Federer takes his place at game's summit | Simon Barnes: statistics back up artistry | Federer has a hand in women's title as well | Graphic: grand-slam roll of honour | Debate: is Federer really the greatest of all time? | Debate: is Federer really the greatest of all time? | Federer's career in pictures

I expect we can all remember that first Federer moment, the time we saw, blinked and muttered in disbelief: “This could be the greatest tennis player that ever drew breath.” Well, we were all right. Roger Federer really is the greatest tennis player of all time. At last he has the stats to prove it, and the stats don’t lie.

He won the French Open yesterday. He has now won 14 grand-slam titles, drawing level with Pete Sampras. What is more, he has now won at every modern grand-slam venue, on all four different surfaces: the only other man to have done that is Andre Agassi. Combine these two Himalayan achievements and there, perched on Everest and in tears once again, is Federer, the greatest mountaineer of them all.

You argue about the lost years of Rod Laver, but this is just pub talk. Federer has the numbers, 14 and four, and they add up to greatness. Greatness is one of the few sporting terms we treat with caution, but yesterday Federer countered every possible objection.

He stood soaked by rain and tears before the massed parapluies of Paris, revealed to all as one of the greatest performers to take part in any sport.

His victory over Robin Söderling at times touched the loftiest height of brilliance. His dominance was complete: as we moved into the last fraught couple of games, it was clear that the only obstacle in Federer’s way was history. History filled him with last-lap nerves, but his serve on match point was a killer, Söderling duly netted his return and the rest was all weeping and rejoicing.

Federer has earned this. He has paid for yesterday’s triumph in the pain and suffering caused by a huge ambition — to be the best ever — and an implacable opponent over the years in Rafael Nadal. When Nadal beat him in the final of the Australian Open in January, Federer looked a broken man, weeping the salt tears of a man who fears he will never reach his heart’s desire.

It has been a hard and bitter road at this championship alone. Federer has been involved in two five-setters and looked a goner in both. Every five-set victory is a triumph of the will, to collect two in a single tournament is extraordinary. He has stuttered and faltered, played some truly ugly points, made some hideous unforced errors and played at times in a way that made his millions of supporters despair.

But again and again he found something more. That, every bit as much as his wonderful racket skill, is what Federer does best. He can raise his game and then raise it again. He has more raises than any one else in history. In the second set yesterday, Söderling kept pace. Federer had given us a first set close to perfection, but the appalling security lapse that allowed an intruder on court to frolic unhindered for 18 seconds broke the spell. Söderling then went toe to toe with Federer until the tie-break, but then Federer made one of his epic raises and that was the match.

It was in this passage of play that we had a sudden, piercingly clear vision of the real secret of Federer’s greatness. Federer raised as only Federer can. In the eight points of the tie-break, he served four times and served four aces. He also dismantled Söderling on his own serve, winning 7-1. After that, it was just a matter of counting down the games and keeping pulse and respiration under some kind of tenuous control.

There is a connoisseurs’ stat we should look at. Federer has now played in the semi-finals of the last 20 grand-slam tournaments. This consistency, on all surfaces and all climates against all opponents and over five years is devastating. It’s not the same as winning: the point is that he has been in there with his best chance every single bloody time.

Federer’s game is a thing of wonder and beauty: we all know this. Most of us realised that we were in the presence of something truly special at Wimbledon in 2003, the first year he won. Magic, we called. Or art. At his best moments Federer seems to be looking beyond victory to create a masterpiece.

But beyond this, he has this quite extraordinary consistency, a testament to mental and physical strength, and above all, testament to the fact that tennis enthrals him. He is never bored by its triumphs nor cowed down by its inevitable reverses.

Consistency is an unromantic virtue, but not every aspect of greatness is romantic. Just being there over and over again really matters.

Nadal has pursued Federer like the furies across the tennis world, and holds a winning record over him. But Nadal was beaten in the fourth round here and Federer was there, as always, and he took his chance. And now Federer knows that he is the greatest of all time, perhaps he will set about Nadal in a different frame of mind.

Indeed, now Federer has got rid of the weight of history, we may see him freed from the fear that he would fall short of his goal. And perhaps he will play now with total freedom, total confidence, total certainty in his new role as the unquestioned champion of all champions. At Wimbledon, a fortnight away, we may just see Roger Unbound.