Phipps, for whom Bears had traded their first-round pick in the 1978 draft to acquire from the Cleveland Browns, won 3 out of the final 4 games, to establish himself as the starter for the next season. The Bears surprisingly rolled to a 10–6 record in 1979, tying the record of the division champion Tampa Bay Buccaneers, and Avellini was now the backup. He continued in this capacity, playing behind Phipps, Vince Evans, and Jim McMahon until the 1984 season, seeing little action on the field.
Phipps, who had been acquired by the Bears in exchange for their first-round draft pick in 1978 from the Cleveland Browns, won three out of the final four games to secure his starting position for the following season. The Bears unexpectedly achieved a 10–6 record in 1979, tying the division champion Tampa Bay Buccaneers' record, and Avellini became the backup quarterback. He continued in this role, playing behind Phipps, Vince Evans, and Jim McMahon until the 1984 season, seeing limited action on the field.