"Odds" Are Not Real Things That Are *Obstacles* to Achievements

Y'all know I'm a big fan of Nate Silver, as a prognosticator.

But as a philosopher of probability, he's pretty darned bad. Consider this: "Some of the historical cases of teams that defied even longer odds are well-known. Pennsylvania, in 1979, overcame what we estimate were 500-to-1 odds against reaching the Final Four."

 Pennsylvania did not "overcome" these odds to reach the Final Four. "The odds" were not out on the court, blocking Penn's shots or grabbing rebounds away from them. Silver should read his Keynes: "500-to-1" is a prognosticator's subjective judgment about what will happen in the future, not something real* that a team must "overcome." The best way to understand such odds is to see them as a statement that the person positing them would be willing to make a 501-to-1 bet that Penn would get in, and a 499-to-1 bet that they would not.

* Yes, as Oakeshott said, everything is real if we do not take it for other than what it is, i.e., dragons are real creatures of the imagination, and Murphy's "boyish good looks" are real in the imagination of that one Austro-libertarian chick at the bar in Auburn. But you know what I mean here: these odds are real thoughts of the prognosticator, but not real factors a team must "overcome"... unless the odds get in the players heads!

7 comments:

  1. You're right Gene...females who don't know of my scholarly work think I have manly good looks.

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  2. Odds that are 500 to 1 certainly imply that there are significant obstacles to overcome. Isn't it fair to say that the odds (assuming they are accurate (and assuming a frequentist framework)) are a measure of *how much* must be overcome in order to win?

    It seems like a very useful turn of phrase to me.

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    1. OK, John, but what I'm objecting to is reifying the odds as if they are something real. No, what Penn had to overcome was that their players were shorter and slower than the other teams players, not "the odds."

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    2. I see your point, but it seems like a semantic nitpick. I think if pressed he would say he was quantifying the obstacles. Saying "overcoming a lot of obstacles" is a lot less precise than "overcoming 500 to 1 odds".

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    3. "I think if pressed he would say he was quantifying the obstacles."

      Yes, he would, and he would be wrong. That is exactly what I am objecting to. He is giving a subjective estimate of what the odds are here. He is definitely not, in any sense, measuring anything objective. There is no way to do so, since the situation is unique.

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  3. In your post you said Silver should speak of the obstacles, rather than the odds; that he was reifying the odds. But if you want to compare obstacles facing different teams in any useful way, you're going to naturally want to quantify them. Measuring the obstacles in terms of odds doesn't reify odds, any more than measuring your height with a ruler reifies inches.

    It follows from the success of knowledgeable gamblers that obstacles can be quantified in a way that reflects some underlying reality. Of course this measurement is naturally an approximation, and we don't always understand all of the "hidden" factors very well.

    Ok, the Penn case is a unique event, just as a single coin flip is. But if predictions are right over time and pay off in betting terms, then the odds must be reflecting *something* about the underlying reality (the difficulty of the obstacle or the bias of the coin).

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    1. OK, but John, don't you sense the vast difference between a single coin flip, which, while unique, hardly differs from any other coin flip, and a particular basketball game, which differs from any other game in highly significant ways?

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