Sumich made his debut for South Fremantle in 1986, having also played cricket for the Australian national under-19 team. After leading the club's goalkicking in 1988, Sumich was selected with a pre-draft selection by the West Coast Eagles prior to the 1988 National Draft. He made his debut for West Coast the following season, and established himself as the team's first-choice full-forward, leading the goalkicking for six consecutive seasons between 1989 and 1994. Sumich played in West Coast's 1992 and 1994 premiership sides, before retiring from AFL football at the end of the 1997 season. In 1998, he was co-captain of South Fremantle, and led the club's goalkicking in what was his final year of playing football. During this time, Sumich also represented Western Australia in five State of Origin and interstate matches.