First, let me be clear about what I am not saying. I'm not comparing Muhammad Ali and Brendon McCullum. And I am not saying that sporting reputation can be entirely separated from achievement.

But the coincidence of Ali's death and McCullum's MCC Cowdrey Lecture did, however, reinforce a complex truth. Sportsmen must seek measurable achievements - runs scored, matches won - but the full nature of their achievement can never be measured. Sport is both literal and also metaphorical, simultaneously a logbook of achieved deeds and also a form of mythic storytelling. The second dimension is far more important.

There is no need to recap, once again, Ali's achievements in the ring. Instead, let me direct you to Norman Mailer's The Fight, one of the most compelling sports books and ample evidence of Mailer's brilliance as well as Ali's (both had absurd streaks too, of course).

What is revealing, in terms of understanding sport, is how Ali's significance extended far beyond boxing. This is partly because his career coincided with the ascent of television and mass media, which gave his exuberant personality new platforms and reach; partly because Ali's stand against the Vietnam War, though it initially left him horribly isolated, chimed with a profound re-evaluation of American identity (so Ali was proved not only brave but also prescient); partly because Ali's character was so magnetic and his early boxing style so beautiful; partly because, in his later career, he showed very different virtues - the dancer became a warrior - giving his sporting journey a completeness that echoed the story of his life. Much of this is historically unique: a moment in sport's growth when boxing mattered, a moment that is unlikely to be repeated.

All this is impossible to disentangle from Ali's reputation as a boxer. After all, if you watch all three of his fights with Joe Frazier in one continuous loop - not for the faint-hearted - it is difficult to say that one man clearly "won". The same can be said about Ali's trilogy of fights with Ken Norton. The scoreboard reports that Ali leads in both head-to-heads, two wins to one. But Ali's heroic significance? Here his lead - despite his unforgivable taunting of Frazier - cannot be measured.

The discrepancy between playing achievement and lasting impact can be demonstrated from the opposite perspective in the sad example of a great player who has been understandably written out of the script. Baseball's highest average does not belong to Babe Ruth, Ted Williams or Joe DiMaggio. That accolade resides with Ty Cobb, the monstrous racist and violent cheat. "Baseball is something like a war," Cobb believed. His play was powered by hatred, effectively so. His reward has been to be quietly forgotten. The last baseball fan who believed Ty Cobb to be "the greatest" was Ty Cobb - the greatest accumulator of runs became the most eagerly forgotten high achiever.

"Sport is both literal and also metaphorical, simultaneously a logbook of achieved deeds and also a form of mythic storytelling. The second dimension is far more important"

McCullum's superb Cowdrey lecture also underlined these distinctions between on-field metrics and lasting contribution. In all international cricket, he has scored 19 hundreds. In Tests, ODIs and T20s respectively, his averages are 38, 30 and 35. As a captain, he has led extremely well, but with nothing like the dynastic supremacy achieved by West Indies and Australia during their dominant phases.

Yet I have no hesitation in saying that McCullum's cricket career is one of the most significant of this generation. After his lecture, a New Zealand friend of mine - resident in London, formerly a first-class cricketer - wrote to me saying it was his proudest moment as a Kiwi in London. A small example of McCullum's achieved goal: to make his country proud.

At one level, sport is a zero-sum game. Your victory, though personally enjoyable, is someone else's defeat. Hence a "neutral" victory - with nothing added in terms of aesthetic, dramatic, heroic or moral contribution - does not advance the ascent of man by even a micro-step. Yes, it is an athlete's job to win matches, yes it keeps him employed, no it doesn't matter much.

In another respect, however, sport is clearly not a zero-sum game. The Federer-Nadal Wimbledon final of 2008, the 2005 Ashes, Barcelona in 2009 - these spectacles provided meaning and value to millions of people. The final result, though it mattered intensely to the combatants, was, in fact, incidental. Their real value lay in the extent and quality of the fan's engagement, the creation of memories, the lifting of worries, the suspension of banal anxieties, the stilling of time, the glow of nostalgia.

So sport, at the most exalted level, approaches alchemy. Two opponents or teams are locked in battle, apparently wrestling for dominance in a highly bounded and limited sphere, while in fact raising the possibility of creating something much more important. The tricky bit, of course, is that the participants have to remain, to a large degree, locked on to the narrow task at hand. If sportsmen turn away from competing and take up grandstanding, the show is diminished; that would be like actors puncturing the suspension of disbelief in a theatre. The real value of sport can only emerge, by obliquity, when athletes pursue victory with authenticity.

Sportsmen can, however, choose to become more - or less - open to sport's higher potential. They can reduce and narrow the terms of engagement, like Cobb, or expand and elevate them, like McCullum.

The chair umpire during that 2008 Wimbledon final said that he was conscious, from the outset, of an unusual degree of eye contact from the players. It was as though the players knew what was happening, what might unfold. They were open to it, while never, for a moment, becoming distracted by it.

Sport, with its rich reserves of statistics, naturally invites arguments, couched in apparently rational terms, about measuring greatness. They are diverting enough, but also beside the point.

Time, not numbers, is the ultimate arbiter. As with the artist, the athlete's real achievement is not just to lodge in the record books, but to leave a mark in memories.