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1540s, "to disgrace," perhaps a Scottish respelling of bauchle "to disgrace publicly" (especially a perjured knight), which is probably related to French bafouer "to abuse, hoodwink" (16c.), possibly from baf, a natural sound of disgust, like bah (cf. German baff machen "to flabbergast"). Meaning "to bewilder, confuse" is from 1640s; that of "to defeat someone's efforts" is from 1670s. Related: Baffled; baffling.
"shielding device," 1881, from baffle (v.).