What is the greatest Wimbledon final of all time?

It’s a deeply personal matter, of course, like choosing your favourite Beatles song. On what grounds do you choose?

Partisanship? In that case, you must go for Andy Murray’s first win in 2013, or perhaps Virginia Wade’s historic win in 1977.

Drama? That will be Goran Ivanisevic’s victory over Pat Rafter in 2001, or the agonising, eternally oscillating struggle between Roger Federer and Rafael Nadal in 2008 – though, on that occasion, I felt that the tension became genuinely unbearable. A human dramatist would never have let things get so out of hand.

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On the women’s side, there is the parade of brilliance from the Williams sisters, the victory of the 17-year old Maria Sharapova over Serena in 2004, and the athletic glory of Martina Navratilova. But in the end, my choice is the 1995 final between Spain’s Arantxa Sánchez Vicario and Steffi Graf of Germany.

The eleventh game of the final set, with Sánchez Vicario serving at 5–5, went on for 20 minutes. They played 32 points, with 13 deuces and 18 game points, of which six were break points. When Graf finally broke the Spaniard’s serve, the crowd stood and applauded throughout the changeover.

It was a classic example of the minute difference between the very, very good players and the all-time greats. Sánchez Vicario had attacked Graf’s backhand relentlessly, a policy that took her within touching distance of victory: and yet Graf won that extraordinary 11th game of the deciding set with a backhand blaster that could have taken your head off, and went on to win the match. It seemed there was nothing to choose between the two players… and yet Graf won 22 grand slam singles titles to Sánchez Vicario’s four.

My choice for the best men’s final is the all-American showpiece of 1999 that many remember as dull and one-sided, when Pete Sampras beat Andre Agassi in straight sets. It wasn’t boring, but perhaps you needed to have a ridiculous number of sporting hours on the clock to see it for what it was: the greatest display of fast-court tennis in the sport’s history.

Agassi was at his absolute peak that year and he delivered three sets of perfection. Sampras did the only thing he could do – or perhaps the thing only he could do – and went beyond perfection. There are times in sport when you stand up and cheer: there are other times when you just want to sit in silence, wondering how such brilliance can be, and marvelling that you had the privilege of witnessing it.

No tennis player in history – not Rod Laver, not even Roger Federer – could have lived with Sampras that day. His serving reached such lofty levels of skill that Agassi knew the tiniest error on his own serve would cost the game, the set, the match, the championship.

Partisanship is great, drama is great, but the greatest of all is excellence. In those two finals, both players contributed: the loser forcing greater excellence from the winner. These duels show how sometimes the difference between two brilliant players is tiny. Almost the only place it can be seen is on the scoreboard – where you find the uncompromising truth.

Wimbledon's women’s final airs Saturday at 1.15pm, on BBC1. The Men's final shows Sunday at 1pm, on BBC1.