**#1**

**UNDERSTANDING THE DAMAGE REDUCTION**

The damage reduction is applied, of course, to the damage that a hero receives. Thus if a defender hero with 3/5 stone skin (15% reduction) receives a raw damage of 15,000, the damage actually received by the hero is only 85% (100% -15%) of the initial damage: 15000 * 85 % = 12750

**Trick Question:** What happens if this defender hero with 3/5 stone skin is actually a paladin with skill 5/10?

**The Wrong answer would be**: Well, the skill of the paladin when activated reduces incoming damage by 70%, moreover the stone skin reduces over 15%. So the total reduction is 85% !!!

Indeed that's the most immediate answer that comes to mind, but in fact what happens is not a direct sum! Far from it!

**The Right answer would be:** Due to the talent, he will receive only 85% of the gross damage (because the talent reduces 15%) and from this amount he will receive only 30% (for his skill reduces 70%).

Then the 15,000 damage will be reduced to 15,000 * 85% * 30% = 3825 which corresponds to a total reduction of 74.5% (much lower than the 85% who thought at first and almost nothing better than the original paladin's 70% shield)

Overall formula:

**Damage taken = Gross Damage* (1 - %reduction from talent)*(1-%reduction from some shield due to an allied skill)**

**TENACITY VS STONE SKIN**

Within the scope of damage reduction, we have the classical comparison tenacity vs. stone Skin:

Tenacity will increase the hero of HP directly as follows: HP * (1+%tenacitybuff)

Stone skin, on the other hand, will not increase the actual HP, but will reduce the damage as we saw earlier.

Suppose a hero with total 60000 HP (inscription and crest HP bonuses included)

If this hero has 5/8 tenacity then that HP will increase by 30%. The actual HP will be 60000 * 1.3 = 78000

Now suppose instead of tenacity, he has 5/8 stone skin that reduces all damage taken by 25%. Thus, for this hero to die, he should receive a damage X such that 75% (=100% -25%) of it is equal to 60 000 HP !!

Mathematically we have:

X * 75% = 60000

X = 60000/75% = 80000

You may notice the stone skin hero will have to receive more damage to die! So it is said that effective HP due to damage reduction is greater than an directly increased HP (by tenacity or bulwar for instance)

The same analysis can be done for 8/8 talents level (or any level):

Tenacity 8/8 = 100% hp buff

Increased HP = HP*(1+100%)=2*HP

Stone skin 8/8 = 60% damage reduction

Effective HP = HP/(100%-60%) = HP/0,4 = 2,5*HP

**At the table below you can compare the HP improvement factor for these talents at different levels:**

From that table we can afirm that for level 4 stone skin or tenacity have the same efficiency. For talent level lower than 4, tenacity gives better results. But for talent level 5 or higher, stone skin is imensely better.

**INTERACTION WITH HEALING**

Another interesting thing is the interaction of damage reduction with healing. Imagine, for example, a hero that receives a 15,000 HP heal from Druid.

For these 15,000 be lost again, a greater damage than those 15,000 have to be received precisely because of the damage reduction! Therefore it is said that healing is actually more effective on heroes with damage reduction!

**FLAME GUARD**

It has been proven in several videos that talent flame guard, by reflecting the damage to attackers will also reduces damage taken by the defender!

So it is better than the stone skin at levels 1 and 2 for it offers a higher reduction. However from level 3+, stone skin will be better due to greater % of dmg reduction!!

Recommended video:

https://youtu.be/z5l2f9DFax4

**Extra: RESIDUAL HP ANALYSIS **(for 5/8 talents but can be done for other lvls aswell)

This analysis explain the treshold of the effectivenss between tenacity and stone skin. What the amount of dmg taken which will make dmg reduction better than increasing HP?

**Hope it helps **

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