Dave Dombrowski deserves a hat tip for getting the deals done, and kudos to John Henry for keeping the checkbook open, but don’t overlook Alex Cora’s role in the discounted extensions of the past two weeks.

These guys want to play for Cora with the culture he’s created.

They’ve been saying it for over a year now, but their recent re-signings speak louder than any “we love A.C.” could.

Free agents that could cash in on the open market are putting their money where their mouth is – err, leaving some on the table to stay.

Nine days after Chris Sale inked a below-market-value extension, Bogaerts did the same.Rather than hitting free agency ahead of his age-27 season, the shortstop signed a six-year, $120 million deal.

Scott Boras is known for advising clients to test the market, but Bogaerts went to super agent on Opening Day with a simple message: I want to stay. Let’s get a deal done.

“At the very end, I will say that Bogey was very influential in this,” Dombrowski told reporters in Oakland. “He really made an emphasis on how much he wanted to be a Red Sox (player).”

As Bogaerts, Boras and Dombrowski fielded questions, the shortstop’s smile never left. Cora and Red Sox teammates lined the walls in the back of the room, listening intently as they had to Sale the week before.

When Boras spoke, the Boston manager was the first person he mentioned.

“Alex Cora, you can stop leaving me those dirty messages on my phone about getting this done,” Boras cracked. “The overriding theme I heard from Xander was, ‘We have a lot more left with this. I want to be with these guys. I want to travel through this career in a way.’

“What he wanted to do is participate in a true team concept and yet do it in a major market that has a lot of just brilliant players. One of the real issues in Boston always is in these decisions is it has so many great players and that’s a hard thing to manage. You certainly want all the guys to remain with one team for a long time but in professional sports, we know that there’s limitations.”

Those limitations are lessened when All-Stars like Bogaerts and Sale don’t hold out for every last dime. The shortstop will be paid well – $20 million a year is no joke – but his salary will likely soon be eclipsed by peers Francisco Lindor and Carlos Correa.

Manny Machado landed a 10-year, $300 million deal, and his stats are surprisingly similar to Bogaerts’ over the past three seasons; the Sox shortstop could have held out for far more, but why mess with a good thing?

“It’s a very special place to play, man,” Bogaerts said. “The fans, the organization in general expects winning. I know my teammates know how much I love winning. Regardless if it’s cards, baseball, dominoes, I don’t care. I just enjoy winning.”

In 2018, Cora created a culture where winning wasn’t just expected but celebrated, too.

All 108 regular-season victories were immortalized with photographs on the manager’s wall, as were the team’s 11 wins in October. There was joy in the journey to a World Series win.The goal is to continue that for years to come, and with Bogaerts’ bat staying in the middle of the lineup, that’s a real possibility.

“Thanks to Scott and his group, and to Alex and everybody else here that makes it possible and a place where our players want to play,” Dombrowski said. “We’re thrilled to get this done and happy to have Bogey on board for a long time.”