Some days, Troy Tulowitzki would pause his trash talking, slide on a glove, and put on a demonstration that accomplished two things. The first was giving hands-on instruction to a willing student in Brett Baty. The second was reminding the highly regarded Mets prospect just who he was dealing with.

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“He’d be trying to show me up,” Baty said in a recent phone interview. “And, I mean, most of the time he would.”

Ahead of what could be a critical 2023 season, Baty sought help to improve defensively at third base. He turned to a former star shortstop in Tulowitzki, who essentially gave Baty a no-nonsense master class on how to be a pro. It was exactly what he wanted.

“He’s not going to beat around the bush about anything and he’s not going to sugarcoat anything,” Baty said. “If he doesn’t see something he thinks will play at the next level, he will tell you straight up.

“And I love that in people. I don’t really like people who are just there to tell you how good you are, tell you how good you look and stuff like that. I like the people that are actually going to be honest with you, and help you get better.”

Over 13 years in the major leagues, Tulowitzki earned five All-Star appearances and captured two Gold Glove awards. But beyond those accolades, Tulowitzki’s credentials include being a first-round pick, something he shares in common with Baty.

First-round picks must navigate expectations and scrutiny. They’re the ones pocketing big bonuses. If they fail, organizations often afford them second or third chances — opportunities other prospects might not receive. Resentment from others festers. The dynamic extends to major-league clubhouses where some veterans see flashy rookies as youngsters who have been coddled. Sometimes, those older players are right. Tulowitzki knows all of this. He wanted Baty to know it, too.

“That’s probably the biggest thing that I’ve really tried to do for him so far,” Tulowitzki said, “is just be that guy for him that challenges him because I don’t think probably many people do.”

The relationship between the two started a couple of years ago, when Tulowitzki, 38, joined the University of Texas at Austin baseball coaching staff as a volunteer assistant. Baty, who went to high school in Austin, once was committed to Texas. In the offseason, the Longhorns allow Baty and other professional players to use their facilities. In the winter before the 2022 season, Tulowitzki would often observe a group of players that included Baty. He’d offer advice and jump in on fielding drills. The more that players like Baty asked Tulowitzki for pointers, the more he obliged the requests.

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By the end of that winter, Baty felt comfortable enough to ask Tulowitzki for his phone number. Tulowitzki no longer coaches at Texas but still lives in the area. Once this offseason began, Baty knew where he wanted to spend it.

“Normally when I’m around different people, it’s always, like, ‘Oh my gosh, you’re so good and you’re such a good athlete.’ Like, ‘You don’t really need to work on all that much,’” Baty said. “And that’s not the case at all. Any big-leaguer will tell you that they just have so much to work on, and especially me as a young dude — I have so much to get better at and so much to work on.”

Baty’s big bat and large frame — 6-foot-3, 215 pounds — provide a strong foundation to build upon.

“Athleticism sticks out for how big of a kid he is,” Tulowitzki said. “That’s the first thing you see and you go, ‘OK, well, he’s a corner guy, let’s see what kind of athleticism he has.’ And that’s off the charts. So I was impressed by that. Then, the hit tool is there. I always like guys that are hitters first. The power kind of follows after that. He’s right in that mold where he’s a good hitter first and then the power is going to eventually get there because it’s big-time raw power.”

The Athletic’s Keith Law ranked Baty No. 31 on his Top 100 prospect list, a testament to his high ceiling. But evaluators think Baty could be smoother at third base, with one scout saying recently that Baty can operate too mechanically and react too slowly. With time, though, that can change.

“Third base, he still needs to work at it, but I think he’d be the first one to tell you that,” Tulowitzki said. “He needs to get better over there. But some people need to get better because they aren’t athletic enough or don’t have arm strength. He’s got all the tools. He just needs some reps.”

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Baty’s time with Tulowitzki should only help.

Training with Tulowitzki, it turns out, includes getting instruction from guests. A couple of weeks ago, Blue Jays third baseman Matt Chapman and shortstop Bo Bichette joined the workout group at Texas. Tulowitzki, who played for Toronto near the end of his 13-year career, is close with Dante Bichette, Bo’s father, because of their deep ties to the Rockies. As a three-time Gold Glove award winner at third base, Chapman’s presence was especially beneficial.

“That was a really good experience,” Baty said. “He is one of the very best third basemen in the game. Just to be able to pick his brain about how he goes about his business over there, and how he fields, his cues and what helps him out was really good.”

Last week, Baty arrived early for spring training, in hopes of continuing the work he put in with Tulowitzki. A critical season awaits. Baty lingers as an intriguing option at third base for the Mets. He has showcased tantalizing offensive skills in the minors. And late last year, while the Mets dealt with injuries to their infield, Baty received a call-up to the majors. For now, Eduardo Escobar projects to be the club’s starting third baseman, and a club option could keep him under control through 2024. The Mets may not immediately give Baty another major-league look. But it may not be long until they do.

Throughout the Carlos Correa saga, club officials such as third base coach Joey Cora and bench coach Eric Chavez consistently checked in with Baty. There was a window in which it appeared that Correa would be locked in at third base for the long term. During that time, Baty remembers Chavez delivering a message: “You’re still gonna be a player for the Mets and we want you to be part of this future whether it be somewhere else on the field or whatever.”

Negotiations with Correa ultimately failed. There won’t be a long-term contract attached to the position after all, which offered some measure of clarity. Last week, Mets general manager Billy Eppler told The Athletic that although Baty can play other positions like left field, the club wants him to focus on third base.

All the while, Baty kept working.

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Being proactive in his own development relay signs of maturity — he appears to embrace the work required to get to where he wants to be, where some Mets officials believe he can be.

“That’s my biggest goal, for them to trust me over there to play every single day at third base for the New York Mets,” Baty said. “I’m just going to do that by just staying within myself and working every day on the little things. If they want me to play over there every single day, then I’m gonna do it. If they want me to play somewhere else, then I’m going to do it, too.

“But I’ve just got to get better and just got to get more solid, especially with little things. And I feel like I’m doing that right now.”

(Photo of Brett Baty: Gregory Fisher / USA Today)