Can sportsmen be called geniuses?

A silly, trivial problem leads me into a much wider (though perhaps insoluble) argument. My problem is merely partisan. As a fan of Roger Federer, I've been grappling with a troubling leap of logic. Federer keeps losing to Novak Djokovic (0-3 in grand slam finals), yet I am no closer to admitting that Djokovic is a genius, nor that Federer might not be a genius.

The consoling argument that Federer is six years older won't quite do. Given the superior quality of his peers, it is increasingly possible that Djokovic at his best is even better than Federer was at his best. The data-led website 538 recently proposed that Djokovic's excellence may touch greater heights than Federer's, even if the longevity (for now) of the Swiss makes him "the greatest of all time".

You will have guessed the logical problem here: my conception of "genius" appears to be distinct from my recognition of achievement. It feels more apt to describe Shane Warne as a genius than Glenn McGrath, though it is hard to say Warne was a "better" bowler. So can I hold on to a concept of genius, distinct and separate from the reality of scores and results? Is this right or even possible?

There is no exact cricketing equivalent of my tennis comparison because batsmen and bowlers cannot play directly against rivals from the same discipline. But here is another version of the Federer-Djokovic debate: how do we weigh Brian Lara (Test average 52.88), who I would describe as touched by genius, against Jacques Kallis (Test average 55.37, plus all those wickets), whose achievements were comparable but whose "genius" was not? Of all the players I've played against or watched live, Lara toyed with opponents more than any other, with a lightness bordering on indifference. He peered down on his opponents from a great height of fully justified loftiness.

From everything I hear about him, Garry Sobers was a genius: his peers were in awe of him, his ingenuity was boundless, everything seemed absurdly easy and natural. Don Bradman was cricket's greatest achiever, but Sobers was cricket's greatest genius.

The theme applies across sports. Lionel Messi is a genius, Ronaldo less so. I do not say Messi is the better player, merely the greater genius. For all his great skill, Ronaldo's achievements owe more to physical attributes (especially pace and power) and less to mystery. (Mystery is another dimension we cannot escape in trying to define genius.)

The same point applies to rugby union's pairing of Barry John and Gareth Edwards. John was the greater genius but not necessarily the better player. John left spectators wondering, "But how did that happen?" Edwards left them counting the ways in which he was superior to everyone else. Unfair as it sounds, transparency is not a trait of genius. In the same way, John McEnroe had more genius than Jimmy Connors, though Connors won one more grand slam title. McEnroe inspired more wonder.

Ty Cobb, a relentless and unpleasant competitor, owns baseball's highest batting average. But everyone considered Babe Ruth the greater genius. Cobb said baseball was "something like a war". Ruth liked to "swing big or miss big - I like to live as big as I can". Exuberant playfulness was bound up with the magic.

Mastery, playfulness, naturalness, style, wonder, mystery - all these concepts are relevant to the idea of genius. But is the term relevant to sport at all? And can we learn from other disciplines, especially literature and music, in making sense of it?

Not everyone approves of the term "genius" taking to the sports field. In a provocative essay for Commentary magazine in 2013, the American writer Joseph Epstein complained about the debasement of the word, now so devalued that even sportsmen and chefs are called geniuses. "[N]one of these men is a genius," Epstein complained, "not even close." He then argued that "geniuses tend to emerge in those areas of life dominant in specific cultures at specific times".

Precisely. Our culture values sport a great deal. Hence it is open to the possibility of producing a genius. While I am certain that "genius" is wildly overused in sport, I am equally sure the term is, very occasionally, appropriate to athletes.

But what do we mean by genius? I think genius is an idea best understood as being subtly distinct from a series of overlapping concepts.

Andrew Robinson's thoughtful book Genius: A Very Short Introduction asks the central question: do talent and genius form a continuum (with genius simply an instance of extreme talent) or are they separated? I tend to the latter view. All geniuses are exceptionally talented but not every exceptional talent is a genius. "Talent is like the marksman who hits a target that others cannot reach," wrote Arthur Schopenhauer; "genius is like the marksman who hits a target others cannot even see."

This element of mystery feels central to any definition of genius. A genius does things that cannot be fully explained by what he has learned or experienced. Genius is not an expression or even a distillation of received wisdom or technical expertise. It is as though the genius is asking the questions afresh, uncontaminated by what everyone else thinks. That is why the emergence of genius is not correlated with formal education: that kind of knowledge would only have to be "un-thought" anyway.

What about the relationship between genius and skill? Genius cannot be expressed without great skill but skill alone cannot add up to genius. With his relentlessly consistent passing, the Spanish footballer Xavi was the pivot in the greatest club side of recent years, Guardiola's Barcelona. Xavi was the definitive player of his era without being the star most clearly touched by genius.

Must a genius be an original? Genius is not quite analogous with originality, even if it is part of the equation. After all, in athletics, the outstanding instance of originality was Dick Fosbury's high jump "flop". But it feels silly to argue that Fosbury was a greater genius than Jesse Owens or Usain Bolt.

It makes more sense when we analyse originality in the arts. I would argue that DH Lawrence was a greater genius than Jane Austen, though I prefer Austen's novels and admire her achievements more. Why, then? Because the prism through which Lawrence described the world was more original and surprising. Once exposed to it, the Lawrentian world-view is harder to forget. In music, a similar point applies to Richard Wagner. When musicians and composers are polled about music's greatest geniuses, Wagner almost always comes high on the list, even among musicians who don't greatly like his work. By this criterion, the sportsman is constrained by the nature of the discipline: sport is (usually) practical where the arts are more naturally transcendental.

But sport can, I believe, occasionally touch the heights of the arts; sportsmen of genius do so disproportionately often. Taking a career as a body of work, what was the ratio of the inspired to the everyday? That is one measure of genius in sport.

As a sports fan, there are moments, very rare but real nonetheless, when I feel not only elation and admiration but also reconciliation. The experience feels complete. Adding to it or taking something away would diminish the whole. As an agnostic I feel slightly hypocritical about using the term, but in these moments sport seems almost divine.

When skill, self-belief, tenacity, technique and even talent have run their race - here genius takes over.