Elemental Skills Deal X% more damage Fully Explained

Credit: Druid - Banned of Gamers

Hello everyone,
I am here to fully explain the affix that has become popular with loot 2.0 that reads:
<Element> skills deal X% more damage
Along with MANY more cases of this affix, Blizz has implemented a pretty solid elemental system for our skills. For the most part, this system works as you would expect it to. However, in some cases it breaks down completely.
I will do my absolute best to write this in a readable way but I want to warn those with a weak-constitution ... thar be Math ahead!
Basics behind the Elemental Affix​Here is an example of the stat in question --

In this example, we see that Azurewrath can roll with "Cold skills deal 15-20% more damage"
For the rest of this example, we will assume it rolled with 20%.
For the most part, this stat is easy to understand ... if you use a skill that is designated as "cold damage" it will do more damage than the same skill if it were designated as something else.
An example skill is --

As you can see, Ray of Frost normally deals 510% weapon damage.
However, If you have the Azurewrath equipped, it will instead deal 510% * 1.2 = 612% weapon damage.
Now let's say you have Azurewrath and Frostburn Gauntelets equipped giving you one source of 20% cold skill damage and another source of 15% cold skill damage.
This is an "additive" stat and your total bonus to cold skills is simply the sum of all your bonuses.
You will have a total bonus of 1+ [0.2 (Azurewrath) + 0.15 (Frosties)] = 1.35
Ray of Frost will now deal 510% * 1.35 = 688.5% weapon damage.
As you can see, this stat is immensly powerful. A normal character will usually get about 9.23% total damage increase from the 6% Critical Hit Chance stat on your Bracers. If, instead of that stat, you went with 15% <elemental> skill damage you would be getting a massive 15% total damage increase to your <element> skills.
This is 1.63x as much damage increase as the CHC!!!
Critical Hit Chance has historically been the best stat for DPS so it's awesome to see a stat beat it out completely.
What Skills Does it Affect?​ This has been a very popular question over the last couple of weeks and it's a very strait forward one.
The <Element> skills deal X% more damage affix only applies the skills that deal X% weapon damage in some way.
Example --

Un-runed Cyclone Strike will always deal Holy damage and is therefore subject to the Holy Skills deal X% more damage stat.
However, the ONLY part of the skill that will be affected is the 261% weapon damage.
This will be increased by X%.
The number of enemies and yards they are pulled will not be altered in any way.
Any skill that has an effect other than X% weapon damage will not have that effect altered by <Element> skills deal X% more damage.
Note: this includes skills that deal damage that is not tied to weapon damage such as Exploding Palm's explosion (the DoT will still do increased damage).
Elemental Affixes and Weapon Elements​ How does your X - Y <element> Damage affix on your weapon interact with your <Element> skills deal X% more damage affixes?
The short answer --
It has no effect what-so-ever
In a hotfix, the following change was made --

This change fixed the last "buggy" issue with this stat and correctly changes ALL elemental type-skills to change your damage type TO the element they are labeled as.
Elemental Affix and Skill Bonus Affix​ Some items have another affix that reads Increase <Skill> damage by X% that interact VERY favorably with <Elemental> Skills deal X% more Damage.
Here is an example --
This staff directly increases the damage done by --

If the Diabo rolls 50%, Deadly Reach will go from 109% to 109*1.5 = 163.5% weapon damage.
However, if we throw some Physical Skills deal X% more Damage into the mix you start to see some incredibly high numbers.
Let's say you have 20% Physical damage on bracers and 20% Physical damage on Andy's helm.
Combine with this staff you will now have a DR that does 109% * 1.5 (staff) * 1.4 (bracers+helm) = 228.9% weapon damage. This is 2.1x higher than it normally is!
The take-away here is that <Elemental> Skills deal X% more Damage and Increase <Skill> damage by X% stack multiplicitively with each other.
Conclusion​All in all, the stat <Elemental> Skills deal X% more Damage is extremely strong when used correctly and will make or break your build. Selecting skills carefully and stacking this affix in the right places will drastically increase your effective DPS!
Best of luck and thank you so much for taking all the time to read this.