bottom of the inning vs bout

bottom of the inning and bout both are nouns.

Word	Noun	Adjective	Verb	Adverb
bottom of the inning	Yes	No	No	No
bout	Yes	No	No	No

As nouns, bout is a hypernym of bottom of the inning; that is, bout is a word with a broader meaning than bottom of the inning:

bottom of the inning: the second half of an inning; while the home team is at bat
bout: (sports) a division of a game during which one team is on the offensive

Other hypernyms of bottom of the inning include round, turn.

bottom of the inning (noun)	bout (noun)
the second half of an inning; while the home team is at bat	an occasion for excessive eating or drinking
	a contest or fight (especially between boxers or wrestlers)
	(sports) a division of a game during which one team is on the offensive
	a period of illness