Several people have inquired about the CHODR probabilities and how the
various playoff formats used in the different leagues affect the
likelihood of the possible outcomes. First let's briefly recap what the
first round format is in each league:
ECAC:
Two games with no OT. If series tied, third game with sudden death OT.
Hockey East:
Two games with 5 min OT. If series tied, sudden death after 2nd game.
CCHA and WCHA:
Best of three games, each to completion (sudden death OT).
Now let's look at the various scenarios for three upcoming series under
the three different formats. The examples we've chosen are Northeastern
at Maine (a predicted blowout), St Lawrence at Clarkson (a fairly average
case), and Alaska-Fairbanks at Ferris State (the closest matchup).
First, the predicted regulation score for each game in these series:
Northeastern 1.98 at Maine 7.57
St Lawrence 2.78 at Clarkson 4.87
Alaska-Fairbanks 3.65 at Ferris State 4.00
Now for some probabilities for each series in the different formats:
Northeastern 1.98 at Maine 7.57: ECAC Hockey East CCHA/WCHA
Format Format Format
-----------------------------------------------------------------------
Chance Maine wins series: 99.8% 99.0% 99.8%
Chance Northeastern wins series: 0.2% 1.0% 0.2%
Chance of third game/SD OT (HE only): 3.6% 4.1% 4.6%
If Northeastern wins game #1,
chance Northeastern wins series: 6.5% 23.3% 4.7%
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Note that under the Hockey East format, Northeastern has a five times
better chance to win the series than under the other formats. The main
reason is that Hockey East plays sudden death overtime if the series is
split after two games. If they get to the sudden death overtime,
Northeastern is given a 20.7% chance of scoring first and winning the
series. Note especially how Northeastern's chances are drastically
improved in the Hockey East format if they win the first game. Then the
worst case for Northeasten is Maine wins the next game and they play
sudden death, where Northeastern's chances are still relatively good.
The rules regarding overtime in the first two games have a slight effect
on the chance of the third game/SDOT. The CCHA/WCHA play to completion
format increases the likelihood of a split, since each game produces a
winner. The ECAC no overtime format lowers that chance, since the series
can be won with a win and a tie. The five minute overtime in Hockey East
puts the chances right about in the middle of the other two.
Now let's look at the other two series:
St Lawrence 2.78 at Clarkson 4.87: ECAC Hockey East CCHA/WCHA
Format Format Format
-----------------------------------------------------------------------
Chance Clarkson wins series: 87.8% 83.6% 88.5%
Chance St Lawrence wins series: 12.2% 16.4% 11.5%
Chance of third game/SD OT (HE only): 25.8% 28.9% 33.4%
If St Lawrence wins game #1,
chance St Lawrence wins series: 43.5% 52.2% 37.8%
-----------------------------------------------------------------------
Alaska-Fairbanks 3.65 at ECAC Hockey East CCHA/WCHA
Ferris State 4.00: Format Format Format
-----------------------------------------------------------------------
Chance Ferris State wins series: 57.7% 56.5% 57.9%
Chance Alaska-Fairbanks wins series: 42.3% 43.5% 42.1%
Chance of third game/SD OT (HE only): 38.1% 42.7% 49.4%
If Alaska-Fairbanks wins game #1,
chance Alaska-Fairbanks wins series: 73.6% 73.2% 69.4%
-----------------------------------------------------------------------
The same patterns seen in the Maine-Northeastern series hold true for the
closer cases as well. The chances of the third game/SDOT are highest in
the CCHA/WCHA format, lowest in the ECAC, and Hockey East is in between.
If the underdog, wins the first game, their chances are worst in the
CCHA/WCHA, where they still have to win one more game. In Hockey East,
they need at least a tie in the next game, or they can win in sudden death
OT. This is the best chance for St Lawrence as it was for Northeastern.
If Alaska-Fairbanks wins the first game, they do best in the ECAC format.
This is because they win the series with a tie in game two, and since the
predicted score is so close a tie is very likely.
In general, the Hockey East format gives the underdog the best chance of
winning the series, mostly because they have a better chance of winning in
a sudden death overtime than they do in a full third game. The CCHA/WCHA
format is the worst for the underdogs, because they must win twice with no
ties allowed in the format. The ECAC is in between because the third game
favors the favorite, but the possibility of winning with a win and a tie
favors the underdog.
To keep it all in perspective, in doesn't make all that much difference.
Clarkson had an 83.6% chance in the Hockey East format, 87.8% chance in
the ECAC format, and an 88.5% chance in the CCHA/WCHA format. It made
even less difference in the other cases.
Some people have found it strange that Northeastern had a better chance
of taking series from Maine than Ohio State had against Miami and Notre
Dame had against Michigan. One reason for this, as demonstrated above,
is that the Hockey East format is the best for the underdog, especially a
strong underdog such as Northeastern. But there is also another factor
which has to do with the predicted score. The projections for each game
of these series are as follows:
Northeastern 1.98 at Maine 7.57 (+5.59)
Ohio State 1.47 at Miami 6.73 (+5.26)
Notre Dame 1.14 at Michigan 6.72 (+5.58)
We see that although, Maine was projected to score almost a full goal more
than Miami or Michigan, Northeastern was projected to score half a goal
more than Ohio State or Notre Dame. Looking at the probabilities
published yesterday, we see that Ohio State was given a 1.6% chance of
winning a game in regulation, while Notre Dame had a 0.9% chance in
regulation. Northeastern meanwhile had a 1.9% chance of winning in
regulation, even though they were the largest pointwise underdog.
The reason is that Northeastern's projected score was large enough to
offset the higher predicted score for Maine. (Northeastern's games are
high scoring, they rate #17 in offense because they score alot, but they
rate #40 in defense, because they allow even more. Thus Northeastern is
usually projected to score a fairly large number of goals, even though
their opponents score could be much higher). In order to win a game, you
have to score at least one goal. The lower the projected score, the
greater the likelihood that no goals will be scored. Let's look at the
probability of each of these three underdogs scoring zero goals according
to the Poisson random variable distribution.
According to the distribution, the probability that a team will score i
goals is given by:
P = ( e ^ -S ) * ( S ^ i ) / i!
where S is the expected score. In our case i = 0 (0! is defined as 1,
and S ^ 0 = 1), so P(0) is given by:
P(0) = ( e ^ - S )
Plugging in our projected score for the underdogs, we have:
P(Northeastern scores 0 goals) = ( e ^ -1.98 ) = 13.8%
P(Ohio State scores 0 goals) = ( e ^ -1.47 ) = 23.0%
P(Notre Dame scores 0 goals) = ( e ^ -1.14 ) = 32.0%
From this it is easy to see that because Ohio State and Northeastern have
a much greater probability of getting shut out, because of their lower
projected score, they are much less likely to win.
And just for the sake of it, let's look at the probability that each team
will score exactly one goal. With i = 1 (1! = 1), the probability is
given by:
P(1) = ( e ^ - S ) * S
P(Northeastern scores 1 goal) = ( e ^ -1.98 ) * 1.98 = 27.3%
P(Ohio State scores 1 goal) = ( e ^ -1.47 ) * 1.47 = 33.8%
P(Notre Dame scores 1 goal) = ( e ^ -1.14 ) * 1.14 = 36.5%
For Notre Dame, that leaves only a 31.5% chance of scoring two or more
goals. For Norteastern, that chance is much better at 58.9%. Thus with
opponents projected to score 6+ goals, it is unlikely that Notre Dame will
win with such a small chance of scoring two or more. Northeastern's
chances aren't great, but they are significantly better, more than enough
to offset the higher projected score for Maine.
And that concludes today's lesson in probability theory.....
Timothy J. Danehy [log in to unmask]
Robin H. Lock [log in to unmask]
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