I'm flattered to be brought up as a standard for testing things

. I just saw this thread, I would have been wrapping up my final school projects at the time. I wish I could live up to the (possibly ironic) claims that I could make an obvious test for something like this.
Disclaimer
I make mistakes all the time, think carefully before spending a lot of eds based only on what I am saying. With that in mind, the rest of this post is probably irrelevant to new players besides curiosity.
Analysis
I see 4 attributes differences, between a relayered BC ring and the azurite ring, for analysis.
- +5 RPD
- -5 SDI
- -5 Strength
- +10 Healing
Everything else can be compensated for by other relayers (if we're talking about end game gear).
RPDs benefit is completely dependent on the damage the enemy you're facing is doing. A 200 damage hit on yourself will result in 10 damage to them at +5% RPD. I am unsure if RPD ignores enemy armor. Note that this is when any enemy hits you. If 9 enemies hit you with physical damage at the same time (or more if there are archers), each hit will have have RPD applied to them.
SDIs benefit is applicable to every hit you make, but may vary based on enemy resistances. If you have 58% lightning (27), 58% fireball (15), 58% harm (20), Magic Arrow (7) (damage based on a dragon), then with -5% SDI the average hit is going to do 2 damage less.
Strengths benefit is applicable to every hit you make, but may vary based on enemy resistances. The formula for base damage %(strength) = .3*strength + 5*(strength > 100). Tactics, Anatomy, Lumberjacking (if weapon is an axe), strength, damage increase, exceptional weapon tag (if weapon has it), and weapon damage all affect the base damage calculation. -5 strength results in a 1.5% decrease in damage. Using a 20 damage weapon (yumi) will result in .3 less base damage. If that adds to a previous fraction you might get 1 damage, which would approximately double with enemy of one, consecrate weapon, and divine fury. At most the average hit will do 2 damage less.
Healing power would really only be helpful in bandage cost savings. The healing amount equation is anatomy/6 + healing/6 + 3 -> anatomy/6 + healing/3 + 10. At 130 Anatomy and 120 Healing you'd be healing 45-72 per bandage. At 130 Anatomy and 130 Healing you'd be healing 46-75 per bandage. I'm not sure that's really enough to even be considered an improvement with instant healing.
Summary
- +5 RPD will result in 5% damage per physical hit point of damage an enemy does. With my DCI and Physical resist capped, I don't get hit anywhere close to as often as I'm hitting mobs and the average mobs don't do that much physical damage. I have definitely killed balrons before they hit me.
- -5 SDI results in at most 2 damage less.
- -5 Strength results in at most 2 damage less.
- +10 Healing results in 1-2 more health healed per bandage.
To make the azurite ring worth it, you'd need to fight mobs that do an average of 4/.05=80 physical damage per mob per 1.25 seconds. With max physical resists and dci, there aren't many places where that is true. Perhaps event areas and perhaps Sgail would benefit more from the RPD on the ring. RPD has enough of an effect that I think with a low enough DCI and Physical Resistance a player may experience more damage in the average area with the Azurite Ring. Though I am worried that such a low DCI/RPD build would be hard/expensive to correct for high damage area.
This would be the testing point. What mobs or group of mobs are capable of doing 80 dmg/mob/1.25 seconds.
I do not feel like it is worth investigating in game. Though I suppose any investigation into this matter could also be viewed as an investigation into the low DCI, low Physical Resist, and high RPD damage play style, which has been theorized and used to some extent, but not thoroughly tested.
[edit]: Someone asked me a question in game which made question my strength math. Looked a little funny, but I was tired and my braces hurt. You'd need 16 and 2/3 strength for each base damage increase on a Yumi and DLS (+2 damage). I verified this by unequiping my 20 strength SoT.
I went to see how much of a damage difference enemy of one, consecrate weapon, and divine fury do. Extremely experimental results (hitting a drake) showed a 2x damage bonus, though I know enemy of one and consecrate weapon effect will vary on the enemy I feel like I've seen at least a 3x bonus.