Winning/Losing Pitcher

Question
This is a high school baseball game going into the 7th and final inning tied 1-1.  Pitcher A starts the inning and faces the #2 batter in the lineup who doubles.  The #3 batter is walked.  Pitcher B comes in with runners on 1st and 2nd and no outs.  He faces the #4 batter and gets him to fly out to left field.  Faces the #5 batter and gets him to fly out to short on an infield fly rule.  He walks the #6 batter.  So we have bases loaded with 2 outs.  He faces the #7 batter who grounds to 2nd base, but the 2nd baseman mishandles the ball and the winning run scores.  Who is the losing pitcher.  The run is the responsibility of Pitcher A, but he left with the game tied.  The run would not affect the ERA of either pitcher since it was an unearned run, but does Pitcher B get the loss?  The coach says the loss would be Pitcher A since the run scored was on the double hit by the batter he faced but I am not sure.  By the way, my son is Pitcher B.

Answer
Good Day...What a great question but it carries a very simple answer....The losing pitcher is simply the pitcher of record at the time.  Therefore no matter what happens or in what order pitcher B is the losing pitcher officially.

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Thanks, Andy