If you watched the end of last night’s Meltdown in Beantown, you probably wondered a little bit about what the odds of such thing happening were. Tom Tango took a stab at estimating it on his blog – I thought I’d push it a little further and try and come up with an estimate of the odds of seeing a collapse happen to your favourite team.
Imagine an NHL in which all teams are equally good. Every team has a 53.33% chance of making the playoffs. Once you’re in the playoffs, you have an equal chance of winning or losing a playoff series. It’s a 6.25% chance that you’ll sweep, a 12.5% chance that you’ll win in five games and a 15.625% chance that you’ll win in six or seven games. Obviously, the chances of you losing in those numbers of games are the same – it’s Gary Bettman’s dream NHL.
In order for you to have a chance at a loss as agonizing as that suffered by the Maple Leafs last night, you need to lose a series in a seventh game. What are the chances that your season ends in a seventh game? In any given series, the probability is 0.15625. What we need to know is the probability of making the playoffs and losing in G7 in R1, R2, R3 and R4. It’s easy enough: R1 is (16/30 teams in the playoffs)*(0.15625 chance of losing in G7). R2 is (16/30 teams in the playoffs)*(0.5 chance of making it past R1)*(0.15625 chance of losing in G7). And so on. Add it all up, and you come up with a probability that your season ends in a G7 of 0.15625.
OK. Now what are the odds that you’d be leading that G7 by two goals with two minutes to play? If you assume that our perfectly average NHL sees teams average 2.6 goals per game, which is close to what they do average, the probability of your team being ahead by two after 58 minutes is 0.118. Now, if you assume that the other team will play 6v5 to the end of the game, you need to alter the probabilities to allow for the fact that the scoring environment changes – I don’t think Tom Tango did this in his post.
There’s a paper published through SFU that says that in the 2007-08 season, teams at 6v5 scored 7.1 goals/60 and allowed 21.3 goals/60. I used those numbers and calculated the probability of the team up two goals getting outscored by two over the final two minutes of the game if it played the entire two minutes at 6v5. I come up with .0114. I’ve already allowed for the fact that your team has to blow it in overtime by specifying that the season ends in a G7 above so I don’t need to
So now it’s just a matter of multiplying the three probabilities: 0.15625*.118*.0114=0.00021019. You can then convert that into years by dividing 1 by 0.00021019. Which gives you once every 4757.65 years. I don’t want Leaf fans to feel too despondent about what they’ve witnessed, so I’ll be kind and round it down to make it sound more common than it is: once every 4757 years, your favourite team will go out of the playoffs like this. Given that it’s a 30 team league, if I’ve done my math right, you’ll see a team go out like this once every 159 years. It’s about twice as rare as a Halley’s Comet sighting.
Leafs fans might not appreciate it but it’s pretty cool that we were all alive to witness such an event. So what if your grandfather saw a bunch of Maple Leaf Stanley Cup wins? Winning a Cup happens to someone every year – who cares. See this happen to your favourite team? It’s a once in sixty lifetimes event. Revel in it.Email Tyler Dellow at firstname.lastname@example.org