Paul Vallely: Sometimes the only person to beat is yourself

The expectations of the public, says Rebecca Adlington, can be different from those of the athlete

The Olympics are not really about sport. What makes us engage with them is something deeper. The London Games have reached through our television screens to bond us emotionally with individuals engaged in a succession of small struggles that say something universal about what it means to be human.

The past two weeks have told the stories of men and women wrestling in an arena bounded by triumph and failure, elation and pain, euphoria and disappointment. They are our modern myths which show that the human spirit is truest under pressure, win or lose. There was something awe-inspiring about the effortless elegance of the modest Kenyan 800m runner David Rudisha, who became the first person to break a world record on the Olympic Stadium track. And there's a magnificence about the exuberant arrogance of the double-gold sprinter Usain Bolt who capped his 100m and 200m victories with the words: "I'm now a legend. I am the greatest athlete to live."

But for all the gold medals it has been the losers who have taught us most, and not because, as Brits, we have a self-indulgent predilection, in the tradition of Dunkirk, to snatch reassurance from defeat. Team GB was tactically outman-oeuvred in the very first big event, the men's cycling road race, for which Mark Cavendish, the reigning world champion and a three-times stage winner at this year's Tour de France, was the favourite. As the Games progressed Cavendish's 29th place was overshadowed by the grace with which, as a BBC commentator, he analysed the performances of others.

There was a similar magnanimity from Louis Smith, the first Briton in a century to win an individual gymnastics medal. He tied on top score but, after seeing gold awarded to his arch-rival for finesse, said: "To come second against one of the best pommel-horse workers the world has ever seen? I'm a happy guy." And Tom Daley refused to blame his partner when they came fourth in the synchronised diving, saying: "We're a team. We win together and we lose together."

We are used to hearing sports coaches say things like: "Nice guys finish last" or "Winning isn't everything, it's the only thing." The Olympic ideal proclaimed by the founder of the modern Games, Baron Pierre de Coubertin, that "the most important thing is not to win but to take part", appeared to have given way to the ad slogan used by Nike for the 1996 Atlanta Games: "You don't win silver, you lose gold."

We have had touches of that cynicism again, with the Badminton players from China, South Korea and Indonesia doing their best to lose in order to secure an easier opponent in the next round. Then there was the Briton who admitted that he deliberately crashed his bike, the Algerian runner who pulled out of one event with a "bad knee" and then won 1,500m gold the next day, or the Japanese women's soccer team which played for a draw to avoid having to travel to Scotland for their next game.

The difference between success and merely winning was clear when the Australian gold medallist, Anna Meares, nudged Victoria Pendleton into veering out of her lane in the cycling sprint final. Pendleton was penalised but Meares, who has ridden with her elbows throughout her career, was not. It deprived us of what would have been a thrilling deciding run. Yet Pendleton, who was distraught at the penalty, gave her rival a hug and next day brushed aside the incident which had so unnerved her. The women's reactions highlighted the difference between gamesmanship and sportsmanship. "I'm so fucking proud of you," her coach whispered to her after the race, not realising the microphones were on. So were we all.

Some victories are hollow, then, but some defeats are glorious. Curtis Beach did not even make the Olympics. But in the US decathlon trials beforehand he sacrificed his lead and pulled over to let Ashton Eaton pass him. Beach knew Ashton could set a new world decathlon record that day – which he did – and did not want to block his route to glory. Beach didn't make the Olympics (where Eaton won gold) but in his hometown strangers approach him and asked to shake his hand.

Losing is a relative business. There are those for whom only gold counts. "Even though I'm holding a silver medal, it still feels completely heart-wrenching," said a distraught Zac Purchase after the sculling-pairs final. By contrast, gold-hopefuls Rebecca Adlington and Beth Tweddle seemed genuinely delighted with bronze. Much depends on whether an athlete sees themselves as in competition with others or with themselves in the struggle to achieve personal best. Sometimes, as Adlington admitted, the expectations of the public are different from those of the athlete which is why, after bettering her time at Beijing, she was so "pleased and proud" of her bronze.

All of which explains why on the wall of the players' entrance to Centre Court at Wimbledon is written Kipling's line: "If you can meet with Triumph and Disaster and treat those two impostors just the same...". Failure is not about not winning. It is about not having done yourself full justice.