I used data from David Pinto's Day-by-Day Database. I found all the pitchers who had 2500+ PAs with runners on base (ROB) and no runners on (NONE). There were 274 pitchers.
The correlation between the batting average (BA) allowed with ROB and BA allowed with NONE was .723. For slugging percentage (Slug%) it was .740. Those are both fairly high.
But I did expect it to be even higher based on some recent posts where I compared BA differential and Slug% differential between the two cases for consecutive years were extremely low. That suggests very little ability to pitch to the situation.
The table below shows the 25 best pitchers in terms of lowering their BA with ROB compared to NONE.
Now for Slug%
The next two tables are the worst pitchers. That is, they gave up a higher BA and Slug% with ROB than with NONE.