This award is given annually to honor the best relief pitcher in each league. It replaces the Delivery Man of the Year Award that was awarded between 2005-2013. The National League award is named in honor of Trevor Hoffman who spent his entire 18-year career in the National League. The American League award is named in honor of Mariano Rivera who spent his entire 19-year career in the American League. Although all winners thus far have been closers all relief pitchers are eligible. The awards are voted on by a nine-member panel that is currently made up of Mariano Rivera, Trevor Hoffman, Dennis Eckersley, Rollie Fingers, Goose Gossage, Bruce Sutter, Lee Smith, John Franco, and Billy Wagner. Each voter selects three pitchers from each league based on their performance during the regular season and ranks those three. A weighted scoring system of 5-3-1 is used to determine the winner.
|Year||NL / Trevor Hoffman Award||Team||AL / Mariano Rivera Award||Team|
|2017||Kenley Jansen||Los Angeles Dodgers||Craig Kimbrel||Boston Red Sox|
|2016||Kenley Jansen||Los Angeles Dodgers||Zach Britton||Baltimore Orioles|
|2015||Mark Melancon||Pittsburgh Pirates||Andrew Miller||New York Yankees|
|2014||Craig Kimbrel||Atlanta Braves||Greg Holland||Kansas City Royals|