World number one Novak Djokovic put in a ruthless display to beat Kevin Anderson and reach the final of the ATP Finals in London.

The Serb will play Germany’s Alexander Zverev in Sunday’s season finale after a 6-2 6-2 victory.

In what was a re-run of July’s Wimbledon final, Djokovic dominated in the same way this time to reach his seventh final of the year.

The 14-time Grand Slam champion has not dropped a set all week.

“I think it was the best match I’ve played so far this week,” Djokovic said after sealing victory in one hour and 16 minutes with a forehand that bounced off the top of the net.

“It came at the right time. Kevin has been playing great tennis this week.

“He lost serve in the first game which was big because he relies so much on his serve. I tried to win as many points on his second serve as possible. It worked very well.”

• Zverev beats Federer to reach final
• ‘I hope ball boy doesn’t have sleepless night’

Djokovic serves up a masterclass

Widely seen as the best returner in the game, Djokovic has in fact been notable for his impeccable serving this week.

He is yet to be broken in four matches – facing just two break points – and it took Anderson until the sixth game of the opening set to win his first point on the Serb’s serve.

The South African won only seven points on the Djokovic serve in the entire match.

Where Anderson delivered big serves that averaged more than 130mph, Djokovic’s were about the 114mph mark but were all about accuracy, placement and setting up the next shot.

He beat Anderson 6-4 on aces – no mean feat against a player so known for racking up the aces that he has been donating money to charity for each one this week.

And his total of first-serve points won was a huge 85%.

Asked in his on-court interview if it was some of the best serving he has produced, Djokovic replied: “Possibly. It is not very common to serve more aces than Kevin. That stat helps the confidence.”

Anderson was making his debut at the ATP Finals, having enjoyed a successful year where he won two titles and reached a career-high ranking of five.

But he was outclassed and under pressure from the off, with Djokovic breaking in the opening game and creating two further break points in Anderson’s next service game.

While the South African held off that challenge when Djokovic hit wide, he gifted him another break in the seventh game when he sent a forehand long.

The second set followed the same pattern with Djokovic capitalising on an Anderson double-fault to establish another early break.

A crosscourt forehand earned the top seed a break for 4-1 and while Anderson limited the damage in the next game with a hold, Djokovic served out the match with style.

Next up, Zverev… again

Standing between Djokovic and a record-equalling sixth title at the season-ending tournament is 21-year-old Zverev, who beat 20-time Grand Slam champion Roger Federer 7-5 7-6 (7-5) earlier on Saturday.

The pair have already met this week, with the German pushing the Serb hard in the opening set of their group match before seeming to run out of steam as Djokovic won 6-4 6-1.

“I played very well in the group stage against Sascha [Zverev] but I don’t think he was close to his best,” said Djokovic, who also beat Zverev in the Shanghai semi-finals in October.

“He had a great match today against Roger and he has been serving well, so it will be a similar approach as today, trying to get as many first serves back.

“It is the last match of the year for both of us, so let the better player win.”

Victory for Djokovic would cap a remarkable year in which he came back from elbow surgery to win Wimbledon and the US Open and returned to the top of the world rankings for the first time in two years.

Alexander Zverev had no need to be sorry for stopping play and did not deserve to be booed, Roger Federer said after his ATP Finals last-four defeat.

Zverev halted play in their second-set tie-break after a ball boy came on to the court to retrieve a dropped ball.

The point was replayed according to the rules but that did not stop the jeers.

Interviewer Annabelle Croft told fans to be “more respectful” during Zverev’s victory speech and Federer hoped the boy did not “have a sleepless night”.

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Zverev, who should have been celebrating the 7-5 7-6 (7-5) victory that put him into Sunday’s final of the season-ending tournament at London’s O2 Arena, was instead taking time to compose himself in his on-court interview and apologising to Federer and the crowd.

“I was really upset afterwards in the locker room, I’m not going to lie. I had to take a few minutes for myself,” Zverev, 21, said after one of the biggest wins of his career.

“But, you know, I hope the crowd and the people who were booing maybe look at what actually happened, maybe just realise that I’ve maybe not done anything wrong.”

Croft came to his defence, sharply telling the crowd: “I’m not sure why you are booing; he is telling the truth. The ball boy moved across the court and disrupted play.

“I think you need to be a little bit more respectful; they are the rules.”

Federer said the whole episode had been “unfortunate”.

He said: “Sascha [Zverev] doesn’t deserve it. He apologised to me at the net. I was like, ‘Buddy, shut up. You don’t need to apologise to me here.’

“He shouldn’t be apologising. He didn’t do anything about it. He just called it how it was. He felt it affected play. There is a rule that if something like this happens, obviously you replay points.”

It was 3-4 in the second-set tie-break on Zverev’s serve when the German stopped a baseline rally when the ball boy fumbled a ball at the far end of the court.

Initially Federer looked perplexed by what was happening but umpire Carlos Bernardes checked with the ball boy and the point was replayed.

The partisan Federer crowd were unhappy, even more so when Zverev delivered an ace to level at 4-4 and went on to win the tie-break and the match.

“It’s a bold move by Sascha to stop the rally because the umpire can just say: ‘Sorry, buddy, you’re in the rally. I don’t care. You lost the point. I didn’t see it.’

“That’s where I just wanted to double-check with the umpire, what is the situation. But not for a second was there a sportsmanship situation there.

“Booing, I never like it. We see it in other sports all the time, but in tennis it’s rare. So when it happens, it gets very personal and we take it very direct.”

Federer, who was seeking a seventh title here, said he was not cross with the ball boy.

“It’s OK, no problem, that happens,” the Swiss said. “It’s all good. It’s all good. I hope he doesn’t have a sleepless night. It’s not a big deal at the end of the day.

“I’m definitely not mad at him.”

Roger Federer must wait until 2019 for another chance to reach 100 career titles after semi-final defeat by Alexander Zverev at the ATP Finals.

Zverev, 21, tipped by many as a future Grand Slam champion, triumphed 7-5 7-6 (7-5) at London’s O2 Arena.

On Sunday, he will face Novak Djokovic, who beat Kevin Anderson 6-2 6-2.

Zverev faced boos at the end of the match after he had – legitimately – stopped a point in the tie-break when a ball boy dropped a ball.

In scenes reminiscent of Naomi Osaka’s victory speech at the US Open when her win was overshadowed by Serena Williams’ outbursts, Zverev was left apologising to both the crowd and Federer after one of the biggest wins in his career.

“I apologised to Roger at the net already, he said it is OK and it is in the rules,” the world number five said.

“I’m sorry this happened. I didn’t mean to upset anybody.”

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‘The Pretender’ beats ‘the King’

Former Wimbledon champion Boris Becker, commentating for BBC TV, had said before the match between ‘the King and the Pretender’ that he believed Zverev was a future world number one.

With three Masters titles to his name, the young German has yet to make his mark on the Grand Slams – although his French Open quarter-final this year was a breakthrough.

But now he will get the chance to win the season-ending title, which is second only to the Slams in terms of prestige.

There were moments when Zverev seemed to show a bit too much respect for Federer.

His body shot at the Swiss in the sixth game of the first set was half-hearted and cost him a point, while he volleyed a ball that was well on its way out of the court in the next game – as if not quite believing that the great Federer was able to hit long.

But he oozed confidence when it mattered the most, setting up three set points on Federer’s serve in the 12th game.

Getting there had included a fantastic passing shot after he raced to Federer’s drop shot, and the roar that followed said it all.

He sealed the set when Federer hit a forehand wide and then kept the momentum going early in the second set when he immediately held to love.

The German was never going to get it all his own way, with Federer setting up three break points of his own with a stunning forehand on the line, and taking the game when Zverev could only get a racquet edge to the Swiss’ forehand.

But Zverev wasted no time in breaking back when a Federer forehand went wide and from then on they matched each other to set up the tie-break.

After setting up two match points, Zverev sealed victory on the second one with a fantastic backhand that Federer could not get anywhere near.

Why was Zverev booed?

Zverev should have been beaming after one of the biggest wins of his career, yet looked emotional and ended up feeling “lost” in his post-match interview after some Federer fans jeered.

Presumably they felt the German had showed gamesmanship when he stopped play in the tie-break after the ball boy came on to the court, although the rules state the point must be replayed in such circumstances.

Former British number one Annabel Croft, who was conducting the on-court interview, scolded the crowd for their negative reaction.

“He was playing by the rules so I think you all have to be a little more respectful,” she said.

BBC Sport presenter Sue Barker said she was “quite embarrassed” by the crowd’s reaction, while colleague Tim Henman called it “disappointing”.

“You have to play a let,” added former Wimbledon semi-finalist Henman. “Once Federer understood what had happened, he accepted it.”

Federer’s wait for 100th title continues

After Federer sealed his 99th career singles title in front of a home crowd in Basel last month, all eyes have been on when the great Swiss player will reach triple figures.

His chance to get there in Paris at the start of November was ended in the semi-finals by world number one Djokovic and in London he has once again fallen just short.

He did, however, get closer this week than looked likely after his poor – and grumpy – performance as he lost his opening round-robin match to Kei Nishikori.

Time is not on Federer’s side – with the Swiss having turned 37 in August – but the fact he won four titles this year, including his record-extending 20th Grand Slam title at the Australian Open, means few would bet against him reaching the milestone very soon.

Analysis

BBC tennis correspondent Russell Fuller

Winners having to apologise for winning is becoming a habit in 2018.

The atmosphere was not nearly as hostile as that faced by Naomi Osaka at the US Open, but Zverev was subjected to whistles and jeers by a significant minority of the crowd.

The decent majority, and the sure-footed intervention of interviewer Annabel Croft, helped salvage the situation.

Adulation can know no bounds, and it is by no means the first time devotion to Federer has overstepped the mark.

The match itself was a triumph for Zverev. He looked extremely assured throughout as he broke Federer to love to win the first set, and then held his nerve in the second set tiebreak.

The 21-year-old has won all four tie-breaks he has played this week.

Britain’s Jamie Murray and Brazilian partner Bruno Soares must continue their wait for an ATP Finals title after they lost to American pair Mike Bryan and Jack Sock in the semi-finals.

Murray and Soares were beaten 6-3 4-6 10-4 at London’s O2 Arena to go out at this stage for the third straight year.

Bryan and Sock only started playing together earlier this year when Bryan’s twin brother Bob was injured.

The fifth seeds will find out their final opponents later on Saturday.

French pair Pierre-Hugues Herbert and Nicolas Mahut face Colombians Juan Sebastian Cabal and Robert Farah at 18:00 GMT.

Sock reached the ATP Finals in the singles last year but, after dropping dramatically down the rankings, has found more success alongside 18-time Grand Slam champion Bryan.

“This is extremely special,” Sock said.

“My singles year wasn’t spectacular, there have been some low moments mentally, so to have success in doubles with a friend has been great.”

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Analysis

BBC tennis correspondent Russell Fuller

Mike Bryan and Jack Sock have proved themselves a formidable team since pairing up mid-season when Mike’s twin brother Bob needed hip surgery.

They have won both Wimbledon and the US Open. Mike has more Grand Slam men’s doubles titles than anyone in history, and Sock – who has had an awful year in singles – is an unpredictable and richly talented doubles player.

His forehand, packed with power and spin, made the difference in this match. Murray and Soares, despite the disappointment of a third successive semi-final defeat, may feel they could not have done much more.