1976 World Series: The Big Red Machine Sweeps Their Way To A Dynasty One team was the powerful defending champions, already one of the dominant teams of the decade and looking to secure the legacy of a dynasty. Another was the team making its first World Series appearance in over a decade. It was the Cincinnati Reds and New York Yankees.But unlike what we would expect today, it was the Reds aiming for a dynasty and the Yankees who were thrilled to be back at the party, when they met in the 1976 World Series.