DENVER -- For much of the time he was building a notable Major League career, mostly with the Rockies, Troy Tulowitzki was preparing for the next act.

Tulowitzki retired last week as a member of the New York Yankees and accepted an unpaid assistant coaching job at the University of Texas.

But almost the whole time he was playing shortstop for the Rockies (2006-15) and accumulating the third-highest Baseball-Reference WAR at 39.4, he was pushing teammates to improve. Players such as current Rockies Nolan Arenado and Trevor Story, Cardinals outfielder Dexter Fowler and retired first baseman Jason Giambi all accepted invitations to work out with Tulowitzki at his Las Vegas home.

That’s the spirit Tulowitzki, who conducted a conference call with media on Monday, wants to bring while working with the Longhorns under head coach David Pierce.

With Tulowitzki at shortstop, the Rockies went to the postseason twice -- including the World Series in 2007 -- and Tulowitzki appeared in five All-Star Games and won two Gold Gloves and two Silver Sluggers. But he is also proud of the influence he has had, and believes he can have, on other players.

“I felt early on in my career I was coaching,” said Tulowitzki, who added he is focused on his current job, although Major League field and front-office work are conceivable in the future. “I always took pride in it. Even with the Rockies, in the offseason I would have numerous players come out to my house and work out with me. That was all part of trying to make them better as players, but bottom line, I was trying to coach them to help us be a better team.

“Oh, man, I like teaching this game. I like getting guys to realize their full potential and trying to maximize their potential. I knew from a young age that it was in me.”

The young Longhorns can expect a tough coach who will bring out their best.

“In the beginning, middle, to the end, he was always tough, until maybe after he got traded," Arenado said. "He was like, ‘Nolan’s starting to figure this out a little bit,' but he still was getting on me about things.

“He was intense. He’d be mean at times, but I really appreciate everything he did. He’s like an older brother. That’s what he was.”

Most objective analysts would say Tulowitzki had a shot at a Hall of Fame career before injuries reduced his participation. A calf strain this year, after bone spurs last year during his final season with the Blue Jays, ultimately led to retirement.

But Tulowitzki rejects the notion -- cliched, unless it holds true -- that a standout player can’t coach players who aren’t as gifted. Tulowitzki insists his success wasn’t a gift.

“I don’t consider myself a natural,” Tulowitzki said. “I didn’t get drafted out of high school. I had to basically beg Long Beach State to take me. While I was there, I feel like I turned myself into a good player. But, honestly, everything I did was through hard work, and I taught myself how to get better.

“And I explained that with Coach Pierce. I feel like a lot of things I can do on a baseball field aren’t natural. It’s things I taught myself through hard work. I want to share those experiences with the kids and get them to realize that, at this point in time, if you were to line up our careers, they probably are more talented than I was.”

The Rockies sent Tulowitzki to the Blue Jays in July 2015 in a deal that left Tulowitzki rankled, with stories of the discord spilling into the next year. But beyond saying he “wished communication would have been a little bit better, but it’s a business,” Tulowitzki devoted Monday’s press conference to fond Colorado memories.

“My legacy as a Rockie is someone who came in as a young kid with some energy and helped us win ballgames,” he said. “That was, for me, helping my teammates and working on my game, preparing myself to help us win. I feel like I gave it the best effort I had throughout my career. I’m proud to say that.”