Two comeback kids met in Miami and played a very fine match of tennis this week. One was Juan Martín del Potro, the lanky, lugubrious Argentinian who has suffered two career-threatening wrist injuries. Since returning last year, after a two‑year hiatus, he narrowly lost to Andy Murray in the Olympic final and led Argentina to their first Davis Cup win.

His is an uplifting story of triumph over adversity, stalwart determination in the face of debilitating physical and psychological setbacks. He played beautifully this week, with his elegant backhand slice and his thunderous slap of a forehand. But unfortunately for him he was up against Roger Federer, who, at 35 and following his own long lay-off with a knee injury and then a back injury, is playing perhaps the best tennis of his life.

Given that Federer is arguably the best player in history, that would make his tennis right now the best there has ever been. That’s an extremely large claim that is probably easier to shoot down than support. But there is no doubt that Federer, that most heavenly of players, is enjoying a second coming at an age when most top players are either retired or long past their peak.

He went through Delpo like Delhi tap water through a tourist. Some of the shots he played were, even by his own exalted standard, jaw-dropping. And there is certainly no question that his single-handed backhand, so ruthlessly targeted by Rafael Nadal and Novak Djokovic, is now a weapon of match‑winning destruction. Federer’s supreme 2017 continues to defy all expectations as he booked a place in the Miami Open final and with it the 37th episode of his rivalry with Nadal.

Has sport, let alone tennis, witnessed such an astonishing comeback? First we must acknowledge that Federer wasn’t exactly a spent force. During his injury-riven doldrums last year his ranking was 17, his lowest since 2001 but still among the world’s elite. That said, at the start of this year he hadn’t won a grand slam title for five years and the only way forward seemed down or retirement.

He had retained his competitive instinct during that spell, three times finishing runner-up in grand slams to the seemingly unbeatable Djokovic – but the plain fact was he hadn’t defeated the Serb or his great rival Nadal in a grand slam final since 2007.

Even though he had accumulated an astounding 17 grand slam titles, it was almost painful to see him try so hard, want it so much, and get further away from his goal of an 18th. Moreover, the slow decline started to cast a shadow backwards over his early glorious years. Between 2004 and 2007 he was by so far the best player in the world that he resembled a god among men – except on clay, where he had feet of clay.

Yet this superiority was now held against him. He was only so successful, said his critics, because the rest of the field wasn’t up to the job. Once Nadal found out his backhand weakness and Djokovic started to outlast him, Federer, for all his peerless grace, began to look all too mortal. And the man who never seemed to break a sweat, much less strain a tendon, started to get injured.

In January at the Australian Open in Melbourne, the stage was set for the world’s new No1, Andy Murray, to confirm his position with his fourth grand slam title, especially once a psychologically troubled Djokovic fell by the wayside. That didn’t happen.

Instead Federer and his nemesis Nadal fought an epic five-set final, with the Swiss emerging triumphant. Since then he’s scarcely lost a set. His game is not just revived but in many respects, not least with his backhand, improved.

When he was a promising teenager, the imperturbable Federer was known for his fierce temper – not with other players, but himself. He couldn’t forgive himself for his mistakes. As he reasoned at the time: “One should just be able to play a perfect game.”

He really started to beat everyone else only when he stopped beating himself up. The paradox was the less he demanded perfection, the closer he got to it. And this may be a clue to this splendid Indian summer of his sparkling career.

He didn’t expect to win the Australian Open, or to be back in the top five by this time of the year. It’s not that he stopped trying – it required enormous effort to regain fitness and change technique – more that he lightened the load of expectation and allowed his phenomenal talent to enjoy one last season in the sun.

Roger Federer with the trophy after defeating his nemesis Rafael Nadal to win the Australian Open, his 18th grand slam title, in January. Photograph: Clive Brunskill/Getty Images

It can’t last. Nothing can. That’s the ephemeral beauty of sporting genius. It’s very hard to believe that Federer could maintain his current form into his 37th year. There is a biological point at which even the finest athletes must succumb to irreversible physical decline. In the same way, it beggars belief that the 35-year-old Manchester United striker Zlatan Ibrahimovic could squeeze another season like the current one out of his monumental frame.

Ibrahimovic is a colourfully contrasting character to Federer. The Swede revels in an arrogance that the Swiss works overtime to suppress. Where Federer could win prizes for humility, Ibrahimovic likes to speak of himself in grand historical terms. But in reality these are superficial differences, because at their core both men possess a cast-iron self-belief, and are willing to do what is needed to retain their competitive edge, long after they are under any obligation to prove themselves.

Andre Agassi, who himself came back from another kind of crisis – the usual: worrying about marrying Brooke Shields and dabbling with crystal meth – recently said that he and his wife, fellow legend Steffi Graf, watched Federer and Nadal in that Melbourne classic. “Why do they do it?” Graf asked her husband. “Can you believe what these guys are willing to put themselves through?”

It’s certainly not for money. Federer could live long and well on his vast wealth and global celebrity. But he’s still striving to be better, to win one more, to reach the top. As a result we can see now that there was a misconception about the arrival of Djokovic and Nadal in Federer’s pomp. They didn’t bring him down to size. He lifted them up to where he was. They would never have reached those heights without his leading the way. And now, like the indomitable champion he is, he’s stepped out in front once again.