Semi-finals day. The two-time Wimbledon champion against the US Open finalist. Carlos Alcaraz vs Taylor Fritz. What will it come down to?

Those of a mathematical bent will rely on the numbers; after all, what is sport without a good stat? But if we start there, we are none the wiser.

Fritz, according the numbers, has the better serve in that he is second on The Championships leader board with 95 aces to Alcaraz’s 62. As for the return games of both men, Alcaraz has landed 71 per cent of his returns successfully – seven of them were outright winners – and has won 31 per cent of his return games. Fritz has landed 65 per cent of his returns, with 11 winners, and won 20 per cent of his return games.

Does this mean that Alcaraz’s return will, undoubtedly, nullify Fritz’s serve? If only it were that simple.

What makes all sport so riveting is that it is played by people. Human beings with emotions, with ambitions and anxieties, with strengths and frailties – all of which can be on display in the course of one rally. No amount of number crunching can account for that.

What we do know is that both men are feeling remarkably relaxed after their first five rounds and both are supremely confident.

Fritz came here on the back of an excellent grass court run-in – two titles won – while Alcaraz played (and won) only one event on grass after winning the trophy at Roland-Garros almost five weeks ago.

The American and world No.5 is playing his first semi-final here. In past years, he has reached the quarter-final stage and regarded it as a hurdle to overcome rather than another stage on the journey to the final. But not this year. The stress levels have been reduced by the experience of reaching the final in New York last summer and that, he believes, will help him as he faces Alcaraz.

“It gives me a lot of confidence that I've been here before, and I've played the pressure matches,” he said. “I don't think anything's going to get more stressful than me playing Frances [Tiafoe] in New York for a spot in the final.

“I also really do think I'm a much better tennis player than I was a year ago or even two years ago. I think right now I'm playing at a much higher level in tennis than I was.”

That certainly helps, but Alcaraz has been here twice before – and then gone on to lift the trophy. After struggling with his serve for the first couple of rounds, everything has clicked into place this week and he is playing with freedom and with a smile. And as he always says, when he smiles, he wins.

“I say that every time, once I started to enjoy the match, enjoy the moment, I think my level showed up, my good level showed up,” he explained after beating Cameron Norrie on Tuesday. “I think today was the key that I didn't think about anything. I just enjoy every single second out there.

“Playing a quarter-final at Wimbledon is a gift. I just tried to make the most of my time stepping on the court, Centre Court. Such a great atmosphere out there. It's a pleasure for me. I try to enjoy as much as I can. I think I show really great tennis.

“It's difficult to compare the level from previous year. But what can I say right now is just my confidence is really high, to be honest. Just feeling great.”

His serve started to fire in the fourth round against Andrey Rublev (apparently the problem was the ball toss) and once he was happy with that, the rest of his game took off.

“On grass when you're serving great or you feel you're serving great,” he said, “then playing from the baseline or playing the return games, you’re just going with more confidence and just playing more calm and thinking clearly. So I think feeling great in the serve, it gave me a lot of calm then to playing great tennis from the baseline.”

Despite his 95 aces, Fritz, too, thinks his serve has improved as the rounds have gone by and he thinks that the surface could favour him rather than the defending champion. 

“[Grass] can be an equaliser,” he said. “So I trust in how I'm playing. I truly know the way that I played the first two sets today [against Karen Khachanov] there's not much any opponent on the other side can do.”

That match went to four sets as, after playing two brilliant sets, Fritz lost his way for a spell. But he did what few players can: having been in “the zone” and then been shut out of it, he retraced his steps and found a way back into that mental state of calm and confidence that allowed him to play as he had at the start. That takes some doing in the heat of battle.

What will it come down to? Fractions. Not numerical fractions but fractions of difference in how each man is feeling, how he reacts to the moment and the opportunity. In other words, none of us knows how the match will pan out which is why we are all fascinated by the prospect.

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