D&D 5E Armor as partially DR

Monster / spell damage does vary but it follows a pattern at least.

It doesn't follow *A* pattern, it follows (at least) two. Damage can increae multiple wats. One pattern is more attacks and the other is more damage per attack. These are affected very differently by your proposed rule.
 

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I suppose it would be possible to have armor half the damage. Hit or miss could be determined by 10 plus DEX modifier, then anything that hits the armor only does half damage, and anything that hits above what the armor provides does full damage. Double the range of numbers the armor provides protection for to make up for it not stopping damage completely.

If a character had DEX 20 and leather armor, AC would be 15 no damage/ 17 half damage.

same character in chain shirt would be AC 12 no damage/ 18 half damage

Half Plate would be AC 12 no damage/ 22 half damage

Chain would be AC 10 no damage/ 22 half damage

Plate would be AC 10 no damage/ 26 half damage
 

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