Dice-Based Armour for Fantasy Oddhacks and similar OSR games

Thanks to Kahva and Duan’duliir in the OSR discord for helping me with the math.
If you're interested in alternative armour systems, you should also look at Kahva's.

I really like combat in Into the Odd, and its bigger cousin Electric Bastionland. Getting rid of to-hit rolls makes it fast and dangerous, and far easier for me to wrap my head around narrating. However, the armour system has some issues outside of its intended setting. 

The armour system uses damage reduction, where a flat amount of damage is deducted from each attack every time. As of Electric Bastionland, armour gives DR1, and a shield gives another DR1. DR3 is reserved for monsters that are practically made of armour, such as living statues. This works well for settings where firearms are the norm, and where a cloth gambeson won’t protect you from a musket ball or a dose of buckshot.

The issue comes with converting the traditional three fantasy armours (leather, chain, plate) to this system. If we give leather DR1, chain DR2 and plate DR3, and shields give +1DR, then a character in Plate and Shield would have DR4. This would be absurdly strong, making them immune to unarmed and impaired attacks, and making them more armoured than a living statue.

We could try what other fantasy oddhacks have done: merge chain and plate into one category, Heavy, and give them DR2. However, this doesn’t sit right with me either. Wearing solid metal plates should offer more protection than just chainmail. Additionally, a character in chain/plate with a shield still has DR3, on par with living statues and Dragon scales. This won't do!

Do not trust the bread

 
Introducing High Pass Filter Armour Dice (HPFAD)
(Or just Armour Dice if you’re not feeling fancy)

The System
When someone is attacked, the attacker rolls their damage di(c)e, and the defender rolls their armour die (AD).

If the Armour Die is equal to or greater than their attacker's highest damage die, the defender takes no damage.

If the Amour Die is less than the attacker's highest damage die, the defender takes the rolled damage, with no reduction.

Light (padded, leather etc) gives AD4
Medium (mail, metal lamellar, brigandine, breastplate etc) gives AD6
Heavy (plate) gives AD8
Shields increase the Armour Die size by one (d4 to d6 etc), or give AD4 if unarmoured.

Bonus damage from ganging up, dual wielding etc is calculated as normal using Electric Bastionland rules: Take the highest single damage die and compare it to the Armour Die.

Monsters can be converted using As Leather, As Chain, As Plate, and given a further increase if their AC looks like it'd involve a shield. Save the AD12 for serious armour, such as dragon scales, living statues and rock golems.

The Math
(For the purposes of the upcoming math discussion, assume the creature in question always fails it’s saves vs Critical damage). 
Here are two tables showing how many hits, on average it takes to bring down a character with 6HP. 

Damage Reduction

Armour Dice

Difference between DR and AD

Difference in average damage the character takes per hit

There's a few conclusions we can draw:

The Armour Dice system is far more scalable. With a DR of 4, it takes 12 hits on average to down a character with 6HP using a d6 weapon. With an equivalent AD of d10, it only takes 6 hits. This becomes even more pronounced at DR 5, where is takes 36 attacks, vs a mere 7 with an equivalent AD of d12. With a DR of 4 of above, it's impossible to damage anything with unarmed or Impaired attacks!

Using more than 3 for Damage Reduction thus won’t do, and even 3 is going to take an eternity to take down if attacks against it are Impaired.

There’s not a great deal of difference between DR and AD at typical levels (d4-d10 damage, d4-d8/1-3 DR), except for 3 DR and d4 armour die, with a whopping 14. However, at higher levels we see the ridiculous amount of protection DR provides compared to AD.
 
From the difference in average damage incurred, in the typical range, Armour Dice provide between 0.20 and 1 less damage reduction than equivalent DR. Thus, giving PCs and monsters armour dice won't cause things to be a slog, even if it's more armour than they'd have under damage reduction (some oddhacks simply give leather DR0). Combat will also move slightly quicker than oddhacks which give it DR1, so it seems like a good balance.   

Another Difference
Another potential difference between Armour Dice and Damage Reduction is the lack of chip damage (attacks doing 1-2 damage, gradually chipping down their HP). 

Damage Reduction

Armour Dice

As we can see, someone with damage reduction will be taking a lot of chip damage, and in some cases, it will be all the damage they can take. In the armour dice system, characters either take a good chunk of damage, or take no damage. While this is a bit swingy, I personally find it more engaging than gradually whittling down characters. Due to the random nature of the armour die, it's not so swingy that a character will always be taking 0 or 10 damage, but it's still more swingy than DR.

The potential issue with this is with Electric Bastionland's Scar-based advancement. This system relies on a dropping to exactly 0HP in order to take a Scar, which might give you extra HP. The potential issue is that people will be taking a smaller range of damage using Armour Dice, than with Damage Reduction, which may result in characters not dropping to exactly 0HP as much. I'm not really sure what to do about this, maybe I'll try and math it out later. 

Final Thoughts
The goal of this was to create a system that game meaningful differentiation between the three classic fantasy armours, while being playable and enjoyable. I think I've succeeded, but this is all speculation at this point, as I haven’t actually playtested it.
 
Stay tuned for updates on this ramble. At some point I'll have to playtest it, and I also want to experiment with durability, disposable armour dice, and armour for structures and vehicles. I’d love to hear your feedback.