This question, along with Murray's merits, was considered in the wake of his second-round defeat at the Newport, Rhode Island tournament in the United States last week by three former British Davis Cup captains: David Lloyd, Roger Taylor and Tony Pickard. For Lloyd and Taylor, Murray's fitness and choice of tactics were a matter of concern.
"If I was in charge, I would work very quickly to ascertain if the fitness problem is physical or mental," Lloyd says. "If it's physical, you can do some- thing about it. Mental, that's something different altogether.
"For an 18-year-old kid to be getting tired like that on grass is a big worry. Two weeks in a row, at Queen's and Wimbledon, he got tired. The worst thing in tennis is to have a weakness, everybody else homes in on it pretty quick. It's no good playing a great five-set match and not winning it. Andrew Castle played a great five-setter against Mats Wilander once, and though he didn't win it he lived on it for about five years. Andy hasn't got that long. The next two years will decide whether or not he is going to be a world-class player."
For Taylor, Murray's abandonment of the third set against David Nalbandian was a mistake. "That match was there for the taking. I would prefer to see him going flat out all the time." Pickard agrees: "Two sets to love up, dumping the next set makes no sense whatsoever to me."
Taylor also prefers Murray to keep the profanity and temper buttoned. "It's OK if it doesn't affect you, but it is affecting him because these matches are slipping away. But it seems his personality will always be like that. He is always going to be fist-pumping when he is up and showing the pain when he is down. That actually makes him interesting, as long as it doesn't cost him matches."
Lloyd agrees: "There's nothing wrong with swearing if it is in your attitude, but not if you are doing it from frustration or showmanship. I like to see that Jimmy Connors-type aggression, but make sure it doesn't make you play worse or put your opponent off."
Pickard spotted the temper in Murray's early junior days. "Obviously, nobody has been able to bounce it out of him; now it will be a hell of a problem to get rid of it. To be doing that shows that when the going gets tough, somebody can't handle it. He isn't John McEnroe. He used it to break everybody else's concentration. Murray is only breaking his own concentration."
Lloyd is convinced the temper is a result of the weight of expectation. "TV went over the top at Wimbledon, praising him every five minutes. Connors, somebody who died a million times on court, was saying Murray was the greatest thing since sliced bread. He should not have made a comment like that about a kid who didn't try in the fifth set against Nalbandian.
"Murray is an 18-year-old who played pretty good on grass, that's as far as you can go. You can't say he is going to win a Grand Slam. But because we are so desperate, he already has a noose around his neck. We have to be careful with him. It is hard to live with that expectation and hype.
"He has the ability to get into the world's top 50, and therefore to become a top 10 player. He is as good a prospect as we have had for years. But he needs a strong person with him. He needs someone like Ion Tiriac. When Ilie Nastase was growing up, Tiriac used to grab him, physically lift him in the air, pack him off to bed. Bjorn Borg had Lennart Bergelin. He was brutal too.
"Mark Petchey is a very good guy and a pretty good coach. It is not Petch's fault, but you need a dictator type, someone exceptionally strong as a coach, like Bob Brett or Brad Gilbert."
Taylor feels that, on the strength of reports of tantrums in Newport, "Murray appears to be getting away with a bit. Petchey has to explain it is going to be detrimental to do that. His wins at Wimbledon showed he can perform well under pressure. Now it's all about learning. It isn't the juniors any more, is it?"
Pickard is convinced that, after what he calls "the glamour trip to Newport" the urgent need is for Murray to get back to his own level. "He is off now to play some Challengers in the US, and if he can win a couple that would set the fire, it would mean he has taken away an awful lot from Wimbledon. But he has never won a match at Challenger level yet, and that worries the hell out of me. It is a very important month coming up for him."
As someone of firm opinion himself, Lloyd is a believer in Murray's chances. "This kid has caught the imagination of youngsters, definitely more than Tim Henman, because he has shown more emotion. He is not as clean-cut, not so prim and proper, as Tim, but if you are going to get people to follow you they want to see an earring, something they can relate to. If he can become as good as we hope, he will get the kids to follow him and start playing tennis themselves, and that would be great."
As long as he can keep away from flying rackets and the verbal volleys.