There are plenty of perks, like free changeover towels (which cost 25 pounds for the general public), loads of Slazenger yellow balls and practice time at the picturesque Aorangi Park.
But when your life flashes before your eyes, you gain a deeper appreciation for the simpler pleasures of chasing a ball. Fish said he thought he was going to die two months ago when he awoke with his heart beating three times too fast. Baker was out of tennis for six years with a series of gruesome injuries.
Tuesday, they both played their way into Wimbledon's second round.
Fish, seeded No. 10, handled Spain's Ruben Ramirez Hidalgo 7-6 (3), 7-5, 7-6 (1). Baker, playing in his first tournament here, looked like a 10-year veteran and promptly dispatched Portugal's Rui Machado 7-6 (2), 6-4, 6-0.
Fish completed his match in 2 hours, 47 minutes and did not appear to be in any distress. Still, his unusual decision to cancel his postmatch news conference will raise questions about the state of his health.
"Mardy is feeling unwell," said ATP Tour spokesman Nicola Arzani.
Is it something serious?
"It's fine," Arzani said. "He will come back for an interview tomorrow."
Fish told ESPN's Tom Rinaldi via a text that he was not feeling well and needed to lie down but that the issue was "not heart-related."
Baker, meanwhile, basked in the reflected glow of his growing accomplishments. He did an extended news conference and a number of television interviews.
"I'd be lying if I sat here and said that I expected all this to happen right now when I was going through all those surgeries," Baker said. "But I never gave up the hope that I would be able to come back. I was always confident in my abilities that if I was ever able to stay healthy that I would have success.
"I don't think I ever imagined that at this point this year that I was going to be playing both at the French and Wimbledon and winning rounds and winning challengers and getting to the finals of an ATP. So it's been a pleasant surprise."
It's been six weeks since Fish lost to Michael Russell in Houston, six weeks since he contemplated a harrowing journey to the other side. Once doctors diagnosed heart arrhythmia, they solved the problem with a cardiac catheter ablation. After 10 days off, Fish was jogging again, and when the second week of the French Open began, he was hitting balls.
Fish had hoped to play a few matches at Queen's Club, but he decided he needed more practice before arriving at Wimbledon. He was comforted by the fact that a grass surface generally leads to shorter points than clay. The only real concern going in was the length of his match with Ramirez Hidalgo, at age 34 the oldest player in the men's draw.
The sets were all close, but Fish -- still the world's No. 12-ranked player -- was better in the crucial moments. In the end, Fish was just a little bigger, serving 24 aces, hitting 61 winners (versus 34 unforced errors) and cashing one more break point than the Spaniard.
On the day the U.S. Olympic team was announced, Fish's name was notably absent. As the No. 2-ranked American man, it was his right to play singles. Fish declined, he said earlier, less for health reasons than mental health concerns. Eight years later, the scars of losing the gold-medal match to Chile's Nicolas Massu in Athens still linger.
Although Fish's swift return is remarkable, Baker's saga might be one of the best comeback stories in all of sport in recent years. The same year he graduated first in his 2003 class at Hillwood School in Nashville, Tenn., he reached the junior final at Roland Garros, beating Marcos Baghdatis and Jo-Wilfried Tsonga along the way.
After Baker suffered through five serious surgeries -- the most complex was a Tommy John-style reconstruction of his right elbow -- his battered body finally allowed him to return to the sport he loved. He was a college assistant coach at the time playing in a men's league with his father.
Baker earned a wild card into Roland Garros and qualified his way into the ATP World Tour event in Nice, France. He went all the way to the final. Then he won his first-round match at the French Open. He won three matches to qualify here and is now a career 4-for-4 at the All England Club -- all in the past week.
Forgive him if he's having an out-of-body experience.
"I haven't been back home," Baker said. "I'm sure it will be a lot of fun when I get to go back home and share it with some friends that I haven't seen. But I think, just all the press that I've been getting at Roland Garros there was -- I feel like I was doing stuff every day, and then it calmed down a little bit.
"Now here I feel like it's been kind of like a whirlwind ride. I'm enjoying it right now, looking forward to continuing to play well, and hopefully this summer I will have a good summer and get into the U.S. Open."