Bench. Rose. Perez. Morgan. The Big Red Machine is the nickname given to the Cincinnati Reds baseball team which dominated the National League from 1970 to 1976 and is recognized as among the best in baseball. Over that span, the team won five National League Western Division titles, four National League pennants, and two World Series titles. The team's combined record from 1970-1976 was 683 wins and 443 losses, an average of nearly 98 wins per season.