I don't think we actually know that much about red hair at all. There are theories, but there are theories for intelligence too.
I would be surprised it it were literally impossible to make a number correlated with people's ability to hit a ball in a game.
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I agree that you couldn't perfectly measure underlying hitting-ability, but I don't think anyone thinks you can perfectly measure g.
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I feel like if Yankees consistently got higher batting average than Red Sox, would be a good start to saying Yankees are better at hitting.
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Though maybe my lack of knowledge of baseball means I've accidentally stumbled into a terrible analogy that disproves my point.
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if you can figure that out in a useful way many baseball front offices would pay you large amounts of money
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You think no statistic is even *correlated* with underlying ability?
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That if we know one guy has highest batting average in league, and other guy has lowest, we have literally no clue who's better?
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oh sure there are correlations but positing a single underlying factor isn't useful the system (batter vs pitcher) is too complex
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I'm not sure that's true. Wouldn't I (not athletically skilled) do worse than Babe Ruth at pretty much everything?
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And if we invented some completely new baseball statistic, wouldn't we have high probability Ruth would beat me in it?
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If this is true, lack of correlation between all measures of good hitting in preselected players might be example of tails coming apart.
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look at publicly available projection systems for minor league players (e.g. KATOH) and look at the range of outcomes
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