• Once in Sixty Lifetimes

    by  • May 14, 2013 • Hockey • 33 Comments

    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 tyler@mc79hockey.com

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    33 Responses to Once in Sixty Lifetimes

    1. David Staples
      May 14, 2013 at

      Best post ever.

    2. May 14, 2013 at

      I’m glad I witnessed it hen, thanks for the informative post!!!!

    3. RMGS
      May 14, 2013 at

      LOL. Send this to the Globe and Star as an op-ed. If it’s published, hide or go into exile in Ottawa.

    4. May 14, 2013 at

      This means that us Leaf fans will (likely) experience winning a Stanley Cup before having to live through a half hour like that again.

      • Tyler Dellow
        May 14, 2013 at

        The Leafs should win 159 Cups before having to deal with that again.

    5. Jamie
      May 14, 2013 at

      6.25% chance to sweep + 12.5% chance to win in five + 15.625% chance to win in six or seven = 34.375% x 2 (chance to lose) = 68.75%. So there’s a 31.25% chance the series will wind up tied?

      • Math
        May 14, 2013 at

        The chance to win in 6 or 7 needs to be counted twice. So 6.25 + 12.5 + 15.625 + 15.625 = 50% chance of winning the series.

        • Jamie
          May 14, 2013 at

          Gotcha, did the math myself afterwards as well, just got confused by the wording.

      • Mathematician
        May 14, 2013 at

        Your math is wrong. 6.25% chance to sweep + 12.5% chance to win in five + 15.625% chance to win in six or seven = 50% to win there for the other 50% chance is to lose.

      • David Attenborough
        May 14, 2013 at

        6.25% + 12.5% + 15.625% x 2 = 50% – the probability for 6 and 7 games is the same.

        Maths.

    6. Saj
      May 14, 2013 at

      Score effects must also increase those odds, no?

      Also, given how bad the Leafs were this year (from a Corsi point of view), the odds of them getting scored on in this particular case were probably a little higher than the average numbers you used.

      • Tyler Dellow
        May 14, 2013 at

        No – I calculated the odds for the two minute turnaround based on 6v5 data, which would include score effects.

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    8. Ryan V
      May 14, 2013 at

      I think you forgot to multiply by the probability your team makes the playoffs. In which case, it should happen to your favourite team every 8921 years. And it’d happen to any team every 298 years.

      • Ryan V
        May 14, 2013 at

        Never mind, I’m wrong. I was fooled by the fact that the chance of losing a best of 7 in G7 = .15625 = the chance of your favourite team losing in any G7 in any round.

    9. Matt McKinnon
      May 14, 2013 at

      I’m oddly proud that a paper on that came from my alma mater. I suppose I shouldn’t be surprised, considering I took an upper division class on Hockey and Canadian Culture there.

    10. PopsTwitTar
      May 14, 2013 at

      This is so great. I actually wanted the Leafs to win, since Marchand and Lucic should never experience joy of any kind (and as an NYR fan Id much rather play the Leafs), but this is too shocking an outcome to not just laugh at the randomness of it.

    11. Showerhead
      May 14, 2013 at

      Oh this is fun. Fun fun fun. Fun!

    12. Showerhead
      May 14, 2013 at

      Whoops. The real reason I came to comment:

      A friend is a Flyers fan and says that in 2010, they were down 0-3 in their series vs Boston. In Game 7, they were down 0-3 (in the 1st period, if said friend is to be believed). Boston’s loss and Toronto’s loss can’t be too far off the same probability, no?

      • Tyler Dellow
        May 14, 2013 at

        Boston blew a 3-0 lead with 45 minutes to go. Assuming that the teams were exactly equal, Philly’s probability of forcing a G7 was 0.125. Their probability of coming back from 3 goals down with 45 minutes left and winning in regulation was about 0.175.

        Not even remotely close to the same stratosphere.

        • Showerhead
          May 14, 2013 at

          This makes me happy. Thank you.

        • Max Power
          May 15, 2013 at

          This is b/c the teams have exactly the same chance of winning in each game, right? Like flipping a coin. Always 50% chance of getting heads no matter how many time you flipped heads in a row already.
          Drawing this out – Boston still sucked hard on that loss – once every 46 years and change.
          TOR/BOS was a real tough one for me, but I have nothing against Patrice Bergeron, and so I’m fine with it. If it had been TOR/NYR – the best outcome I could have hoped for would have been “Series cancelled due to influenza.”

          • Max Power
            May 15, 2013 at

            And I should state clearly that I was in no way prepared to see that result happen. I didn’t start cultivation anywhere near early enough.

    13. Jonny
      May 14, 2013 at

      The odds of having any exact outcome in round 1 is exceedingly rare, and yet one of them happens in eery series..

    14. nausso1@sympatico.ca
      May 15, 2013 at

      Please send your findings to the CEO of the TML organization. They need to see these stats to prepare for next year and give an increase to our captain who cannot play defence and watched Chara screen Reimer as the puck went in for the tying goal, then pinched on the winning goal.

    15. R
      May 15, 2013 at

      Very interesting work, appreciate the analysis. One comment: since it was the magnitude of the loss that is staggering, should one sum up probability of being outscored assuming they’re down by 2 *or more* goals? E.g., P(down by 2)*P(scores 2 or more) + P(down by 3)*P(scores 3 or more) + …? I suspect the additional probabilities become vanishingly small, however… But, if in 3 years, the leafs waste a 4 goal lead with 2 minutes to go in Game 7, I think this would qualify as the same ‘sort’ of event. Maybe this is done in the hidden work on the 6v5 stuff (did you model as a Poisson process?). Again, thanks!

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    18. Navi
      May 15, 2013 at

      Top notch work.

    19. Franklin Jameson
      May 15, 2013 at

      They had the historical probability of the Game 7 loss at WhoWins.com. Low ebb for Boston was at the end of the two goal lead for the Leafs.

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