MESA, Ariz. — The Chicago Cubs made Alex Bregman an offer they knew he could refuse.

Even after the negotiations dragged into spring training, league sources indicated the Cubs were outbid by multiple teams in all the ways free agents keep score: years, average annual value and total guaranteed money.

As Bregman remained unsigned, Cubs president of baseball operations Jed Hoyer pitched the Ricketts family on a unique opportunity to add a two-time World Series-winning All-Star third baseman to a team emerging from a disciplined, multiyear rebuild.

The ownership group — led by chairman Tom Ricketts and board members Todd and Laura Ricketts — authorized Hoyer to proceed with a four-year, $115 million proposal that included opt-out clauses after the second and third seasons.

Bregman’s decision came down Wednesday night, reaching an agreement with the Boston Red Sox on a three-year, $120 million deal that’s structured with opt-out clauses after each year and a significant amount of deferred money.

“Obviously disappointed,” Hoyer said Thursday morning at the team’s Arizona facility.

But not all that surprised.

Cubs pursuit of Alex Bregman came up short.

Bregman had already turned down a reported six-year, $156 million offer to return to the Houston Astros, the organization that selected him with the No. 2 pick in the 2015 MLB Draft. Coming off an unexpected playoff run, the Detroit Tigers offered Bregman six years and about $171 million, according to The Athletic’s Cody Stavenhagen, viewing him as a missing piece.

“No,” Hoyer said, he never felt like the Cubs were on the verge of a deal with Bregman. “The Red Sox got a great player. They were aggressive. Kudos to them.”

It was unrealistic, Hoyer said, for the Cubs to match the $40 million average annual value the Red Sox presented to Bregman, “given where we are with our budget right now.”

The Cubs have roughly $209 million committed for this season, according to FanGraphs’ database, which includes expenses tied to the competitive balance tax. Maybe the team will approach the $241 million luxury tax threshold by the end of the year, as Tom Ricketts suggested during Cubs Convention, but Hoyer made it clear that Bregman was viewed as an exception.

“He’s a great player,” Hoyer said. “He’s a great fit. We definitely recognized the opportunity. I was really thankful to Tom and Todd and Laura. I spent a lot of time talking about the pursuit of him, and they were willing to green-light us pushing our budget.

“It’s free agency. Ultimately, they got a deal in structure and amount that we couldn’t match. But that’s just the nature of it. I’m thankful that I was able to pursue it. It was a really good opportunity. And now we move forward.”

The money approved for a potential Bregman deal will not be automatically redistributed within baseball operations, team sources said, making it difficult to envision bigger moves in the middle of February.

“The things we’re going to be doing now are probably going to be smaller things financially,” Hoyer said. “We’ll always look, but I think that right now the big blocks, so to speak, are sort of on this team. We’ll be able to make moves in-season. We’ll be able to be opportunistic as things come up. But my expectation is that the group we have right now is really close to what we’re going to go forward with.”

The Cubs could add complementary pieces to improve their overall depth. Previously, The Athletic reported that Justin Turner could be an option if Bregman were to sign elsewhere. Others, such as Mark Canha and J.D. Martinez, who are still available, could be seen as fits. Additionally, the front office never stops looking for more pitching.

But there will be no sequel to the return of Cody Bellinger. Hoyer and agent Scott Boras, who also represents Bregman, finalized Bellinger’s three-year, $80 million contract in late February last year, creating a false sense of hope that the Cubs could close another deal for an All-Star during spring training.

“We were at our budget last year, and Bellinger was still available,” Hoyer said. “I was really thankful that the (Ricketts) family allowed us to go way over budget last year to sign Belli. It was the same thing. We’re really close right now (to our budget limits). We have a little bit of money for some small in-season things. But this was obviously a significant exception.

“Certainly, I had no expectation on Feb. 12 that Alex Bregman was going to sign. It’s important to be opportunistic. That was sort of the case I was making: I realize this is a financial stretch above our budget, but I realize this is the moment to do it.”

The arrival of Bregman in Mesa would have made the Cubs the heavy favorites to win the National League Central, one of baseball’s weakest divisions. The Baseball Prospectus PECOTA system already projected the Cubs for 90 wins, and the less optimistic forecast on FanGraphs still gives them a 54.9 percent chance to make the playoffs.

The outlook, though, would have changed dramatically with Bregman, who reached the postseason in eight of his nine seasons with the Astros. The Cubs had already traded for two of Bregman’s good friends — Kyle Tucker and Ryan Pressly — in separate deals with the Astros that signaled a strong sense of urgency.

Hoyer, however, indicated a financial mechanism used by other big-market franchises is largely unavailable to his front office: “Philosophically, deferrals have been something that the organization has avoided.” In the final calculations, those deferrals are expected to lower the average annual value of Bregman’s deal with Boston.

“We made the best offer that we could make,” Hoyer said. “To me, that’s competitive. That’s free agency, right? Within the structure and our finances, we made the best offer we could make.”