Wednesday, 20 April 2016

What are the Odds? Canada and the Stanley Cup Playoffs

What are the Odds?  Canada and the Stanley Cup Playoffs

Another year has come and gone, with no prospect of a Canadian team winning the Stanley Cup.  This will be the 22rd year in a row, without a win.  This year comes with a special twist, as none of the Canadian teams even made the playoffs, so we know for certain that there can’t be a Stanley Cup winner based in Canada this year.

So, what are the odds of all 7 Canadian teams missing the playoffs in the same year.  One might intuitively think that it is not all that unlikely - after all, 16 teams have to miss the playoffs, and that means there were actually 7 American teams that missed as well as the 7 Canadian teams.  That’s not really such a big deal, you might think.

Actually the odds against this occurring are pretty low.  You can calculate it at about 2 chances in 1000, or 0.0017 or 0.17%, depending on how you like to describe it.  There are several ways to calculate this:

·        1 - The first way, is the classic “coloured balls in an urn” technique.  In this case, we frame the problem as “you have an urn with 30 balls (the number of teams in the NHL).  23 of those are blue (U.S.) and 7 are red (Canadian).  What is the probability of drawing 16 balls, with all of them being blue?”.  And as we might remember from mathematics that probability is:

o   (23/30)X(22/29) X(21/28) X(20/27) X(19/26) X(18/25) X(17/24) X(16/23) X(15/22) X(14/21) X(13/20) X(12/19) X(11/19) X(10/17) X(9/16) X(8/15) = 0.0017.

o   The basic idea here, is that on the first draw there are 23 blue balls (U.S. teams), out of 30 in all.  So, that gives 23/30.  On the second draw, there are now 22 blue balls, out of 29 in all, left in the urn.  We keep doing that for all 16 draws (the number of playoff spots), decrementing both numerator and denominator each time.  Then, we multiply out all of those probabilities to get the overall probability.

·        2 - The second technique, is to calculate the number of ways there are to form the numerator (how may ways can you create a list of 16 teams from 23 U.S. teams), then calculate how many ways there are to form the denominator (how many ways can you create a list of 16 teams from 30 teams).  Then divide one into the other, and you have your probability, which is again .017.  You can work this out from the formula for combinations, which is N!/(N-K)!K!, where N is the total number of items in the list and K is the number you want to choose.  Or, you can use the excel COMBIN function.

·        3 - Alternatively, you can write a little Monte Carlo program or set up a Monte Carlo spreadsheet in excel.  In this, you would set up a list of 16 random numbers, then check them to see if the first in the list was less than 23/30 (that would indicate a U.S. team in the first playoff spot), the second was less than 22/29 (that would be a U.S. team in the second playoff spot), and so forth, until all 16 spots were filled.  For a given list of 16 spots, check whether zero Canadian teams were included.  Then, repeat that a few hundred or a few thousand times, and calculate how many times you had zero Canadian teams in a given list of 16 spots.  You should find a small number of occasions where that happens, about 1 in every 500 sets (0.0017) of 16 playoff lists (or simulated seasons).  That’s what my excel spreadsheet gave.

The other question is “what are the odds of no Canadian team winning the cup for 22 straight years?” .  That’s a pretty low probability event as well, at about .0053.  One way to calculate that is via the binomial theorem.  You can look that up in a table (lots of them can be found on the internet, or you can find one in a stats textbook), or use the excel function BINOM.DIST.  The calculation can be described as “how many times would you get 0 successes in 22 trials, assuming the probability of success in any given trial was about 7/32” (actually, I used .212 instead, to reflect the changing percentage of Canadian teams in the league over the 22 years).

You can also set up a Monte Carlo for this, as a check.  The procedure is similar to before:

·        Make a list of 22 random numbers.

·        Test them to see if any of them are less than .212.

·        If so, then a Canadian team won in that run of 22 seasons.

·        If not, you have uncovered a simulated streak similar to the one that we are living through.

When I did this, I found 3 occasions in my 22 season streaks, out of 500 trials, where no Canadian team won the cup.  That’s about .006, very similar to what the binomial theorem predicted.

You can do other things, like simulate this procedure with playing cards instead of computer generated random numbers.    Remove the King and Queen of clubs from the deck, then deal cards from a shuffled deck until you hit a club.  Record how many cards you had to turn over to do this.  I did this, and found only one club-free run in 250 trials (equivalent to no Canadian team winning a Stanley Cup).  That represents a 0.004 probability of this event occurring, very similar to what the Binomial theorem predicted. 


So, we have two awfully unlikely events occurring.  It begins to stretch credulity to consider this merely bad luck.  Some other theories have been propounded:

·        It’s related to the Canadian dollar.  But that doesn’t work, as the Canadian dollar has varied considerably during this time period, sometimes being lower and sometimes higher than the U.S. dollar, as the accompanying graph shows (the graph shows how many Canadian dollars it would take to buy a U.S. dollar, from about 1970 to the present day).  Indeed, during the 1980’s Edmonton Oilers dynasty, the Canadian dollar was quite low, and during the 2000-2010 part of the recent Stanley Cup drought it was quite high.

·        Another theory states that hockey players can’t stand the pressure of playing in the Canadian cities, where the sport is taken very seriously by the fans. Therefore, the players choke, basically.  That theory falls down in two ways:

o    First, professional athletes are not given to choking, especially so many athletes over such a long period. 

o   Second, they should have been choking in hockey-mad U.S. cities like Chicago, Boston, Detroit and New York, too.  They didn’t , as all of those teams have won cups during the Canadian drought.

So, the only theories left, are:

·        conspiracy (the league let the U.S. teams win, to help the U.S. marketplaces),

·         economics (Canadian teams can make as much money losing as they can winning, so they don’t manage business affairs with winning as a significant priority), 

·        or plain bad luck. 

 Truly a conundrum.


If you have some spare time, possibly due to lack of interest in the NHL playoffs, you might want to consider a nice road trip, exploring the non-hockey contrasts between Canada and the U.S..  If so, then “On the Road with Bronco Billy” is definitely your book. 

Sit back and go on a ten day trucking trip in a big rig, through western North America, from Alberta to Texas, and back again.  Explore the countryside, learn some trucking lingo, and observe the shifting cultural norms across this great continent.  There's even some hockey playoff talk (Oilers-Denver and Oilers-Dallas), for those nostalgic for Canadian playoff representation.

It’s on Amazon (ebook), for a mere 99 cents (U.S.).

No comments:

Post a Comment