late Old English scoru "twenty," from Old Norse skor "mark, notch, incision; a rift in rock," also, in Icelandic, "twenty," from Proto-Germanic *skur-, from PIE root *sker- (1) "to cut."
The notion probably is of counting large numbers (of a passing flock of sheep, etc.) by making a notch in a stick for each 20. The prehistoric sense of the Germanic word, then, likely was "straight mark like a scratch, line drawn by a sharp instrument." That way of counting, called vigesimalism, is widespread and also exists in France and left its trace in the language: In Old French, "twenty" (vint) or a multiple of it could be used as a base, as in vint et doze ("32"), dous vinz et diz ("50"). Vigesimalism was or is a feature of Welsh, Irish, Gaelic and Breton (as well as non-IE Basque), and it is speculated that the English and the French learned it from the Celts. Compare tally (n.).
By early 13c. it is attested in the sense of "a financial record" (perhaps one kept by tallies), and it is attested from early 14c. as "reckoning, total amount." The specific sense of "a reckoning or account kept by means of tallies" is clearly attested by c. 1400, especially (1590s) "mark made (by chalk, on a taproom door, etc.) to keep count of a customer's drinks."
This was extended by c. 1600 to "amount due, one's debt," and by 1670s to "mark made for purpose of recording a point in a game or match," and thus "aggregate of points made by contestants in certain games and matches" (1742, in whist).
The sporting score-card is by 1877 (in cricket). The newspaper sports section score line is by 1965. Score-keeping in sports is by 1905. From the tavern-keeping sense comes the meaning "amount on an innkeeper's bill" (c. 1600) and thus the figurative verbal expression settle scores (1775; as cut scores, 1610s).
Meaning "printed piece of music" is recorded by 1701, said to be from the practice of connecting related staves by scores (in the "line drawn" sense). Especially "music composed for a film" (1927). In underworld slang, "money obtained in a crime," 1914. Meaning "an act of obtaining narcotic drugs" is by 1951.
The meaning "a cut, notch, scratch or line made by a sharp instrument," without reference to counting, is attested from c. 1400. By c. 1600 as "a line drawn."
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.
late 14c., "one who or that which makes notches," agent noun from score (v.). By 1732 as "one who keeps record of a score" (in a match or game), by 1884 as "one who makes a score" in a match or game.
1590s, "cut a notch or notches in," from notch (n.). Earlier verb (before misdivision) was Middle English ochen "to cut, slash" (c. 1400). Meaning "to place in a notch, to fit (an arrow) to the string by the notch" is from 1630s. Meaning "to mark or score" (1837) is sporting slang, originally in cricket, from the old method of keeping score; notch (n.) as "a nick in a stick, etc., as a means of keeping score" is from 1570s (also compare score, tally). Related: Notched; notching.