In most hunting situations, you're not going to have a lot of time to decide whether to take a shot. So you need to use every trick possible to make this decision quickly and reliably. This decision is especially tough if a branch is sticking out between you and the deer.
Here's how you determine whether your arrow will clear that branch -- or hit it. Hold your bow at full draw and aim at the animal with the right sight pin. Now look at all of your other sight pins -- they'll tell you exactly where your arrow will be at each corresponding distance.
For example, if you're shooting at a deer 40 yards away and a branch 20 yards away covers the deer's vitals, your 20-yard pin will tell you exactly where your arrow will be when it passes that branch. If your 20-yard pin is in line with the branch at 20 yards, your arrow will hit the branch. Don't shoot. If your 20-yard pin rests above or below the branch, your arrow will have a clear path to the deer. Go ahead and release. On any shot, simply match up your pins with the openings in the trees to find a clear path for your arrow.
If you do this on every shot you take in the woods, all of those mysterious deflections you used to get will disappear.