Here's one example that I can give because I have the run expectancy data for the two situations.
Let's say that there's a runner on 1B, no outs, in the bottom of the 9th, with the team down by one run. Your #9 hitter is up at the plate. Do you have him sac bunt or swing away? Let's assume the sac bunt will be successful.
From a run expectancy viewpoint, the team's chances of scoring a run in that inning dropped by 1.9%, from 41.6% to 39.7%. The difference is not very significant at all.
Sadly for me, I don't have access to all of the run expectancy data on how Pitcher A would fare in a situation versus Pitcher B, but the stat geeks do. From what I've read, that difference is surprisingly small.