SCOTTSDALE, Ariz. — When the Yankees’ Brian Cashman arrived here for Major League Baseball’s general manager meetings, it was not to pick up a World Series ring or a handsome playoff bonus.  But he could have made an argument for them.  “He had a huge impact on the postseason in his own way,” Jed Hoyer, the general manager of the Chicago Cubs, said with a smile.  Cashman was merely an observer of this year’s World Series, just as he has been every season since the last appearance by the Yankees in 2009. But this time Cashman’s fingerprints were all over it — thanks to his decision in late July to trade his two difference-making relievers, Andrew Miller and Aroldis Chapman, to the Cleveland Indians and the Cubs.  Both became indispensable in their new teams’ title chases — Miller as a dominating tool that Indians Manager Terry Francona used early, late and liberally, and Chapman providing some ballast to a wobbly Cubs bullpen.  Asked if it was an unusual feeling to watch two players he had dealt end up in the World Series — the Yankees have not often been in the business of trading away their best assets for prospects — Cashman shook his head.  “It wasn’t foreign to me,” he said.  Nor was he surprised. It unfolded just as Cashman had laid it out for the Cubs, the Indians and other teams after he received the green light from the owner Hal Steinbrenner to dismantle a disappointing team.  “I told clubs I’ve got your World Series appearance in the palm of my hand,” Cashman said. “Whoever gets them: ‘You’re going to the World Series. You’re going to the be mayor of your city. You’re going to get Champagne sprayed all over yourself. So you’re going to have to step up because somebody’s going to do it, and you’re going to want it to be you.’  “That’s how it worked out — not because I said it was going to work out — these guys are true difference-makers and they proved it.”  Cashman can only hope he is as prescient in how the trades will turn out for the Yankees. The point of making the deals — along with others for Carlos Beltran and Ivan Nova — was to continue refurbishing the Yankees’ farm system with a haul of prospects.  From the Cubs, they extracted shortstop Gleyber Torres, the Cubs’ top prospect who had Addison Russell and Javier Baez in front of him, and three others. From the Indians, they got a four-player package that included outfielder Clint Frazier, one of the top prospects in a system flush with them, and three promising pitchers.  An indication of how the trades were viewed was evident Monday night when the results of the Sporting News executive of the year voting were announced. Theo Epstein, president of baseball operations for the Cubs, won with 13 votes from the 56-member panel of baseball executives. The Indians’ Chris Antonetti finished second with nine votes.  Cashman was third with eight votes — this after a season in which his team won 84 games, equaling the Yankees’ worst record since 1992.  “I think Cash, of all the G.M.s in baseball — and I want to be respectful of the Cubs and the Indians — had as good a year as anybody,” Seattle Mariners General Manager Jerry Dipoto said. “They took their moment to hop in and collect talent as quickly as they could collect it. And it’s not that far away with potential impact players.”  Hoyer added: “One of the most important things in this game is giving an honest, realistic evaluation of what you are. I think Brian did a great job of that — I think he realized he didn’t have a championship club this year. It just goes to show you a good deadline or two and a good draft or two can get you right back to where you need to be.”  Cashman said on Tuesday that the Yankees’ position players are probably set for next season, with Aaron Judge getting a shot to play regularly in right field and Greg Bird, in his return from shoulder surgery, and Tyler Austin sharing first base.  Brian McCann, who lost the catching job to Gary Sanchez, could return as the designated hitter and backup catcher. But Cashman said he has informed McCann’s agent, B. B. Abbott, that he will listen to offers. McCann has a full no-trade clause in his contract, but he could be willing to waive it for a chance to remain a starting catcher. If McCann is traded, it could open a path to the acquisition of a position player.  Cashman said his priority this winter will be acquiring pitching — both starting and relieving. The free-agent market is thin on the former and flush with the latter. Three of the best closers in baseball — Kenley Jansen, Mark Melancon and Chapman — are free agents, and Cashman said he has already contacted the agents for Chapman and Jansen and plans to do so for Melancon.  He acknowledged that Jansen could be less attractive since signing him would require the Yankees to forfeit a draft pick — which would not be the case for Chapman or Melancon, since they were traded in their last season before free agency.  As for starting pitching, the targets are expected to be more modest.  “We’re not in a position yet to back the truck up,” Cashman said. “That’s a finish-off deal where you’re feel like you’re one player away maybe. And I feel like we’re still building.”  He continued: “It doesn’t mean we can’t accomplish special things next year, but in the winter time I don’t anticipate us making that type of move. I can’t speak to him specifically, but generally, one of these high-end guys, it’s going to take four or five guys, a blockbuster deal; I don’t see that happening.”  The blockbuster deals may be the ones the Yankees have already made. Cashman planned to watch Torres on Tuesday afternoon in the Arizona Fall League. He will begin next season at Class AA Trenton.  “If he goes on and plays in a lot of All-Star Games we’ll be happy for him,” Hoyer said of Torres. “Because there’s no way that flag is flying without Chapman.”  A version of this article appears in print on November 9, 2016, on page B8 of the New York edition with the headline: Cashman Played Winning Hand. Order Reprints| Today's Paper|Subscribe
By trading top-flight relievers to build his ball club, the Yankees’ general manager played a key role in helping the Cubs and the Indians.