Earned v. Unearned Run Following an Error (Dropped Foul Ball)

Question

Suppose that Paul the pitcher begins an inning by striking out Adam, and then he walks Billy. The next batter is Charlie, who hits a foul ball that the first baseman drops. Subsequently, he is charged with an error on the play. Charlie proceeds to hit a home run. Paul concludes the inning by striking out David and Ed.

How does this inning get scored in terms of earned v. unearned runs? Clearly, Charlie's run is unearned because of the error. But what about Billy's run?

I would assume that there are 3 options available for the official scorer:

1) Ignore the end result of Charlie's at bat (the homer, which implies Billy's run is unearned).

2) Assume that the next hitter (David) would have the same end result as Charlie (i.e., David would hit a homer, which implies Billy's run is earned).

3) Which ever approach is more favourable for the pitcher.

How would the answer change if instead of David and Ed striking out, David hit a triple (which would have scored Billy had the foul ball been caught), and then Ed and Fred strikeout? My guess is that the scorer would take approach 1, assume Charlie was actually out, and proceed from there.

Answer 1

1. Both of the runs are unearned because Billy would not have scored if there had been no home run by Charlie. The clear method to draw the line is

What would have happened if an error had not been committed?

In other words, if Charlie's foul ball had been caught, none of the runs would have been scored. That's why both of the runs are unearned.

2. David had hit a triple, Billy's run would have been earned as there was no error committed for David and Billy.

For more information, you can read the Wikipedia article on Earned run. There is a quite interesting example in the link as follows.

A batter or runner advances one or more bases on an error or passed ball and scores on a play that would otherwise not have provided the opportunity to score.

...

Under the last circumstance, for example, with two outs, a runner on third base scores on a passed ball. For the time being, the run is unearned since the runner should still be at third. If the batter strikes out to end the inning, it will stay that way. If the batter gets a base hit, which would have scored the runner anyway, the run now becomes earned.