Tuesday, September 29, 2009

On The Fallacy of Probablistic Thinking

Let us imagine that we are brilliant, and came up with a way besides the classic Hockey League Simulator 2 to simulate 10,000 2009-10 seasons, from start to finish (in all of them, Marian Gaborik gets injured). Let us imagine these simulations are pretty darned accurate - the Gaborik injuries are a dead giveaway that they are.

Now we have a list of teams who've won the Stanley Cup in these 10,000 simulations - let us look at their average playoff wins. Someone like Detroit might have 9 or so, someone like the Islanders might have 0.1 or less. These numbers, however, are inherently meaningless when imagining who's going to win the Stanley Cup simply because some team has to win 16 games in the playoffs.

There's a lot of luck in the playoffs - it's rather improbable that despite the fact that Detroit and Pittsburgh were likely the two most talented teams in each of the last two seasons that both teams made it to the Stanley Cup Finals. When wondering about whether they'll repeat that feat, citing the above is not particularly important - it is certainly improbable, but still more probable than most Stanley Cup Finals pairings.


  1. I'm not sure I get your point. Can you maybe say it in a different way?

  2. haha, it's so simple, that's why you're missing it. i got into an argument in the 2p2 regular season thread where it basically turned out i was using the gambler's fallacy (i.e. pittsburgh, detroit are 'due' to lose, using NJ and detroit's playoff records over the last 15 years). buoying this was my partly mistaken notion that even if pittsburgh are 65% to win any given playoff series, they're not 50% to win 2, which is true, but they are still more likely than any given team X to win 2 playoff series. even so, this is silly because you can't lose the first and win the second - there's therefore a 35% chance that they go out in the first round, then a 35% chance again that they go out in the second round.

    so like i said, so elementary that it probably went right under your head. i just had to get clear on it myself.

  3. has anyone made updates for HLS 2 recently. I'm looking for them. arkham@roadrunner.com