Averhoff’s father was a member of the iconic Cuban jazz ensemble, Irakere, which was led by pianist Chucho Valdés. The outstanding group was one of Cuba’s chief cultural exports, making Averhoff, Sr. lead a very busy life as a performing and touring musician. Though he did not get much direct instruction from his father, Averhoff, Jr. would get the benefit of his father’s teaching through Juan Felipe Tartabull, Averhoff Jr.’s first saxophone teacher and once a disciple of his father.