Nobody could fail to appreciate Sampras's talent, or the work he puts in to support it. Doing his gym exercises, watching his diet, never touching a drink during a tournament. A more professional pro you couldn't wish to find. But the problems and setbacks that can bring out more of the character in a player - these things had not figured in Sampras's world. Until now, that is, when they have hit home with a vengeance.
With the death of his coach, Tim Gullikson seven weeks ago, Sampras has suffered in a way that goes far beyond the experience of most players. Indeed, all Sampras's performances since halfway through the 1995 Australian Open, when Gullikson collapsed and was diagnosed as having brain cancer, have to be seen against a background of emotional distress that puts the normal run of sporting ups and downs into their proper context.
Sampras and Gullikson, a former world No 18 but best remembered for his doubles partnership with his twin brother Tom, teamed up at the beginning of 1992. They were friends first, coach and player second, and Gullikson's light touch and instinctive understanding were just right for the mellow Sampras as he set about honing his game to a state of near-perfection.
Guided by Gullikson, Sampras rose to be the world No 1 and added four Grand Slam titles - the US Open in 1993, Wimbledon in 1993 and 1994, and the Australian Open in 1994 - to the US Open he had won as a 19-year-old in 1990.
When Gullikson fell ill, the man who took over his role was Paul Annacone, another former doubles specialist and a man whose sensitivity to the circumstances of his arrival on the Sampras scene was one of the main reasons why the transition was almost seamless. Gullikson continued to be consulted, and the idea, to begin with at any rate, was that Annacone would be strictly a stop-gap.
Gullikson made some progress towards recovery, and was well enough to work alongside Sampras in an unofficial capacity during the United States' Davis Cup tie with Sweden towards the end of last year. But his condition deteriorated and he died on 3 May at his home in Wheaton, a suburb of Chicago. He was 44.
"For Pete and for everybody who was close to Tim there's always going to be a void there now," Annacone said during the French Open earlier this month. "But I think it keeps things in perspective and makes you realise, yes, this is your job, this is what you do, it's the limelight, it's the spotlight, but there are some things that are more important than that.
"Towards the end the most important thing was for Tim to have a decent quality of life and to have as little pain as possible. Now all his friends and family are having to deal with that, and it's very, very tragic. There's no other way to describe it."
Gullikson's death threw a shadow over Sampras's clay-court season and his preparations for the French Open. "After Tim's funeral, we went down to Pete's house in Tampa and there was nothing in the gas tank," Annacone said. "It took a few days to get going again. But that was fine. I would have been worried about him as a person if all of a sudden he was ready to go out and train four hours a day. So we took a few days to let it all sink in and get some peace, and then we started back to work again."
In the end, Sampras missed four weeks on the Tour and played only one clay-court event before the French, the World Team Cup in Dusseldorf where, not surprisingly, he struggled. Yet in reaching the semi-finals of the French - his best performance in seven visits - Sampras claimed to have benefited from not playing much on clay beforehand. He was fresher, he said. The French still took a huge amount out of him emotionally and physically, and instead of playing the Stella Artois at Queen's he went back to America to rest before Wimbledon.
Sampras has spoken little about Gullikson in public since his death. "I think the best one can do is respect Pete's feelings and leave him in peace to work through the situation," Annacone said. And certainly when Sampras turned up at Wimbledon last week after 10 days that had comprised a mixture of golf and grass-court practice, he looked and sounded relaxed. "I'm mentally fresh," he said.
Given the build-up he has had, though, it is hard to predict whether Sampras will be able to win his fourth Wimbledon in a row, which would take him to within one of Bjorn Borg's modern-era record of five successive titles. But his friend and fellow-American Todd Martin is in no doubt. "He's been the best player this year, I think," he said during the Stella two weeks ago. "Week in, week out, he's the guy people respect the most. Anybody who doesn't think Pete's the favourite for Wimbledon is really going out on a limb."
Martin knows Sampras better than most players do and can speak for the depth of character that has only become obvious to the outside world since the time of Gullikson's illness. "He's very humble," Martin said. "That's the first thing people get a glimpse of when they're with him in a personal situation. For any 24-year-old who's accomplished as much as he has, that's about as good a quality as you could have. He's very quiet and reserved, but in many moments you see the person behind all that. He's very human for a superstar."
A man who has twice cried in public certainly doesn't deserve to be regarded as the somewhat remote figure that Sampras seems to be in the eyes of many tennis followers, especially those at Wimbledon. He will surely win their admiration over the next fortnight. He will surely win their sympathy as well. And, who knows? He may even win their love.