I think that might be a question for the sports psychologists! I don’t know about improving it, but I do know that there has been a lot of research looking at how we coordinate our eye and hand movements. Some of this research has come from looking a patients with specific types of brain damage – for instance, people who suffer from optic ataxia can see properly, but aren’t able to guide their hand towards an object that they’re looking at. On the other hand (ba-dum!), patients with visual agnosia can guide their hands to objects, but can’t recognise them. Then, there’s something else called ‘blindsight’ – people who have had damage to certain parts of their brain that control vision are effectively blind, but if you were to hold out your hand to them to shake, they would be able to grasp it and shake it back! That’s because they can still ‘see’ by using different parts of the brain, even though they aren’t aware that they can see anything!
So given that we know quite a lot about how the brain can coordinate our hand and eye movements, I’m sure we’ll know something about how to improve it!