When you look at something, most people will see the object with both eyes. Each eye is looking at the object at a slightly different angle, giving slightly different images to the brain. The brain is able to take both images and do miraculous things with it. It judges distance, and forward or backward motion, by the change in focus and by the change in the angle between the 2 eyes. Some people, like myself, only use 1 eye. That makes it very hard to judge distance and motion because we can't use the difference in angles, only the focusing action.
Just about everyone has a dominant eye. The dominant eye has priority over the other one. It provides the main picture to the brain while the other one provides more details and data. There are many ways to figure out which eye is your dominant one.
1) Look at something far away and slowly bring your right hand in front of your right eye, then take it away and slowly bring your left hand in front of your left eye. You will notice that in one case very little happens, but in the other, as the one eye gets covered, the image shifts. That means you covered your dominant eye.
2) Form a circle with your hands and look at something through that circle with your hands away from you. Slowly bring the circle closer to you keeping what you are looking at in the center of it. When your hands contact your face, that circle will be around your dominant eye.
What's this gotta do with bowling perspective?
Most of us bowl by aiming for a certain arrow part way down the lane. We want the ball to cross that arrow. We aim by looking at the arrow to get our angle, and throwing the ball. Now here's a minor complication. When we look at the arrow, we are looking down the lane at a certain angle, but for the ball to cross the arrow, it's angle has to be slightly altered. Why? Because your eye is slightly off to the side of where the ball is. That makes the 2 angles a bit different. With practice, the brain calculates the difference and makes the adjustment.
Now the difference between right-eyed and left-eyed bowlers:
If you're a right-handed bowler, and your right eye is the dominant one, the difference in the angles between the ball path and what the eye sees is small, but if you're left eye is the dominant one, that angle is bigger and therefore harder to adjust for accurately. If you're a left-handed bowler, it would be reversed. A dominant left eye would be closer to the actual path than a dominant right eye.
Look at the following image to see what I mean. The red, blue, and black dots near the bottom of the image are your left eye, right eye, and the ball, respectively. The image isn't meant to be perfectly to scale, just a way to show the different angles and the difference in angle adjustments.
Want to have some fun?
Figure out which eye is your dominant eye, then next time you go bowling, throw a normal shot, then close or cover your eye that IS NOT the dominant one and bowl again, then close or cover your dominant eye and try once more.
While you are waiting for the chance to try that, try this. It will show you how important the dominant eye is.
Get a ball and someone to play catch with. Play normally, then cover each eye one at a time and try again. You will miss frequently when you cover your dominant eye because the other eye isn't used to doing all the work.