My impression was that it's shot by shot. So obviously a player might do better from one season to another. But one shot is no more or less likely to hit than the one immediately preceeding it, statistically. Obviously in the real world something or other may affect a shot. A minor hand injury, for example.

Yup. It's shot by shot, but for large sample sizes. As a fan or coach, the take-home message is that whatever is going on, you can safely treat the "hot hand" as irrelevant or absent. Give the ball to the guy who looks open, not the guy who hit the last shot. (The broader take-home is that your intuition is often wrong.)

Interestingly, if you add enough variables the system becomes chaotic and the results become as unpredictable as the weather. It's not quite accurate to say that it's random (I don't think... could be wrong), but chaos and randomness are often indistinguishable.

This is probably how I'd try to explain the observations. I mean, a coin flip isn't truly random either. What side lands face up is affected by the imparted torque, the air density, the precise angle of contact between the coin and the surface it hits, etc. Precisely-calibrated coin flippers operated in a vacuum could, with sufficient engineering, (nearly) always toss a heads. But as far as the coin flips you've done, it's random and uncorrelated, just like how you should treat CF's RNG.

valguarnera@carrionfields.com