At first this may sound surprising, but if you think about it, sports is not just a matter of physical practice but also of mental practice. Sports requires motor coordination, discipline and skill learning. According to Chris and Erik, the main cognitive function of importance that connects physical and mental prowess is executive control. Executive control, located in the frontal areas of the brain, concerns our goals and the handling of our goals. It keeps us focussed on what we do, help us in determining our actions in the absence of outside information, and plays a role in juggling all the items that we needs to maintain in working memory. Sounds familiar? Those are exactly the functions that are needed for multitasking.
In my own talk, I showed a picture of brain pictures associated with sequential multitasking: an area in the frontal cortex and an area in the parietal cortex (made by Jelmer Borst). To my surprise, both Chris and Erik showed pictures of roughly the same areas.
If we connect the two together: physical exercise improves executive control, and executive control is the main factor of success in multitasking, then we can conclude that physical exercise can make us better multitaskers.
The pitfall of this line of reasoning is that most evidence is correlational. We cannot be sure whether physical exercise actually causes better executive function. Apart from that, it is an interesting thought that this is another reason why body and mind are maybe not as separate as we tend to think.