I always thought that the armor rating was the threshold of damage that had to be cleared before it started to take away from the shield's hit points.
Is it a linear thing like that or does it function like normal armor soak?
Its like armor soak. So if you have a 0 resistance shield hit by 30 damage, the shield takes 30. If you have a shield with 20 resistance, it will take 10 damage.
That's why I love my knightly heater shield and the 33 armor rating (but it has only like 230 hit points, so I can take a lot of sword hits, but hardly any axe hits)
Axes have such high damage to shields from their own high base damage plus the huge bonus that they overwhelm most soak. against axes a high HP shield is better than a low HP, high armor shield but still something like a bardiche will chew through those extra 200-300 HP pretty quickly, maybe takes 2-4 more hits.
Also Egan, I believe resistance is just for ability to stop arrows/bolts from punching through. I think you mean armour.