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Originally Posted by bob jenkins
I think the manager can choose the batting order spots of Smith and the new pitcher -- one has to bat in the original DH spot and the other in the original right fielder's spot (assuming the substitutions were made at the same time).
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J/R goes on to say that the manager must announce his intentions to the umpire before signaling for a new pitcher. If he signals for a new pitcher without telling the umpire his intentions the pitcher has to leave the game. So "at the same time" is only after discussion with the umpire.