This was pulled from the combat mechanic thread and would explain why you don't notice anything when using Ring of Pain.
Ring of Pain:
Costs 10 stamina to activate and 5.1% of max stamina per second to sustain.
Damage dealt by Ring of Pain counts as DoT. Therefore it ticks every 2 seconds, ticks cannot be critical hits and do not benefit from flanking. Each tick deals 15% weapon damage.
Damage bonus from missing health is 1.25% per 1% missing health and is added as a flat value to damage_multiplier. This bonus only affects the DoT damage from Ring of Pain.
[Mistake/Bug - Patch 5] In-game description incorrectly lists damage bonus from missing health as 1% per 1% missing health.
[Bug - Patch 5] While active, reduces health cost of Dragon Rage to 4% max health per attack even without the Torrent of Pain upgrade.
[Bug - Patch 5] While active, reduces stamina cost of Devour by 15 stamina even without the Torrent of Pain upgrade.
[Bug - Patch 5] While active, reduces cooldown of Devour by 4 seconds even without the Torrent of Pain upgrade.
Torrent of Pain (Upgrade)
[Bug - Patch 5] Currently has no effect. All listed improvements to Ring of Pain are already included in the un-upgraded version.
While active, Ring of Pain grants a flat +50% to Dragon Rage's damage_multiplier value (all 3 attacks).
If this is the case, it would actually make more sense to use Ring of Pain in a build that uses Rampage constantly...would be almost useless for the devour spam builds that are trying to take advantage of Bloodfrenzy and Dragon Rage damage bonus while at low health.
Who tests Ring of Pain at full health? Well, I started up my game just to see if this is correct, but I was not able to get any conclusive results. At times it seemed like it added around 500-800 damage at full health, but then my next hit would do much more than that, regardless if I had Ring of Pain activated or not. If this is in fact how Ring of Pain works, then it is no wonder I couldn't see it working before; Fervor, damage bonus' while at low health from Blood Frenzy and Dragon Rage, Hakkon's Valor's Horn of Valor proc, etc. would all add up to make it virtually unnoticeable while at low health.
The spirit damage is the only part of Ring of Pain that seems to increase the lower your health gets. Tested against a Black Wolf: at full health it ticked for 100, at low health for 130. Also tested against a Bogfisher, Rage Demon, Terror, and Venatori Archer. All showed a very linear increase in damage the lower my health got.
InB4 Drasca says he knew that this is exactly how Ring of Pain works, and that I am an ignorant n00b for not seeing it after he so thoroughly explained it to me at length multiple times.
Edit because I just saw this and couldn't stop laughing. 
RoP is health based damage increase just like DR is, so its actually hard to keep track unless you're extremelly diligent about your scientific method-- which most people don't even know exist.
I guess that noticing that Ring of Pain doesn't seem to do much damage, forming a hypothesis (Ring of Pain doesn't work correctly), testing the hypothesis through simple and reproducible testing by
- Removing all variables that increase damage other than the one I am testing
- Having a consistent baseline damage (basically any damage done without Ring of Pain active, because the only ability that modifies damage relative to health level at that point was Ring of Pain)
- Gathering results from multiple enemies
then analyzing my results and sharing them and my test footage with others so they can see exactly what I did, is nothing remotely like the scientific method. Instead, go and watch Bruh's video where there are plenty of variables at play and is just a normal quick and dirty run through two zones. Much more scientific that way. 