left hander vs left-hander

left hander and left-hander both are nouns.

Word	Noun	Adjective	Verb	Adverb
left hander	Yes	No	No	No
left-hander	Yes	No	No	No

As nouns, left hander and left-hander are synonyms defined as:

left hander and left-hander: a baseball pitcher who throws the ball with the left hand

Other synonyms of left hander include left-handed pitcher, lefthander, lefty, southpaw.

left hander (noun)	left-hander (noun)
a baseball pitcher who throws the ball with the left hand	a person who uses the left hand with greater skill than the right
	a baseball pitcher who throws the ball with the left hand