The trio made up half of the class that was inducted into the Baseball Hall of Fame Sunday afternoon.
"I can honestly say, I would not be standing here today if it weren't for you guys," Cox said of Maddux and Glavine. "Together, these guys earned six Cy Young Awards wearing Braves uniforms."
Frank Thomas, Tony La Russa and Joe Torre were also honored at the Hall in Cooperstown.
While Maddux didn't go into the Hall of Fame officially as a Brave, it's clear he was largely responsible for Atlanta's success. The winner of four consecutive National League Cy Young Awards from 1992-95 and a record 18 Gold Glove Awards in a 23-year career, Maddux was the first one inducted on stage behind the Clark Sports Center.
"My first day in the big leagues, the starting pitchers were Nolan Ryan and Jamie Moyer. Twenty minutes before the game, I was sitting on the bench, and my first manager Gene Michael thought I was the bat boy," Maddux said during his speech. "The nickname stuck for a few years, but faded over time."
During his career, Maddux compiled a 355-227 record with a 3.16 earned run average and 3,371 strikeouts, playing for the Chicago Cubs, Braves, Los Angeles Dodgers and San Diego Padres.
Maddux and Glavine became the first "primary teammates" elected together by the BBWAA since Whitey Ford and Mickey Mantle in '74. They are the first pair of 300-game winners inducted in the same year since 1973 -- Warren Spahn (363) and Mickey Welch (307).
Glavine, a longtime teammate with Maddux in Atlanta, was a two-time NL Cy Young Award winner (1991 and '98) and 10-time All-Star. He posted a 305-203 record with a 3.54 ERA over 22 seasons with the Braves and New York Mets. The left-hander was a five-time 20-game winner and won four Silver Slugger Awards.
In 1984, Glavine was drafted by the Braves and also by the Los Angeles Kings. Glavine turned down a career in the NHL and instead chose baseball, and the lefty vaulted to Hall of Fame status. Glavine was actually drafted two rounds ahead of future star Brett Hull and five rounds in front of Luc Robitaille.
"I had a difficult choice to make and as a left-handed pitcher I thought that was the thing that would set me apart and make baseball the smartest decision," Glavine said. "Of course, I always wonder what would have happened if I had taken up hockey. In my mind, of course, since I was drafted ahead of two Hall of Famers, Luc Robitaille and Brett Hull, that obviously means I would have been a Hall of Famer in hockey too."
Cox, La Russa and Torre were dominant managerial figures in baseball since the mid-1990s. They all rank in the top five in managerial wins, all with well over 2,000 to their credit.
Torre, who is fifth on that list with 2,326 victories, started his managerial career as a player-manager for the New York Mets and also skippered the Atlanta Braves, St. Louis Cardinals and New York Yankees.
"I might as well cut to the chase. I'm here because of the New York Yankees," Torre said.
Of course, it was with the Yankees that Torre had his most success, as he racked up 1,173 of his wins, while leading them to four World Series titles, six American League pennants, 10 AL East titles and a postseason berth in all 12 of his seasons with the club.
Cox, meanwhile, is fourth on the all-time managerial wins list with 2,504 victories. He guided the Atlanta Braves to the 1995 World Series title. His Braves teams lost four World Series in his time at the helm.
La Russa managed the Chicago White Sox, Oakland Athletics and St. Louis Cardinals for 33 seasons. He compiled 2,728 wins to rank third all-time behind Connie Mack and John McGraw and won three World Series titles, one with the A's in 1989 and twice with the Cardinals in 2006 and 2011.
"I think leadership is more important than ever in baseball," La Russa said. "Because of free agency and guaranteed contracts, guys seeking fame and fortune, they grew up kind of entitled, it's more important than ever, the people who are trying to put (players) into position to win have real leadership skills and really work at it."
Nicknamed the "Big Hurt" for his immense power and the plate, Thomas won consecutive American League MVP Awards with the Chicago White Sox in 1993 and '94, placing in the top three in the voting five times overall. He finished his 19-year career with 2,468 hits, including 521 home runs, 1,704 RBI and 1,494 runs scored.
"In my career I had so many magical moments in all three uniforms," Thomas said. "I will always be thankful, for all of you."