>I know I feel it when I play. It's very intuitive, yet
>completely wrong. That's why the field is interesting to me.

I'd have to look at the research, but I can think of a number of mundane reasons why players might be more "streaky" than random chance would dictate. For instance, if a player believes he's on a cold streak then his performance may decrease purely on the basis of that (incorrect) belief. Sort of like a psychosomatic illness- it happens because he believes it's already happening. If a player believes he's on a hot streak, that belief might cause him to modify his style of play (regardless of the sport) in such a way that he becomes more effective.

Think of it this way. Your point is based on the idea that a player has a fixed skill level. Maybe he's a 0.333 hitter. Every time he steps up to the plate there's a 1/3 chance he'll get a hit. Given that, over the course of a season you'd expect there to be any number of hot and cold streaks just based on chance. If the guy happens to hit 0.800 over a two-week span, he's still just an 0.333 hitter for the next game.

Where this breaks down is when you consider that the player's attitude may make him more or less than an 0.333 hitter at any point in time. Maybe the belief that he's on a cold streak modifies his technique, his concentration, you name it, such that he becomes a 0.200 hitter. Maybe when he's on a hot streak, pitchers become intimidated and pitch to him differently so that he gets better balls to hit. I'm just not sure it's accurate to treat human beings as if they were perfectly random variables.