Mens Sana in Corpore Sano

The ancient Romans used to say, "A healthy mind in a healthy body" to express a correlation between physical and mental health. Is that really true? Looking at the raw numbers, publications and medals do seem to correlate, although there are a few outliers. Russia, UK, Australia, Ukraine, and Hungary all perform notably better in sports compared to scientific productivity. Meanwhile the opposite is true for India and Taiwan, where they appear to be strong publishers but weak in the Games (Olympic, not tenure).