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Selig said those who have violated the anti-drug rules are “a very small percentage” of players.

“A great majority really, really have been terrific,” Selig said, “and I give the players’ association a lot of credit. We had lots of problems two decades ago, 10 years ago, but I’m confident that Michael and Rob will sit down, because I feel very strongly about this.”

Cabrera, who was leading the NL in hitting for the San Francisco Giants, was suspended for 50 games last year. After asking for a rules change that prevented him from winning the NL batting title, he signed a $16 million, two-year contract with Toronto during the offseason.

Selig would not comment on the now-defunct Biogenesis of America clinic in Coral Gables, Fla., other than to say it is the subject of a “very thorough investigation” by MLB.

The facility was alleged in media reports to have provided performance-enhancing substances to several players, including Cabrera, Alex Rodriguez and Nelson Cruz. The players have denied they obtained banned drugs from the clinic. MLB has been trying to obtain purported records of the clinic posted online by The Miami New Times, which initially revealed the allegations.

“The program is working fine,” Selig said, “but I’ve come to the conclusion the more I’ve thought about this that obviously there are some people, small in number, who need to be given a tougher lesson.”

In the year ending with the 2012 World Series, there were seven positives for performance-enhancing substances and 11 for stimulants among 3,955 urine tests and 1,181 blood tests, according to a report issued in November by baseball’s independent program administrator, Dr. Jeffrey M. Anderson.

“We’re way ahead of what anybody could have thought, but my father used to tell me life is nothing but a series of adjustments,” Selig said, “and this is an adjustment that you have to make based on what you see.”

Joe Torre and Tony La Russa, retired managers who work for Major League Baseball, both voiced support for the tougher penalties at Selig’s news conference.

Torre, the former New York Yankees and Los Angeles Dodgers skipper who will manage the United States in the World Baseball Classic, said it is important to remove questions fans may have about whether players are clean.

“Until we can gain the total respect back from fans and have them trust us again, we’ve got work to do,” he said.

La Russa, longtime manager of the St. Louis Cardinals, said although the punishment already is severe, it apparently isn’t enough.

“Just make that risk so punishing that we can eliminate this,” he said.

Selig said stiffer penalties are in the best interest of baseball.

“Anybody who will be dismayed by this announcement is living in a world that I don’t understand,” he said, “and in my own feeling frankly doesn’t exist.”

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