My hypothesis was that hitting any number of shots in a row does not improve your chances on the following shot. You'll still hit your percentages on any shot in a large sample regardless of whether you hit or missed the previous few shots. That's how I'm defining it.
If the hot hand is real, then after hitting, say, 5 shots, the 6th should go in at a higher rate than your normal fg%. This should show up regardless of any complexities because we're averaging out all the times you've hit that many shots, ideally.
But it's shown most players take harder shots and become more closely guarded once they hit multiple shots in a row. I think those "complexities" would be significant. That's why I like the idea of doing the study off the 3 point contest, because there arent as many variables.