NATIONAL HARBOR, Md. >> Rich Hill’s voice cracked as he described his emotions upon re-signing with the Dodgers on Monday.Sure, the $48 million he’ll be paid over the three-year deal is a notable reward for what he’s endured in his baseball career.But Hill was clearly also thinking of the infant son he lost three years ago, whose name he mentioned as he was describing the emotion of the day in a press conference at the winter meetings.“I told myself I wasn’t going to do this,” Hill said, explaining the pauses when he could not get out any words. “It’s been an incredible journey to get to this point.” Newsroom GuidelinesNews TipsContact UsReport an Error “You see guys like R.A. (Dickey) and Bartolo (Colon) who are still pitching into their 40s, and that’s inspiring,” Hill said. “It’s something I’d love to do. We all know the body clock says other things. Right now I’m trying to make the most out of the next three years and be as productive as I can be. I would love to go out and have 30-plus starts the next three years.”As for the blister issue that caused Hill to miss the first three weeks after the Dodgers got him, he said it won’t be a problem.“It wasn’t your typical pitcher’s blister,” Hill said. “It was more of a wound. Moving forward, there will be no issues.”Andrew Friedman, who had not signed a major leaguer to a deal more than this amount since taking over as the Dodgers president, said his confidence in Hill’s future comes from the time they spent with Hill after acquiring him in July.“No matter how much work you do (researching) a guy, it’s different once you get to experience it first-hand and see it,” Friedman said. “Having that chance and that opportunity for those three months is what gave us the confidence to bet on him, in terms of what kind of person he is and the work ethic.”Of course, the Dodgers also liked the results they got from Hill, who had a 1.83 ERA in six regular-season starts with the Dodgers after they acquired him from the Oakland Athletics.In three postseason starts with the Dodgers, Hill gave up five runs in 13 innings. He pitched six scoreless innings in a victory over the Chicago Cubs in Game 3 of the National League Championship Series.Hill’s deal is the latest development in what has been a remarkable career rebirth.He has bounced around eight organizations and pitched for the independent Long Island Ducks. It was after the Boston Red Sox signed him away from Long Island that his career turned around. He parlayed four good starts with Boston into a $6 million, one-year deal with Oakland last year.And now this.“It’s been amazing,” Hill said. “This is a great day for us.”A smaller Puig?If Yasiel Puig is back with the Dodgers next season, there could be less of him.Manager Dave Roberts said Monday that the organization would like Puig to lose some weight, although he wouldn’t specify how much. He said Puig will be in Los Angeles in early January to work with the trainers on slimming down.“With Yasiel, there is so much natural strength, it’s more trying to focus on leaning out a little bit,” Roberts said of Puig, who was listed at 240 pounds last season.Roberts also said he’s expecting Puig to be a Dodger next season, despite the widely held assumption that the Dodgers could trade him to clear their outfield logjam.Seeking a closer Andrew Friedman said the Dodgers continue to move towards acquiring a closer. “I think things are starting to bubble toward the surface a little bit,” he said. Kenley Jansen – the Dodgers incumbent — and Aroldis Chapman are the two prominent free agent closers left now that Mark Melancon signed with the Giants. The Dodgers may also be looking to trade for a closer like Kansas City’s Wade Davis. …Dodgers prospect Cody Bellinger was named on Monday to the Arizona Fall League all-prospect team, selected by the league’s managers and coaches. Bellinger, a first baseman, hit .314 with a .424 on-base percentage and a .557 slugging percentage in 20 plate appearances this fall. Bellinger, 21, is rated the Dodgers No. 1 prospect by MLB.com, and the 31st best prospect in baseball. … Clayton Kershaw, at the winter meetings for a promotional event, told reporters he hasn’t yet decided if he will pitch in the World Baseball Classic. Adrian Gonzalez was on the list of players who have committed to play for Team Mexico. The 36-year-old Hill had bounced from organization to organization, a reliever who dealt with injuries that prevented him from getting a foothold in the majors.Those struggles were nothing compared with the loss of his son, Brooks, who died of complications shortly after he was born.“Baseball teaches you how to deal with things off the field that are far greater than you can deal with on the field,” Hill said.Later, as Hill addressed reporters, he held his 5-year-old son, Brice, and looked ahead to what he hopes is a bright future.It’s unusual in this era for a pitcher his age, with his injury history, to get a three-year deal, but Hill said he’s confident he can deliver on the Dodgers’ faith.