Wednesday, January 23, 2013

NHL and luck: simulation results

Last post, I calculated that in an 82-game NHL season, luck is almost as important as talent.  Talent accounted for 53 percent of team variance in the standings, while luck accounted for the other 47 percent.

That makes it seem like the standings are hugely unpredictable.  But, that's not really the case.  Fifty-three percent is still enough for the best teams to come to the top, for the most part.

I ran my NHL season simulator a bunch of times, using the 2010-11 season.  I'll show you one of the seasons that came out with typical randomness ... in this case, 48 percent luck. 

Teams are ranked in order of simulated points.  Assumed talent (goal differential, regressed 22 percent to the mean) is in parentheses.  ("Assumed talent" is based only on the raw stats.  I'm pretty sure the Canucks aren't really a true +61 -- based on their seasons before and after -- but I'm not making any team-specific adjustments for that.)

OK, here's the Western Conference:

113 Nashville Predators (+22)
109 Vancouver Canucks (+61)
107 St. Louis Blues (+8)
104 Chicago Blackhawks (+25)
 99 Anaheim Ducks (-3)
 98 Phoenix Coyotes (+9)
 96 Los Angeles Kings (+12)
 94 Detroit Red Wings (+13)
-----------------------------
 91 San Jose Sharks (+27)
 86 Calgary Flames (+11)
 84 Dallas Stars (-4)
 77 Colorado Avalanche (-51)
 74 Edmonton Oilers (-53)
 69 Minnesota Wild  (-21)
 57 Columbus Blue Jackets (-31)

 
And here's the Eastern:

112 Boston Bruins (+46)
108 New York Rangers (+22)
 99 Buffalo Sabres (+9)
 97 Philadelphia Flyers (+33)
 95 Washington Capitals (+19)
 95 New York Islanders (-26)
 92 Tampa Bay Lightning (+3)
 90 Montreal Canadiens (+5)
---------------------------
 89 Florida Panthers (-25)
 87 Carolina Hurricanes (-2)
 86 Ottawa Senators (-41)
 86 New Jersey Devils (-31)
 82 Toronto Maple Leafs (-23)
 81 Pittsburgh Penguins (+25)
 77 Atlanta Thrashers (-38)


Generally, the good teams did well and the bad teams did poorly.  But, there were a few exceptions that contributed to the 47 percent luck. 

In the East, the Islanders and Penguins basically swapped positions.  Pittsburgh had a horrible simulated year, finishing next to last despite actually being the fourth best team.  Other than that ... the East finished very much as expected: all the plus teams making the playoffs, and all the minus teams missing out.

In the West, the Sharks missed the playoffs despite being the second-best team.  Effectively, they switched with the Ducks, who wound up in fifth place despite being worse than average.  Also of note: the Blues wound up a few spots north of where they should have been.

Other than those five teams ... nothing really that notable.  But you can imagine how the big stories of the year would be the Penguins' collapse and the Islanders resurgence.

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That's pretty typical for what you get with around 50 percent luck.  If you want to get a better feel, here's a few more.  I won't give you the whole record, but I'll just tell you what happened.  (If you want some more sets of random season standings in full, e-mail me and I'll run a bunch off for you.) 

1.  The simulation showed 45% luck.  The Anaheim Ducks (-3) finished fourth, but the Red Wings (+13) finished tenth and out of the playoffs.  In the east, Tampa Bay (+3), Montreal (+5), and Buffalo (+9) took the first three spots.  The best teams took four of the next five, except that the Leafs (-23) took the eighth spot.  Washington (+19) finished ninth.

2.  Luck was 44%.  The Kings (+12) missed the playoffs in favor of the Wild (-21), who finished seventh in the West.  In the East, two bad teams, the Leafs (-23) and Panthers (-25), finished fifth and sixth, respectively, while Pittsburgh (+25) missed the playoffs by two points.

3.  Luck was 47%.  In the West, nothing too serious ... Anaheim (-3) and Minnesota (-21) took the last two playoff spots from the Flames (+11) and Kings (+12), who were right behind them.  But in the East ... the top three were the Sabres (+9), Hurricanes (-2) and Habs (+5).  The Islanders (-26) tied with Boston (+46) and Philadelphia (+33), for 5/6/7th.  The Capitals (+19) missed the playoffs by a point, and the Penguins (+25) by nine points. 

4.  This one was 52% luck ... but, strangely, it wasn't that big a deal.  In the West all the plus teams made the playoffs except the Sharks (+27).  In the East, six of the top seven made the playoffs (Buffalo, +9, was the odd man out); the surprises were the Devils (-31) and Islanders (-26) snatching seventh and eighth.  Toronto (-23) also surprised, missing the playoffs by only two points.  I guess what happened here was that the randomness was mostly *within* the playoff and non-playoff groups, instead of *between* them. 

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Those were all typical seasons, with around 45% luck.  But some seasons had more, and some seasons had less.  Here's a summary of all one hundred.  Explanation follows the chart.


Team (talent)     Pts    Pos  1st/POff/Best
------------------------------------------
Vancouver (61)    113    1.6   64  99   1
Chicago (25)      100    4.9   11  88   1
San Jose (27)      99    5.3    7  83   1
Nashville (22)     98    5.6    6  82   1
Detroit (13)       97    6.1    6  74   1
Los Angeles (13)   96    6.5    1  71   1
Calgary (11)       95    6.7    1  73   1
Phoenix (9)        93    7.7    0  58   2
St. Louis (8)      93    7.3    3  60   1
Dallas (-4)        90    9.1    0  38   2
Anaheim (-3)       90    9.0    1  35   1
Minnesota (-21)    84   11.1    0  21   3
Columbus (-31)     81   11.8    0  15   3
Edmonton (-53)     74   13.4    0   3   6
Colorado (-51)     73   13.9    0   0  10

Boston (46)       108    2.7   40  98   1
Philadelphia (33) 102    4.2   14  93   1
Pittsburgh (25)   101    4.4   13  89   1
Washington (19)   100    4.9    4  94   1
Rangers (22)      100    5.1   12  83   1
Tampa Bay (3)      94    7.0    8  65   1
Buffalo (9)        94    7.3    2  65   1
Montreal (5)       93    7.4    2  64   1
Carolina (-2)      91    8.2    3  53   1
Florida (-25)      85   10.5    0  25   2
Islanders (-26)    85   10.5    2  24   1
Toronto (-23)      84   10.5    0  27   2
New Jersey (-31)   80   12.0    0   9   5
Atlanta (-38)      79   12.5    0   5   5
Ottawa (-41)       77   12.8    0   6   5



Reading across the bottom line of the chart as an example: we assumed the Ottawa Senators had a talent level corresponding to a regulation goal differential of -41.  On average, that team wound up with 77 points in the simulated standings.  It finished, on average, 12.8th in its conference.  It finished first zero times in 100 chances, and made the playoffs six times.  The highest position it ever reached was fifth place.

The chart looks pretty reasonable, overall; the outcomes corresponded to the talent.  But, for single seasons, we see that strange things happened.  The New York Islanders, at -26, finished first twice, just by luck.  The Washington Capitals, a good team, should have finished first a lot more than 4 times.  And it looks like Colorado had miserable luck; they never finished higher than tenth, while Edmonton, which was actually two goals worse, made the playoffs three times and finished sixth at least once.

Also, it looks like the Canucks, by far the best team in the league, missed the playoffs once just by random chance. 

(By the way, I ran the simulation again, just to make sure it wasn't a programming error; the Washington and Colorado outliers disappeared.  Also, the Canucks made the playoffs all 100 times.)

You can get a feel for the number of anomalies in the average season, just by adding up some numbers.  Of course, it depends how you define "anomaly".  Suppose we say an anomaly occurs in a conference when:

-- one of the best three teams misses the playoffs.
-- one of the worst three teams makes the playoffs.
-- the first place team is not in the top five in talent.

Those frequencies, respectively, were 50, 38, and 23.  So we have 111 anomalies total, 1.11 per season.  That's an average; some seasons have more than one, some seasons have none.  But, typically, there will be one big regular-season surprise that's completely due to luck.

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There were still a couple of things I wanted to check.  One is, in one hundred seasons, what's the weirdest, most luck-filled one look like?  Another one is, what's the typical talent difference is between, say, sixth place and tenth -- that is, the five teams fighting for the last three playoff spots?  My gut says there won't be much ... but I haven't checked yet. 

I'll do those in future posts.


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