WHEN Novak Djokovic beat Roger Federer to win the Wimbledon men’s singles championship on July 12th, he gave his supporters fresh ammunition to argue that he is playing better tennis than anyone in history. It was his 14th victory in his past 21 matches against the Swiss maestro.

Younger fans might presume that only Mr Federer’s superlative run from 2004-09 could compete with Mr Djokovic’s dominance. But those with longer memories could make a compelling claim for Rod Laver, who won a record 200 tournaments from 1956-76, or even Bill Tilden, who dominated the 1920s. Mr Federer’s oft-cited status as the best player ever, and Mr Djokovic’s as the heir apparent, rest on a widely held but hard-to-prove assumption: because the quality of play has increased so much over time, today’s finest sportsmen must be superior to their predecessors.

Cross-era comparisons are easiest in sports like running, jumping and weightlifting, which are measured in units like time, distance or mass. In general, performance in such contests has improved substantially over the years: the average top-ten finisher in the men’s 100-metre sprint has cut his time from 11.2 seconds in 1900 to just under ten now, and in the marathon from around two hours and 35 minutes in 1939 to two hours and five minutes today. The gains have been greater still in events that require complex equipment or techniques: the current pole-vault world record, at 6.16 metres, is over 50% higher than the best height a century ago.

However, the pace of progress has tended to slow. Most events—with the men’s 100 metres an exception—have settled into a plateau, where new world records are set less often and surpass the old marks by smaller margins. For example, the best men’s 800-metre time has shrunk by a mere 0.82 seconds since 1981, versus almost four seconds in the 26 years before that. And in a few disciplines, improvement has ground to a halt completely. The average times for female short- and middle-distance runners have not budged in 30 years (though some 1980s records by eastern European competitors may have been aided by performance-enhancing drugs). Some “speed limit” is inevitable—humans will never run as fast as an aeroplane, or jump into outer space—and athletes may be approaching it much faster than is widely believed. Mark Denny of Stanford University calculates that most human race times are within 3% of their potential best. Outside athletics, performance is harder to measure. In bowling, for example, the number of perfect 300 games per year in America rose nearly 40 times during the 30 years to 1999. But connoisseurs attribute much of this to strategically oiled lanes that guide the ball towards its target, rather than any broad-based gain in skill. Golf has demonstrated the opposite pattern: in response to better players wielding better clubs, designers have built longer golf courses with more hazards, such as lakes and bunkers (see article). Yet even these measurement difficulties pale in comparison with those in interactive sports, in which opponents affect each other. If players improve at the same rate, scoring levels will remain flat. The challenge of comparing players from different eras in games like football—Pelé, Maradona or Messi?—has fuelled many a bar-room brawl. But analysts have devised a few statistical methods to resolve these debates, and estimate how the greats of the past might fare against modern competition.