Born into a musical family (biographies differ on his date of birth), Rich began dancing in his parents' vaudeville act at the age of 18 months, soon acquired the stage name “Baby Traps, the Drum Wonder,” and by the age of 11 was leading a band. He began playing jazz in 1938 and soon was the rhythmic inspiration of popular swing bands, working longest with Tommy Dorsey (1939–42, 1944–46, and 1954–55) and Harry James (1953–54, 1957, 1961–66). Meanwhile he served in the U.S. Marines in 1942–44, toured frequently with Jazz at the Philharmonic beginning in 1947, had short-lived careers as a singer and an actor, and acquired a reputation as a technically brilliant swing drummer who combined showmanship with good musical taste. Occasionally he formed short-lived big bands; he finally found lasting popular success in 1967–74 leading a band of 16 young musicians, which played jazz arrangements of rock and pop music. He often reorganized the band for tours after 1974; he also led occasional small groups and appeared often as a soloist on television.