The Barclays ATP World Tour finals in the O2 Arena in Greenwich will open with a spectacular match-up between the 22-year-old Scot and Juan Del Potro, who turned 21 just after his victory in the US Open.

The tour finals have been described at tennis’s fifth major. They are not. Murray knows to his cost that there are only four majors to a season. He has failed in all of his attempts at a Grand Slam event. However, the events this week will be significant far beyond casually
adding huge sums to already rich players’ bank accounts. Murray finds himself in a 
situation and in a group that is almost exquisitely fashioned to replicate the highs and lows of a remarkable career and a turbulent year.

First, it must be observed that the Scot arrives in London on the back of a season that only needed a victory in a major to have been highly rewarding and deeply satisfying. Only. It is a four-letter word that will outrage Murray. His dedication to win a major has slipped into a barely concealed desperation. The absence of a Grand Slam triumph on his cv forms an insidious fog that obscures every other achievement.

Stripped of the Grand Slam events, this has been an outstanding season for Murray. He finally broke the Roger Federer-Rafael Nadal four-year stronghold at the top of the rankings by becoming world No 2, though he has slipped back to four. His early season form saw him become the first player to record 50 tour victories, eventually
reaching 64 wins, a record only bettered by Novak Djokovic. He won six tour titles despite being sidelined for six weeks by a wrist injury.

All this is impressive testimony to a superb player but it lacks the definitive statement of greatness that a series of Grand Slam victories articulates. Most tennis commentators, and all the great players, say Murray will win a major. The tennis obsessive from Dunblane knows these testimonials ultimately mean nothing. He simply has to grind one out before he can be satisfied in any way with his career. Murray is a man who will describe being No 1 in the rankings as “nice”. Already a rich man, he is not playing simply for money.

A Grand Slam is not just his target, it is his very reason for playing. The tourn-ament this week throws up almost a definitive guide to how he has failed in the majors in the shape of the three players in his group.

Federer, Del Potro and Fernando Verdasco offer lessons that have inflicted pain on the Scot. The Swiss all-time great presents the most obvious
reason as to why Murray has not won a Grand Slam. With Nadal, Federer has formed a firm that dominates Grand Slams. Federer, too, denied Murray in 2008 when the Scot reached his first, and so far only, Grand Slam final at the US Open. But Murray’s 6-3 record against the Wimbledon champion suggests he should not recoil in horror when matched up with him. And he does not. Murray fancies his chances against Federer. The greatest accum-ulator of Grand Slam titles knows this. And it grates.

The Federer problem for Murray is this: he must find a way to play him again in a Grand Slam final or semi-final. And this brings up the most pressing problems. The Del Potro problem is that Murray is no longer the sole pretender to the joint crown of 
Rafaroger. The young Argentine showed at Flushing Meadow that he will be a contender for every Grand Slam, save perhaps Wimbledon. There are others, too, who are progressing. Murray is no longer the lone, young gun.

The Verdasco problem is the most intriguing. The Spaniard defeated Murray at the Australian Open in an astonishing match. This victory pointed to two Murray vulnerabilities. The first is that Murray has been dogged by bad luck in major tournaments. He would not admit it but he was suffering from flu in Australia. The wrist injury in the US Open was similarly downplayed but it ultimately led to a break from playing for six weeks.

The second susceptibility is much more frustrating for Murray and his supporters. He is a genuinely great player who finds a way to lose against those of inferior talent. The Grand Slams of 2009 illustrate this point 
graphically. Murray lost in the fourth round in Melbourne to Verdasco, in the semi-finals at Wimbledon to Andy Roddick, in the second week of the French Open to Fernando Gonzalez and to Marin Cilic at Flushing Meadow. Some will jump to his defence by saying that Murray was injured against Cilic, sick against Verdasco, playing Gonzalez on the Chilean’s best surface and encountering a Roddick who was in the form of his life. But he lost them all. Murray will simply look at the matches as failures and try to address the issues they raise.

He has already changed his schedule so his immune system is not as vulnerable to long-distance travel before the Australian Open. He has also carefully considered just how much training he has to complete before a Grand Slam after there were indications that he had done too much before arriving in New York for the US Open.

He will also have considered how he lost to Roddick’s simple but hugely effective game-plan at Wimbledon. Murray, a devout student of tennis, must improve his passing shots and raise his willingness to come to the net.

His group matches this week personify the challenges the young Scot must confront. There is every reason to suppose he will take them on robustly. Murray is a player of sublime beauty while in full flow, seeming to pluck shots out of the air. He is a careful, cunning strategist, too. But his greatest, most enduring quality is his ability to come back from setbacks. He takes his knocks and returns stronger.

Justifiably, there is a clamour for him to win a Grand Slam. But its ever-increasing volubility should not drown out the words of those observers who insist Murray is improving. The Scot will face an unforgiving examination
against the best in the world this week. He has lessons to learn. But it is not just a Caledonian chauvinism that insists that Murray can be the inspiring teacher and not just a willing pupil in a teeming classroom on the Thames.