Some attacks miss by a wide margin, sometimes the character outright dodges, and a lot of time it will just 'plink' off the armor; this all depends on how close it was to beating the AC of the target. In real world you usually have a DM describing the attack in the same terms. Hell, even attacks that do damage are sometimes described as "the arrow hits you, but your armor and/or training (depending on character) allows you to channel the deadly force of the blow away from your vitals: that will probably leave a bruise though." .etc
I would really like this happen --get rid of the HP bloat and replace it with compelling animations. Dodge is great but what about animations for "thunk" on armor, grazing to the side, swords crossing, ducking under or jumping over the slash of a weapon . . .