A right-handed hitter should face the pitcher with a keen left eye.
Hand dominance plays a key role in gross and fine motor development, but it's unclear whether there's a true link between hand dominance and eye, or ocular, dominance. The correlation between hand dominance and eye dominance appears to occur in most cases and is strengthened over time due to use, but many right-handed people find they have developed a cross-dominance, or a proclivity to use their left eye to position objects. When training for sports or recreational activities that require sharp vision and exacting hand-to-eye coordination, there may be some advantages to cross-dominance.
Percieved Problems with Cross-Dominance
Shooting sports generally require a dominant hand to aim and support a firearm and a traditional one-eyed positioning method. For shooting, dominance in the right eye appears to be necessary for right-handers. Archery bows are an example of a mechanism constructed for the use by a shooter who's dominant in the same hand and eye. Right-handed archers with left eye dominance may need to develop a left-handed shooting method in order to use the proper bow and their dominant eye for correct vision.
Altering Eye Dominance
Though it appears that in many cases eye dominance strengthens over time, it may be easier to train the right eye to become dominant in positioning. Hunters use an eye patch to develop focusing strength in the "weak" eye. Archers who want to benefit from cross-dominance may utilize their binocular vision to shoot with both eyes open while using a left-handed bow.
Hand-to-Eye Coordination
In sports such as baseball and golf, cross-dominance may hold some advantages. Generally, dominant-handed hitters use this hand as the direction and force behind a swing, while their opposite eye faces the object more directly. In baseball, for example, it appears to benefit a batter to use his dominant eye -- in the case of right-handed hitters, their left eye -- to face the pitcher and the oncoming pitch. Although studies conducted in the major leagues have shown no correlation to cross-dominance and batting average, this may be due to several other circumstantial factors.
Natural Development
Because it appears that eye dominance develops and strengthens over time, it also appears eye dominance can be trained and re-learned. In the case of baseball, it could be possible that right-handed hitters, over time, develop left eye dominance as a way to adapt to the skill requirements of hitting. In shooting sports, the opposite may be true, as eye dominance may develop as a method for utilizing the dominant hand and achieving accurate positioning.
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