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With a man on first, a batter hits a ball in the infield, the fielder makes an error and both runners are safe. While the next batter is up, the runner at first is picked off (the batter that got on via error). A few pitches later, the batter hits a ball for extra bases and the man on second scores. Is that run earned or unearned?
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I'm not an expert on this, but I'll give it a try. First off, you didn't mention the outs to start, so I'll assume there were no outs.

With the runner on first and a groundball, you can't assume the double play, which means (I think) that you have to make a decision on which runner would have been thrown out had the ball been handled. For example, if the grounder was hit to SS and he booted, you might could assume the out would have been recorded at second....but if the ball was hit to the first baseman and he booted, you probably have to assume the out would have been recorded at 1st.

If you assume the out would have been recorded at 2B, then the run is unearned because that runner should have been out. However, if you assume the out would have been recorded at 1B, then the pickoff would never have happened and the run is earned.

I'll warn you that this is my best guess, and again I'm not an expert. But I think you had to be there to make that judgement call.
The general rule is that you cannot, for purposes of determined earned vs. unearned, presume that a DP will be turned. You can only score on a presumed DP if, e.g., the DP is turned but the sole reason you don't get the 2nd out is because the 1B drops a perfectly fine throw on the relay.

So, Emanski is right, and you still haven't really provided enough info to answer the question.

I would decide based on where it appeared the fielder was going to make the play before he booted it. If it looked like he was going to 2nd, then with the E, I would recreate the inning as if there were 2 outs and a man on 1st. After the pickoff, there should've been 3 outs, therefore all runs would be the result of the runner rendered safe and the "extra out" and thus all unearned.

But if the fielder were going to go to 1B all along, then the pickoff essentially cured the E and all runs would be earned.

I guess since you say it was a DP ball, you're saying the fielder would have made the play to 2nd base, so as indicated, all runs are unearned. You would recreate the inning as follows: 1 out already; E should've been 2nd out; pickoff should've been 3d out, end of inning.
I would concur with Midlo Dad.

In another thread, I just complained about W/L being the thing most frequently screwed up by scorers. I was actually wrong on calling it 'most frequent'. Although more frequent but less annoying is how most HS scorekeepers handle ER/UER.

You've asked an excellent question. This one is tough and involves making a jugement call. Many other's require only a few seconds where 3 or 4 neurons have to connect to get it right.

My son on Friday night gave up three walks and a single in the same inning. No errors or PB or anything else. He walked the run in, yet the official scorer said it was unearned.

I love my son (and my daughter) more than life itself, but there is no way on God's green earth that I could enter that run in my son's spread sheet as anything but earned.

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