Spritely Roger Federer continues to defy his years to dispatch Jack Sock at the ATP Finals in London

Federer beat the American in straight sets at London's O2 on Sunday

Federer has only lost four matches all year (Getty)

Two weeks after Steely Dan and the Doobie Brothers enthralled a capacity crowd here in the O2 Arena, Roger Federer proved on the same stage that advancing years can be brushed aside by veteran tennis players as well as by ageing rockers.

Federer is the oldest player to qualify for the season-ending Nitto ATP Finals since the tournament’s first incarnation as the Masters in 1970, but the 36-year-old Swiss looked as spritely as ever when he opened the singles proceedings here on Sunday with a 6-4, 7-6 victory over Jack Sock.

Wimbledon, where Federer became the first man to win the singles title eight times this summer, is the tournament above all others with which he will forever be associated, but his domination of this event is almost as impressive. He holds the record for the most titles (six), most finals (10), most appearances (15) and most prize money won ($14.35m or £10.9m).

Federer's run of 14 successive appearances in this tournament ended when he missed the second half of last season because of a knee injury, but he has bounced back in stunning style in 2017.

The oldest world No 2 in history has lost only four matches this year and won 12 of his 13 meetings with top 10 opponents. Despite having played a limited schedule of only 12 tournaments, he has already won seven titles, which is his best return since 2007.

When Federer made his debut in this competition in 2002 Sock had just turned 10 and was starting to find his way around a tennis court, having first picked up a racket two years earlier. At 25 he is enjoying the best season of his career and will end the year as the highest-ranked American for the first time, ending John Isner’s five-year reign.

Only a week ago Sock was ranked No 22 in the world and outside the qualifying places for London, which are filled by the eight men who have earned the most ranking points in the year. He qualified by becoming the first non-European to claim a Masters Series title for seven years, winning in Paris last Sunday, having trailed 5-1 to Britain’s Kyle Edmund in the final set of his opening match.

Federer has only lost once against a top 10 player this year (Getty)

Federer withdrew from that tournament, saying his body needed rest, and admitted here that it had taken him time to recover from his exertions the previous week in Basle, where he played five matches in six days. After beating Sock, however, he said he felt good and ready to go “full steam ahead in every match that comes”.

Sock had not won a set in his three previous meetings with Federer and that pattern rarely looked like changing. Although the only one break of serve came in the opening game, Federer never seemed in any danger.

The Swiss served with all his usual guile and consistency, dropping just 11 points in his 11 service games. Sock, who is the first American to play here for six years, made very few punishing returns, unlike Federer. Sock was regularly made to work hard on his own serve, though it was to his credit that he stuck to his task throughout. "I don't think I played too badly," he said afterwards.

On the very first point Federer hit an apparently effortless backhand winner down the line and on the second his clever shot to feet forced Sock into a volley error. Three points later a winning inside-out forehand took the Swiss to break point, which he converted with a sumptuous backhand winner down the line.

Federer served out for the first set and had Sock in trouble on his serve for most of the second. The American saved two break points at 3-3, two more at 4-4 and one more at 5-5. In the tie-break he retrieved a mini-break before serving his sixth double fault at 4-4, after which Federer served out to complete his victory in just over an hour and a half.

Sock will end the year as US No 1 (Getty)

The only embarrassing moment for Federer came at the end of the seventh game of the first set. Sock’s poor drop shot set up what should have been the easiest of kills, but after the American had given up on the point by turning round, bending over and inviting Federer to drill the ball at his backside, the Swiss netted his forehand.

“It was a big distraction, I'll tell you that, because it was very big,” a laughing Federer said afterwards. “That's what I should have aimed for. That target was bigger than the down-the-line court that I had.”

In the ninth game of the second set, nevertheless, it was Sock’s turn to look sheepish. The world No 9 hit a showboating volley between his legs only for Federer to return it with a winning backhand, which his opponent chose to leave.

“It was a minor shank and I figured it was going to go out,” Sock said later with a smile. “It’s Roger, I guess. He can do no wrong. Everything goes in.”

Federer, who said he was pleased with the way he had managed his opening match, was asked afterwards how he felt Andy Murray had played when they met in a charity event in Glasgow last week. It was the Scot’s first match since he struggled through Wimbledon with a hip injury.

“I think in some ways it was a brave move for him to just put himself out there and give it a go because nobody really knew how he was doing,” Federer said. “I was actually happy how he was playing. Definitely he can move better, he can serve better. We know all these things. For a start, I think it was actually quite encouraging and actually OK.

“He still has a lot of time before Australia comes around, but only he knows at what level he wants to return to competition. But I thought he was actually pretty good. I didn't expect him to be this good yet.”

In his second round-robin match on Tuesday Federer will face the 20-year-old German, Alexander Zverev, who in his very first match in the tournament recovered from a break down in the final set to beat Marin Cilic 6-4, 3-6, 6-4. Rafael Nadal, the world No 1, will play his opening match against David Goffin on Monday evening.