"But for the most part, those studies always show that the variance in the real-life performance is identical to the variance that would be expected if nothing was operating except the normal randomization"
Ah...so variance in real life is somewhat random. Holy cow? Of course it is. Hot streaks do come up randomly. You can't control it...or they would be streaks. A Boston 3B named Boggs felt that by eating chicken before every game he could have more control over his "randomness"(or so I've read). If you slipped him a mickey and gave him turkey nuggets instead, would his performance have suffered? Probably not...you can't control "hot" like that.
Streaks come and go, randomly, surely But random comes and goes in the middle of such streaks. For example, a guy who is a .300 career hitter, but has hit .450 for the past 3 weeks, is certainly more likely to get a hit in his next AB than the .300 career hitter who is hitting .150 over that period.
Wanna bet on it?
In a coin flip proposition the coin has no control over the result. In a hitting proposition the batter certainly does.
moe
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