I play basketball too, and have had 'hot' nights and crummy nights -- and subjectively, on the few really good nights I've had, I knew when shots are going to go in, and when they were going to miss, and I knew, much more clearly than normal, where the hoop was and how to get the ball there. This did not feel like post-hoc rationalization of a successful basket. I was predicting accurately which shots would hit, and which would miss, before the ball when in.

Yet, analyzing players' performance, their streaks are indistinguishable from what would be expected statistically.

The explanation that reconciles both set of observations is that the ability to attend to salient data (weight of ball, position of feet, etc.) is itself a random process.

Note also that this attention may not be conscious: your motor control circuitry is doing huge amounts of processing that you're not at all aware of during a game.