Well. IMHO it matters a lot. Hard to break any target if your dominant eye (i.e. your rear sight) is 3"off the barrel. Having said that, nothing is absolute as people vary in the degree of eye dominance as to one side or the other. Some lucky shooters are very strongly eye dominant to their hand dominant side. But many of us are dominant to one side but not strongly so. This means that, for example, you are right eye dominant but targets from the far left get picked up first by your left eye. This is not uncommon and I have have this affliction myself. I have been largely successfull in overcoming this problem by doing a couple of things. First, I have learned to recognize which targets can cause my left eye to take over. In my case, it is mostly quartering or crossing targets from the left. The problem is exacerbated if the trap is even with the shooting stand or behind it. When I encounter such a target I, do a couple of things. First, I move my head to as far left as I can reasonably get it. That forces me to use my right eye to pick up the target (before the left eye does)if possible. If you can acquire the target with your dominate eye at the instant that you first see it, your dominant eye will, in most cases, continue to focus on the target. If that strategy doesn't work, I will next try closing my left eye very briefly at the moment I hear the trap throw. I don't reopen the left eye until I acquire the target with my right eye. The left eye is closed for just a split second. Any longer and you will find that the target is getting away from you and out too far from your chosen break point. The last adapting strategy is to let the target get way out in front of you to where your dominant right eye will most likely take over. This only works if the break point is still within a reasonable range at the point where your dominate eye takes over. Hope these tips help. The most important thing is to realize the problem and then you can work on strategies to overcome your built in problem of your non-dominant eye taking over when you don't want it to do that. There are other things you can do other than what I mention above. Some are more radical like an eye patch, the magic dot or putting vaseline on your glasses. No problem with whatever works for you. Just keep trying things until you find the solution and you will break a few more targets than you are now.