Don’t mind me; I’m on a math bender

As the paid-up holder of a Mainstream Media club card, can I warn the sportswriters away from making too much of the statistical fluke of all eight first-round NHL playoff series starting out tied through two games? The warning will arrive too late for some, but others may yet be saved.

As a landmark of NHL parity, the large number of 1-1 results in 2010 is not going to prove very useful. Imagine that game outcomes are statistically independent of each other and that the better team has a p chance of winning each individual game in the home team’s rink. If that’s the case, then the chance of a given series standing level after two games is 2(p)(1-p).

The 1-1 tie is always, for realistic values of p, the most common outcome. In a world of perfect parity—all teams are equal, no home-ice advantage, p = 0.5—half the series will be tied 1-1 after two games. And because the chance of the better team going up 2-0 is counterbalanced by a decreased chance of the other team going up 2-0, the overall chance of a tied series doesn’t drop off very fast as you depart from the parity condition, p = 0.5. For p = 0.6, about 48% of the series are still tied 1-1 after two games. (The better team is ahead in 36%, or 0.6²; the worse team is up 2-0 in 16%, about 0.4².)

But you can see that having eight series tied 1-1 will be incredibly rare even in the world of perfect parity. The probability of that happening in a given year will be the total product of the chances of a 1-1 tie in each of the series. Given an average overall value of p, the odds of all eight series starting out equal works out to, at most, (2(p)(1-p))8—a pretty small number, demonstrating the great flukiness of the “eight ties” outcome. Even in the perfect-parity world the expected frequency works out to 1 time in every 28, or 256, years. In the real world, the right average figure for p is probably around .54, giving us an “eight ties” year about 1 time in 269. In a fairly extreme non-parity world where the 1-4 seeds had an average 60-40 edge—that is to say, p = 0.6—the “eight ties” outcome would happen once every 355 years.

In other words, using this fluke as any kind of sign, indicator, or test for parity is about like insisting on reading a book only by the light of Halley’s Comet. You’d better have a comfortable chair. And plenty of kids, so they and their progeny can continue the observations (over several millennia) after you die in it…




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Don’t mind me; I’m on a math bender

  1. Killjoy

  2. Thank you!!!!! Please go after "momentum" and the use of small sample sizes to prove some lame theory next…..

  3. "… the overall chance of a tied series doesn't drop off very fast as you depart from the parity condition…

    That's debatable. At p=0.3 it's 1 in 1000. At p=0.2 it's 1 in 9000, and at p=0.1 it's 1 in 90000 years.

    So one thing in which we can have some confidence is that the odds are high that these teams are within 10% of parity.

    • It is unfortunate that Canada has lost one of its most promising young leaders. Given this post, if Gaunilon was to run for office now, his opponents would no doubt run a devastating:
      "Gaunilon, not a mathematician" campaign.

      • The real question is whether Gaunilon would pretend to object most strenuously to the government's agenda while simultaneously failing to vote it down in Parliament, and then make the Global Warming fad the centrepiece of his campaign.

        …oh yes, and then set up a Coalition government to take over after getting completely destroyed in an election…

        • My stats classes are too far behind me to argue the math, but your memory is cleary very good Gaunilon! Perhaps like yourself I'm still looking for "soldiers"…."on the streets"…in Canada…cue ominous music.

          btw, great quote from the weekend, " the worst day in power beats the best day in opposition", wonder how the Igster feels about tht one?

        • Gaunilon is not that much of a fool. Not many people are that much of a fool.

          • "Gaunilon is not that much of a fool. Not many people are that much of a fool. "

            Thanks….I think.

            To be fair, though, Gaunilon does manage to come pretty damn close from time to time.

  4. They pay you to do this, right?

    Or, more accurately given Macleans subsidy, WE pay you to do this, right?

  5. But what of the fact that after game 3, no team has more than a one game lead? Parity!

    • What about the fact there will be no sweeps in the first round? Parity!

      • NONE of the series will be over after the first three games. Parity!

        • How are the Oilers doin" Colby :)

  6. Great post, Colby. It's always nice to have a rational voice cautioning us not to read too much into improbable coincidences like this one.

  7. Ooh, Colby, I love it when you talk statistical analysis.

  8. Colby you are from Edmonton, remember the Dallas/Oilers series where Dallas was able to put it into 5th gear most years. As an Oiler fan you could look to 2nd or 3rd lines and the disparity in payrolls was evident.

    I believe there is increased parity in the NHL now, not necessarily by design, and certainly not based on the current 8 1-1 playoff series.

    • Yeah, things are way more awesome for the Oilers now in the world of "increased parity". It's working out great.

      • You wait , Old Boy…I was talking league wide,

        GOILERS!!!!!

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