What actuaries can learn from Canada’s Stanley Cup struggles

Well, it happened again. For the second straight year, the Edmonton Oilers had a chance to defeat the Florida Panthers and bring the Stanley Cup north of the border, and once again they came up short. This marks an incredible 32 years since the National Hockey League championship was won by a Canadian-based team, an embarrassing situation for our de facto national sport. (Sorry, lacrosse fans.)

Inevitably, we start to wonder what the probability is of enduring such a championship drought, and, as an actuary, I thought I would try to figure that out.

 A simple model for a long wait

To do so, let’s set up a simple model. If we are looking at championship droughts, I think we can assume that the probability of winning a title in any given year is 1/n, where n is the number of teams in the league. That’s obviously not going to be strictly true at any point in time (2025 Colorado Rockies, I’m looking at you), but if we are looking at a prolonged period, I think we can assume that teams generally average out in terms of competitiveness. Given this, we can express the probability of a championship drought of z years to be:

,

where n_t is the number of teams in the league in season t.

 History’s harshest droughts

Now we can crunch some numbers to see what we get. Let’s start with the champ of all championship droughts, Major League Baseball’s Chicago Cubs, who went 108 years between World Series titles, winning in 1908 and not again until 2016. Take a moment to think of everything that happened in between: the Great Depression, two world wars, the rise and fall of the Soviet Union, the emergence of commercial air travel, space travel, nuclear power, nuclear weapons, television, computers, the internet, streaming services, and Tim Horton’s donuts.

Given how much history occurred between those two events, you would think that the probability of winning zero titles over that time would be minuscule, and you would be right. Our simple model produces a value of 0.38%. But a century of futility by the Cubs seems like an anomaly, so let’s look at some more modest recent droughts.

Maple Leafs and misery

You all knew where this was eventually going – let’s consider the Toronto Maple Leafs, who won the last Stanley Cup of the Original Six era, in 1967, and have never been back. Thanks to being knocked out in the playoffs last season by Florida again (we need to do something about that team), the Leafs are mired in what is now a 58-year championship drought. Intuitively, you may think that, even though it likely won’t be as bad as the Cubs’ ignominy, what the Leafs are experiencing is in the same realm of improbability.

Actually, it’s not: our model gives a probability of 7.63%. I was surprised by this result. Yes, it is low, but not ridiculously so. Expressed another way, we are looking at roughly a 1-in-13 chance. With 32 teams in the NHL, does that mean we can expect two to three other clubs to be in a similar situation? Considering that the Vancouver Canucks and the Buffalo Sabres both entered the league 55 years ago and have yet to win a Stanley Cup, it looks like we’re almost there.[1]

When intuition misses the net

So, what can we learn from this? When it comes to making completely intuitive assessments, there is a good chance that we are going to be wrong.

A classic example of this is the well-known birthday problem (often called the birthday paradox by those who don’t understand there is nothing paradoxical about it). In this question in probability theory, we are asked how many people need to be gathered in a room for there to be a 50% probability that at least two of them share a birthday. The answer, 23, seems unreasonably low to most observers, but it can be proven relatively simply. The difference between the intuitive guess and the actual answer is often quite large if we have no frame of reference.[2]

So, the cautionary tale for actuaries is that, even though we rely on intuition from time to time, any assumptions we make need to be at least partially informed with data. To further highlight the gap between intuition and reality, here’s how actual Stanley Cup wins stack up against what we’d expect based on probabilities over the past 32 years:

This stark contrast reinforces just how misleading gut feelings can be when they’re not backed by math.

Going totally on gut feel, in the absence of supporting information, can be perilous. Maple Leaf fans may feel that they have been hard done by, but what they are experiencing is at the low end of the probability scale – and it is not unreasonable. I realize that provides little to no comfort, so all we can say is better luck next year.

The Canadian Stanley Cup curse?

To close, let’s go back to the question at the start. How likely is it that we have gone 32 years without a Canadian-based team winning the Stanley Cup? To do so, we need to modify our formula slightly, to:

,

where c_t is the number of Canadian teams in the league in year t. Going back over the past 32 years, we end up with a probability of 0.04%, or roughly 1 in 2,500. Which goes to show that “highly unlikely” is not the same as “impossible,” and that sometimes – despite the odds – you just get unlucky.

This article reflects the opinion of the author and does not represent an official statement of the CIA.

[1] In fact, there is a 100% probability that at least one NHL team is going to experience at least a 32-year drought going forward. If we assume there is a different winner every year, then that means one team will be the last one on the list. We just don’t know who.
[2] “You’re out of your element, Donnie!”