Earned or unearned?

[Howboys37]

Here's the situation:
Men on 2nd and 3rd, no outs (both reached on base hits)

Ok, now next batter hits ball to shortstop who errantly tries to throw runner from third out at home. Runner safe at home, batter reaches first base on fielders choice. After runner on first steals 2nd, the next batter grounds to second baseman who tries to throw runner on 3rd out at home but overthrows catcher also allowing the runner on 2nd to score as well.

My question is are these three runs earned or unearned? Here is the rest of the inning:
With the previous batter reaching first on fielder's choice, next batter strikes out (1 out). Subsequent batter singles, men now on 1st and 2nd. Next batter grounds to shortstop who flips to second base for 2nd out of inning and on to first base for attempted double play, runner beats out throw and man previously on 2nd base scores. Next batter strikes out for 3rd out of inning.

Next question, is the runner who scored this fourth run of the inning earned or unearned since he initially reached base on second baseman's errant fielder's choice throw to home?

Hope I was clear, thank you in advance.

[bmclaurin]

All runs unearned. OBR 10.16 states in part:

...In determining earned runs, the official scorer shall reconstruct the inning without the errors (which exclude catcher's interference) and passed balls, giving the benefit of the doubt always to the pitcher in determining which bases would have been reached by runners had there been errorless play...

It goes on to state:

No run shall be earned when scored by a runner whose presence on the bases is prolonged by an error, if such runner would have been put out by errorless play. [10.16(c)]

No run shall be earned when the scoring runner's advance has been aided by an error, a passed ball or defensive interference or obstruction, if in the official scorer's judgment the run would not have scored without the aid of such misplay. [10.16(d)]

So, in reconstructing the inning, we have R3, R2, no runs scored, no outs.

3rd batter: FC, E6 (R3 assumed out at home) --> we now have R3, R1, no runs scored, 1 out

R1 steals 2nd --> R3, R2, no runs scored, 1 out

4th batter: FC, E4 (R3 assumed out at home, R2 advances to 3rd on the throw) --> we now have R3, R1, no runs scored, 2 outs

5th batter: K --> inning over, no runs scored, 2 LOB

Subsequent action is irrelevant to determining earned runs.

An interesting question would arise if the 5th batter singled on a line drive to the outfield instead of striking out, thus scoring R3, followed by 3 straight strikeouts by batters 6-8 to end the inning with no further runs scored. In that hypothetical case, would the 3rd run of the inning be earned? Recall that this is the run that actually scored from 2nd during the 4th batter's at bat on the E4. Under the reconstructed inning scenario, that run would be earned, even though he actually scored as a result of an error. In this hypothetical case, that particular runner wouldn't have been put out as a result of errorless play; rather, he would have advanced safely to 3rd but no further. The subsequent base hit by the hypothetical 5th batter would have then scored R3, thus resulting in an earned run.

[PetroGuy]

I'm not sure about the wording of the question. You mentioned the SS 'errantly' tried to throw the runner out at home. Did you mean the SS made a bad throw or a bad decision to throw home? If it is just a bad decision, then that run is earned.

[bmclaurin]

Agreed. I have assumed that "errantly" means that a throwing error was committed. If no error, then that changes things.

[Howboys37]

Sorry for the confusion, 'errantly' was intended to mean that it was a bad throw, both by SS and 2nd baseman.

[Howboys37]

Just to clarify, the fourth run of the inning is also unearned?

[bmclaurin]

Was it the "bad throw" that allowed the runner to score (i.e., he would have been put out with a good throw), thus causing an error to be charged to the thrower? I assumed this was the case in my initial reply, but the answer would change if this wasn't the case.

If the answer to the preceding question is yes, then all runs are unearned, including the 4th.

[OhioTex]

@bmclaurin... Well done. I liked the reconstruction explanation.. And the hypothetical 5th batter..