ATP Finals: Rafael Nadal knocked out of ATP Finals after Alexander Zverev beats Daniil Medvedev

Nadal beat Stefanos Tsitsipas 6-7(4) 6-4 7-5 earlier to keep his semi-finals hopes alive, but he needed Medvedev to beat Zverev on Friday evening in order to go through.

And unfortunately for him, defending champion Zverev was on fine form. The German was imperious on serve once again, and after breaking Medvedev early in the first set things looked bad for Nadal waiting in the wings.

Medvedev took Zverev all the way in the second and threatened a deciding set, but the defending champion saw off his opponent in the tie-break and goes through to play Dominic Thiem in the semi-finals. Tsitsipas plays Roger Federer.

In Nadal's earlier match against Tsitipas, neither player faced a break point in a tight first set that went to a tie-break, with the Greek world No 7 edging Nadal after the Spaniard struck the net and sent a forehand long, leaving his ATP Finals hopes on the brink.

But the stubborn Spaniard bounced back in the second set, landing 86 per cent of his first serves before finally breaking Tsitsipas in game five and serving out the set to draw level.

And Nadal only improved, especially at the net where he was at his imperious best, and remarkably survived the entire match without facing a break point while unforced errors began to creep into his opponent's game.

In the third and final set the world No 1 twice went close to breaking a resilient Tsitsipas before the Greek finally relented and was broken in the 11th game, giving Nadal a chance to serve out for the match.

Nadal made no mistake, but with Tsitsipas having already confirmed his semi-finals spot with wins over Medvedev and Zverev, Nadal - who lost to Zverev on Sunday - needed a Medvedev win.

It wasn't to be, but Nadal at least had already ensured he will end the year as world No 1 after Novak Djokovic was knocked out of the finals by Federer yesterday, and was presented with the trophy after beating Tsitsipas.

"It's a real honour to receive this trophy. Honestly, what can I say? I am super happy," said Nadal.

"After all the things I went through in my career in terms of injuries, I never thought at the age of 33 and a half I would have this trophy in my hands again. It's something really, really emotional for me, a lot of work. Without all my team and family that is here, this would be impossible, so thank you very, very much."