Torre and Cox retired as managers after the 2010 season and La Russa after leading St. Louis to the 2011 championship. Torre won four World Series titles with the Yankees, La Russa three with Oakland and the Cardinals, and Cox one with Atlanta.
"They say when you're voted to the Hall of Fame your life changes," Cox said. "And it has. I've got goose bumps, and it's the greatest honor that we could ever have."
Among the nine managers with three or more World Series titles, Torre and La Russa were the only ones not in Cooperstown.
"It's a stunner," said La Russa, revealed he'd like to join a club front office, "I miss the winning and losing. ... Some day I'll be with a team, I think. I'd like to be part of the competition again."
La Russa is third among managers with 2,728 wins; Cox had 2,504 and Torre 2,326.
Torre had an unusual experience when he learned of his election from Hall chairman Jane Forbes Clark.
"I was always trying to be like blase about this, saying that it's something I never obsessed about, because I had no control over it," he explained. "But when the phone call comes and -- I hung up on Jane Clark the first time she called this morning, not meaning to, but I didn't have my glasses on -- it hits you like a sledgehammer."
The trio of retired managers was joined on the 12-man ballot by a pair of much-debated figures who died in recent years: New York Yankees owner George Steinbrenner and pioneering players' union head Marvin Miller.
Clark said no other candidates received more than six votes.
Miller was on a Hall ballot for the sixth time and Steinbrenner for the second.
"Over the past fifty years, no individual has come close to matching Marvin's impact on the sport," union head Tony Clark said in a statement. "Despite the election results, Marvin's legacy remains intact, and will only grow stronger, while the credibility of the Hall of Fame continues to suffer."
By the time the vote was announced, the lobby in the Dolphin hotel near Walt Disney World was filled with agents and team officials arriving for the four-day session.
Even before the meetings, 42 of 168 major leaguers who became free agents after the World Series already had agreements, with at least seven more deals in the process of being finalized.
Since Boston finished off St. Louis for its third title in 10 seasons, Prince Fielder, Ian Kinsler, Doug Fister, Jim Johnson, David Freese and Heath Bell have been traded in a busy swaps market.
"It's not the best free-agent market," Texas general manager Jon Daniels said, "and so I think that teams realize they weren't going to be able to fill all of their needs, or wouldn't necessarily want to fill all of their needs on the open market, and that led to a lot more accelerated trade conversation, and we're seeing that play out."
Robinson Cano, Jacoby Ellsbury, Joe Nathan, Jhonny Peralta, Tim Hudson and Curtis Granderson are some of the top free agents who have already changed teams.
Outfielders Shin-Soo Choo and Nelson Cruz are among the free agents still available, joined by designated hitter Kendrys Morales, shortstop Stephen Drew and pitchers Bronson Arroyo, Bartolo Colon, Matt Garza, Ubaldo Jimenez, Fernando Rodney and Ervin Santana.
"It's a bit like an art auction," Oakland general manager Billy Beane said. "This is a time the industry is very active, you want to make sure you're a part of what's going on so you don't miss anything."
Cano has the largest package, a yet-to-be-finalized deal said to be worth $240 million over 10 years for the All-Star second baseman.
"Nothing should be surprising anymore. Therefore I wasn't surprised -- after a moment," New York Mets general manager Sandy Alderson said. "That kind of money has been spent before. The thing about baseball (that) is funny is that all 30 teams are on a continuum and nobody is in the same point psychologically, competitively and financially at any point in time."
After missing the playoffs for only the second time in 19 seasons, the Yankees have been big spenders despite the loss of Cano. New York has committed $307 million to add Ellsbury, Brian McCann, Carlos Beltran and Kelly Johnson and to retain Hiroki Kuroda and Brendan Ryan.
"We have enough voids that we don't have to prioritize any one," Cashman said.
New York also is interested in pitcher Masahiro Tanaka if he is made available by his Japanese team. Major League Baseball and Nippon Professional Baseball have an agreement in principle on a new posting system. If ratified by both sides, there would be a $20 million cap on the fee going to Japanese clubs for players put on the posting market, and any MLB teams bidding the specified price would be able to compete to sign the players.
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