Postpublished at 19:36 GMT 18 November 2018
Djokovic 4-6 3-6 Zverev
Alexander Zverev becomes the ATP Finals champion and the first German to win the tournament since Boris Becker. Only had to beat Roger Federer and Novak Djokovic to do it.

Alexander Zverev beats Novak Djokovic 6-4 6-3 to win ATP Finals
German, 21, wins season-ending title for first time
'The biggest title I have ever won,' says Zverev
Zverev lost to Djokovic in straight sets in the round-robin stage
World number one Djokovic had not lost a set until the final
Emma Sanders
Djokovic 4-6 3-6 Zverev
Alexander Zverev becomes the ATP Finals champion and the first German to win the tournament since Boris Becker. Only had to beat Roger Federer and Novak Djokovic to do it.
Djokovic 4-6 3-6 Zverev
The first is saved with a serve and volley from Djokovic and Zverev asks the umpire to tell someone in the crowd to turn their flash off on their camera.
Another rally then breaks out and Zverev gets the break and the title with a sublime forehand passing shot!
He falls to the ground in disbelief and Djokovic comes over to congratulate him.
Alexander Zverev beats Novak Djokovic to win ATP Finals
*Djokovic 4-6 3-5 Zverev
Djokovic volleys a forehand into the open court. 15-0. But Zverev's return pushes the serb wide and he puts away a forehand into the court to draw level. 15-15.
A double-fault brings up 30-15 for Zverev and he gets two championship points when Djokovic overcooks a backhand.
*Djokovic 4-6 3-5 Zverev
One service game down, one more to go.
*Djokovic 4-6 3-5 Zverev
Zverev swats a lovely wide ace to move 15-0 up. His second serve can only be swept into the net by Djokovic. 30-0.
Djokovic returns the next one long but Zverev can't put away the passing shot. 40-15. He holds comfortably though with a cross-court forehand.
Djokovic 4-6 3-4 Zverev*
Zverev needs to hold two more service games to win the ATP Finals title. He's only got the world number one, the US Open and Wimbledon champion and the best returner in the game on the other side of the court.
No pressure.
Boris Becker
Three-time Wimbledon champion on BBC TV
Novak's got a different look on his face today. It's the whole body language, his whole attitude.
Djokovic 4-6 3-4 Zverev*
Djokovic's backhand flops into the net again but he responds coolly with an inch-perfect backhand slice volley.
Zverev then hooks a forehand wide before a fizzing serve is returned long. 40-15. Zverev then blasts a backhand into the net and Djokovic unconvincingly holds.
Tim Henman
Former British number one on BBC TV
Djokovic was winning 81% of second-serve points in the tournament. He's yet to win a second-serve point in this second set.
Boris Becker
Three-time Wimbledon champion on BBC TV
It's going to bother Djokovic that the crowd are supporting the young gun, the 21-year-old. That's bothering him.
*Djokovic 4-6 2-4 Zverev
A double-fault from Zverev is greeted with a huge groan from the German. The crowd fall silent and ripples of nervousness spreads around the arena.
He falls to 30-0 down but recovers to tip the ball into the corner after moving into the net. And Djokovic sends a forehand long. 30-30.
He moves onto 40-30 with another good serve and holds when Djokovic's passing shot fails to beat the net.
Leon Smith
GB Davis Cup captain on BBC Radio
Djokovic has to test the agility of Zverev and somehow get him off balance. But it's easier said than done when Zverev is serving so well and has been coming out on top more often than not when Novak has had him on the run.
Djokovic will have to come out of his comfort zone and take a few more risks, which is not in his nature, but he needs to inject more pace into his shots.
#bbctennis
Arantcha Sanchez: A great game, it does not matter who wins!
Vincent James: Come on Alexander. You can get this done. I am rooting for you Alex. I know how hard it is to beat Novak. But you can do it.
Helen Fothergill: This is a different Zverev to the one we saw on Wednesday.
Get in touch using #bbctennis on Twitter or via text on 81111.
Boris Becker
Three-time Wimbledon champion on BBC TV
Sooner or later, these 20-somethings have to step up to the plate. Zverev is the best of the lot and he's the first one to do it.
Djokovic 4-6 2-3 Zverev*
Djokovic is up to 40-0 in no time and he comfortably holds with an ace. That's how to keep up the pressure...
Now, what does Zverev have?
*Djokovic 4-6 1-3 Zverev
He makes a good start with a 140 mph ace. Nice! But Djokovic quickly storms ahead to 30-15 as Zverev sends his forehand over the baseline in another intense rally.
The German serves down the T and Djokovic can only hook it over the baseline. 30-30. And the world number one sends his next forehand long. 40-30.
Zverev holds, just, when his passing shot is saved by Djokovic at the net but only for the Serb to volley into the cords on the next time of asking.
#bbctennis
Chanice Hird: Novak you ok Hun? Someone want to tell him to hold his serve?
Brendan: It's not often you see Djokovic out-rallied by an opponent, but Zverev has brought his A-game today. Some brilliant tennis on display.
TJ Hilton: COME ON ZVEREV XX
Get in touch using #bbctennis on Twitter or via text on 81111.
Djokovic 4-6 1-2 Zverev*
Djokovic is feeling it.
He's gasping for air following those lengthy rallies and Zverev gets the break back again on the first time of asking as the Serb flops another forehand into the net.
Now, can the German hold on to his advantage this time?
*Djokovic 4-6 1-1 Zverev
Djokovic is still not quite there yet. He falls down to 30-15 as a 28-shot rally ends in Zverev's favour when he plants one into the net.
The Serb crouches down to catch his breath and slices his backhand into the net. Two break points for Zverev...
*Djokovic 4-6 1-1 Zverev
Tim Henman
Former British number one on BBC TV
It will be interesting to see how Zverev reacts to that. He's obviously still in a great position but it certainly wasn't one of his better games this week.
On the other side of the net, it is the kind of reaction you expect from the best player in the world.