baseball game vs hitting average

baseball game and hitting average both are nouns.

Word	Noun	Adjective	Verb	Adverb
baseball game	Yes	No	No	No
hitting average	Yes	No	No	No

baseball game (noun)	hitting average (noun)
a ball game played with a bat and ball between two teams of nine players; teams take turns at bat trying to score runs	(baseball) a measure of a batter's performance; the number of base hits divided by the number of official times at bat