins game #1:
      Chance St Cloud           wins series:           9.4%
      Chance Michigan Tech      wins series:          90.6%
   -------------------------------------------------------------------
 
 
 #5 Denver               3.31 at
 #4 Northern Michigan    4.68                     In      Sudden Death
                                     Overall  Regulation    Overtime
   -------------------------------------------------------------------
   Chance Denver             wins:    30.5%     25.1%     5.3% (41.4%)
   Chance Northern Michigan  wins:    69.5%     62.0%     7.5% (58.6%)
   Chance of a tie:                             12.8%
   -------------------------------------------------------------------
   Expected time of Game Winning Goal (in Overtime):              5:12
   -------------------------------------------------------------------
   Chance Denver                wins in two games:     9.3%
   Chance Northern Michigan     wins in two games:    48.3%
   Chance of a third game:                            42.4%
   -------------------------------------------------------------------
   Chance Denver                wins series:          22.2%
   Chance Northern Michigan     wins series:          77.8%
   -------------------------------------------------------------------
   If Denver             wins game #1:
      Chance Denver             wins series:          51.7%
      Chance Northern Michigan  wins series:          48.3%
   If Northern Michigan  wins game #1:
      Chance Denver             wins series:           9.3%
      Chance Northern Michigan  wins series:          90.7%
   -------------------------------------------------------------------
 
 
Timothy J. Danehy                     [log in to unmask]
Robin H. Lock                            [log in to unmask]

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