Born in Detroit, Michigan, Radatz led the American League in saves (24), games (62) and relief wins (9) in , his rookie season with the Red Sox, and was named Fireman of the Year by The Sporting News.
In Radatz saved 25 games and went 15-6 with a 1.97 ERA, becoming the first pitcher in history to have consecutive 20-save seasons. The same season he was selected to the All-Star Game, and impressed with strikeouts of Willie Mays, Dick Groat, Duke Snider, Willie McCovey and Julián Javier in the two innings he pitched. In 1963, Yankee manager Ralph Houk said, "For two seasons, I've never seen a better pitcher," and reporters apparently agreed: Radatz finished 5th in MVP voting despite Boston's 7th-place finish.
Radatz received his second Fireman of the Year award in for his league-leading 29 saves with 16 wins and a 2.29 ERA in 79 games. Again, he was selected an All-Star (but was saddled with the loss in that game when Johnny Callison hit a dramatic home run). Most notably, he fanned 181 batters in 157 innings, setting a record that still stands for most strikeouts by a relief pitcher in a single season.
Sportswriter Jim Murray wrote that "Dick Radatz brings one weapon - a fastball. It's like saying all a country brings to a war is an atom bomb." However, Radatz's one-pitch arsenal was a worry for Boston, and Ted Williams encouraged him to develop a sinker. Radatz complied, but in changing his mechanics to incorporate the new pitch, he permanently lost the edge on his fastball.
In 1965 Radatz went 9-11 with 24 saves and a high 3.91 ERA. He was diagnosed with injuries in his arm and shoulder which required season-ending surgery. He never recovered his form, was traded to the Indians at the 1966 mid-season, and was sent to the Cubs the following year. Out of action for the 1968 season, he finished his career with the Tigers and Expos in 1969.
Overall with Boston, Radatz saved 104 games (a team record later broken by Bob Stanley) with a 49-34 record and 646 strikeouts in 576.1 innings pitched. With the other four teams he went 6-20 with 26 saves in 117.2 innings.
Dick Radatz was selected to the Boston Red Sox Hall of Fame in . He died in March 2005 after falling down a flight of stairs at his home in Easton, Massachusetts. The Red Sox held a moment of silence during their 2005 home opener in his honor.