The accuracy needed to shoot a basketball successfully does not leave much margin for error. The slightest deviation on line or distance and the ball will carom off the rim. Consequently, any elements of vision or dexterity which don't work together can produce consistently errant shots and complicate the efforts of the shooter.
Although you may not realize it, everyone has a dominant eye. The website sportsci.org defines the dominant eye as the one which processes and transmits information to the brain a few milliseconds faster than the other. To establish which eye is dominant, extend one arm forward at shoulder height and form a small circle with your thumb and forefinger. Pick an object in the distance and center it in the circle with both eyes open. Your dominant eye is the one which still sees the object within the small circle when the other is closed.
With very few exceptions, people are either right-handed or left-handed. Although you may enjoy some facility with both hands, it's unlikely that you write equally well with both hands or find equal strength in each. Basketball players, for instance, typically prefer to shoot with the dominant hand. It is also one of the few sports where players may elect to execute a fundamental skill movement involving a target with either hand, depending on the circumstances.
Orientation of Vision and Motor Skills
Clearly, basketball players must use their vision to locate the target and judge distance and line before the motor skills take over to send the ball on its way. Neither of these skills can accomplish the goal of making a basket alone. Consequently, they must work together and in proper sequence. Basketball Shooting Coach.com states that you should direct your vision to the metal hook on the far side of the rim--from whatever angle you happen to be facing the basket. From there, the motor skills respond to execute the shot.
Dominant Eye vs. Dominant Hand
According to an article in "Experimental Psychology," the proper sequence of vision and action in shooting a basketball is not conclusively affected by crossed hand-eye dominance. Experiments testing the accuracy of basketball players shooting the ball through a variety of visual stimuli showed that, among other things, individuals tend to adjust to whatever dominant hand-eye combination they possess. Shooting a basketball simply reflects their hand-eye skills in general. Poor shooting more likely results from inferior mechanics or poor overall vision.