Yes, whatever the reason, we all have good days and bad days.
What you're talking about is what the statisticians call nonstationarity: on one day you make 30% of your shots, while on another day you make 40%, or whatever. Then your teammates, estimating your probability of making the next shot based on how they've observed you playing that day, decide whether to give you the ball more or less often. That would be one explanation -- and to my mind, a perfectly reasonable one -- of the "hot hand" theory.
But that's not what the authors of the original paper measured; and interestingly enough, it's also not the theory that Collins has now un-debunked. That involves a different measure, called autocorrelation, which measures "streakiness": how the odds of your making the next shot change based on whether you made the previous one. Autocorrelation and nonstationarity are orthogonal -- you can have either one without the other.
If you create a shot-vector per day, then any vector will lack autocorrelation.
If you you create a shot-vector for the whole season, then there will be autocorrelation.
Why?
P(n = good | n-1 = good)
= P(n = good | currently good day) P(currently good day | n-1 = good) + P(n = good | currently bad day) P(currently bad day | n-1 = good)
> P(n = good)
Also regarding verhausts example, the process he describes clearly has autocorrelation.
What you're talking about is what the statisticians call nonstationarity: on one day you make 30% of your shots, while on another day you make 40%, or whatever. Then your teammates, estimating your probability of making the next shot based on how they've observed you playing that day, decide whether to give you the ball more or less often. That would be one explanation -- and to my mind, a perfectly reasonable one -- of the "hot hand" theory.
But that's not what the authors of the original paper measured; and interestingly enough, it's also not the theory that Collins has now un-debunked. That involves a different measure, called autocorrelation, which measures "streakiness": how the odds of your making the next shot change based on whether you made the previous one. Autocorrelation and nonstationarity are orthogonal -- you can have either one without the other.