Roger Federer does not own Centre Court. Nobody does, nobody ever has. The most singular arena in sport does not go in for being owned, rather it will lend itself on a complex lease-hire system and is always ready to foreclose at the cruellest and least convenient moment.

The architecture does odd things to people's heads. Even with the roof half-finished, there is a strange sense of interiority about the place. It is disturbingly private and intimate. Sometimes it feels as if you are having 15,000 friends round to tea, at other times it's as if you were loitering in the bedroom of 15,000 strangers.

The court will let people have a taste of ownership, but then it will kick them out on to the street without a moment of remorse. It is an arena that dotes on its favourites and is generous and sporting to everybody else, but it is also the cruellest arena in sport. Those whom the place loves best end up suffering the most.

Which man has ever had a better right to call himself owner of Centre Court than Bjorn Borg? He won 41 successive matches at Wimbledon, the bulk of them on Centre. But in the end, when love was at its highest, the supreme court turned against him. Not the people, only the place itself, allowing a foul-mouthed interloper called John McEnroe to beat him. The one thing you can never do with Centre Court is to take it for granted.

Yesterday Federer won his 41st successive match at Wimbledon; most of them have been on Centre Court. He is through to the final tomorrow after playing three sets of marvellously controlled and accurate tennis against Marat Safin, winning 6-3, 7-6, 6-4. By the end Safin was reduced to chucking rackets, spreading his palms as wide as he could and trying to touch his ears with his shoulders, gestures not directed at his failings but at the ineffable futility of trying to beat Federer on Centre Court.

There is no question that the world No1 has been a changed man since he stepped out here 12 days ago. Illness, a stuttering clay-court season and a walloping by Rafael Nadal in the final of the French Open - all these things have filled everybody's mind with doubt. Everybody except Federer. And if you saw his absolute comfort and ease on the green grass of Centre Court, you could almost start believing it.

Yesterday he played like a man with home advantage. Safin never truly believed that he had a right to be on the court with Federer, save as a passing guest. Federer has yet to drop a set here this year.

Home matters. It is an atavistic thing. Everything to do with territory is about breeding and feeding. And it is a fact throughout nature that the holder of the territory has a considerable advantage over the invader, not only because he knows the place but also because being at home gives him strength. There is a species of fish for whom the mere fact of being at home makes it the certain winner of every fight over every invader.

Other species are less clear-cut and I suspect that tennis players are among them. But Federer has as much claim to ownership of this court as Borg. The question remaining is whether or not he can take the step that was beyond Borg.

Yesterday Federer's sense of being in his own place did for Safin from the start. The Russian lost his first service game in the match and, therefore, the first set, beaten before he had started. The combination of Federer and Centre Court had got to him.

In the second set Safin played six marvellously strong service games, only to chuck it away in the tie-break. Two unforced errors - but were they unforced? Against Federer, if you don't play your best shots every time, they will come howling back at you. So you go for your super-plus-best and that's why you miss straightforward shots, you just put too much on them. Federer not only plays good shots, he forces his opponent to play bad ones.

Sports psychologists make a big thing of the idea of making friends with the place of competition. They tell you to get the arena on your side. You will see competitors in all sports walking aimlessly about, idly playing with a ball, or just sitting about. Some do mental exercises, visualising themselves winning, others just absorb the vibes, telling themselves that they like the place, that the place likes them. Everybody just wants to feel at home - that's the crucial thing.

But Centre Court is always capricious. Sometimes it seems not so much like a court as a courtesan - beautiful, generous, but always capable of withdrawing her favours for no apparent reason, just because she happens to feel like it, or more usually, because she has a thing for a younger man.

The wresting of Centre Court from Borg was the biggest happening in men's tennis in the Open era. Now, more than a quarter of a century later, we have another great champion fighting to keep his ownership of the greatest arena in sport. It is Federer's place and so Federer has the edge, at least to start with. But you presume on Centre Court at your peril. In the end, it always eats the ones it loves the best.