I promised to total up the numbers on the before and after portions of J.J. Hardy's streaks a last week in this post. I took Hardy's 5 streaks of more than 5 games in a row reaching base two or more times and found his total slash line during these hot streaks. Last time, I showed the five weeks following the hot streaks and found that they were very inconsistent.
This time, I've removed the selective sampling issue by finding the total slash line of the hot streaks and the total slash line of the week following the hot streak, excluding the first game after the streak-- which could skew the information, because that game has less than 2 times reached base.
So your hypothetical situation is that you are playing Hardy, and he goes on a hot streak over 5-7 games, reaching base 2 or more times in each of these games. Then he has a poor day, reaching base only once or not at all. Do you continue to play him, in hopes that the "hot streak" is still going?
The five hot streaks together produced a line of .516/.556/.871 in 122 at-bats. After the poor day, Hardy went on to hit .228/.286/.500 in the following week in 136 at-bats. What would we have expected him to hit in the following week? I would have said .270/.329/.446, which is his career line. Balancing out the higher-than-usual slugging and lower-than usual OBP, he looks to be pretty close in line with the expectation.
When I saw the high slugging percentage, I was going to theorize that J.J. presses to hit home runs after a hot streak and forgets about patience-- but the gap in his OBP-BA stays close to the same after these hot streaks.
What conclusions can we draw? All I can say is, even when you have an incredibly streaky hitter like Hardy, you still cannot predict what he will do in the future based on his recent performance. You are much better off looking at the bigger picture to decide on playing time instead of trying to "play the hot hand".