Shortly after Roger Federer had defused Milos Raonic’s power game with a deftness and elan that ranked alongside many of his great Wimbledon performances he was asked whether he could explain how, aged 35 years and 342 days, he was playing so well. His response was startling. “This year I’m just a normal tennis player again.”

Normal was not an adjective anyone who watched Federer’s 6-4, 6-2, 7-6 (4) victory in his 100th match at the All England club would have chosen. The No3 seed was sensational, winning 90% of his first-serve points, thumping 46 winners to nine unforced errors, and moving like a panther around the court.

“I am much better prepared for Wimbledon this year,” the Swiss said. “In 2016 I had a hard time practising – back and knee injuries. In matches I couldn’t play freely. But I am normal again so I can focus on tactics.”

Certainly the sustained quality of his play made a believer out of Raonic, who had beaten him over five thrilling sets in the semi-final last year, with the Canadian saying an eighth title is within Federer’s grasp.

“I think the most significant things are he’s mentally sharper, and he’s moving better,” Raonic said. “You can see there’s not much doubt in his mind. He’s feeling it.” He was then asked whether he was disappointed. “No, I did everything I could.”

No wonder that with Andy Murray and Novak Djokovic slinking out of the tournament on Wednesday, Federer is a prohibitive favourite with the bookies – with the No11 seed Tomas Berdych lying in wait in the semi-finals and either the No7 seed Marin Cilic or the No24 Sam Querrey due in the final. But Federer is not getting ahead of himself.

“These other guys are all big-hitters,” he said. “All three guys are taller and stronger than I am. I’ve got to figure out a different way, carve my way through the draw somehow with my slice and my spins, my consistency maybe.”

Federer barely got a look-in during Raonic’s first service game but quickly began firing winners from both sides – and was rewarded with a break in the fifth game. With his service game seemingly a foreign language to Raonic, Federer ran away with the set. It seemed there was no way he could keep up his level. Instead it went even higher as he broke Raonic twice to win the second set 6-2.

At this stage Centre Court was in raptures at the sight of vintage Federer – blunting his opponent’s power, getting into the rally, and then squeezing Raonic until his pips squeaked. The Canadian could have wilted. Instead he fought back and had the better of the third set only to squander a breakpoint in the second game and then four more in the eighth.

That did not appear to matter when the No6 seed went 3-0 up in the third set tie-break. Yet Federer then went on a five-point run which included a running backhand winner which had his opponent shaking his head in disbelief. An ace then brought him to match point before a loose forehand from Raonic into the tramlines ended matters after one hour and 58 minutes.

Play Video 2:02 Wimbledon 2017: Murray and Djokovic down and out on day nine – video highlights

On Friday he will play in his 12th Wimbledon semi-final – one ahead of Jimmy Connors – and it makes him the second oldest man in the open era to reach the semi-finals after Ken Rosewall, present in the royal box and who finished runner-up to Connors in 1974 three months before his 40th birthday.

After this stunning victory, however, Federer will have his eyes on the biggest prize of all. And on this evidence, few would bet against him.