Rethinking Weapon Damage

Using average weapon damage instead of rolling speeds up the game. I've been doing it in Roll20 because the system doesn't automatically roll the damage (at least I haven't found the correct setting yet) but this is unsatisfactory.

I've always felt that the hit roll and weapon damage should be linked. A really good hit should do more damage and a barely successful hit should less damage, so here is what I'm thinking. This applies to the raw roll without any modifiers and only when the roll is a hit of course.

    20         A critical, double damage

    15-19    Maximum damage

    10-14    Average damage

    05-09    Minimum damage 

For example: 

Thug's mace: Max is 8, Ave is 5, Min is 3. Easy enough.

Thug's Heavy Crossbow: Max is 10, Ave is 5, Min is 1.

Since Roll20 automatically calculates weapon damage for the players this will only be done for the foes but I think it should work.

My only question is would the critical be double the max damage or double the average? I'll have to think about that.