In the twilight of his greatness Roger Federer chases the ball with the dignified desperation of a man who is running out of tomorrows. He's late to the ball against Marin Cilic yet he hustles for it. In the early segments of their five-set fisticuffs in the Wimbledon quarter-finals, his backhand is like a used-car part, his forehand lacks whip but he keeps playing.

One shot, then another, in the hope that timing will return and feel will arrive and he'll stop being this misspelling poet. At times the most awkward truth abruptly lies before us: This game no longer looks simple to this player. And yet even in his misery he looks unruffled.

Every champion has a quota of wins, an allocation of titles, and then they revert to mortality. But Federer's not done yet, he'll play as long as Centre Courts will host him and crowds rise for him; he'll play as long as the crisp beauty of a flicked forehand is still fun for he is the anti-Kyrgios who finds pleasure in his work; he'll play as long as men look up at break point before serving and occasionally still think, "S***, it's Roger".

Federer still wants to compete and people still want to watch. They're invested. No, they're emotional. My nephew, 25, in Delhi, messages me an emoticon of hands folded on Wednesday. My son-in-law, 34, in Melbourne, can't bear to watch. My neighbour, 45, in Singapore, is so nervous after the fourth set that she calls to say she's coming over. My mother, 83, hangs up the phone if I question Federer's chances. There's more prayer at work here than assurance.

People of every age want him to win because if he does win he stays in the tournament and in tennis, and if he stays they don't lose something, and what they are scared of losing isn't just another athlete but an entire style of sport. He's the one, a fan tells me, who will be "exhibit A when we say 'it was better in my day'."

People have trust in the old guy maybe because the old guy has some faith in himself. Else how does he stagger into a Wimbledon semi-final in a year when he's played only 22 matches (Novak Djokovic has played 47), not won a title for the first time since 2001, been beaten by a 19-year-old kid called Alexander Zverev, had his knee surgically repaired, his back worked on and part of his confidence cut away?

Champions in distress rummage through their memories for reassurance: Oh, we've been here before. And yet he has never done this before, nothing quite like this, not at 34, not when he hasn't played a five-setter since 2014, not when five-setters make you wonder, as he says, "Can your shoulder, your back, your legs, can they sustain 3 hours 17 minutes of just hitting big serves, running, being explosive?"

Anyway his memory is clogged with other stuff, crammed with artfully angled backhands and inventive half-volley flicks, but this was another Federer, an original work, scrappy and scrapping, digging and grinding, not the imperious strokemaker but a survivor with dirt under his manicured fingernails. In his grit lay a different beauty.

Two lefties from a more rugged tennis school would have approved of this Federer. Jimmy Connors, whom he equalled with 84 Wimbledon wins, would have spat at his feet in congratulation because this was a Jimbo-type comeback, raw and tense, if a little better behaved. Nadal would have just smiled. Federer can be a casual narcissist, aware of his own beauty, yet when he said "I fought, I tried, I believed," it sounded like a phrase borrowed from the Spaniard's vocabulary.

Eventually Federer warmed up like a slow-starting car, his game returned and he stroked one backhand down the line, on the run, of such precision that it seemed hit with a set square, not a racket.

He will need this today, early on, consistently, for Milos Raonic is nine years his junior, his fastest serve (230kmh) is 11kmh quicker than Cilic's, he's served 114 aces, he's beaten Fed this year and he'll be all over the net like a famished pterodactyl.

Will Federer be ready for Raonic? Who knows, but he will be there, in his 11th Wimbledon semi-final, headband on, all white, twirling his racket. In a beautiful story recounted in The Guardian, the Japanese artist Hokusai, dying at 88, said: "If heaven would only grant me 10 more years, I might still become a great artist." Federer knows he is a great artist but he just hopes life will grant him more tennis to show it off.

The game, of course, no longer belongs to him and yet stadiums still do and Raonic will be given audible proof today. Once the Swiss needed no help, not even a coach, now he needs the cheering mob; once spectators sipped Pimm's and swooned and now they tightly hold four-leaf clovers in hands whose fingers are crossed. Federer-watching has become harder work. Perhaps because subconsciously no one's ever sure if this is the last goodbye.