Canada’s Long Stanley Cup Drought, 2023 Edition

May 2023 Update:

As I write this (May 8, 2023), there are two Canadian teams left in the 2022-23 Stanley Cup playoffs, Edmonton Oilers and Toronto Maple Leafs. The Oilers have a decent chance of going on, while the Leafs have dug themselves into a hole, but may still climb back out. So, there is still some chance that a Canadian team can win the cup, though I would estimate the odds at maybe 25%.

This brings up the well-known fact (among Canadian hockey fans, anyway) that no Canadian team has won since 1993. That is a string of 29 seasons of futility.

This raises the question of just how unlikely it is to have a run of failures like this. There are a number of ways to calculate this likelihood:

The binomial theorem now shows odds of 0.10% for this event to occur. Basically, the binomial theorem gives the answer to the question, if the probability of an event occurring is P, and you repeat the experiment N times, what is the probability of the event occurring exactly X times. In this case that would be:
- P is the probability 0.212 (the fraction of Canadian teams in the NHL over this period, which can also be expressed as 21.2 percent). This is because, over a long enough period of time, the other factors that influence the event will tend to even out (i.e. good and bad luck), making the probability of the event equal to the proportion of Canadian teams. This is similar to how a series of coin tosses is expected to become very close to 50:50 heads and tails, as you do more and more flips of the coin.
- N is the 29 year streak (the length of the experiment),
- X is 0, the result that 0 Canadian teams win the Stanley Cup during the length of the experiment. what is the probability of there being exactly 0 Canadian teams in that span of time.

You can plug this into Excel’s BINOM.DIST function, with the following syntax (BINOM.DIST (0, 29, .212, FALSE)) and the answer is 0.00100. That’s two-tenths of one percent. Below is a screenshot of that.

Another way to calculate this is to raise 0.788 (the proportion of non-Canadian teams) to the 29^th power, giving .00100 or 0.10%. That’s just the probability of the event Only Non-Canadian Team Win multiplied by itself 29 times

(.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788) X (.788)= 0.00100

The advantage of using the binomial function is its versatility; you can calculate the probability of 1 win in 29 years, 2 wins, etc.. This “power” method is only good for the “0 wins” case, but that’s what we are primarily interested in, so that’s ok.

The third way is to create a computer simulation, that plays a 29 game schedule thousands of times, counting the number of Canadian teams that win the Stanley Cup (7 teams) in each simulated season, given that the Stanley Cup winner was chosen at random. I set up the simulation, with 1000 trials of 29 year periods and ran the simulation 10 times. That gave a value of 12 29-year stretches out of a possible 10,000 where Canadian teams were shut out. So, that is an overall probability of 0.0012, which is very close to the analytic solution of 0.00100 obtained by the other two methods. The results for each trial of 1000 seasons were: 3, 1, 1, 0, 2, 0, 0, 0, 0, 5. That also shows the apparently quirky nature of randomness.

Below is a histogram of a typical run of the R simulation, with 1000 trials of 29 game seasons, showing the number of times Canadian teams won the Stanley Cup in each of these simulated seasons.

The R simulation code is given at the end of the blog, if you want to try it yourself. (Yes, I know my R code would be considered sloppy by the folks on Stack Overload).

So, we have an awfully long stretch of losses occurring, far longer than could possibly be the result of random chance, or “just one of those things”. It strains credulity to consider this to be 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.
Canadian teams are mostly located in small markets, so they can’t pay their players top dollar. But Toronto and Montreal can hardly be called ‘small markets’. Plus, many of the American-based Stanley Cup winners of the last 3 decades are note exactly big markets, at least relative to Toronto and Montreal (e.g. New Jersey Devils, Tampa Bay Lightning, Carolina Hurricanes, Colorado Avalanche).
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 seems unlikely – after all, professional athletes have come through a grueling system of training and preparation to make it to the big leagues. They know how to handle stress.

So, the only theories remaining (that I can think of), are:

It’s a conspiracy – the league helps the U.S. teams win (say, via referee decisions or Board of Governor actions), to help out teams in the more financially uncertain U.S. marketplaces. But, that seems like a difficult to conspiracy to actually make work, as the league simply doesn’t have that sort of control over the referees or the owners.
Economics - Canadian teams can make as much money losing as they can winning, so they don’t manage their business affairs with winning as a significant priority. Indeed, playing rope-a-dope with Canadian fans might be an optimum strategy, keeping player payrolls relatively low, while holding out “wait until next year” hopes for the hockey-mad fans, who will show up, come what may.

Plus, this strategy helps out American teams, some of which don’t have the sort of “stick with the team through thick and thin” fans that Canadian hockey teams have. Canadian teams need American teams to survive, in order for the NHL to reach a continental market, which of course includes that money-generating American TV market. In addition to generating TV and related revenue, such a strategy increases the value of a team enormously on the theoretical hockey team market and therefore increases the wealth of the owner or owners of the Canadian team. After all, if weak market American teams fold, that devalues the franchise of every owner in the league, including the strong Canadian markets.

None of these theories seems all that persuasive, but neither does “its just one of those things”.

Perhaps the Canadian sports media will give another go at explaining this peculiar run of failures on the part of Canadian teams. In recent years they have nodded towards the strange phenomenon each spring, almost as a ritual now. Their explanations are usually pretty lame, and they also reveal their weakness with statistical reasoning during these efforts. Not that I expect much from a journalist, when it comes to math.

At any rate, we will see in a few weeks whether the Great Canadian Stanley Cup Drought continues and thus becomes even more inexplicable.

# R Simulation Code

# ***************************************************************

# This is as simulation adapted to the Stanley Cup question:

# How likely is it that a Canadian Team wouldn't win a Cup

# for 29 years in a row.

# ***************************************************************

# Load any required libraries, etc.

# ---------------------------------

#Using the dplyr library

library(dplyr)

#Using the plyr library

library(plyr)

start_time <- Sys.time() # For testing the models execution time.

# Create a list of winners for each season.

# This will be filled in for each run of a season.

# trial - holds trial number

# season - holds season (each trial has 29 seasons)

# stanley_winner - holds team# of the cup winner that season

# country - holds country number (1=Canadian, 0=American)

# ----------------------------------------------------------------

stanley_winners_list <- data.frame(matrix(ncol = 4, nrow = 0))

x <- c("trial", "season", "stanley_winner", "country")

colnames(stanley_winners_list) <- x

stanley_winners_list

num_trials <- 1000

num_seasons <- 29

for(trial in 1:num_trials) {

for(season in 1:num_seasons) {

# This is for a single season simulation.

# -------------------------------------------------------

# Create a population vector of eligble (possible) teams.

# There are 34 teams in the NHL, during this period.

# This is just a list of numbers from 1 to popsize.

# --------------------------------------------------------

# season <- season + 1

leaguesize <- 34

NHL_teams <- seq(from = 1, to = leaguesize)

NHL_teams

# Create a uniform random test variable vector, to select

# the team that wins the Stanley Cup in a given year.

# This is just a list of random numbers, of size leaguesize.

# --------------------------------------------------------------

stanley_test <- runif(leaguesize, min = 0, max = 1.0)

# hist(stanley_test, freq = FALSE, xlab = 'x', density = 20)

#stanley_test

# Put those together in a dataframe

# Now, have a list of (sequence number, random_number).

# -----------------------------------------------------

season_run <- data.frame(NHL_teams, stanley_test)

#season_run

# Pick a single winner, choosing the team with the highest

# the highest value for the test variable, stanley_test.

# -----------------------------------------------------------

stanley_winner <- which.max(season_run$stanley_test)

#stanley_winner

country <- 0

if(stanley_winner <= 7)

{

country <- 1

}

#country

# Put that "winner" record into a dataframe

# of winners, to run numerous seasons.

# -------------------------------------------

stanley_winner_season <- data.frame(trial, season, stanley_winner, country)

#stanley_winner_season

# Build a list of winners for each season.

# ----------------------------------------

# Use rbind() function to insert above observation

# into a cummulative list of winners.

# -------------------------------------------------

stanley_winners_list <- rbind(stanley_winner_season, stanley_winners_list)

#stanley_winners_list

} # End of num_seasons Loop

} # End of num_trials Loop

# testing execution time

# ----------------------

end_time <- Sys.time()

end_time - start_time

# This is the list of Stanley Cup winners in each season,

# within each trial.

# --------------------------------------------------------

head(stanley_winners_list)

#histogram shows that each team number wins approx same num of times

winners <- stanley_winners_list$stanley_winner

hist(winners)

# --------------------------------------------------------

# Summarizing the data

# --------------------------------------------------------

# using standard R function, get number of Canadian teams that won

# for each trial of 29 years.

stanley_trials_canada_count <-

aggregate(stanley_winners_list$country, list(stanley_winners_list$trial), FUN=sum)

head(stanley_trials_canada_count)

stanley_trials_canada_count2 <- aggregate(cbind(country) ~ trial, data=stanley_winners_list, sum)

stanley_trials_canada_count2

#histogram shows how many Canada-based teams win during 29 games

Canadian_winners <- stanley_trials_canada_count2$country

Canadian_winners

hist(Canadian_winners, breaks=50)

# subset the data, with only trials where Canadian teams

# did not win a Stanley Cup in 29 simulated series.

subset(stanley_trials_canada_count2, country < 1)

===================================================

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.).

Amazon U.S.: http://www.amazon.com/gp/product/B00X2IRHSK

Amazon U.K.: http://www.amazon.co.uk/gp/product/B00X2IRHSK

Amazon Germany: http://www.amazon.de/gp/product/B00X2IRHSK

Amazon Canada: http://www.amazon.ca/gp/product/B00X2IRHSK

==============================================================

Or, if you want to continue contemplating mysterious runs of luck, you could try “The Devil Rides A Dark Horse”, which concerns the troubling run of good luck that a (fictional) horse player experiences.