[1] For the many meanings of βάλλω (cf. beta 70, beta 71, beta 72, beta 73, beta 74, beta 75, beta 76, beta 78, beta 79, beta 80) see LSJ (web address 1). The particular distinction here, from verbs of close-range hitting, is repeated at nu 614, omicron 968, and tau 1240.
[2] Homer, Iliad 5.52, which reads βάλλειν ["to hit"] for the lexicon's unmetrical βάλεν . See web address 2 below for the text. The uses in Homer are well analyzed in Lexikon des frühgriechischen Epos II (fasc. 10, 1982) 23-37. The verb τυγχάνω is commonly used in Homer as a synonym of βάλλω "hit", e.g. Iliad 5.582 Ἀντίλοχος δὲ Μύδονα βάλ'… χερμαδίῳ ἀγκῶνα τυχὼν μέσον "Antilochus struck Mydon, hitting the middle of his elbow with a rock", cf. 23.857. See Cunliffe, Lexicon of the Homeric Dialect, and Dyer 660-61 (Bibliography below, citing A.W. Gomme on Thucydides' use of the word, A Historical Commentary of Thucydides III 488-89). It probably originally meant "hit the mark, succeed," an antonym for ἁμαρτάνω "miss the mark, fail" (as at Iliad 5.287).