His goal on 57 minutes at the Estadio Félix Capriles on 31 March 1963 made it 5-4 against Brazil and held as the winner, with 25,000 in Cochabamba watching Bolivia finish the tournament unbeaten. That win sealed the 1963 South American Championship, Bolivia's only continental title, and he finished the tournament on five goals; three Bolivian league championships with Jorge Wilstermann in 1957, 1958 and 1959 came before it, along with 13 goals in 22 caps. Career record: 22 caps and 13 goals for Bolivia; club career at C.D. Jorge Wilstermann, Club Always Ready, Deportivo Municipal de La Paz.
| 1956–1960 | C.D. Jorge Wilstermann |
| 1960–1961 | Club Always Ready |
| 1961–1962 | Deportivo Municipal de La Paz |
| 1962–1963 | Club Aurora |
| Bolivia | 22 caps, 13 goals |
Bolivia legends whose careers overlapped Alcócer's
One rank above: Marco Sandy at #22.
One rank below: Ovidio Messa at #24.
Bolivia's editorial top five: Marco Etcheverry · Erwin Sánchez · Julio César Baldivieso · Víctor Agustín Ugarte · Marcelo Moreno Martins.