IT HAS been a year to remember for Andy Murray. In July the Scot won Wimbledon for the second time, marking his third major championship in total. The next month, he became the first tennis player in history to win two Olympic gold medals in the singles tournament, after defending his title from the London games of 2012 in Rio de Janeiro. And on November 7th he claimed the top spot in the official men’s rankings as measured by the Association of Tennis Professionals (ATP)—the first time that he has done so, some seven years after he first clawed his way into second place. Mr Murray’s rise followed his victory at last week’s Paris Masters event. Novak Djokovic, who had been sitting atop the table since July 2014, endured his fourth consecutive tournament without a trophy, ensuring his demotion.

Mr Murray’s newfound lofty perch represents long-overdue recognition for a player who was already building a stealthy legacy as an all-time great. He is only the 26th man to hold the top slot since the system was introduced in 1973, and the first from Great Britain. In a sport played across six continents, on a variety of surfaces, with differing tournament sizes and formats, the ATP rankings are the one yardstick that players and fans have generally agreed upon to determine the best player in the game.

Other unofficial indicators support the claim that Mr Murray is at the top of his profession. His record since mid-June has been formidable: he has lost just three matches and won seven titles. And betting markets regard him as the favourite to add to this collection at next week’s season-ending World Tour Finals in London, even though he faces more difficult preliminary-round competition than Mr Djokovic does.

But Mr Murray’s journey to the apex of the rankings has also exposed some of the flaws in the official system. The ATP awards points exclusively on the basis of the importance of a tournament and the round each player reaches. Grand Slams count for twice as much as the next tier of events, the Masters series, and winning a competition is worth two-thirds more than losing in the final. This method suffers (at least) one major weakness: it fails to account for the strength of a player’s opponents, which can vary widely over short time periods. And Mr Murray’s hot streak has coincided with a stretch of very soft competition: he has not faced a single rival from the official top five since June, when he lost the final of the French Open to Mr Djokovic. In total, the Serb has won three of their four meetings this year.

Fortunately, there is an alternative rating system available, which does factor in quality of opposition. It’s called Elo, in honour of its inventor, the Hungarian physicist Arpad Elo. Originally designed to measure the ability of chess players, it requires nothing more than a record of each competitor’s wins and losses to calculate, and has become a standard method for assessing the strength of teams or players in various sports.

Elo works by exchanging points between opponents after a contest. If you beat a much stronger rival, you take a large number of his ranking points, causing him to move down the rankings as you climb them; if you win against a weaker player, you take only a small portion of his points. As an example, Mr Djokovic gained just 0.3 Elo points for beating the low-ranked Frenchman Adrian Mannarino in the second round at Wimbledon this year—but lost 16 points to Sam Querrey when the American 28th seed beat him in the third round. The number of points swapped depends both on contestants’ Elo ratings before a match and on a parameter, derived from historical data, that measures how fast the model should adjust its estimate of a player’s strength based on new information. In tennis, this figure is fairly low, suggesting that abrupt changes in a player’s ability are rare (excluding the effect of injuries). As a result, it takes a large number of disappointing match results for Elo to conclude that a once-outstanding champion has become an underdog.

Elo ratings have proven to be better forecasters than the ATP’s. During the past 15 years, it has correctly picked the winner in 68.2% of matches, compared with 66.4% for the official rankings. And when the two systems have disagreed on who the favourite should be, Elo’s picks have prevailed 55% of the time.

Compared with the ATP rankings, Elo is both far less impressed with Mr Murray’s string of victories—he did not face a single player from inside the ATP’s top ten during his run to the title last week in Paris—and far less concerned by Mr Djokovic’s slump. Since his victory at the French Open, Mr Djokovic has triumphed in just one of six tournaments, a miserable run for a player of his ilk, and has suffered a number of upset losses. Meanwhile, Mr Murray has done his part to chip away at Mr Djokovic’s lead. But a five-month barren patch for a player who has won 12 grand slams, coinciding with a hot streak for one who has collected three, has not convinced the Elo algorithm that the two have traded places. In that time, each man has lost to Juan Martín del Potro, a hard-hitting Argentine, and to Marin Cilic, a Croat with a booming serve. Mr Djokovic was also on the receiving end of an inspired performance by Swiss slugger Stanislas Wawrinka in the final of the US Open in September.

As a result, the current Elo ratings still consider Mr Djokovic to be the world’s best player, and by a decent margin: they have him beating Mr Murray 63% of the time. That is a far cry from his advantage in March, when Mr Djokovic reached the highest score of anybody in the modern era, and would have been an 81% favourite against Mr Murray. But the magnitude of his edge even after such a decline simply confirms how stratospheric the heights that Mr Djokovic reached were when he was playing his absolute best. Despite the rough patch for Mr Djokovic, Elo still believes that the chasm between him and Mr Murray is larger than the gap between the Scot and the ageing Roger Federer, in third place. It pegs Mr Murray as a modest 60-40 favourite over the Swiss champion.

The imminent ATP World Tour Finals, which begin on November 13th, could help clarify the standings at the top. Mr Federer will miss the tournament due to injury. But with a round-robin format and a field of eight elite competitors, Mr Murray will play at least three matches against formidable opposition, giving him the chance to accumulate more high-quality victories. Mr Djokovic could simultaneously find himself struggling against players he once thrashed. It will take more instances of both to prove that the old king is dead, and that a new one has dethroned him.