Hoffman, who at 38 years old, posted the second-highest save total of his career with 46, could also garner some votes for the NL Cy Young Award that will be announced on Nov. 14.
"I am very honored to have been named the Rolaids Relief Man of the Year Award winner," Hoffman said. "However, this award would not have been possible without the work of my fellow relievers in the bullpen, one of the top bullpens in the League in 2006."
Rodriguez edged Hoffman by one save to lead Major League Baseball with 47. It was his second straight 40-plus save season and broke the Angels' franchise mark of 46 set by Bryan Harvey in 1991.
Based on a formula that awards points for saves and wins but subtracts from that total for blown saves and losses, Rodriguez posted a 2-3 record for a total of 134. He also had a 1.73 ERA. Hoffman went 0-2 with a 2.14 ERA and a Rolaids point total of 124.
"Every year has been a progression," Angels manager Mike Scioscia said of Rodriguez. "His challenge now is to maintain his level of achievement for his career, and that will be very important for our organizational goals, to have Frankie Rodriguez in our bullpen, because for any team to reach their goal, you have to have that presence."
The 2006 season was just the second year as full-time closer for Rodriguez, who has become one of the premier pitchers in his specialty. At 24, Rodriguez is the youngest pitcher to reach 100 saves in his career. Last season Rodriguez notched 45 saves and finished the year with 18 straight.
The right-hander carried that streak into 2006 and rattled off another four straight saves before having his string broken at 22, which also set a new franchise record. Later in the year, Rodriguez put together a 30 2/3 scoreless innings streak.
Rodriguez made $3.775 million this past season, the first year he was able for salary arbitration, and the Angels are looking to sign him to a multiyear deal.
"His fastball command this year was the best that we've seen it," Scioscia said. "The power combination that he has is incredible. His ability to get the fastball over for strikes was impressive, and he understands the importance of his fastball command. He wants it and he wants to achieve."