As an official Mentor for the National Bowhunter Education Foundation, I support the NBEF's recommendation that you should take only broadside or quartering-away shots at animals. These are high-percentage angles that allow the best soft-tissue arrow access to the vital heart/lung zone.
However, I am amazed at how lethal sharp broadheads can be with less-than-perfect hits. If your target jumps the bowstring, or if you make a poor shot because you are tired, cold, or excited, do not assume the animal will get away. If your broadhead has solidly hit the rump, paunch, or liver, you still have a chance for success.
Years ago the late, great Fred Bear told me he had great confidence in a rump shot. Like Fred, I have never lost an animal hit solidly in the ham. Similarly, a gut-shot or liver-hit deer should be yours if you follow up correctly. You should never shoot for such marginal parts of an animal on purpose, but if your shot goes astray, do not despair.
In my experience, game seldom travels more than a half-mile with solid hits to the rump, paunch, or liver. Wait several hours after such hits, and then start searching cautiously. If you cannot find blood or tracks, you should grid-search the entire area. With enough persistence, you will probably find your animal. Sharp broadheads are deadlier than you might think!