That is when the home team is batting in the ninth inning. If the home team is ahead after the visiting team makes its three outs in the 'top' of the ninth (their turn to bat in the ninth inning) there is no bottom of the ninth because the game is over and the home team has won. If the home team is tied or behind the visiting team after the visiting team makes their three outs in the ninth inning, the home team comes to bat and it is called 'batting in the bottom of the ninth inning'.
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There are many phrases in sports, baseball included. The phrase bottom of the fourth refers to the end of the fourth inning.