Old English scot, sceot "an act of shooting, that which is discharged in shooting," from Proto-Germanic *skutan (cf. Old Norse skutr, Old Frisian skete, Middle Dutch scote, German Schuß "a shot"), related to sceotan "to shoot" (see shoot).
Meaning "discharge of a bow, missile," is from Old English gesceot; extended to other projectiles in Middle English, and to sports (hockey, basketball, etc.) 1868. Another original meaning, "payment," is preserved in scot-free. Meaning "drink of straight liquor" first attested 1670s. Meaning "try, attempt" is from 1756; adjectival sense of "exhausted" is from 1930. Sense of "hypodermic injection" first attested 1904; figurative phrase shot in the arm "stimulant" first recorded 1922. Meaning "remark meant to wound" is recorded from 1841; hence cheap shot (1973). To call the shots is first attested 1967; shot in the dark is from 1895.