by saying "Home Run" you imply that it was ruled a hit, so then no it cannot be an error on the play. However, there are situations where a batter can round the bases and people call it a "Home Run" when in actuallity there was an error on the play so it goes down officially as a 4-base error (i.e a fielder is standing on the warning track and the ball bounces out of his glove and goes over the fence) -- this examply would not technically be a "home run", but that is more then likely what fans will call it
A run can never be counted as earned if scored due to an error by ANY player. (But, I do see your point)
The batter is credited with a home run in his personal statistics (and the pitcher is charged with allowing one,) but no runs score.
If the batter got on base with the original pitcher and he scores of the new pitcher, the previous pitcher is charged with the earned run.
it matters if the run that scored got on by a hit or by a walk
One of the greatest home run hitters of all time was a pitcher. Babe Ruth was a pitcher
If the inning should have been over, but was prolonged by a fielding error, any subsequent run that scores is considered unearned. Thus, even a home run does not impact on a pitcher's ERA in this instance
'Give up a home run' is a term for a pitcher who has thrown a pitch that a batter has hit for a home run. When a batter hits a home run you might here the announcer say 'That was the 4th home run given up by [pitcher] this season'. That means the pitcher has thrown four pitches that batters have hit for home runs.
Mulder was the first pitcher to hit a home run at the new Busch stadium!
Yes. Even though the run is not charged to the pitcher, due to an error by his defense, the player scoring is credited with a run scored. However, the batter may or may not receive a Run Batted In. The official scorer will determine if the runner, would have scored, regardless of the error, and then determine if the player should or should not receive a RBI.
E.R.A. stands for Earned Run Average. It is the average earned runs scored upon a pitcher per nine innings of work. It is called Earned because if a fielder makes an error allowing a runner to advance a base and that runner eventually scores, that run will not be charged to the pitcher's E.R.A.
No anybody that's on because of an error is an unearned run no matter how they score