So, we're not giving you live text updates from this match - that's the bad news.
The good news is you have no excuse not to listen to ball-by-ball coverage by our BBC Radio 5 Live Sports Extra team at the O2 Arena instead.
Click the audio tab to tune in. We're sure Rafa Nadal will be...
That's because Nadal can still qualify for the semi-finals, as can Alexander Zverev, but Rafa needs the already-eliminated Medvedev to do him a favour.
Here are the possible scenarios for Saturday's semi-finals:
If Medvedev beats Zverev, Nadal faces Federer and Tsitsipas plays Thiem
If Zverev beats Medvedev, Tsitsipas faces Federer and Zverev plays Thiem
Goodbye!
I am off for a lengthy lie-down .
You can catch up on that cracker of a match over here and 5 live sports extra will guide you through the final group match between Alexander Zverev and Daniil Medvedev.
We'll be back tomorrow for the semi-finals.
Until then!
Video content
Video caption: ATP Finals: Rafael Nadal beats Stefanos Tsitsipas in ATP FinalsATP Finals: Rafael Nadal beats Stefanos Tsitsipas in ATP Finals
Post update
More from Rafael Nadal: "There have been some bad moments and you [my team] have been always there so honestly, like this year, before Monte Carlo, after Monte Carlo, without the support of all these people, things will be much different to me. They encourage me to keep going and I can't thank them enough.
"This trophy is an achievement for all year around so personally today I can't thank enough to all of you for all the support in this personal match and all the time I have been playing here in London.
"But at the same time I have to say because it's something I really feel from the bottom of my heart, to all the fans that give me their support from around the world.
"I don't know if i see you tomorrow because it depends on this afternoon's match but I did all that I could today. If i am able to play in front of you tomorrow against Roger, it will be a huge honour.
"If not, I really hope to see you next year."
Post update
World number one Rafael Nadal, speaking on court: "It's a real honour to receive this trophy. Honestly, what can I say? I am super happy.
"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."
Post update
Nadal 6-7 (4-7) 6-4 7-5 Tsitsipas
Nadal's going to pose for some photos and watch a highlights reel of his year so far.
He probably just wants a nice sit down and a bottle of water.
Live Reporting
All times stated are UK
Post update
So, we're not giving you live text updates from this match - that's the bad news.
The good news is you have no excuse not to listen to ball-by-ball coverage by our BBC Radio 5 Live Sports Extra team at the O2 Arena instead.
Click the audio tab to tune in. We're sure Rafa Nadal will be...
That's because Nadal can still qualify for the semi-finals, as can Alexander Zverev, but Rafa needs the already-eliminated Medvedev to do him a favour.
Here are the possible scenarios for Saturday's semi-finals:
Goodbye!
I am off for a lengthy lie-down .
You can catch up on that cracker of a match over here and 5 live sports extra will guide you through the final group match between Alexander Zverev and Daniil Medvedev.
We'll be back tomorrow for the semi-finals.
Until then!
Video content
Post update
More from Rafael Nadal: "There have been some bad moments and you [my team] have been always there so honestly, like this year, before Monte Carlo, after Monte Carlo, without the support of all these people, things will be much different to me. They encourage me to keep going and I can't thank them enough.
"This trophy is an achievement for all year around so personally today I can't thank enough to all of you for all the support in this personal match and all the time I have been playing here in London.
"But at the same time I have to say because it's something I really feel from the bottom of my heart, to all the fans that give me their support from around the world.
"I don't know if i see you tomorrow because it depends on this afternoon's match but I did all that I could today. If i am able to play in front of you tomorrow against Roger, it will be a huge honour.
"If not, I really hope to see you next year."
Post update
World number one Rafael Nadal, speaking on court: "It's a real honour to receive this trophy. Honestly, what can I say? I am super happy.
"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."
Post update
Nadal 6-7 (4-7) 6-4 7-5 Tsitsipas
Nadal's going to pose for some photos and watch a highlights reel of his year so far.
He probably just wants a nice sit down and a bottle of water.
From the press box
Nadal 6-7 (4-7) 6-4 7-5 Tsitsipas
Post update
Nadal 6-7 (4-7) 6-4 7-5 Tsitsipas
Rafa is going to celebrate his win by being presented with the trophy for finishing as the year-end number one.
Lovely stuff.
Post update
Nadal 6-7 (4-7) 6-4 7-5 Tsitsipas
That was an absolute corker.
Still, there could be some tired bodies in those semi-finals.
Post update
Nadal 6-7 (4-7) 6-4 7-5 Tsitsipas
Rafa will need Daniil Medvedev to beat Alexander Zverev this evening if he is to advance to the last four and play Roger Federer.
We'll hear from him shortly - he's just, er, nipped off for a comfort break.
Game, set and match - Nadal
Nadal 6-7 (4-7) 6-4 7-5 Tsitsipas
He's done it!
A proper grinding victory from Rafael Nadal - and he might not even make the semi-finals!
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*Nadal 6-7 (4-7) 6-4 6-5 Tsitsipas
Very, very good from Rafa Nadal!
He outfoxes Tsitsipas on the run and, after two hours and a lot of minutes, he's got two match points.
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*Nadal 6-7 (4-7) 6-4 6-5 Tsitsipas
Tsitsipas picks a horrible time to shank a forehand flick over Nadal's head.
30-15.
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*Nadal 6-7 (4-7) 6-4 6-5 Tsitsipas
Rafa can't buy a first serve at the minute, and his second is promptly battered back past him by Tsitsipas for a winner.
15-15.
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*Nadal 6-7 (4-7) 6-4 6-5 Tsitsipas
Long goes a Tsitsipas forehand, by the tiniest of margins!
Tsitsipas challenges but the line judge is proved right.
15-0.
Nadal serving for match
*Nadal 6-7 (4-7) 6-4 6-5 Tsitsipas
Rafa bounces the ball and goes through his pre-serve routines.
Off we go...
Post update
*Nadal 6-7 (4-7) 6-4 6-5 Tsitsipas
Tim Henman
Former British number one on BBC Two
The quality has just never dipped. Side to side, incredible athleticism, racquet head control on the run, balance.
Post update
*Nadal 6-7 (4-7) 6-4 6-5 Tsitsipas
Two hours 48 minutes and we've got at least another game to go.
The semi-finals are tomorrow, by the way. Ouch.
Nadal breaks to serve for match
*Nadal 6-7 (4-7) 6-4 6-5 Tsitsipas
Tsitsipas gets to the net, in the perfect place for the volley... and he pushes it wide!
My WORD. Nadal will serve for the match!
Post update
Nadal 6-7 (4-7) 6-4 5-5 Tsitsipas*
A lengthy baseline exchange, and it's Tsitsipas who pushes his backhand into the foot of the net!
Break point for Nadal, once again...
Tsitsipas saves break point
Nadal 6-7 (4-7) 6-4 5-5 Tsitsipas*
A strong serve out wide and Nadal eventually pushes his shot just, just, wide of the tramline.
Deuce.