The Detroit Pistons selected Alcorn in the third round (18th pick overall) out of California State University, Fresno in the 1959 NBA Draft. He played two seasons in the league, one with the Lakers during the 1960-61 year. A 6-foot-9 forward, Alcorn averaged 3.3 points and 4.2 rebounds in 78 career games.
- Five-time NBA champion (1980, 1982, 1985, 1987-1988)
- NBA Defensive Player of the Year (1986-87)
- Five-time NBA All-Defensive First Team (1982, 1984, 1985, 1987, 1988)
- Three-time NBA All-Defensive Second Team (1981,1983, 1986)
- Ranks fifth all-time in Lakers history in assists (3,666) and steals (1,033)