[3] Stanley was selected by the Los Angeles Dodgers in the ninth round of the June 1973 MLB draft, but did not sign with the team,[4] choosing instead to attend college.

[7] While he was not named to the All-Star team, Stanley was recognized with down-ballot votes for the Cy Young and Most Valuable Player awards.

He was named to his second All-Star team the following season, 1983, appearing in 64 games and pitching 145+1⁄3 innings, while recording 33 saves and a 2.85 ERA, and he remained a fixture of the Red Sox bullpen in the years which followed.

[8] Stanley was a key member of the 1986 Red Sox team that came within one strike of winning the World Series but ultimately fell to the New York Mets in seven games.

Stanley entered Game 6 with the Red Sox one out away from clinching their first World Series since 1918, holding a one-run lead with runners on first and third.

Stanley was also the team's all-time saves leader, a record he held for 20 years, until Jonathan Papelbon tied him on June 29, 2009, and then passed him on July 1, 2009.