## Friday, January 25, 2013

### How much luck in a shortened NHL season?

Last post, I showed examples of the typical amount of luck in an 82-game NHL season.  For this year, though, we're interested in a 48-game season instead.  We'd expect significantly more luck with the shorter schedule.

It's hard for me to simulate a 48-game season, because I don't have a schedule handy.  So I took a shortcut.

For a shorter season, the typical r-squared between standings and talent should be about .4.  So, what I did was, I ran the "regular" simulation, and I pulled out all the occurrences where the r-squared was between .35 and .45.  That should give us some "typical" 48-game seasons.

(How do we get .4?  Well, we know, from the previous post, that the SD of talent in the NHL is 8.95 points per 82 games, which is 5.24 points per 48 games.  And, we can calculate that the SD of luck in 48 games is 6.45 points.

Therefore, the typical r-squared between standings and talent should be about 5.24 squared divided by (5.24 squared + 6.45 squared).  That's around .4.

It might really have to be slightly less, taking into account that real-life has no inter-conference games, but I'm going to ignore that.)

Here's the first simulated season that meets the criterion.  The r-squared was .42, which means 58 percent luck.  The left column is points in 48 games; the number in parentheses is the presumed talent.

69  Vancouver (61)
68  Phoenix (9)
64  Dallas (-4)
61  San Jose (27)
59  St. Louis (8)
59  Calgary (11)
55  Los Angeles (12)
54  Minnesota (-21)
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53  Anaheim (-3)
50  Nashville (22)
48  Chicago (25)
47  Columbus (-31)
47  Detroit (13)
40  Edmonton (-53)

62  Pittsburgh (25)
62  Boston (46)
59  Rangers (22)
59  New Jersey (-31)
58  Montreal (5)
56  Tampa Bay (3)
55  Washington (19)
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54  Florida (-25)
53  Buffalo (9)
52  Atlanta (-38)
50  Ottawa (-41)
47  Carolina (-2)
45  Islanders (-26)
44  Toronto (-23)

In the West, the third- and fourth-best teams missed the playoffs.  A below-average team finished third.  And Minnesota, a bad team, squeaked into the last playoff spot.  In the East, third-worst New Jersey tied the Rangers for fourth, and Buffalo was the only good team to miss out.

Maybe we can do this in kind of a summary way.  Let's create "anomaly points", to count up the number of surprises.  It'll be one point for a +10 or more team missing the playoffs, or a -10 team making the playoffs, which is a "small" surprise.  Two points for "medium" surprise of +20 and -20.  Three points for +30 and -30, and so on.

(Hopefully, when I say "points," you'll be able to tell by context whether it's anomaly points or standings points.)

By this scale, we have 2 anomaly points for Minnesota making the playoffs, 2 for each of Nashville and Chicago missing out, and 1 for Detroit's failure.  In the East, we have 3 points for New Jersey's unexpected success, and that's all.  So, 7 points in the West and 3 points in the East, for a total of 10 points.

OK, here's the next one, which was 55 percent luck:

68  Vancouver (61)
66  Nashville (22)
61  Chicago (25)
61  St. Louis (8)
60  Los Angeles (12)
59  Phoenix (9)
59  Dallas (-4)
58  San Jose (27)
--------------------
54  Calgary (11)
50  Minnesota (-21)
47  Anaheim (-3)
46  Columbus (-31)
43  Detroit (13)
39  Edmonton (-53)

67  Tampa Bay (3)
62  Buffalo (9)
60  Washington (19)
59  Boston (46)
57  Islanders (-26)
55  Atlanta (-38)
54  Rangers (22)
----------------------
53  Montreal (5)
53  Florida (-25)
47  Pittsburgh (25)
47  Carolina (-2)
46  Ottawa (-41)
44  New Jersey (-31)
40  Toronto (-23)

In the West, only 2 points (Calgary and Detroit missing the playoffs).  In the East, though, 7 points: the Islanders and Atlanta somehow made it in, while Pittsburgh finished well out of the playoff picture.  Total: 9 points.

I'll just give you summaries from here on.  These are the next few random seasons I found with 55 to 65 percent luck:

-- 15 anomaly points.  Edmonton, the worst team in the West, finished eighth, ahead of Detroit and Chicago.  New Jersey finished seventh in the East, ahead of Pittsburgh and the Rangers.

-- 5 points.  Nashville was 12th, Chicago 15th, and Washington 9th.

-- 13 points.  Only Chicago in the West (they finished 12th).  But in the East ... Boston, the best team, finished 10th, two points out of the playoffs.  The Rangers were 12th.  But the Devils and Islanders made it in.

-- 10 points.  New Jersey and Toronto (third and fourth!) in, Rangers and Capitals and Sharks out.

-- 5 points.  Atlanta makes it in by a point; the Rangers finish second last.  In the West, there were zero points ... Vancouver, by far the best team, finished only fourth, but we're not counting that even though it's very unlucky.

-- 12 points.  Columbus swapped with Nashville, and New Jersey swapped with Boston.

-- 5 points.  New Jersey (8th) finished three points ahead of Pittsburgh (9th).  So, this one almost had zero!

-- 16 points.  Edmonton made the playoffs, winning a three-way tie for eighth (I chose randomly).  Minnesota finished sixth.  The Islanders, Leafs, and Devils made it, while the Rangers missed out.  (Also: Buffalo finished last, despite being an above-average team (+9).)

-- 6 points.  Below-average Carolina (at -2) finished first in the East, five points ahead of Boston ... maybe we should give that some points, but I won't.  San Jose missed, while the Leafs and Islanders were the surprises in the East.

Taking an average of all these ... it comes out to a bit less than 10 points.  That's around five "medium" surprises (like Toronto or Minnesota making the playoffs).  Or, if you like, one "medium", one "large", and one "extra extra large" -- say, Chicago, Columbus, and Edmonton.

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To see how the shorter season compares, I ran the points for a hundred normal, 82-game seasons.  The average was only 5.8 points (with an SD of 3).

The more luck, of course, the more anomalies.  Here's how the anomaly points vary by the r-squared of the individual seasons:

.35 - .45 (~ 60% luck): 10.5 points ( 6 seasons)
.45 - .55 (~ 50% luck):  7.0 points (26 seasons)
.55 - .65 (~ 40% luck):  5.4 points (42 seasons)
.65 - .75 (~ 30% luck):  3.6 points (23 seasons)
.75 - .85 (~ 20% luck):  2.0 points ( 3 seasons)

Since 48-game seasons are around 60% luck, a typical short season will come from the top group, and so we should expect around 10.5 points.  That's pretty close to the just-about-10 we got in the ones I described earlier.

So: perhaps we can say, a typical 48-game season has around 70 percent more surprises than an typical 82-game season (roughly 10 divided by roughly 6).

That's almost exactly equal to the difference in games (eighty-two games is 71 percent more than forty-eight games).  I think that's just a coincidence, but I'm not certain.

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One thing I want to clarify here: the short seasons we looked at are very "average", close to the center of the distribution (which is 40% luck).  There will be seasons with a lot more luck, and there will be seasons with a lot less luck, that go very much according to talent.  In the seasons we looked at, we found that *typical* seasons have around ten points, with a range of 5 to 16.  However: overall, there will be a much wider range.

Just for fun, let me show you a season with a lower talent correlation, where luck was 66 percent:

70  Vancouver (61)
63  Detroit (13)
57  Nashville (22)
56  Minnesota (-21)
56  Anaheim (-3)
55  Calgary (11)
55  Los Angeles (12)
55  Columbus (-31)
-----------------------
54  St. Louis (8)
54  Phoenix (9)
52  San Jose (27)
49  Dallas (-4)
48  Chicago (25)
40  Edmonton (-53)

70  Rangers (22)
58  Islanders (-26)
57  Pittsburgh (25)
56  Montreal (5)
54  Buffalo (9)
54  Carolina (-2)
53  Tampa Bay (3)
52  Ottawa (-41)
-----------------------
52  Boston (46)
52  Washington (19)
51  Florida (-25)
46  New Jersey (-31)
44  Atlanta (-38)
43  Toronto (-23)

That's 20 points, if I'm adding it up right.  Breaking it down:

-- 2 extra large surprises (Boston, Ottawa)
-- 1 large surprise (Columbus)
-- 4 medium surprises (Minnesota, San Jose, Chicago, Islanders)
-- 1 small surprise (Washington)

An 82-game season this extreme should happen around one or two times in a hundred.  But, in a 48-game season, it'd be a lot less rare.  Remember, the average r-squared in a short season is .4, and this one isn't that much worse, at .34.

So, this year in the NHL, we should expect "10 points" worth of surprise teams, but it could, with a little more luck, be as many as 15 or 20 points.

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