outscore v.

in Old English a common prefix with nouns, adjectives, adverbs, and verbs, "out, outward, outer; forth, away," from out (adv.). The use was even more common in Middle English, and also with the senses "outer, outside, on the outside, from without, external, externally; apart; greatly, extremely; completely, thoroughly, to completion." Other senses of out that extended into the use as a prefix include "beyond the surface or limits; to the utmost degree; to an explicit resolution."

In composition out has either its ordinary adverbial sense, as in outcast, outcome, outlook, etc., or a prepositional force, as in outdoors, or forms transitive verbs denoting a going beyond or surpassing of the object of the verb, in doing the act expressed by the word to which it is prefixed, as in outrun, outshine, outvenom, etc. In the last use especially out may be used with almost any noun or verb. [Century Dictionary]

late 14c., "to record by means of notches;" c. 1400, "to cut with incisions or notches;" see score (n.). Meanings "to keep record of the scores in a game, etc." and "to succeed in making or adding a point for one's side in a game, etc." both are attested from 1742 (Hoyle on whist).

Meaning "to be scorekeeper, to keep the score in a game or contest" is from 1846. In the musical sense of "write out in score" by 1839. The slang sense "buy a narcotic drug" is by 1935; in reference to men, "achieve intercourse" by 1960. Related: Scored; scoring.