Help with Scorekeeping

Bob, it's a good question. And yes, there is something about a fielder's choice that apples here.

The answer to your question is that Pitcher 2 gets charged with 2 runs, Pitcher 3 with 1.

Here's why:
OBR 10.18(g): "When pitchers are changed during an inning, the relief pitcher shall not be charged with any run (earned or unearned) scored by a runner who ... reaches base on a fielder's choice which puts out a runner left on base by the preceding pitcher."

In your post, Batter 5 did exactly that -- he reached by a fielder's choice which put out a runner (#2) left on base by Pitcher 2. So Pitcher 3 doesn't get charged when Batter 5 scores.

The key is that when Pitcher 2 departed there were 2 runners on base -- so he's liable for the next two 2 runs that score, whether it's those particular runners or not. The only exception is if those runners get picked off, caught stealing, or called out for interference (with the batter not reaching first).

Hope that helps.

Thanks, that is what I was guessing.