Originally signed by the Angels as a free agent in 1961, he made his debut with them on September 21, 1962 at age 19 against the Cleveland Indians.

He pinch hit for pitcher Fred Newman and singled off Mudcat Grant, driving in Leo Burke in his only at bat.

[1] Before the 1964 season began, Angels general manager Fred Haney touted Simpson as a possible Rookie of the Year candidate.

[3] He batted .301 with 22 doubles, 12 triples, 24 home runs, 29 stolen bases and 79 RBI with the Angels' Triple-A affiliate in Seattle in 1965.

[5] Simpson replaced Curt Blefary as the young outfielder traded along with Milt Pappas and Jack Baldschun from the Orioles to the Reds for Frank Robinson one week later on December 9.