Well, that's it then. That curious hotch-potch of sport known as the modern Olympics is done and dusted for the 27th time (if we exclude the intercalated games of 1906 as all good statisticians should).

As expected, the London 2012 medal table was led by the United States and China, but it goes without saying that the European community, had its member nations all been playing for the same team, would have comfortably beaten both, in fact surpassed the total of the US and China combined. Of course, the Olympic Games has always been, essentially, a European affair. Sixteen of those 27 editions have, after all, been held in Europe.

To give the Olympic movement its due (which is not a phrase familiar to Olympic journalists), it has inched away from a Eurocentric games. But it's not a radical change and the induction of golf and rugby union to the 2016 Games in Brazil only amplifies the feeling that the United States-Europe TV axis is still driving the whole show.

You always know a sport is a dubious recruit if it fails the pre-eminence test; that is, the Olympic competition is not the most-valued for that sport. As an example, no athlete would ever trade an Olympic gold medal for a world title. It's their most valued possession. But it doesn't work for tennis, say, where Andy Murray would swap his Olympic gold for Federer's eighth Wimbledon title in an instant. He would, trust me.

So it is that golf and rugby waved into the Olympics for 2016 are sports that do not need the Games either. It's the wrong way forward. What the Games needs is sports that invest totally in the Olympic ethos, and sports that bring global diversity. How about these?

Foot-volley

As baseball and softball found to their cost, the Olympics is full already, so for every sport that arrives, one must leave. They both went. There are other ways to make room, though. Merging sports is a progressive way forward. Football fails the pre-eminence test (see above), and beach volleyball fails on the grounds that any sport with beach in its title isn't really a sport. So the answer surely is to merge them and, as I'm sure you know, the merged sport already exists. It's called foot-volley, was invented in Brazil in 1965, and was played by such footballing eminences as Romario and Ronaldo.

Sepaktakraw

Another composite sport that bears consideration is sepaktakraw, which is either one word, two words or a hyphenated word (your choice). Sepaktakraw is somewhat similar to foot-volley, but played on an indoor court (or a beach, but we don't talk about that) with a rattan ball (made with palm leaves) and at a tempo that could best be described as prestissimo and some. It's compelling watching – bicycle kicks are de rigueur – but that's not the real reason for inclusion: Malaysia has attended 14 Olympics and still awaits its first gold medal. They would have a serious chance in this sport, though they wouldn't want to meet Thailand in the final.

Capoeira

Not until the Tokyo Games in 1964, when judo joined the fold, did the Olympics embrace martial arts. Taekwondo, having twice been a demonstration sport, was the second to join in 2000. A third martial art has long been on the cards, with karate and wushu persistently arguing their corners. But capoeira has two distinctive claims: firstly that it is not Asian in origin (like judo and taekwondo), but South American; and secondly that it is performed to music. The Olympics is currently obsessed with music. It may seem the last thing a gymnast would need in those precarious moments on a 10cm beam is a rock'n'roll backing track, but that's what has been happening. A disco beat when you're triple-jumping; garage for dressage and hip-hop for the high jump. This is the new Olympic world and capoeira has its place in it.

Dragon-boat racing

Water covers 71% of the Earth's surface, but only three Olympic sports take place on it: sailing, rowing and canoeing (well, if you exclude swimming, diving and a few horsey jumps that take place in it). There must surely be room for another sport on water, and one with a rich tradition and a theatrical flourish should surely prove irresistible. An ornate dragon's head prow, 20 or so paddlers in near-perfect unison, a drummer beating the stroke (think how good Redgrave and Pinsent would have been with that) and a sweep with a 10ft rudder steering the boat. It was good enough for the Asian Games, which adopted the sport in 2010.

Kabbadi

For a country of its size and population, India has exceptionally poor return from its Olympic involvement: nine Olympic titles, eight of them from hockey. There would have been a few more had cricket (by far the most popular sport in India) been Olympic, but that, too, would fall down on the pre-eminence principal. Kabbadi is not the easiest sport to comprehend, and Channel 4's attempt sell it to the British public 20 years ago failed on those grounds, but clarity has never been a major concern of the IOC. Does anyone understand how they score in boxing now?