[Sherman]

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Thank you for your answer.

I think I have been confused because you say "... randomly select ½ of a player’s at bats and compute the average. Then take the remaining ½ of that player’s at bats and compute the average"

But I didn't do the same as you because I didn't calculate the correlation of the mean but the mean of the correlation. This at least where I'm wrong.

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Ah yes. This would be one way of estimating the skill for hitting in baseball for a single season. However, because the database I have has multiple seasons, a better estimate is to take the average r from the pairs of seasons.