Simon Barnes blogs from Beijing

There are three ways of enjoying sport, and they form a hierarchy. The three categories can mingle and merge, any two together or all three at once. But they still form three easily separated categories and there is no question as to which is the highest. I have spent the past 16 days in remorseless, painstaking and thrilling search for the sport of the third kind, and I encountered it on at least four occasions.

The lowest of these categories is partisanship: us lot beating them lot, our bloke beating their bloke - and it's the most wonderful fun, especially when you win. Partisanship is the bread and butter of the sports industry: loyalty, identification, cheering for your team, your man, feeling absurdly glad when you win and suffering the most ridiculous pain when you lose. One world, one dream, and that dream is to beat the crap out of everybody else. Partisanship is Tim Henman at Wimbledon: agonising desperation for a mere result, glorious and painful to experience because of the extreme identification of audience and athlete.

This has been a great Games for British partisanship, but I haven't been around many British medals. I managed only a single gold and that was more by luck than judgment. I had gone to the Water Cube for quite other reasons when I watched the superb Rebecca Adlington win her first gold medal, in the 400 metres freestyle. It was the first British swimming gold for women for 48 years and it was a moment to savour.

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The middle category is drama. Drama effortlessly sheds the chains of partisanship. In Wimbledon terms, this was the Goran Ivanisevic final, in which Ivanisevic kept double faulting on match point, kissing tennis balls, calling to the heavens and, eventually, won. It was an amazing match, but sport can still do better than this.

The men's super-heavyweight weightlifting supplies drama at every Olympic Games and the event is a real favourite of mine. This time, the drama was greater even than usual; an unexpected and glorious victory for Matthias Steiner, of Germany, with the last lift of the competition. He then burst into tears, cavorted about the stage in a mad dance like a giant baby in his romper suit, accepted his gold medal and held it up, holding in his other hand a picture of his wife, who was killed in a car crash last year. As drama goes, this was pretty rich.

You can get partisanship and drama together; very often, in fact, because drama feeds off intensity of feeling. It is partisanship that gives such drama to the doings of the England football team. England's most recent competitive match, in which they lost to Croatia at Wembley, was not without its dramatic side; the strategy was a farce and the result was a tragedy.

But let us move up to sport of the third kind. It is this category I have been looking for at these Olympic Games and, for that matter, at every Olympic Games of the six I have attended. It is a good place to look - you are more likely to find this category at the Games than at any other sporting event. The third category is greatness.

In Wimbledon terms, it is the best of the Sampras finals. Those unaware or unappreciative of the third category found Sampras boring. One can only have pity for people who find greatness boring.

At these Games, I have turned myself into a greatness hunter, a tart for greatness, if you prefer. And I found it, and it was better than all those lovely British medals, and better than all that wonderful drama - the sort of drama that we found at the taekwondo at the weekend, when a Cuban kicked a referee in the head and Sarah Stevenson, of Great Britain, won a bronze medal and left on crutches.

At these Games, I first encountered greatness at the swimming pool, where I watched Michael Phelps make his inexorable way to eight gold medals. Eight at a single Games beats the record of Mark Spitz. Phelps now has 14 in all, five more than anyone else in history - and he's eyeing up London. Some say that swimming medals are cheap. No Olympic medal is cheap. There's only one swimmer - Spitz - among the four athletes who have a total of nine gold medals to their names.

Phelps's eight triumphs were played out without fuss and with little attendant drama. His face, shorn of the louche beard and the tangled mop he wore before the Games, is the essence of blandness, his remarks in victory little better. Being the most decorated Olympian ever is “kinda neat”.