May 6, 2009

The Pirate Kings

The Milwaukee Brewers beat the Pirates Tuesday 8-5, the seventeenth win in a row by Milwaukee over Pittsburgh:

Let’s assume, for a second, that the Brewers have a 60% chance of beating the Pirates in any given game. The chances that they win two in a row at that rate would be 0.6*0.6, which equals 0.36, or 36%. A three-game sweep? The odds of that are 21.4%. The odds of the Brewers winning 17 in a row? The chances of that are 0.17%. Even if you assume the Brewers have a 70% chance to beat the Bucs, the odds jump to 0.23%. If we bump the odds of a Brewers win in any given game to 80% (which is pretty high, even for the Pirates and Brewers), this sort of thing only happens 2.3% of the time.

The thing is, the Pirates aren’t that bad this year, and Milwuakee’s not that good. The teams have nearly identical runs per game, and Pittsburgh has a better ERA. I doubt the Pirates will get swept by the Brewers over the full season.

Maybe the Brewers keep claiming to be orphans, which is a sure way to defeat Pirates.

4 thoughts on “The Pirate Kings

  1. Androcass

    That analysis is fine, as far as it goes, but it’s more valid to look at the probability that any matchup over a period of time might bring about that result, in which case the chances are considerably higher.

    We are looking, right now, at a result that’s caught our eye simply because it’s improbable. But there are 30 MLB teams, and 435 possible matchups. A back-of-the-envelope calculation with the 60% figure shows us that there’s actually a 52.3% probability that one of the 435 matchups leads to a 17-game streak.

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  2. Ed

    You are forgetting black swans. Low probability events will always occur at some point. There are lots and lots of cases where one team plays the other seventeen times in a row. If the odds of a seventeen game winning streak against a particular other team are one in three hundred, this will happen at one point. In any particular matchup it is unlikely, but over several hundred matchups eventually it will happen.

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  3. Androcass

    Given the mistake in the original article (at 60%, the probability of 17 in a row is 0.017%), I’ve revised my estimate, but it doesn’t change the questionable nature of the quote from the original article (“When one team loses to another seventeen straight times, it’s not just a case of good vs. bad. It’s a case of good vs. bad with a sprinkle of bad luck and an incredible rash of improbability.”).

    I’ve roughed out an argument at my blog (http://androcass.blogspot.com/2009/05/streaks-and-stats.html), but, to summarize, we could expect a similar streak somewhat more often than every 27 years. Since we haven’t seen one since 1970, it’s actually been overdue.

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