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General manager Farhan Zaidi said doctors put the odds of a recurrence of the same disk damage at 10 percent.
"It's a bit of bad luck," he said.
Zaidi added that the club "feels good about internal options" to replace Anderson.
"We're not on the phone or anything," he said. "But we're always looking to improve."
Anderson, 28, felt discomfort toward the end of a two-inning stint of live batting practice on Tuesday. His condition worsened on Wednesday with discomfort down his leg. He went for tests which revealed the damaged disk and was scheduled for surgery in Phoenix with Dr. Chris Yeung, who performed Anderson's 2014 operation.
Dodgers manager Dave Roberts said Brandon Beachy and Mike Bolsinger are the primary candidates to replace Anderson in a rotation that has Clayton Kershaw, Scott Kazmir, Kenta Maeda and Alex Wood.
"We didn't think our depth would be tested this early," said Roberts. "Others will have to step up. Every day's a test."
Beachy is continuing a comeback from two Tommy John operations. Bolsinger stepped in admirably early last season, but he struggled in the second half.
The Dodgers are hopeful of getting injured starting pitchers Brandon McCarthy (elbow), Hyun-Jin Ryu (shoulder) and Frankie Montas (rib) back in the coming months.
"It's a bummer," said Kershaw. "Just from the team standpoint. And personally, I can't imagine going through one back surgery, let alone two. I feel bad for him. Any time you have injuries, you have to have one more guy almost pitch above expectations. It's one thing playing to the expectations that you have individually, but when guys are constantly having to step up and step up, it's tough. You know, we'll see."
The Dodgers also have young starters Zach Lee, Chris Anderson, Ross Stripling, Jose De Leon and Julio Urias in camp, but Roberts indicated that Beachy and Bolsinger were likely to get the first shots at replacing Anderson, who had hoped to have shaken an injury-prone label last season, when he threw 180 1/3 innings for the first time in his career.
"As a guy who has spent a little time down before, I hate seeing this happen to him," said Beachy. "I really feel for him. He's had more than his share. This is sobering."
Last year was Anderson's healthiest season since 2009. In the interim, he has had a fractured foot, fractured finger, Tommy John surgery and the previous back operation.
A free agent during the offseason, Anderson turned down multiyear deals and accepted a one-year, $15.8 million qualifying offer from the Dodgers, saying he would bet on himself producing a second healthy season and cash in even bigger next offseason.
Zaidi said he did not regret extending Anderson the qualifying offer.
"No, not at all," he said. "He was healthy all last year. The risk of recurrence is very, very low. Considering how free-agent pitchers' prices went, it's looking like a pretty good buy. It's just unfortunate."
"I was shocked," Roberts said of the news. "Two days ago, Brett thought it would be a couple days and it would subside. I'm sure he's disappointed."