What is the limit for throws a relief pitcher may take after being replaced in an inning?

The correct answer indicates that the limit for throws a relief pitcher may take after being replaced in an inning is timed from the first throw. This means that whether the new pitcher is warming up prior to entering the game or immediately upon taking the mound, the official count of warm-up throws starts only when they throw the ball to the catcher for the first time. This rule is in place to ensure that the game continues to move at an efficient pace while still allowing pitchers to adequately prepare to face batters.

The other options suggest different starting points for timing the warm-up throws, which do not align with the established rules. For instance, timing from when the pitcher arrives at the mound may not accurately reflect the actual warm-up process, and focusing on when the change is made does not account for the immediate actions of the pitcher. The idea of timing from the third out of the previous inning would also be misleading, as it does not relate to the particular moment when the new pitcher actively begins to warm up, which is critical for clarity and regulation during the game.