Since Glavine left Atlanta to join the Mets after the 2002 season, he has been wearing rival colors. But those, including Cox, who knew him during his 16-season stay in Atlanta, still view him as a member of the Braves family.
"He did so much for Atlanta," Braves center fielder Andruw Jones said. "There's no doubt that people in Atlanta love Tom Glavine."
Glavine's march toward the immortal 300-win milestone began with the 242 victories he recorded for the Braves. That total doesn't even include the greatest win in Atlanta professional sports history.
It was on the night of Oct. 25, 1995, that Glavine had people dancing in the streets of Atlanta. He'd just limited the vaunted Indians offense to one hit over eight scoreless innings to clinch a World Series title and give his city what remains the only world championship it has ever realized in a major professional sport.
"From my personal standpoint, it's probably the best game I've ever pitched," Glavine said. "When you throw in all the circumstances and what it means, then I think it's easily the best game I've ever pitched."
Cox obviously has great memories of the sheer dominance Glavine displayed on that chilly October night. But his parental-like love for the 41-year-old southpaw dates back two decades, back to a time when he was the general manager of an organization that knew it had something special in this young kid from Billerica, Mass.
When Cox promoted a 21-year-old Glavine to Atlanta during the 1987 season, he saw talent. While watching the young southpaw endure a 17-loss 1988 season with a weak cast around him, the veteran manager began to see a mental toughness that still existed when success soon followed.
After losing more than 10 games in two of his first three full seasons, Glavine came back in 1991 to win the first of his two National League Cy Young Awards -- both with the Braves.
"He's as tough as they come," said Cox, who saw Glavine capture his second Cy Young Award in 1997. "He never gives in. He's like one of those guys in Extreme Fighting, that if you get them in a choke hold, they're not going to tap out."
Glavine gained a partner in crime when a 21-year-old John Smoltz joined the Braves rotation in 1988. The communion of these highly competitive pitchers created a strong friendship that still exists today. In addition, it provided them an opportunity to feed off each other, both mentally and physically.
Of course, this competitive drive was only enhanced in 1993, when they were pushing themselves even harder in their attempt to match the contributions provided by their new Braves teammate, a guy named Greg Maddux.
"Any time you have a chance to play with those guys, you can't help but learn," Smoltz said. "You can't help but get better. From that, I obviously owe a lot of my success to them.
"If you had a big ego, you were going to get crushed. If you thought you were pitching good, you could be brought down a peg the next night when the other guy pitched. It allowed us to sustain a lot of winning seasons."
Glavine played an integral part in 11 of the 14 consecutive division titles that the Braves won. Ironically, he also helped put an end to that streak last year, when the Mets claimed the National League East crown.
Even as time has passed and his ties to the Mets have strengthened, the Braves have maintained a high level of respect for Glavine. His on-field accomplishments in Atlanta have been well documented, and the city can't help but remember the many charitable endeavors he continues to provide.
"He's brought so much to this town, and not just from a pitching standpoint," Cox said.
What can't exactly be measured is the amount of determination and heart he displayed during his 16 seasons with the Braves. Smoltz believes it was during Glavine's 20-win 1992 season that the southpaw pitched through shoulder pain that would have landed many pitchers on the disabled list for an extended period.
Regardless of injury, Glavine was willing to do whatever it took to take the mound every five days throughout his Braves career. Cox remembers different occasions when his determined pitcher continued to compete with cracked ribs or a bad ankle or even sore knees.
As his career progressed, Glavine's left shoulder provided regular discomfort. Still, in every non-strike-shortened season from 1990-2002, he never made less than 33 starts.
As this trend progressed, Cox gained a sense that 300 wins would definitely one day be within Glavine's reach.
"He never missed starts and his stuff was always high quality," Cox said. "It was always just a matter of whether he wanted to keep pitching. If he did, you knew he was going to get it."
Glavine's current commitment remains with the Mets. But his heart remains in Atlanta, where he has maintained his family residence. He wanted to make this final march toward 300 wins while wearing a Braves uniform.
When he never received an offer from the Braves this past winter, he opted to re-sign with the Mets. Still, he never responded with any public bashing of his former organization. But then again, history has shown that wasn't to be expected.
Throughout his splendid career, Glavine has never worn his emotions on his chest. If he did, they would only further cover a heart that continues to draw great admiration from a Braves organization that saw him grow from a boy into the legendary figure that he is today.
"He is very stoic and very professional," Smoltz said. "The reason he has won 300 [games] is he continues to put himself in that position where it seems like nothing fazes him."
Mark Bowman is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.