Rafael Nadal believes he will eventually look back fondly on matching Roger Federer and Novak Djokovic for equal second most year-end number one rankings.

Federer's win over Djokovic at the ATP Finals on Thursday ensured Nadal would end the year as world number one for the fifth time in his career.

The three greats are alongside Jimmy Connors on that tally, while only Pete Sampras (six) has achieved it more often.

Nadal, 33, said it was an achievement he would eventually be proud of.

"At some point for me, it's something that gives me great personal satisfaction," the 19-time grand slam champion told a news conference.

"To have the chance to equal both of them [Federer and Djokovic] after missing a couple of years for injuries means a lot.

"I remember 2012 for example, I had been playing great and I had been in a position that I think I was playing great, after winning Roland Garros I had to stop for eight months for my knee. Then in 2009 something similar happened.

"So, a couple of years I had been there but because of physical issues I was not able to fight for it. To have this trophy with me means a lot and of course it's a great achievement."

Nadal edged Stefanos Tsitsipas at the ATP Finals on Friday, but the Spanish great was eliminated after Alexander Zverev's win over Daniil Medvedev later in the day.

Winner of the French Open and US Open this year, Nadal said being number one at year's end had not been a target.

"Number one was not the main goal for me. I will not follow the number one, I was going to do my normal calendar because you have to make decisions to try to play as long as possible in order to fight for the number one," he said.

"Our decision is to try to do things to play as long as possible so that's why I tried to do the conservative calendar in terms of saving the body.

"But the thing is when I've been playing, I've been playing very well. I achieved almost every single time the last rounds of every tournament. That's why it's put me in a position that I am where I am today, having this trophy with me.

"Of course, after winning the US Open I put myself in a position that it can be a chance to be there, but of course having the rivals I have in front, anything is possible."

Novak Djokovic hopes to play at the Davis Cup Finals despite admitting he felt a "pretty sharp" pain in his elbow against Roger Federer on Thursday.

Djokovic failed to reach the last four at the ATP Finals after suffering a 6-4 6-3 defeat to Federer in London.

The Serbian 16-time grand slam champion was again troubled by his elbow, a worry ahead of the Davis Cup Finals beginning in Madrid on Monday.

"I hope it's nothing that will really unable me to play Madrid. The pain was pretty sharp, but I could play the rest of the match," Djokovic told a news conference.

"If I had something really serious I think I wouldn't be able to hold the racquet so it wasn't, it was probably just an awkward, quick movement that I did, but it did not impose any form of issues later on."

Djokovic suffered his first loss to Federer since 2015, the result handing Rafael Nadal the year-end number one ranking.

The 32-year-old said he was well below his best, while praising Federer's performance.

"There was not much that I did right this match to be honest, realistically he was the better player in all aspects and absolutely deserved to win," Djokovic said.

"He served great, moved well and returned my serve very well so from his end I think he did everything right, from my end I was just playing too neutral.

"I couldn't read his serve well and just a pretty bad match from my side."

Despite not living up to his usual standards to finish the year, Djokovic was happy with his 2019 after successes at the Australian Open and Wimbledon.

"I'm not happy with the way I finished the season. Obviously this is not the way I want to play on the court first of all but you've got to accept that you have these kinds of days and move on," he said.

"If I have to draw the line, I think it was still a very good season winning two slams and five titles.

"Of course I'm still hot-headed off the court but all in all it was a good season."

Serbia are in Group A at the Davis Cup Finals, alongside France and Japan.

Rafael Nadal matched Roger Federer and Novak Djokovic by securing a fifth year-end number one, while also breaking a record set by the Serbian.

Federer was too good for Djokovic 6-4 6-3 at the ATP Finals on Thursday, reaching the semi-finals at the expense of the 16-time grand slam champion.

The result confirmed Nadal will finish the year at the top of the rankings for the fifth time.

The Spanish star joined Federer, Djokovic and Jimmy Connors on that tally, trailing only Pete Sampras (six).

It also marked the 16th straight year in which one of the 'Big Four' – Federer (2004-07 and 2009), Nadal (2008, 2010, 2013, 2017 and 2019), Djokovic (2011-12, 2014-15 and 2018) and Andy Murray (2016) – has finished as world number one.

At 33, Nadal is the oldest year-end number one in ATP rankings history. Djokovic, 31 last year, held that mark previously.

Federer (20) still leads his rivals for most grand slams, although Nadal (19) and Djokovic (16) closed the gap this year.

Roger Federer described his ATP Finals victory over Novak Djokovic as "magical", having come up short when they last met in an epic Wimbledon final.

Swiss icon Federer earned a brilliant 6-4 6-3 victory at the O2 Arena in London on Thursday to join Dominic Thiem in advancing to the semi-finals at the Serbian's expense.

It was the 19-time grand slam champion's first win against Djokovic – whose defeat meant Rafael Nadal will end 2019 as the world number one – since 2015, with the 32-year-old having been triumphant in each of their previous five encounters.

The most recent of those saw Djokovic stave off a championship point before clinching the Wimbledon title following a tie-break at 12-12 in the fifth set.

Asked what he did differently on Thursday, Federer replied: "I won match point, I guess! It was so close at Wimbledon. It was a privilege to play that match, so many ups and downs.

"I thought I played an incredible tournament … and it's just a point or a shot here and there that made the difference and he got it.

"You move on, try harder next time and hopefully luck goes on your side. I stayed calm, I played great until the very end and I couldn't be more happy right now.

"[It was a] great atmosphere, great opponent. It was definitely incredibly special. I enjoyed it from the beginning.

"I played incredible and I knew I had to because that's what Novak does. I was able to produce. It was definitely magical. You guys [the fans] made it super special, I can't thank you enough."

Federer bounced back from losing his opening round-robin match to Thiem by beating Matteo Berrettini in straight sets and the 38-year-old stepped up his game again to overcome Djokovic.

"You always play better as the tournament goes on, that's why I think we played as well as we did at Wimbledon as well," said Federer, who suffered a semi-final defeat to Alexander Zverev in last year's ATP Finals.

"Dominic Thiem has been supreme in our group, made life difficult for both of us and put us in the situation that only the winner goes through.

"There was a lot riding on the match and I came out and I think I served great, had great anticipation, a clear game-plan and it worked great – hopefully not for the last time against Novak.

"I'm happy to stick around. Hopefully I'll go a step further than last year, I played a good match against Zverev last year but he was unreal."

Roger Federer triumphed in a win-or-bust ATP Finals encounter with Novak Djokovic at the O2 Arena on Thursday, meaning Rafael Nadal will end 2019 as the world number one.

Six-time champion Federer was in fine fettle as he restricted the rallies to seal an impressive 6-4 6-3 victory over Djokovic, ensuring it was he who qualified from Group Bjorn Borg behind Dominic Thiem.

The Serbian's defeat – his first in six meetings with the 38-year-old – ended his hopes of regaining top spot in the rankings from Nadal, who only replaced him last week.

Federer surrendered two championship points before falling to Djokovic in a thrilling five-set Wimbledon final in July, but he looked unbeatable as he clinched a first victory over the 16-time major winner since 2015.

Djokovic stayed cool to stave off a break point in game one but successive double faults put him under pressure in his next service game and Federer seized the initiative with a fierce backhand.

The match continued at a high pace – only five points in the opening set lasted for nine shots or more – and, after Djokovic battled back from 0-30 down to complete an essential hold in game nine, the Swiss sent down an ace to seal the set.

Federer kept the pressure on at the start of the second but was met with resistance as the world number two dug in to fight off a pair of break points with impressive work from the baseline.

Djokovic appeared to hurt his right elbow while stretching for the ball in game two yet seemed to be gaining momentum, only for a scintillating Federer forehand to deny him a chance to move 3-1 up.

The Swiss heeded his warning and pounced in the next game after a long forehand from Djokovic ended a baseline exchange on the second of three break points.

A pair of unforced errors helped hand Federer a trio of match points and he leapt into the air when Djokovic failed to get a volley over the net, completing a resounding win for the 19-time grand slam champion.

Novak Djokovic praised Dominic Thiem's "unbelievable" performance after suffering a thrilling loss to the Austrian at the ATP Finals on Tuesday.

Djokovic went down to Thiem 6-7 (5-7) 6-3 7-6 (7-5) after an enthralling contest at the O2 Arena in London.

Thiem hit 51 winners and just as many unforced errors during an aggressive display that eventually paid off with victory in two hours, 47 minutes.

Djokovic, who will face Roger Federer in Group Bjorn Borg for a place in the semi-finals, praised Thiem's performance.

"I thought he deserved to win. He just played very courageous tennis and just smacking the ball, he went for broke, the entire match he played the same way he played the last point," the Serbian 16-time grand slam champion told a news conference.

"I mean, I have to put my hat down and congratulate him because he just played a great match."

Djokovic added: "I don't think I've experienced too many matches like this where my opponent just goes for every single shot.

"I mean, he was unbelievable, in some stages it was just incredible that he was just literally smacking the ball as hard as he can and it was going in.

"Of course his level is super high, today was unbelievable, but whether he can keep that up every match, if he does, chapeau, there's not much you can say, for sure he's playing great tennis."

Dominic Thiem said he was "in the zone" during his thrilling ATP Finals win over Novak Djokovic on Tuesday.

The Austrian booked his spot in the semi-finals in London by overcoming Djokovic 6-7 (5-7) 6-3 7-6 (7-5) at the O2 Arena.

Thiem, who beat Roger Federer in Group Bjorn Borg on Sunday, said it was an unforgettable performance.

"I was in the zone from the first point on," he said in an on-court interview.

"I served for the match at 6-5 in the third set, but obviously I was playing the best returner in the game so I didn't worry too much, I was focusing on the tie-break and coming back from 4-1, a little bit of luck here and there.

"But, in general, it was just unbelievable and a match that I will probably never forget."

Thiem hit 51 winners during his win, coming from 4-1 down in the third-set tie-break to edge past Djokovic.

The 26-year-old was delighted with his performance and said it was the level required to beat the 16-time grand slam champion.

"This was really one of these very special matches that I practised all my life for, what I practised all my childhood for, a really epic one in front of an amazing atmosphere, beating a real legend of our game," Thiem said.

"I couldn't be happier and also I qualified for the semi-finals which is the best."

He added: "I was playing Novak, who is in great shape, who is probably the best player in the world right now.

"I had to do something special and luckily a lot of these balls and these winners went into the court."

Thiem will face Italian Matteo Berrettini in his final match in the group on Thursday.

Dominic Thiem followed up his win over Roger Federer with a stunning performance in an enthralling 6-7 (5-7) 6-3 7-6 (7-5) victory over Novak Djokovic to secure his progression in the ATP Finals.

The most recent meeting between Djokovic and Thiem went the distance at Roland Garros in May, and it was the latter who triumphed again in a two-hour 50-minute classic.

After losing a 66-minute first set, Thiem rallied to force a decider for the first time in a match at this year's edition of the Finals, while ending Matteo Berrettini's slim qualification hopes in the process.

Despite going a break down, Djokovic - who will now battle it out with Federer for a last-four spot - seemed to have turned the tide in the final set, but Thiem thrived under the pressure, fighting back to clinch a remarkable win on a tie-break.

Djokovic looked set to take control after breaking on Thiem's second service game, yet the Austrian returned the favour to draw level at 3-3.

Thiem denied Djokovic a chance to claim the set in game 10, forcing the world number two onto the backfoot with a venomous serve.

Djokovic was at his best to nose himself ahead in the tiebreak with a stunning cross-court shot, but Thiem found a way back, only for an overhit forehand to hand to give last year's runner up an advantage he did not relinquish.

Two sensational backhands saw Thiem respond with a decisive early break in set two, racing into a lead that proved unassailable.

Thiem raised his arms to the crowd as he restored parity on his serve, though it was Djokovic's turn to fire up the spectators in the opening game of the decider, thumping the air after a wonderful defensive shot won him his first point.

It was to no avail as Thiem claimed another break, but Djokovic - after failing to take advantage of three chances to bounce straight back - did manage to swing momentum in his favour in game six.

However, Thiem refused to go down, holding serve magnificently before breaking for a fourth time, though a loss of focus at the vital moment resulted in another tie-break.

A sloppy start put Thiem on the back foot, but three successive winners paved the way for the world number five to force Djokovic into a weak shot into the net and ensure his place in the semi-finals for the first time.

Roger Federer is thrilled to be going head-to-head with world number two Novak Djokovic in what could be a pivotal ATP Finals encounter for both players.

Federer bounced back from his opening defeat to Dominic Thiem by beating Matteo Berrettini 7-6 (7-2) 6-3 on Tuesday, and will face Djokovic for the first time since losing in a five-set epic in this year's Wimbledon final.

Last year's runner up Djokovic, who is aiming to dethrone Rafael Nadal as world number one, would secure his progression from the Bjorn Borg group should he beat Thiem in Tuesday's late match.

Depending on the result, and how Thiem does against Berrettini on Thursday, Federer could potentially have to beat Djokovic to ensure his place in the last four.

However, Federer is merely focusing on making sure his own performance is at its highest possible level, as he goes up against an opponent he has faced on 48 occasions in the past, winning 22 times.

"No, I'm excited playing against him. I'm excited to see how he's going to play tonight, as well," Federer told a news conference after his win over Berrettini.

"It's definitely going to give me some more information about what to expect. But other than that, I think I need to focus on my game, what I do best and regardless of what I need to do, I just hope I play well.

"We have played a lot of matches since [Wimbledon], and I think we both look back at a great match. I think we both can take away some confidence from the match. Him, obviously a lot. Me, maybe a tad bit less.

"But at the end of the day, I wasn't hoping [for] him not to be in my section or in my draw. I didn't hope I was never going to play him again.

"Actually, it's good for me to play him again, and maybe that all helps to get a chance to get him back or whatever it is."

While Djokovic and Nadal are battling it out for top spot in the ATP rankings, Federer claims he is no longer concerned with where he is placed among the world's elite, as long as his fitness remains in tact.

"Points? Yeah, who cares? Who cares if I'm ranked three, five, nine?" Federer said.

"If I feel like I'm 100 per cent fit, then I feel like I have a chance to win the tournament.

"But if I don't feel that way but I'm ranked one or three or five, whatever it may be, I know it's going to be extremely more difficult and sometimes almost impossible, even though I feel like if I'm in a draw, usually I always give myself a chance."

Andy Murray believes he is now back to being capable of taking on the world's elite players after his remarkable comeback from injury in 2019.

Murray looked set to retire due to injury earlier in the year, but after undergoing successful hip surgery, crowned his return by winning the European Open in Antwerp to claim his 46th ATP Tour title.

After taking the best part of a month off, Murray will now head to the Davis Cup finals as part of Great Britain's five-man team.

The 32-year-old intends step things up further in 2020 and the three-time major winner says he would be confident of pushing Rafael Nadal, Novak Djokovic or Roger Federer all the way should he come up against any of the big three.

"I know if I played against the top players tomorrow there would be a very small chance of me winning that match," Murray told BBC Sport.

"But I do feel I could win. That's one of the performance goals I want - when I go out on court against all of the players I want to feel like I have a chance of winning.

"Seven or eight weeks ago I wouldn't have felt that was the case. 

"If I continued along that path then I wouldn't continue playing. It has been an up and down few years but I feel like I'm coming through the other side of it and I'm excited to see what I can do over the next couple of years.

"It's difficult to say exactly where I am. I'm not where I was when I was 25 but I don't expect to be and I don't need to be [in order] to be competitive at the highest level and that's why I'm excited.

"I'm not going to set a target of top 10 or trying to make the semis of a Grand Slam because I've done all of that before and I don't need that.

"I'm happy just being pain free, healthy and love what I'm doing."

Murray defeated Stan Wawrinka to clinch the European Open title, while the Scot overcame world number eight Matteo Berrettini on his way to the China Open quarter-finals in Beijing, where he was eventually defeated by Dominic Thiem.

Novak Djokovic made a superb start to his ATP Finals campaign with a dominant 6-2 6-1 triumph over tournament debutant Matteo Berrettini.

In the first match of this year's season finale, Djokovic – who is aiming to oust Rafael Nadal as world number one after he was dethroned by the Spaniard earlier this week – made a statement of intent in the Bjorn Borg group.

Five successive, clinical breaks of serve saw last year's runner up – a four-time champion at the O2 Arena – ease to an emphatic victory in just 63 minutes.

Berrettini, the last player to qualifier for the finals, walked towards the wrong exit after Djokovic's win was sealed on a first match point, and given the beating he had just taken, it was perhaps no surprise the Italian seemed slightly shocked.

"It feels great to be back in, earlier this year I had a great stay in London, played well at Wimbledon," Djokovic told BBC Sport.

"Over the years I've played really well in this arena. I've been enjoying it very much.

"It's not easy for Matteo, playing his first tour finals match, I knew he'd be a bit more nervous at the beginning, I tried to use my experience.

"I was fortunate to get the break midway through the first set. He's got big weapons with his serve and forehand but I managed to play really solid."

Djokovic beat Roger Federer in a Wimbledon final for the ages in his last appearance in London, and the Serbian was swiftly into his rhythm against world number eight Berrettini.

Having not dropped a point in the opening game, the 32-year-old forced Berrettini to deuce on his first serve before two breaks handed him the set.

Berrettini claimed a brilliant point in game two of the second set, managing to reach for a low backhand that Djokovic could only skew into the air, providing his opponent with a simple volley.

But it merely stalled Djokovic's process for a brief moment – Berrettini, who is renowned for his powerful serves, going 2-0 and a break down.

Another break for Djokovic followed, though Berrettini did capitalise on the only break point he was afforded.

It mattered little, however, Djokovic getting the better of his opponent's serve once more before rounding off the win with a controlled cross-court forehand.

Rafael Nadal is set on ending 2019 as world number one despite doubts over his fitness heading into the ATP Finals.

Nadal overtook Novak Djokovic atop the ATP rankings on Monday but is still not certain of retaining the position at the end of the year.

Djokovic and Nadal are in opposite groups in London, with the Spaniard to face Stefanos Tsitsipas, Alexander Zverev and in-form Daniil Medvedev – who he beat in the US Open final in a five-set epic.

The 33-year-old took to Twitter on Friday to provide an update on his fitness, stating he is "taking it day by day," after he was forced to withdraw from the Paris Masters due to an abdominal tear, though doubt remains as to whether he will be able to participate through the whole tournament in the English capital.

However, Nadal insisted he is still determined to cap off the year at the top of the rankings, should he stay fit.

"Of course I would love to be the year-end number one but I always said it was not my personal goal because I did not follow that [path]," Nadal said in a news conference at the O2.

"If I did, I would be flying to China after New York because I was in a positive position.

"But that doesn't mean I am renouncing to try to be number one. Not at all. I am fighting for it."

Nadal, whose injury has prevented him from practicing, is hopeful of being fully fit for Monday's encounter with defending ATP Finals champion Zverev.

"I'm excited to be here after a couple of years without being able to play. I need to see how things evolve every single day," he said.

"I have good hopes to be 100 per cent ready for Monday. I had been serving very well in Paris, I had good matches, so I am confident that I can be very competitive.

"Of course it's a tournament that you will face the top guys since the beginning so you need to be 100 per cent ready. 

"But I really hope I will be able to serve every single day a little better and my hope is to be on Sunday serving normal."

Novak Djokovic and Roger Federer will meet in the group stage of the ATP Finals after being drawn together on Tuesday.

The pair have won 36 grand slams between them and triumphed at the season-ending tournament a collective 11 times, with Federer leading that head-to-head tally by one.

Joining the Swiss maestro and Djokovic in Bjorn Borg Group will be Dominic Thiem and Matteo Berrettini.

Andre Agassi Group consists of world number one Rafael Nadal, Daniil Medvedev, Stefanos Tsitsipas and reigning champion Alexander Zverev.

Nadal had been a doubt for the event after withdrawing ahead of the Paris Masters semi-final with an abdominal injury. 

The year-end number-one spot is up for grabs in London, with Nadal in the driving seat but Djokovic – the winner in Paris – ready to pounce.

Nadal has never won the ATP Finals, while Djokovic's last victory came in 2015 and Federer has endured an eight-year drought. 

Medvedev, Tsitsipas and Berrettini will each compete in the tournament for the first time, with the action scheduled to start on Sunday. 

Novak Djokovic is under no illusions over the size of the task he faces to claim the year-end number one ranking for the sixth time.

The Serbian beat Denis Shapovalov to seal his fifth Paris Masters title on Sunday, lifting his 34th Masters 1000 trophy in the process.

It kept alive his hopes of beating Rafael Nadal to the summit of the rankings at the end of 2019, but the 16-time grand slam winner knows he cannot afford to relent. 

"That puts me in a better position after this week. But, again, I have to keep on winning," he said after moving 640 points behind the Spaniard ahead of the ATP Finals in London.

"There's always a chance that I win all my matches in London, that I play well. I have done it in the past, and I like playing there. But it's [an] extremely difficult task considering who my opponents are going to be. You're playing a top 10 player every single match.

"So that's a big task on my end that I have to focus on. And as a consequence, if I manage to get the year-end number one, that would be, of course, fantastic."

Nadal withdrew in Paris ahead of his semi-final meeting with Shapovalov, citing an abdominal injury which could yet hamper him in London.

Djokovic was disappointed to see his rival pull out and hopes he is primed and ready to go at the season-ending tournament.

"I'm sad to see that he's injured because that's not what you want to see, not for Rafa, not for any other athlete," he said.

"I know how that feels. Obviously I went through major injuries in my life as well.

"I hope he can recover and compete in London. Because with or without him, obviously, also the battle for number one but also the tournament itself is different. He's a great champion and obviously lots of respect for him."

Novak Djokovic claimed his fifth Paris Masters title on Sunday with a straight-sets victory over Denis Shapovalov.

The number one seed triumphed 6-3 6-4 to lift his 34th Masters 1000 trophy - one short of Rafael Nadal's record haul - and keep alive his challenge to end the year at the top of the ATP rankings.

Having reached his first final at this level after Nadal withdrew from their semi-final with injury, Shapovalov, who lives in Nassau, offered plenty of swashbuckling style but gave up too many free points against a watertight Djokovic display.

The 20-year-old, who has taken only one set in three matches against the 16-time grand-slam champion, won only three of 17 points on his second serve as he lost in 68 minutes.

Shapovalov set about trying to force the ascendancy but two tight forehands when the court was at his mercy gave Djokovic an early break.

The Serbian dropped only four points on serve in the first set and Shapovalov smashed his racquet to the floor when he sent another return long in game seven.

Djokovic served out a clinical opening set with a hold to love and put his opponent under immediate pressure in the second, although Shapovalov dug himself out of a hole with a huge ace.

A terrific Shapovalov passing shot had the crowd on their feet, and he moved 2-1 ahead with a rasping forehand up the line, but he still could not make inroads against the Djokovic serve.

Djokovic was seething when he sent a backhand into the net when given a chance to go 30-0 up on Shapovalov's serve at 3-3, but three errors in succession handed the world number one the crucial break.

A long forehand gave Shapovalov his first break point in the next game, but a timely first serve and a missed backhand from the Canadian saw the opportunity pass him by.

Djokovic eased to three match points and promptly took tour-level title number five of 2019 with a crisp forehand, meaning his battle with Nadal for year-end number one will continue to the ATP Finals in London even though the Spaniard will move top of the rankings on Monday.

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