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When Roger Federer moved back to the top of the rankings last week, the sports world entered a state of uproar. The man is 36.5 years old, we cried. This is unprecedented!

We were only half right. Yes, Federer is breaking new ground in the Open era, a concept which will celebrate its 50th anniversary on April 22. Yet there have been tennis Methuselahs before. Ken Rosewall reached the 1974 Wimbledon final aged 39.

A better comparison would be ‘Big’ Bill Tilden — the 1920s giant who was so influential in spreading the game that he could be considered a racket-wielding WG Grace. As Allen Hornblum writes in his excellent new biography, American Colossus: “A general stampede of the crowd occurred each time an announcement was made on what court Tilden was practising or playing a match.” Remind you of anyone?

Over the course of its 405 pages, American Colossus delivers further parallels. Tilden was a late developer who did not peak until 27, when he won Wimbledon on his maiden visit. The explanation lay in his uniquely broad palette of strokes, which he kept developing so that he was still claiming national doubles titles into his fifties.

Federer, too, was relatively slow off the mark by modern standards. He needed time to harness his uniquely versatile game, and to control what was once a volcanic temperament. Today, Federer is still expanding his options. He subdued Rafael Nadal last year by adding more aggression to his backhand — exactly the same upgrade that allowed Tilden to overcome his own closest rival, ‘Little’ Bill Johnston, in the 1920s.

Throughout that decade, Tilden was the most famous sportsman in the world, eclipsing even boxer Jack Dempsey and baseball’s Babe Ruth. He hung out with royalty, both figurative (Charlie Chaplin) and literal (King Gustav of Sweden), in the same way that Federer cultivates celebrities like Vogue editor Anna Wintour and actor Bradley Cooper.

Tilden was 37.5 years when he delivered his last great season, lifting his third Wimbledon title. So why do we not hear more about a man variously compared to Napoleon, Leonardo da Vinci and Mount Everest? The answer is that Tilden fell upon hard times because of his homosexuality. He repressed his instincts during his playing days, judging by the accounts of young proteges like Vinnie Richards and Sandy Wiener, who would later testify to his rectitude. But in 1946 he was stopped by police on Sunset Boulevard, and found in a compromising position with a 14-year-old boy who had a previous conviction for “immorality”. Jailed by a hard-line judge, he never recovered his standing, dying broke and largely ignored at the age of 60.

Even today, Tilden’s case remains sensitive enough for his native Philadelphia to reject recent calls for a commemorative plaque. He has paid a high price for his late fall from grace, which prevents him from being acclaimed as a sporting legend on a par with Suzanne Lenglen and Rod Laver.

Still, however you judge his colourful and complex story, Tilden remains the closest antecedent we have to Federer’s miraculous longevity.