Is sport getting better? If so, why are some records never broken? Until Roger Bannister managed it in 1954, many thought that running a mile in under four minutes was impossible. As one contemporary writer explained, the figure “seemed so perfectly round — four laps, four quarter miles, four-point-oh-oh minutes — that it seemed God had established it as man’s limit”. Anything faster than that was thought to be beyond human capacity. Some even thought that running that fast was dangerous, perhaps lethal.

These days, four minutes is not even a landmark, let alone a barrier. The present record, 3min 43.13sec — held by Hicham El Guerrouj — is more than 7 per cent faster than Bannister’s time. The four-minute mile was just another step in human evolution.

Marathon-running makes the point more starkly. In 1896 it took the Olympic gold medal-winner just under three hours; now the best marathon runners hover close to two hours.

There are all sorts of reasons for the sharp increase in human athletic evolution. First, modern training is far more scientific and advanced. Secondly, the professionalisation of sport means that athletes can devote their lives to improvement. (Bannister, on the other hand, squeezed his training into hour-long lunchtime breaks from his medical studies.) Thirdly, nutritionists fine-tune athletes’ diets to make sure that they will be in perfect physical condition come race day.

Techniques have also advanced in huge jumps. Before 1968, high jumpers took off from their inside foot and swung their outside foot up and over the bar. But at the Mexico City Olympics of that year, Dick Fosbury, of the United States, raced up to the bar at great speed and took off from his right (outside) foot. Then he twisted his body, going over the bar head first but with his back facing down. Fosbury jumped 2.24 metres and won gold. The world record — by Fosbury flop, of course — stands at 2.45.

Deeper, longer-term demographic trends have also helped records to tumble. Most sportsmen are naturally bigger and stronger than their ancestors. A 12-year-old child in 1990 was about nine inches taller than his 1900 counterpart. Improved diet and health have made us grow bigger and earlier. Worldwide population has exploded, so the talent pool of potential record-breakers has increased hugely.

So, if health and diet continue to improve and training techniques become more scientific, surely sporting aptitude will continue to evolve indefinitely? No. There are some barriers that cannot be broken. “We will never run a mile at the same speed at which we now run 100 metres,” Andrew Berry, the Harvard evolutionary geneticist, has said. “The laws of oxygen exchange will not permit it.”

Racehorses seem to have reached that physical limit. Like human athletes, for years their speed records steadily improved. From 1850 to 1930 the winning times for the Derby dropped from 2min 55sec to 2min 39sec. But then horses simply stopped getting faster. From 1986 to 1996 the average time stayed at 2min 39sec. Racehorses are bred to run, but you can go only so far. You can only breed horses with ultra-light, thin bones to a particular point; the bones will crack under stress if they get any lighter.

The same principles will one day apply to humans. “Human improvement must eventually bow to the basic constraints of biomechanics,” Berry said. There is an outer wall of human endeavour. It is just that no one knows where it is. But we do know that it is not the four-minute mile.

There is an obvious difficulty in applying this scientific method of measurement to other sports. Cricket, for example, is a predominantly skills-based game. There is also the Bradman problem: cricket’s towering achiever played from 1928 to 1948 and in half a century of professional cricket — for all the new training, better diets and vast talent pool — no one has got anywhere near him. How is that for human evolution?

In fact, the Bradman problem is not unique to cricket. Being outstanding seems to be getting harder. In baseball, the holy grail for batters is to average more than .400. No one has done that since Ted Williams in 1941, but if you look at the 50 years before then, eight players managed even better and hit .401.

The same is true for cricket. Twelve English batsmen born before the First World War had an average of more than 50, an achievement matched by only three players born after it.

This is the central paradox of sporting progress. If the standard of sport is improving, why do the greats of the past stand out more? Three reasons: better defence, more information and a higher base level of achievement.

The first thing a coach can do in any sport is to provide a defensive structure. Attack and flair, which rely more on instinct, are harder to systematise. But defence is more a question of alignment and tactics. Given two balanced teams, if one of them takes defence at all seriously it can easily make scoring very difficult for the opposition.

Secondly, professional sports teams now have much better information about the opposition. Access to television footage, newspapers, books and the internet means that you can analyse future opponents in huge detail. As a result, more strategies are devised to counteract exceptional players.

Again, the easiest application of that information is defensive. The Body-line theory was infamously devised to stop Bradman. Bodyline may have been extreme and unsporting, but it was philosophically ahead of its time. These days, devising strategies to limit opposing star players is commonplace — bowling well wide of Sachin Tendulkar’s off stump, for example.

Thirdly, the less good players in professional sport are a lot better than they used to be. Stephen Jay Gould, the scientist, polymath and baseball nut, conducted a study of the history of baseball averages. He found that as the game improved, the lowest averages crept up. An average that once made you a struggling but employed baseball player now leaves you out of a job. And yet the overall batting average has remained reasonably constant. In fact, there is exact symmetry — as the worst have got better, the best have stood out less.

Gould explained all this as a perfect scientific example of “declining variation” — the bunching of elite sportsmen as the professional league improves overall. Gould measured this decline in variation throughout the history of Major League Baseball. He simply took the five highest and five lowest averages in each season and compared them with the league average. He discovered that “the differences between both average and highest and between average and lowest have decreased steadily through the years”.

In a cricketing context, Gould’s argument provides a scientific explanation of why there will never be another Bradman, even — in fact, especially — if the standard of general play does constantly improve. The sophistication of the modern game works against freakish solo domination.

Bradman proves Gould’s point better than any baseball player could. He was better at cricket than anyone has ever been at any other measurable sport. His feats are more remarkable, the second-best player is farther adrift, the chasing pack trails by a greater margin. When Bradman died in February 2001, The New York Times mathematically converted his cricket average into other sporting measures — basketball points per game, baseball hits per inning. Bradman, it concluded, was better than Michael Jordan or Babe Ruth or Ty Cobb.

When I was 5 I met Bradman in Adelaide. We stayed with friends who lived two doors along from the great man. I was crazy about cricket and our friends kindly arranged for us all to have tea with “the Don” and for me to have a net session in the back garden. It was the ultimate dream come true for a cricket-mad kid. I remember meeting a shrewd-looking old man, who seemed to have a sharp, analytical expression.

A few balls were thrown for me to hit into a net. He watched and did not say much. More balls were thrown. I hit some OK with my size 3 Stuart Surridge bat. “For God’s sake stop throwing him half-volleys — make it a bit harder for the lad!” he exclaimed. The Don had spoken and everyone laughed.

I did not realise then, of course, what writing this has helped me to understand. I had been privileged to meet not only a genius — there will always be geniuses — but a genius from an age when they stood taller above their contemporaries. The sporting world was smaller in Bradman’s time, so its giants loomed larger. No one stood higher than him.

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The rundown

— Ed Smith, 30, is captain of Middlesex and became the fifteenth Smith to be selected for England when picked against South Africa in 2003.

— He earned the call-up on the back of scoring hundreds in six successive matches, including a double hundred. He made 64 in his first Test innings but a total of 23 runs in his next four. He has scored more than 1,000 runs in each of the past seven seasons.

— Smith read history at Peterhouse, Cambridge, where he gained a double first as well as averaging 58 for the university.

— His previous books were Playing Hard Ball and On and Off the Field.

A league of his own

— Sir Donald Bradman ended his Test career in 1948 with a batting average of 99.94 from 52 Test matches. The highest end-of-career average to that point had been Herbert Sutcliffe’s 60.73. Graeme Pollock (60.97) and George Headley (60.83) are the only other batsmen to have ended their career with an average of more than 60.

— Mike Hussey, of Australia, is averaging 78.14 after 36 Test innings. At a comparative point in his career Bradman was averaging 95.30 and had scored almost 1,000 more runs.