The Rice University Neologisms Database

Etymology : This is an acronym. The idea of an un-athletic person already existed and people came up with an acronym to match it. Comes from non, prefix meaning "not, lack of," or "sham," 14c., from Anglo-French noun-, from Old French non-, from Latin non "not, by no means, not at all, not a," + athletic, from 1630s (athletical is from 1590s), "pertaining to an athlete," from Latin athleticus, from Greek athletikos +random, "having no definite aim or purpose," 1650s, from at random (1560s), "at great speed" (thus, "carelessly, haphazardly"), alteration of Middle English noun randon "impetuosity, speed" (c.1300) and person from early 13c., from Old French persone "human being, anyone, person" (12c., Modern French personne) and directly from Latin persona "human being, person, personage; a part in a drama, assumed character."(etymonline)