APBRmetrics

Guy wrote:Are you comparing the hit rate after 3 makes to each "player's" expectation, or to the overall average of 54%? If it's the latter, that would explain your result: the better shooters will generate a disproportionate share of the streaks of 3 makes, and their expectation on the next shot will be higher than average.

Well, I actually did this:

Guy wrote:But if you are comparing the post-streak hit rate within each 166-shot sample to that player's specific hit rate, then your result doesn't make sense (your randomization process must have some non-random element).

but for some odd reason I used weighted.mean and thereby calculated the former in which the better shooters got weighted more due to the higher amount of runs. Thus, you explained my results and I can thereby confirm that the bias correction is actually correct, because over those now 400 33-players-samples (or 13200 166-shot-sequences) it averages out to 0.000 after bias correction when using mean instead of weighted.mean. For the creating of the shot sequences I simply used "sample" in R. Would have been very odd, if the process had some non-random elements involved.

Mystery solved!

Going back to an earlier question, does anyone know of any research or on whether individual players tend to have higher 3PT% from certain locations along the 3-point line? Of if not research, does any site generate multi-year shot charts? That would provide some indication of whether players do indeed have "sweet spots."

Guy wrote:Mystery solved!

Indeed. Thanks for your help.

In regard to your question, some of the research by Kirk Goldsberry may be a starting point: http://courtvisionanalytics.com/the-yea ... al-review/
That's for all players in 2012, but I'm pretty sure I saw some work by him for individual players as well. Maybe he even done something with multi-year datasets ...

That's interesting data. It seems clear, at a minimum, that the hit rate is higher in the corners (as we'd expect). The study reports no difference by location, but their sample is probably just too small to get a statistically significant difference (especially since they discard the first two shots in each round, which I assume is always from one of the two corners).

Looking at the 3-point study again, I suspect they made a simple but important error: although they discard the first two shots when examining the hit rate after streaks, they seem to be comparing the post-streak hit rate to each player's overall mean as reported in Table One (54% average overall). However, the real hit rate once you discard those first two shots is two points higher on average, or 56% overall. If the post-streak hit rate is being compared to the overall mean, rather than the mean excluding the first two shots, that alone would account for about half of the increase they report for "hot" shooters. You can't tell from the paper whether they did this, but the way Table One reports results it seems this is a good possibility.

EDIT: If true, this would also explain why they find a hot hand effect but not a "cold hand" effect. Since every shooter's hit rate is being inflated about two points -- whether following a hot streak or a cold streak -- a small cold hand effect would be obscured.

I'm also not clear on how they adjusted for the bias created by the fact that the shot being studied cannot, by definition, include one of the three hits in the streak. For the average player in their sample, that will reduce the hit% after a streak by about 1%. However, their adjustment is about 2x as big, making the adjusted hit rate look still higher. I'm not sure what the justification for that is.

The same authors have a paper (linked in http://andrewgelman.com/2015/07/09/hey- ... -hot-hand/) showing/explaining how certain methods of calculating a hot hand underestimate the value. For example, the classic Gilovich study that found a statistically non-significant hot hand actually found a fairly strong hot hand.

Reading through, it doesn't seem to me that the selection bias they mention is right.
If you use the four-coins example, assuming that each of the permutations happens once, there are a total of 22 coin flips after a head, and 11 of those flips are heads, just what is expected.
The bias the authors suggest only occur if you calculate P(head|previous head) for each permutation and then average those probabilities.
I don't really think that's the way hot hand studies have been done in the past.
Let's use the example of evaluating whether a single player has hot hand by checking whether the probability of a making a shot is higher after a previous made shot.
To have the bias the authors suggested, we would be calculating P(make|previous make) for each game and comparing the average of those probabilities with his overall probability.
On the other hand, if we just count all the shots after a made shot and count how many of them are made, we would avoid this bias.
This is my impression of previous hot hand studies in the past, so the selection bias the authors suggested does not really stand