Greg Maddux always deflected praise and downplayed his pitching brilliance. So, the former Braves ace was asked this week how he remained humble and unassuming through a career that included 355 wins and four Cy Young Awards.

“You think about the things that are important to you, and I guess it’s never really been high on the list, worrying about what other people think,” Maddux said, then recalled something his Cubs pitching coach said when Maddux was a rookie.

“Billy Connors asked me the question one time, ‘Do you ever want to find out how good you can be?’ And I think I just always tried to find the answer to that question. I think it’s just going out there and trying to find out how good you can be.”

Maddux and the rest of the world found out. He became arguably the greatest pitcher of his generation. He also had a considerable influence on another eventual 300-game winner, Tom Glavine.

The two friends were Braves teammates for a decade through 2002, and Wednesday they were elected to the National Baseball Hall of Fame along with former White Sox slugger Frank Thomas, who is from Columbus. All three were on the ballot for the first time.

Not only will the two Braves aces go in together, they’ll be inducted alongside their Braves manager Bobby Cox, who was voted in by the Veterans Committee last month along with fellow retired managers Joe Torre and Tony La Russa.

Maddux was named on 97.2 percent of the writers’ ballots and Glavine on 91.9 percent, far above the 75-percent threshold for election. Glavine wasn’t certain he would get in on the first ballot and said missing out on going in with Maddux and Cox would’ve been the worst part if he hadn’t. They’ll be inducted July 27 in Cooperstown, N.Y.

“It’s such a rare opportunity to go into the Hall of Fame,” said Glavine, who won 305 games and two Cy Young Awards and had five 20-win seasons. “It’s an even more rare opportunity to go in with a teammate and a manager at the same time, particularly two guys in Greg and Bobby who were so influential in my career.

“Bobby is the single greatest influence in my baseball career. Greg had a huge impact on me, both from a standpoint of what he provided for our team, and in doing so made me want to work harder and be better to keep up, but also learning from him about the things that he did to do what he did.

“I think Greg’s greatest influence on me was the way he would go have a game plan and execute that game plan or change that game plan based not only on what he wanted to do, but what hitters were telling him, how they were reacting.”

Glavine and Maddux are the first pair of living 300-game winners elected to the Hall in the same year. They could be joined as soon as next year by John Smoltz, the other of their vaunted “Big Three” starters for much of the time that Glavine and Maddux were in Atlanta. Smoltz retired a year after they did and becomes eligible next winter, as do Cy Young winners Pedro Martinez and Randy Johnson.

“There’s no question that the guys who I ultimately was surrounded with made me a better player,” Glavine said. “Being around guys like John and Greg and so many other guys that were here over the years — people always talk about that competition we had on the pitching staff, and we had it. But it was always in a fun way, always in respectful way, always in a way that we honestly drove each other to be better. Whether it was pitching — ultimately the No. 1 thing — or hitting, fielding, bunting, you name it. We all drove each other to get better in every facet of the game.

“When you’re around Greg and John and (Steve) Avery and Pete Smith and all these other guys who were here over the years, when your rotations are deep like that, you don’t want to be the weak link.”

Glavine’s greatest baseball moment was the 1995 World Series, when he was series MVP after his performance-for-the-ages in Game 6 — eight innings with one hit allowed in a 1-0 win that clinched the only major pro-sports championship Atlanta’s had.

“That’s what you play for,” he said. “There’s certainly some other individual big games, and the Cy Young Awards. But so many of those things are individualistic. Whereas the World Series, that’s the ultimate of what you’re trying to accomplish as a team.

“There was no better feeling than that night when we won the World Series, to be able to run out on the field with 25 or 30 guys you’ve gone to war with all summer long, and jump around like a bunch of morons out on the baseball field. It doesn’t get any better than that. That’s what you want.”