Exsanguinous

Build Tips
Exsanguinous is used to make ward a more permanent source of health than health itself. Even though this is true, increases to your maximum health will increase your stable ward (see math section below). As a result of this, health, ward regen, and ward retention (and by proxy, intelligence) are valuable stats for increasing your survivability. In order to break even on the conversion with your usable health pool, you require at least 100% ward retention. Interestingly, the traditional defense stats like armor and protections actually have diminishing effectiveness, and are not the primary recommended defensive stats.

It is highly recommended to pair this item with Chains of Uleros.

Math
Exsanguinous principally changes how your health pool functions. When equipped it drains your health and increases your ward until it reaches an equilibrium.

The following formulas can be used to determine at what point each will reach a stable value:

$$HP_{Stable} = (HP_{BaseRegen} + HP_{AddedRegen}) * (1 + HP_{IncrRegen}) \div (0.2 + H_{AddedPercDegen})$$

$$W_{Stable} = [(HP_{Max} - HP_{Stable}) * 0.2 + W_{Regen}] * (1 + W_{IncrRet}) \div 0.4$$

Base health regeneration is determined by your character level. (9.22 at level 23, 13 at level 50, 16.5 at level 75, and 20 at level 100)

Calculating your stable ward with Exsanguinous is different than if you just had simple ward regen.

From these formulas some observations can be shown:


 * 1) Increases and reductions to health do not effect your stable health, but effect your stable ward instead.
 * 2) Increases to health regen reduce your stable ward, and inversely decreases to health regen will increases your stable ward.
 * 3) Increases to ward regen and retention increase your stable ward.
 * 4) Increases to your character level increase your stable health and reduce your stable ward.

From here we can continue to draw comparisons between your old health pool and your new health pool. Without Exsanguinous your health pool is your maximum health. With Exsanguinous your usable health pool becomes your stable health plus your stable ward. By default Exsanguinous will reduce your usable health pool. You require a minimum of 100% ward retention to break even on the conversion.

This does however get complicated when you consider how armor and protections effect your survivability. By default each 1 point of armour and protections provides an increase of 1 point to effective health against that type of damage. With Exsanguinous this effect is reduced since it is calculated using your maximum health and current ward, and you are always missing part of your maximum health.

$$EHP_{Without} = HP_{Max} \div \left (1 - {A \over |A| + HP_{Max}} \right )$$

$$EHP_{With} = (HP_{Stable} + W_{Stable}) \div \left (1 - {A \over |A| + HP_{Max} + W_{Stable}} \right )$$

Where A is armor, protections, or some average of those.

To calculate the actual value of each point of armour or protections, use the following formula:

$$EHP_{PerPoint} = (HP_{Stable} + W_{Stable}) \div \left (1 - {1 \over 1 + HP_{Max} + W_{Stable}} \right ) - (HP_{Stable} + W_{Stable})$$

For example:


 * 1) At 500 max health, 50 stable health, and 1000 stable ward, each point of armour and protections is worth 0.7 EHP.


 * 1) At 500 max health, 50 stable health, and 2000 stable ward, each point of armour and protections is worth 0.82 EHP.

As your stable ward increases, the value of each point with continue to approach 1 but never actually get there. As such, it is recommended to not focus on armour and protections, but also not worry about having any.

Trivia
This item was designed by ZiggyD.