This new analysis is all wrong. I simulated basketball players whose number of shots in game is normally distributed with mean 10 and sigma 2. Each player is a 50% shooter and successive shots are independent I played out 1000 players and aggregated over all players the fraction of the time a made shot was followed by a made shot. I get 50% as expected. But if I compute for each player the fraction of the time a made shot is followed by a made shot and average these numbers over all players  I get 44% which is what the new stuff says. But really the first computation is the one that should be used in any study to see if a hot hand exists.