PREDICTING how many medals a country will win in the Olympics has become a cottage industry. Size and wealth are obvious factors: bigger countries naturally have larger pools of talent to draw from, and rich ones tend to have healthier populations and more resources to devote to sport. As expected, economic heavyweights like China, Germany and Russia were among the five countries that collected the most medals in Rio. And America comfortably topped the medal table, just as it did in London in 2012.

Academic studies have found that both population and per-capita GDP are strongly linked to Olympic triumph. No surprise then that total GDP yields a robust predictor of Olympic success—and is thus a convenient benchmark against which to measure countries’ sporting performances. At the Olympics, as in geopolitics, the country that punches the furthest above its economic weight is Britain. Based on GDP alone, we would expect Britons to collect just 36 medals. Yet in Rio, Britain placed third with 67 medals (and second in the gold-medal count), thanks to generous funding for sports like cycling, where it has enjoyed previous successes. Money well spent means athletes well placed.