You could not have asked for a more popular result. Roger Federer, the man whose face was missing from the ATP’s promotional posters, thanked the fans at the O2 after they cheered him into the semi-finals with a 4-6, 7-6, 7-5 win over Juan Martin del Potro.

One had to feel for del Potro, for if crowd support can lift a player to greater heights, he was effectively starting at 0-30 in every single game.

Even the organisers of the Barclays ATP World Tour Finals must have been pulling for Federer, in the knowledge that a victory would set up a show-stopping meeting with Rafael Nadal .

“Having that playing-at-home feeling, maybe in any sport, soccer or tennis, I just feel you give it a shot, you kind of go for it, and the risk pays off,” said Federer afterwards.

“When the crowd is for your opponent, you might play a little more tentative. I think that’s what’s been happening for me. I’ve been willing to take the risk, move forward, even though the unforced errors are piling up.”

Federer v Nadal XXXII can now be inked onto Sunday's schedule, starting at 2pm, and it is a surprisingly tricky one to call.

Yes, Nadal has been almost irresistible in 2013, with a record to date of 74 wins from 80 matches. Federer, meanwhile, only sealed his ticket for this event ten days ago, which is why his image could not be used too heavily in promotions.

But the O2 Arena seems to suit Federer as well as it does Rihanna and the Rolling Stones. In 2011, he simply carpeted his oldest rival here in a 6-3, 6-0 schooling that occupied just 60 minutes and still stands as the most one-sided meeting in their nine-year series.

The memory of that great day could well inspire him to forget his recent frustrations.

“I will maybe play with a little less pressure than I have in previous matches maybe with him,” said Federer.

“I just feel like I need to look at it more as being an underdog a little bit because of circumstances, because of my year, because of the year he’s had.

“Maybe that free swinging is what I kind of need to do a little bit more tomorrow.”

Federer has now played del Potro three times on indoor courts in as many weeks, and each match has gone to a deciding set.

You do at least know what you are getting when you go up against the big Argentine, who is so powerfully built that he could have played second row at Twickenham.

The racket comes through with the force of a sledgehammer.

Like most of the best matches, it was a contrast of styles with Federer darting forwards at every opportunity and throwing in slices, lobs and drop-shots to break up the rhythm.

He was broken early in every set, but showed a level of self-belief that has not always been evident this season to fight back each time. His best tennis came on the biggest points, which is another encouraging sign.

The match threw up the rally of the tournament when del Potro managed to hit a perfect lob through his own legs with his back to the net.

Yet Federer scampered back and produced his own piece of magic, a sort of ramp shot of the kind you sometimes see in Twenty20 cricket, where he flicked the ball over his own head.

As the crowd gasped, he finished the point with a winning forehand pass.

This week has clearly meant a good deal to Federer, whose sheer desire spilled over into a testy exchange with a lineswoman.

Her poor call of “out” led to a rally being restarted, and when del Potro promptly served up an ace, Federer made sure to point out to her that she had cost him a point.

But then such commitment is what drives him on even now, when he has 17 grand slam titles in his pocket and enough earnings to sustain a lavish lifestyle for the next 300 years.

The fans at the O2 were certainly delighted to see him out there, still fighting for every inch.

Standing outside the world’s leading rock-music venue, you would have seen a stream of shiny happy people go past.