In 1969, Goumas moved from Panellinios, to the Mozambican club Sporting Clube de Lourenço Marques (SCLM).

In the 1970–71 season, in a Greek League game against Amyntas Athens, Goumas scored 61 points.

When he retired in 1988, Goumas was the Greek Basketball League's all-time top scorer.

His career scoring record was eventually broken by Nikos Galis, on 29 February 1992.

Goumas was the Greek League Top Scorer four times during his career, in the 1969–70, 1973–74, 1974–75, and 1976–77 seasons.

Goumas played with the Greek Under-17 junior national team at the 1963 Balkan Youth Basketball Championship, where he averaged 13.5 points per game.

Goumas' last appearance with the senior men's Greek national team came on 16 June 1975, in Greece's 74–64 loss to Turkey, at the 1975 FIBA EuroBasket.

At that 1975 EuroBasket, which took place in Belgrade, Yugoslavia, the famous "The Serenade on the Danube" incident occurred.

The Hellenic Basketball Federation had given the Greek national team's caretaker, Panos Metaxas, some bottles of ouzo, brandy, cognac, nuts, and miniature tcholiadaki, that were supposed to then be given as gifts to FIBA's head officials and refs.