His achievements scarcely need elucidation. His record of accomplishment is supreme in his sport. Only Rafael Nadal has a pronounced winning record against him over a meaningful length of time, but even Nadal does not claim to have mastered him. Put it this way: Federer is the greatest player, Nadal the greatest player of Federer.

Compare and contrast players from different sports and eras at your eternal peril. But tennis is a big sport, and broader now than ever, ranking next to golf and only behind soccer for universal appeal. Moreover, it is played in an exacting knock-out format. Together, this means a vast field of would-be usurpers is forever on Federer's case, dwelling on a single slip. All this, he takes in his leisurely stride.

Periodically, some mark down Federer for front-running. Firstly, he is rarely behind. His fifth set record is modest, his least impressive statistical category, but only 10 percent of his best-of-five matches go to five sets. Secondly, fighting spirit does not have to be patent to be real. Ask Kei Nishikori if Federer has fighting spirit. If fighting spirit is a weakness, it's like Don Bradman's supposed vulnerability to short bowling: negligible, beside the point, and in any case, humanising.

Federer's style is also a by-word. Federer on court is both an athletic and aesthetic delight. His forehand ‎will be put in a museum when he is done, and his backhander's least virtue is that it is single-handed (and, he was pleased to say after Nishikori had tried him on it, still worth a few points). Opponents sometimes say they have to stop themselves from watching him, like Odysseus putting wax in his ears, tying himself a mast so as not to lured by sirens to ruin. After losing to Federer in the second round here, perennial top-tenner Tomas Berdych said he would rather have been in the stand watching than out there playing. Crowds have the privilege of never having to take their eyes off him.

Sport is about both contest and spectacle, so is at its peak when they coincide. In Federer's performances, they invariably do. As RC Robertson-Glasgow once wrote of Bradman: "Poetry and murder lived in him together." Extrapolating, some pedants even marked down Bradman for his mechanical style, as they surely never will Federer. Rather, in a famous essay 10 years ago, David Foster Wallace wrote that watching Federer was almost a religious experience.

Graciousness might be Federer's most admirable attainment. Without it, the "sport" in sportsman is redundant. Sportspeople are more intimately watched and seen now than ever, and Federer more closely than most, but after 20 years in that public eye, the worst that he has shown was a minor tiff with compatriot Stan Wawrinka a couple of years ago.

For a long time, only Tiger Woods could compare for apparent virtue, and his unmasking six years ago showed all that might have befallen Federer, but has not. If Federer were to be unmasked as a fraud now, it would be the death of sport. On court and off, he – and Nadal, to be fair – have elevated their sport's standards, for which only the brats will not thank him, since it has left them more exposed than ever.

Deconstructed this way, Federer might be a robot. He is anything but. He gives to fans and media inexhaustibly, but with humour, in many languages. Sometimes, you see glimpses of the competitive fire that animates all great sportspeople, him foremost, and destroys some. Though every force pulls him skyward, his feet stay resolutely on the ground, admittedly in luxuriously comfortable shoes. He says he's embarrassed by the Foster Wallace essay, but understands sport's love of superlatives. His Superman cape is lightly worn.

More space than is available here would be needed to unlock Federer's secret, and yet its essence might have been there for all to hear after the Nishikori match, when he revealed that while on tour, the TV in his room was tuned always to the tennis and that he had seen most of the two great upsets in this tournament, Denis Istomin of Novak Djokovic and Mischa Zverev of Andy Murray. Federer is a rare example of a sportsperson whose sport has loved him back with equal fervour. It is not that he is too good to be true, but that he is so good he can be true.

A fourth but lesser measure of greatness is durability, a subset of achievement. For 15 years, Federer was indestructible. This especially set him apart from Nadal. Federer always affected nonchalance about practice and preparation. It was probably not entirely true, but even he was not above a little innocent myth-making. Suddenly last year, he became brittle. It was the end, of course: what other conclusion could be drawn about a 35-year-old whose halcyon days had long been receding in the rear vision mirror anyway?

But at the Australian Open, his game has come back to him more rapidly even than he dared to hope. And look: the men's draw is like the old video game Minesweeper, opened up with a single touch. It made Monday not so much the start of week two as the first day of the rest of the tournament. If Federer goes on to win it, he would become the oldest man other than Ken Rosewall to win a major in the Open era. Like Jack Nicklaus' Masters victory at the age of 45, it would set the final seal on his greatness. He wells knows it: upon beating Nishikori, he leapt like a child and said it was for him a career milestone.

Also as in Minesweeper, Federer could disappear in an instant, as soon as Tuesday night's clash with the surprising Zverev. Unlike Nicklaus, he must make the cut every time he plays if he wants to go on. That is the nature of tournament tennis; witness Djokovic and Murray. If so, Federer will have lost nothing that he could not afford to lose, without losing his unimpeachable status among sportsfolk.