There was a very intriguing post a few weeks ago at the Hardball Times by Derek Carty called Using FIP to evaluate pitchers? I wouldn’t. The FIP refers to "fielding independent ERA," the idea that pitchers should be evaluated only on outcomes that don't involve the fielders. That would include HRs allowed. But, the article said:
"Here's how things work: a pitcher can influence the rate of fly balls he gives up. By this logic, the more fly balls allowed, the more total balls will clear the fences for home runs (all else being equal). However, while a starting pitcher can control the rate of fly balls allowed, he cannot do a very good job of controlling the rate at which those fly balls become home runs (with very few exceptions).
To put it more simply, starting pitchers don't have any underlying ability to prevent home runs—the best they can do is prevent fly balls. If those fly balls are clearing the fence at too high a rate (or too low), we say that the pitcher has been unlucky (or lucky)."
I am not sure I completely agree with this. It could be that there is a difference in flyballs allowed that accounts for the HR rates allowed across pitchers. But whatever the reason, the year-to-year correlation of HR rates allowed by pitchers, although not as high as they are for their walk rates and strikeout rates, they are not small.
The data I looked at involves year-to-year correlations of various years for pitchers who faced at least 500 batters in both of two consecutive seasons. The table below summarizes the results. Starting with the 1955 season, I eliminated IBBs from the calculations. HBP were counted as walks in all years. The columns show the correlation between the rates allowed for each stat year-to-year. The last line is the simple average of all the correlations.
Overall, the correlations are much higher for strikeout rates and walk rates (the denominator I used in all cases was batters faced). But the correlations do seem to be getting higher for the HR rates. It was very surprising to see how low they were in some of the earlier years.
One more thing that I tried (and this really makes me think that we should keep looking at HR rates) is that I found a high correlation in HR rates from one period to the next using more years. For that, I found all the pitchers that had 1000+ batters faced in both the 2003-05 period and the 2006-08 period. The correlations for walk rates and strikeout rates from period 1 to period 2 were 0.736and 0.767, respectively. But for HR rates it was 0.505. This seems high enough to say that, yes, pitchers do differ in the HR rates they allow, even if the reason is their flyball rates.