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No, I am not committing the gambler's fallacy. Though I can see why you might think that. There are enough things that sound similar. I'm instead talking abo

by btilly 8y ago

No, I am not committing the gambler's fallacy. Though I can see why you might think that. There are enough things that sound similar. I'm instead talking about a more subtle detail. Which is that selecting a group based on performance results in selecting people in part for having been lucky. They were lucky to have done that well that time, were lucky to be in your group, and their future performance probably won't be as good. The result is called regression to the mean. See https://academic.oup.com/ije/article/34/1/215/638499 https://academic.oup.com/ije/article/34/1/215/638499 for an example of statisticians talking about it. See http://onlinestatbook.com/stat_sim/reg_to_mean/index.html http://onlinestatbook.com/stat_sim/reg_to_mean/index.html for a more introductory tutorial. And see http://wmbriggs.com/post/63/ http://wmbriggs.com/post/63/ for an example of an article discussing this counterintuitive phenomena in the context of sports. (Namely the "Sports Illustrated curse" - the future performance of athletes whose performance was good enough to get them on the cover of Sports Illustrated drops after their article appears.)

antidesitter 8y ago
I think I see what you mean now. If you roll 20 dice and select the highest, the next time you throw that very same die it’ll probably have a lower value, simply as a consequence of outcome-dependent selection + a fixed probability. It’s not that the probability has changed, just that you didn’t choose the first outcome according to the true generating distribution. Comparing this highest value with the highest value across all coins when you toss them all again a second time is a different matter. It’s no more likely to be lower than higher. It's best to avoid using the term “luck” altogether in discussions of probability, since it’s easy to misinterpret.
- btilly 8y ago
  That's exactly the right idea.

by btilly 8y ago

antidesitter 8y ago

I think I see what you mean now. If you roll 20 dice and select the highest, the next time you throw that very same die it’ll probably have a lower value, simply as a consequence of outcome-dependent selection + a fixed probability. It’s not that the probability has changed, just that you didn’t choose the first outcome according to the true generating distribution. Comparing this highest value with the highest value across all coins when you toss them all again a second time is a different matter. It’s no more likely to be lower than higher. It's best to avoid using the term “luck” altogether in discussions of probability, since it’s easy to misinterpret.

btilly 8y ago
That's exactly the right idea.