Shields add to your Armor Class. Your armor class is a combination of your characters armor, ability to block with a shield, ability to parry with their weapon, and the fact that people don't stand still in a fight.
So if you do not roll high enough to pass someone's AC, your attack fails. The game calls it a 'miss', though it can be due to missing, the enemy dodging, the enemy parrying, or the enemy blocking.
Mechanically, 5E does not differentiate between ANY of that. There's no 'This is your armor AC. Then this is your shield AC. Then this is your AC for moving around. And this one is for parrying'.
So there's no way for the game, or the devs, to decide what's a miss, a dodge, a parry, or a block.
Well actually, in 5e you could decide what is what. As a DM I do this.
The order of AC is as follows...
Base AC: Always 10
Dex modifier
Armour
Shield.
So as a DM I would maybe do it as follows.
Ifyou roll under 10 - Complete miss
If you roll over base but under dex - they dodge out of way
If you roll over base/dex but under armour - glancing blow(no damage)
If you roll over base/dex/armour but under shield - they block it away with shield
If you roll over total AC thats a hit(with damage)
As a side note, if your DEX modifier is negative then I would just 'reset' their base AC(accordingly) and they don't 'dodge out of the way'
