Just read the Bob Fancher article.....there is plenty of research on eye dominance in Medline or Pubmed, a couple of thousand articles to be exact....just one for example: A new interocular suppression technique for measuring sensory eye dominance.
Yang E, Blake R, McDonald JE.Invest Ophthalmol Vis Sci. 2009 Jul 23. PMID: 19628736
Each eye supplies information to the brain differently. The dominant eye is used to fixate on objects. If you look at a point, the fixation of the dominant eye will fall on the center of the point while the non-dominant eye will fall slightly off-center. By comparing the difference between the images supplied by each eye the brain is able calculate depth information in a scene. The degree to which any eye is dominant varies from person to person as well.
In scenarios where estimating depth is important, the functioning of both eyes in tandem is vital. I don't recommend skiing with an eyepatch any more than driving. However, in scenarios where determining a straight line between two points is needed, using the dominant eye confers an advantage over using both eyes. When shooting a gun, you want to align the sight of the gun with a target. If you kept both eyes open while sighting down the barrel of the gun, when you looked at the sight you would see two targets, and when you focused on the target you would see two sights. In this scenario, the depth information your brain is supplying you is not helpful in aligning the target and sight, and it is easier to sight with one eye.
Pool is an interesting scenario in that it requires good depth perception to estimate the line of sight, generally done while standing up, and in addition requires accurately lining up the cue ball with the contact point on the object ball. If you adopt a high stance and hold the cue under both eyes, you have the best depth judgment, which is needed to estimate the speed and direction of the hit. If you adopt a low stance and use your dominant eye, you have the best ability to line up the cueball and object ball. Most people go somewhere in between, where they can line up the balls while still having a general view of the table to guide the speed of their stroke.
This seems to come into play in the nature of various cue games. In three-cushion billiards players generally adopt a more erect stance that provides a good, continuous 3-d view of the table, allowing them to accurately predict the reaction of the balls. In snooker, the accuracy requirement that smaller balls present requires players to adopt a low stance sighting down the cue. In this game moreso than in billiards, players must first estimate what will happen on the shot and determine the line of sight, then remember the layout of the table when they are down on the shot since they don't have a good view of the balls.
