Avenged Sevenfold have made quite a habit of left-field covers lately, re-interpreting the Mexican folk song “Malagueña Salerosa,” Mr. Bungle’s “Retrovertigo,” an original track (“Dose”) Del Shannon’s 1961 hit, “Runaway” and—most recently—The Beach Boys’ “God Only Knows.” Now, the band have released yet another eyebrow-raising cover, taking on the classic early Rolling Stones song, “As Tears Go By.”