Low correlations indicate that pitchers tend not to be clutch one year and again clutch the next year.
I looked at all pitchers that had at least 250 plate appearances against opposing hitters in both 2009 & 2010 both with and without runners on base. There were 76 such pitchers. Data from David Pinto's "Day by Day Database" which is based on Retrosheet.
I found the differential between the batting average they allowed with runners on base (ROB) and the batting average they allowed with no runners on (NONE). I did the same for SLG. So if a pitcher allowed a .240 AVG with ROB and a .260 AVG with NONE, his differential was -.020. That means he did better in the clutch than otherwise.
Did pitchers maintaing about the same clutch performance in each year? Probably not. The correlation between their differentials in each year was just -.064. A zero correlation means no relationship and this is very close to that.
It was higher for SLG, though. But it was -.196 . That means if a pitcher was good in the clutch one year, he tended not to be good the next year, although the effect is weak.
This is just one year. More years need to be looked at. I will try to do more when I can.