The only way a runner can reach on a passed ball is if he strikes out, and the 3rd strike gets away from the catcher. Since the batter struck out, he should not have reached based, although no errors are charged the run if he later scores is an unearned run
See MLB Rule 10.18 Earned Runs. No earned run if batter reaches on passed ball.
A wild pitch is the pitcher's fault and contributes to the earned run.
Assume 3 players in a row hit singles, and the bases are loaded. The pitcher walks the batter and the first player scores. Since he hit a single, his is an earned run. Now imagine a different situation, where the first player got on base due to an error. Then the next two players hit singles and the bases are loaded. If the pitcher walks the 4th player, the 1st player scores but his is an unearned run. That is, the run is not counted against the pitcher since an error by someone else led to his being on base. Now imagine the next batter gets on due to an error and another run scored. This is the 2nd player, who had a single earler. His is an earned run. Every player on base could become an earned or unearned run, depending on how they got on base-- not how they eventually scored.
if there is two outs and the error would have meant the third out, then no earned runs will be charged. In all other cases, any runner who reached base on an error will not be considered an earned run ( the batter will be an earned run if the error was not supposed to be the third out.) Any runner who reaches base on a hit or walk but advances a base because of an error will still be considered an earned run when the homerun is hit (including runners who already scored on errors)
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