A straight sets win, a place in the third round booked and back in the locker room after a brief 94 minutes on court – Daniil Medvedev could not have been a happier man.

The No.2 seed eased past the 18-year-old Carlos Alcaraz, Spain’s latest, greatest hope, 6-4, 6-1, 6-2. But if the scoreline suggests that it was a one-sided clumping, Medvedev was at pains to point out that it was anything but.

Yes, he won, but he has been to two Grand Slam finals and has been at the very top of the game for a couple of years. Alcaraz is just starting out on his career and already ranked No.75, he has a brilliant future.

“Carlos is an amazing player,” he said, “and I was actually surprised in a way in the first set because grass is not his best surface but he was giving it all there. Of course, second and third sets maybe the gap was too high but I’m sure he’s going to be sooner or later in the top 10 and maybe even higher.

“What he is doing is pretty special because in his first Grand Slams, he’s made a victory in Australian Open, made third round in Roland-Garros [and won a match here]. My first four Grand Slams, I had actually only one victory and it was here in Wimbledon on Centre Court. So Wimbledon is always going to be special for me.”

Alcaraz has been described as the “new Rafa”. This billing is built on a solid foundation of tennis knowledge: he is Spanish and he is good. Punditry can be like that sometimes.

The man himself would not agree – were he vain enough to do so, he would call himself the “new Roger”. But he is not vain at all. What he is is an aggressive player who has a thumping forehand, a deft touch and absolutely no fear of the net.

Juan Carlos Ferrero, Alcaraz’s coach, meanwhile, holds no truck with these predictions and comparisons. As a player, he was never one for flights of fancy; it was hard work, dedication, self-belief and – of course – talent that took him to the Roland-Garros title, two further Grand Slam finals and the No.1 ranking. And that is what he wants from his charge. Alcaraz is not the new anybody; he is the current Carlos and he still has a lot to learn.

That said, by breaking into the top 100 back in May, Alcaraz became the second youngest man to achieve the feat since a certain R. Nadal of Mallorca (who was 16 when he did it in 2003). And as he took to the court against the world No.2, he was trying to become the youngest man to reach the third round here since the 18-year-olds Andy Murray and Novak Djokovic in 2005. And they turned out all right.

Then again, Medvedev has been creating his own little bit of history of late, too. When he made his way to the No.2 spot in the rankings, he became the first man not called Federer, Nadal, Djokovic or Murray to set up camp there since July 18, 2005. That is 16 years ago, almost to the day (and we know that you could have done the maths yourselves but we were just making the point: that’s a very, very long time).

He got there on the back of reaching the Australian Open final in February and then going on to win the Marseilles title in March. Suddenly he found himself looking down on Rafael Nadal and staring at the heels of Novak Djokovic. Not only that but for the past few weeks, he has been in a position to overtake Djokovic at the top.

He could have done it by winning Roland-Garros and hoping that a few other results went his way and he could do it here, too. If Medvedev reaches the final and Djokovic doesn’t, the Russian will become world No.1. And if they both get to the final, as they are seeded to do, it will be a straight shoot-out for the top spot.

But all the mathematical permutations are based around events at the sharp end of the tournament; on Thursday, Medvedev was still navigating his path through the first week and as he got to work against his young rival, it soon became clear that he planned on taking the most direct route.

In his first four service games, he dropped just one point and he had secured an early break, to boot. He was 5-3 up and in total control. And then he went to serve for the set and made a hash of it. Alcaraz perked up – he may have been taking a pasting but this was a glimmer of hope. Medvedev snuffed it out again in the next game, but the young man from Murcia was definitely feeling a bit better about life.

The problem was that Medvedev was just too good and too experienced on this green stuff and just too good and too experienced at this Grand Slam business. As the Russian accelerated into the third round, the new Rafa, the wannabe Roger and the could-have-been Novak and Andy was on his way home. But he would be back and he would be older, wiser and a real threat to the great and the good.