Pitcher "A" completes an inning. Pitcher "B" comes in to start the following inning. Question, when is pitcher "A" officially removed from the game, or when does the pitching change officially occur?
The pitching change officially occurs when the new pitcher takes the mound. For example, let's say Pitcher A finishes a half inning with his team losing. During the next half inning, his team takes the lead and the manager either pinch-hits for Pitcher A or decides to put in Pitcher B to pitch next, Pitcher A would still get a Win assuming his team maintains the lead they got.