According to Google (not me) Baseball is the professional sport which requires the most hand-eye coordination. One of the biggest sports in America, Baseball garners a large pool of viewers and a high-quality standard of player. The sport requires players to be able to grip a shaft just right (the shaft of a bat that is) then scan the field for a pitch, all while having to smash a ball out of the reach of fielders. So even if it is a poor man’s Rounders, Baseball certainly takes some skill to be good at.
Let’s face it, Darts is hardly the sexiest sport in existence. The likes of Michael Van Gerwen and Phil Taylor don’t really compete with the likes of Cristiano Ronaldo or Rafael Nadal in terms of athleticism or looks. Despite this their sport of choice still requires a good bit of hand-eye coordination. Anyone who’s ever played darts knows that your dartboard’s wall of choice soon has more holes in it than the board. Therefore, it takes quite the Darts player to hit the treble 20 and anyone who watched the World Championship over Christmas will know the level of concentration and composure it takes to be a quality player.
Finally, a proper sport (sorry Darts). Tennis is one of the world's most popular sports and the players must develop hand-eye coordination skills that are better than most other sports stars. The top players train to develop fast twitch muscles in their arms and legs in order to react quicker. Most importantly, players eventually obtain fast twitch muscles in their eyes so they can more easily focus on balls. Players also grunt and moan in order to concentrate better, which has very little to do with hand-eye coordination but is quite funny.