MESA, Ariz. — So there was left-hander Hoby Milner at the Chicago Cubs Convention last month, minding his business and meeting new teammates, when Alex Bregman engaged him in conversation.

The two reflected on May 7, when they faced each other at Fenway Park. Milner entered the game for the Texas Rangers to start the sixth inning, protecting a 3-2 lead. Bregman led off for the Boston Red Sox. And on a 2-2 count, Bregman lofted a soft fly to left that matched the unimpressive speed of the pitch — 88.1 mph.

The ball bounced off the Green Monster, about 10 feet up the wall, for a double. Bregman acknowledged to Milner that if not for the Monster, the ball might have been caught. Yet, he also told the reliever something else.

“He let me know of a tip they had on me. He let me know of two tips,” Milner said, referring to something in his body language that indicated to the hitter what type of pitch he was about to throw.

“I knew one of ‘em already. The other one I didn’t. I guess we never caught it with the Rangers. And he knew it off the top of his head. He didn’t have to go to his notes and pull it up. He had thought about it enough to remember.”

The Cubs signed Bregman to a five-year, $175 million contract, valued at closer to $154.5 million after deferrals, mostly for his offensive skill and defense at third base. However, they also signed him for his difference-making leadership, the way he influences hitters and pitchers alike.

Bregman, who turns 32 in March, is the league leader in a metric Scott Boras, his pun-making agent, somehow failed to invent during the 10-year veteran’s free agency — Secondary Teachings Above Replacement.

Call it STAR.

Many players are good teammates. Bregman stands out, particularly for a player of his caliber, because he thinks beyond himself.

“He really wants to help guys get better,” Cubs president of baseball operations Jed Hoyer said. “He’s passionate about it.”

The Houston Astros absorbed Bregman’s wisdom from 2017 to ‘24. The Boston Red Sox benefited from it in ‘25. And the Cubs already are buzzing about the Bregman Experience, even though he officially joined the team less than a month ago and the club has yet to begin full-squad workouts.

“I just want to win baseball games. I just want to be part of a team that plays meaningful games in October,” Bregman said. “Communication is key. The best teams I’ve been on have been the best at communicating, the best at helping one another.”

Bregman talks the game nonstop. He is bilingual, relating to English and Spanish speakers. Cubs center fielder Pete Crow-Armstrong, the player Bregman perhaps will impact most, gushes about the lessons his new teammate already is imparting. And Cubs pitchers marvel at Bregman’s recall of at-bats against them from years ago.

“I’m pretty good at remembering stuff,” said left-hander Matthew Boyd, who also will be Bregman’s teammate with Team USA in the World Baseball Classic. “He’s probably better than me.”

Boyd and Bregman reviewed a recent showdown they had in Game 3 of the 2022 Division Series, when Boyd was with the Seattle Mariners and Bregman with the Astros. Boyd entered in the 16th inning to face a dangerous pocket — Yordan Alvarez, Bregman and Kyle Tucker.

Boyd started Bregman with a changeup after retiring Alvarez on a two-seam fastball, missing with the pitch. Bregman laid off for ball one. Boyd then came back with a fastball.

Wrong choice.

“I was like, ‘Of course he was waiting on that,’” Boyd said. “I should have gone right back to the changeup and induced weak contact. Instead, he hit a single.

“He was like, ‘Oh, man. I was fighting to survive, just trying to get my barrel out.’ He was talking about what he was going through in that moment.” Boyd, chuckling, added, “I walked Tucker in the next at-bat, and I was out of the game.”

The Astros did not score that inning, but completed their sweep on a Jeremy Peña home run in the 18th. To Boyd, his discussion with Bregman about a pitch sequence from almost three and a half years ago was part of his ongoing baseball education, the kind of perspective curious players cherish.

Bregman (center) walks with Pete Crow-Armstrong (left) and Michael Busch (right) on the way to a workout on Tuesday. (Matt Dirksen / Chicago Cubs / Getty Images)

Right-hander Phil Maton — who, like Milner and Bregman, is a new member of the Cubs — first benefited from Bregman’s savviness in 2021 after getting traded from Cleveland to the Astros.

Teams during that period were particularly obsessed with pitch tipping. Bregman was on an Astros team that, in 2019, was found to have engaged in illegal electronic sign stealing. Still, the Astros also excelled in the perfectly legal practice of picking up pitchers’ tells, from teammates and opponents — “the in-game stuff that can win games and change seasons,” Cubs second baseman Nico Hoerner said.

Shortly after Maton joined the Astros, Bregman and other new teammates informed him of his tell, saying, “Hey, you’re doing this with your glove. We know every pitch that’s coming. You need to stop.”

One game after the trade — Maton can’t remember the exact date or opponent — stood out.

“The paranoia was setting in a little bit: ‘All right, I really need to dial this in, clean it up.’” Maton said. “I just remember even in-game, really working on it with (Bregman), (shortstop) Carlos (Correa) and (catcher Martín) Maldonado. It was just like, get my glove angle a little better so I’m hiding pitches from the guy at second base.”

As a right-hander, Maton gave Bregman a full view from third when he came set. Occasionally, he would glance at Bregman between batters. If Bregman fidgeted his glove, it would signal to Maton that his grip was too visible to the runner at second, and that he needed to adjust.

All this information, mind you, was coming not from a fellow pitcher, or even a coach. It was coming from a hitter.

“I can’t even imagine what he’s doing from the hitting side with those guys,” Maton said.

Bregman sat in the Cubs’ video room with the team’s hitting coaches on Tuesday, asking about some of his new teammates what they’re working on and what they’re trying to accomplish.

Young Red Sox hitters such as Roman Anthony, Marcelo Mayer and Ceddanne Rafaela raved about Bregman’s tutelage last season. The Cubs’ position-player group is more established. A number of their veterans — Hoerner, shortstop Dansby Swanson and left fielder Ian Happ — share Bregman’s sensibilities, his cerebral, baseball-first approach and obsession with improvement.

Crow-Armstrong, who turns 24 next month, is still a work in progress.

His chase rate last season was the third-highest in the majors. His on-base percentage was the 11th lowest. His OPS was .847 before the All-Star Game and .634 after.

Bregman intends to help him fix all that.

“He’s excited to see my OBP go up and my swing rate go down,” Crow-Armstrong said Wednesday. “It’s everything that everybody else probably wants to see. But the way he talks about it is really cool.

“It’s a nerdy approach to hitting, but it’s never overcomplicated.”

Cubs manager Craig Counsell said Bregman not only possesses “a wonderful grasp of data,” but also shares it with teammates in ways they can easily digest, making his knowledge all the more valuable.

The Cubs are learning that Bregman is intentional and process-oriented, even in batting practice. Bregman quizzed coaches and teammates on which pitches the right-hander would be throwing and at what velocity before facing Jameson Taillon in a live BP session on Wednesday. Yet, as serious as Bregman is about his craft, Crow-Armstrong describes him as “super-supportive” in their exchanges.

At one point, Bregman told Crow-Armstrong emphatically, “I can tell you’re going to chase less,” citing everything from Crow-Armstrong’s mechanics to his mindset.

“He’s so good already,” Bregman said. “And he has so much potential. I think he’s going to have the best year of his career this year, for sure.”

Crow-Armstrong isn’t about to argue.

“I can already kind of see it’s going to be really easy to apply my conviction and competitiveness into a real thought-out approach,” he said. “The guy has had .400 OBP years. He is probably someone you should listen to in terms of that. I just appreciate it when he can come in, and he’s not just picking apart my swing.

“That’s always a possibility. I would still hear what he has to say because it’s Alex Bregman. It’s a little bit different of an approach to swinging. He just wants to see a little less from me, I think.”

It’s only Feb. 12. The Cubs have yet to play a Cactus League game, much less embark upon their regular-season schedule. And for Bregman to prove a truly meaningful addition, he will need to be healthier than he was last season, when he missed nearly seven weeks with a strained right quad and was less productive after his return on July 11.

He still finished with 3.5 fWAR, not terribly below where he was when healthy in 2023 and ‘24. And even while on the injured list, he contributed, giving starting pitchers pop quizzes and hollering instructions to hitters from the top step of the dugout.

Now it’s the Cubs’ turn.

Bregman made an impression on Taillon last month at the Cubs Convention, just as he did with Milner. One of the first questions Bregman asked him, Taillon said, was, “Why didn’t the Cubs win the division last year?”

Taillon mentioned a couple of reasons, notably the Milwaukee Brewers’ 29-4 run in July and August that extended their NL Central lead.

Then, Taillon thought of something else.

“And,” he told Bregman, “we didn’t have you.”