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How the lineups were created and knowing when to pull pitchers was what greatly affected this game.
Jim Leyland sent in Quintin Berry later on, but instead of taking out Andy Dirks (who didn't get a hit until extra innings), he took out Avisail Garcia, who helped extend the lead in the eighth.
He also kept in Jose Valverde too long after it was clear that he was melting down; even Joaquin Benoit looked shaky on the mound in his role, which won't show up in the stats.
Joe Girardi, on the other hand, didn't make many questionable moves. He took out Alex Rodriguez and Curtis Granderson when they weren't getting it done yet again, and he put Raul Ibanez in a prime spot right after Mark Teixeira, which helped big time.
That being said, David Phelps lost his first postseason appearance coming into extra innings, so using his second appearance for just that was not the best move. Sure, they were running out of pitchers, but that's what happens when you use four pitchers for 2.1 innings.