For Helen Glover, winning a gold medal came down to 7 minutes and 27.13 seconds of overwhelming effort after four years' training. For Bradley Wiggins, it took 50 minutes and 39 seconds. Preparation time: 20 years.
By Olympic standards, these are relaxed ratios. Louis Smith has been waking up in pain everyday for most of the 12 years since he chose gymnastics over singing in the choir. His pommel horse routine takes barely a minute.
Olga Korbut says that Olympians do what they do, enduring agonies most of us cannot imagine, because they enjoy it. This must be true. But they also do it to win; for that instant when enjoyment is distilled to pure, immeasurable joy and oarswomen collapse in each others' arms, sobbing who knows what into each other's ears.
A paradox of such moments is that they are built on self-belief but often followed by disbelief. Glover said that her victory would "take for ever to sink in". Chad le Clos, after swimming the men's 200m butterfly five hundredths of a second faster than Michael Phelps, repeatedly had to remind himself that this really did mean that he had won.
His delight, like that of Britain's first gold medal-winners yesterday, was only slightly alloyed by glee. It had less to do with beating his hero than with having proved himself. Victory feels so good because its essence is vindication.
Victory at the Olympics usually take a little luck, but more than anything, it takes work. This is why it almost never fails to inspire. "If you work hard and try your best, absolutely anyone can do anything," Glover panted on the pontoon at Eton Dorney. Which parent wouldn't print that out and stick it on the fridge?