Smitty- The issue with small sample sizes has to do with the predictability of the results within the sample. A streak is just that - a small sample with no predictive value. Sure, streaks exist and players feel hot and cold. No doubt about it. But it's impossible to predict when those hot and cold streaks will start and/or end. Your Josh Hamilton example is a perfect one to illustrate the volatility and arbitrary nature of streak lengths. Relying on unpredictable data for measurement of future actions, in and of itself, is bad decision making.
JH,
what I'm saying is that hitting is not like a coin toss, in which the next flip is completely independent of the last flip. The probability of a hit is a function of the hitter's performance in the last at-bat, or at-bats. At least this is my assertion. However small the sample size, I believe streaks and slumps exist. Of course they end, but while the streak (or slump) is going the odds are with you if you take this into account in decision making. They only go against you the time it ends.
If a hitter goes 4 for 4 in Wednesday's game and 4 for 4 in Thursday's game and 4 for 4 in Friday's game, there is no predictive value in that to say he will get a hit in his first at-bat on Saturday. He may feel more confident and in rhythm at the plate, but there is no way to quantify that he will get a hit strictly based on the sample size of the previous streak he had. As a decision-maker, it would be a bad idea to base in-game decisions on small sample sizes of results because of this. I'm not saying streaks don't exist, I'm saying they aren't usable predictive values.
JH,
I'm not sure if you and I are disagreeing or getting crossed on terminology. I am not suggesting that there's an ability to predict with certainty the outcome of an at-bat based on recent performance, but I do believe that the probability of the outcome changes based on recent performance. Perhaps the math being used to analyze this today is too simple. Algebra shouldn't be used to solve a calculus problem.