How does the "Obsidian Ring of the Zodiac" work in Diablo 3?

In Diablo 3, the legendary ring Obsidian Ring of the Zodiac has the following legendary power since patch 2.2 (patch notes):

Reduce the remaining cooldown of one of your skills by 1 seconds when you hit with a resource-spending attack.

This can potentially allow for permanent uptime of certain skills (Champion of Akarat, Wrath of the Berserker, Epiphany, etc). However, it does not appear to scale as expected in situations with high density.

How does the ring's legendary power really work?

Solution 1:

The description is slightly misleading, as the cooldown reduction is only triggered on the first hit by each spender cast. This means a multishot or blessed hammer can only reduce a cooldown by one second, no matter how many enemies are hit.

The legendary effect does not appear to be affected by proc coefficients (source, source), and conflicting reports are likely due to people expecting the ring to be able to reduce the cooldown every time a spender hits, not just the first (as per the first paragraph).

The cooldown that is reduced is randomly picked among your current remaining cooldowns (source).

This leads to a few conclusions:

• As long as you're hitting at least one monster, further increasing mob density will not help you reduce your cooldowns.
• Attack speed translates directly to cooldown reduction provided enough resources are available (given that at least one monster is being hit). The maximum cooldown achievable is directly tied to how many spenders you can put out in the given time frame. If you have a skill on a 90s cooldown, with a 30s duration, you need to hit with 60 spenders during that 30s duration to sustain permanent uptime.
• If resources are abundant, casting extra spenders instead of letting present ones finish mobs can be beneficial (for example, casting a second Blessed Hammer to kill a mob that would otherwise die from a previously cast one).
• To efficiently reduce the cooldown of a specific skill, one should avoid casting other cooldown-dependent skills unless necessary. The other skills will "steal" some of the random reductions and may prevent you from reaching permanent uptime on the specific skill.

All in all, a better (or at least more accurate) description could be:

Reduce a randomly chosen remaining cooldown of one of your skills by 1 seconds the first time you hit with a resource-spending attack.

Also note that it is triggered when hitting debris or breakable containers, which can be useful for fast-moving builds.