View source for Template:Collapse top/testcases

;Main
{{Collapse top|Derivation of the mana/life ratio}}
{{c|mod|When Hit, X% of Damage is taken from Mana before Life}}

Let {{math|display=inline|formula=k = {X \over 100} }}, to completely remove all mana the damage, {{math|dmg}}, has to be:
{{math|nr=1|formula=
mana - k \times dmg = 0
}}

The life removed can then be written as:
{{math|nr=2|formula=
life - (1-k) \times dmg = 0
}}

Solving equation {{EquationNote|1}} for {{math|dmg}}:
{{math|nr=3|formula=
dmg = {mana \over k}
}}

{{EquationNote|3}} in {{EquationNote|2}} gives:
{{math|nr=4|formula=
life - (1-k) \times {mana \over k} = 0
}}

Solving {{EquationNote|4}} for {{math|mana}}:
{{math|nr=5|formula=
mana = {k \over 1-k} \times life
}}

The ratio {{math|display=inline|formula={mana \over life} = {k \over 1-k} }} leads to exactly all life and mana being removed from a one-shot. 
If the ratio is less, i.e. {{math|display=inline|formula={mana \over life} < {k \over 1-k} }}, then mana will have run out before all life is removed.

The table below show the necessary mana/life ratio required for varying amounts of Mind over Matter.
{| class="wikitable" style="text-align: center;"
! X
! mana/life ratio
|-
| 0 || 0
|-
| 10% || 11%
|-
| 20% || 25%
|-
| 30% || 43%
|-
| 40% || 67%
|-
| 50% || 100%
|-
| 60% || 150%
|-
| 70% || 233%
|-
| 80% || 400%
|-
| 90% || 900%
|}
{{cob}}

;Sandbox
{{Collapse top/sandbox|Derivation of the mana/life ratio}}
{{c|mod|When Hit, X% of Damage is taken from Mana before Life}}

Let {{math|display=inline|formula=k = {X \over 100} }}, to completely remove all mana the damage, {{math|dmg}}, has to be:
{{math|nr=1|formula=
mana - k \times dmg = 0
}}

The life removed can then be written as:
{{math|nr=2|formula=
life - (1-k) \times dmg = 0
}}

Solving equation {{EquationNote|1}} for {{math|dmg}}:
{{math|nr=3|formula=
dmg = {mana \over k}
}}

{{EquationNote|3}} in {{EquationNote|2}} gives:
{{math|nr=4|formula=
life - (1-k) \times {mana \over k} = 0
}}

Solving {{EquationNote|4}} for {{math|mana}}:
{{math|nr=5|formula=
mana = {k \over 1-k} \times life
}}

The ratio {{math|display=inline|formula={mana \over life} = {k \over 1-k} }} leads to exactly all life and mana being removed from a one-shot. 
If the ratio is less, i.e. {{math|display=inline|formula={mana \over life} < {k \over 1-k} }}, then mana will have run out before all life is removed.

The table below show the necessary mana/life ratio required for varying amounts of Mind over Matter.
{| class="wikitable" style="text-align: center;"
! X
! mana/life ratio
|-
| 0 || 0
|-
| 10% || 11%
|-
| 20% || 25%
|-
| 30% || 43%
|-
| 40% || 67%
|-
| 50% || 100%
|-
| 60% || 150%
|-
| 70% || 233%
|-
| 80% || 400%
|-
| 90% || 900%
|}
</div></div>

----

;Main
{{Collapse top|Calculations of the efficiency}}
Assuming the player allocates the [[Chaos Inoculation]] keystone, the "value" of this effect is as follows for various maximum elemental resistance breakpoints. (The "Damage Taken" is an arbitrary amount corresponding to a large elemental hit for the purposes of calculation and percentages are rounded up or down to conform to the way the game displays resistances (whole numbers)).

{| class="wikitable"
! Elemental Resistances
! Elemental Damage Taken
! NET Damage Taken w/ IH + CI
! NET Damage Taken w/o IH + CI
! IH + CI Mitigation (Effective Max Resists)
! "Bonus" Effective Max Res provided by IH Effect
|-
| 85%
| 30000
| 3375
| 4500
| 89%
| 4%
|-
| 80%
| 30000
| 4500
| 6000
| 85%
| 5%
|-
| 76%
| 30000
| 5400
| 7200
| 82%
| 6%
|-
| 75%
| 30000
| 5625
| 7500
| 81%
| 6%
|-
| 70%
| 30000
| 6750
| 9000
| 78%
| 8%
|-
| 65%
| 30000
| 7875
| 10500
| 74%
| 9%
|-
| 60%
| 30000
| 9000
| 12000
| 70%
| 10%
|-
| 50%
| 30000
| 11250
| 15000
| 63%
| 13%
|-
| 45%
| 30000
| 12375
| 16500
| 59%
| 14%
|-
| 40%
| 30000
| 13500
| 18000
| 55%
| 15%
|-
| 30%
| 30000
| 15750
| 21000
| 48%
| 18%
|-
| 25%
| 30000
| 16875
| 22500
| 44%
| 19%
|-
| 20%
| 30000
| 18000
| 24000
| 40%
| 20%
|-
| 15%
| 30000
| 19125
| 25500
| 36%
| 21%
|-
| 10%
| 30000
| 20250
| 27000
| 33%
| 23%
|-
| 5%
| 30000
| 21375
| 28500
| 29%
| 24%
|-
| 0%
| 30000
| 22500
| 30000
| 25%
| 25%
|}

For characters with less than 76% Chaos Resistance, '''Incandescent Heart''' acts as an elemental damage taken multiplier, increasing the total amount of elemental damage taken as illustrated in the following table:

{| class="wikitable"
! Elemental Resistances
! Chaos Resistance
! Elemental Damage Taken
! NET Damage taken w/ IH
! NET Damage Taken w/o IH
! (Percent of) Elemental Damage Taken
|-
| 75%
| -60%
| 30000
| 17625
| 7500
| 235%
|-
| 75%
| -40%
| 30000
| 16125
| 7500
| 215%
|-
| 75%
| -20%
| 30000
| 14625
| 7500
| 195%
|-
| 75%
| 0%
| 30000
| 13125
| 7500
| 175%
|-
| 75%
| 20%
| 30000
| 11625
| 7500
| 155%
|-
| 75%
| 40%
| 30000
| 10125
| 7500
| 135%
|-
| 75%
| 60%
| 30000
| 8625
| 7500
| 115%
|-
| 75%
| 75%
| 30000
| 7500
| 7500
| 100%
|-
| 75%
| 100%
| 30000
| 5625
| 7500
| 75%
|}
{{cob}}

;Sandbox
{{Collapse top/sandbox|Calculations of the efficiency}}
Assuming the player allocates the [[Chaos Inoculation]] keystone, the "value" of this effect is as follows for various maximum elemental resistance breakpoints. (The "Damage Taken" is an arbitrary amount corresponding to a large elemental hit for the purposes of calculation and percentages are rounded up or down to conform to the way the game displays resistances (whole numbers)).

{| class="wikitable"
! Elemental Resistances
! Elemental Damage Taken
! NET Damage Taken w/ IH + CI
! NET Damage Taken w/o IH + CI
! IH + CI Mitigation (Effective Max Resists)
! "Bonus" Effective Max Res provided by IH Effect
|-
| 85%
| 30000
| 3375
| 4500
| 89%
| 4%
|-
| 80%
| 30000
| 4500
| 6000
| 85%
| 5%
|-
| 76%
| 30000
| 5400
| 7200
| 82%
| 6%
|-
| 75%
| 30000
| 5625
| 7500
| 81%
| 6%
|-
| 70%
| 30000
| 6750
| 9000
| 78%
| 8%
|-
| 65%
| 30000
| 7875
| 10500
| 74%
| 9%
|-
| 60%
| 30000
| 9000
| 12000
| 70%
| 10%
|-
| 50%
| 30000
| 11250
| 15000
| 63%
| 13%
|-
| 45%
| 30000
| 12375
| 16500
| 59%
| 14%
|-
| 40%
| 30000
| 13500
| 18000
| 55%
| 15%
|-
| 30%
| 30000
| 15750
| 21000
| 48%
| 18%
|-
| 25%
| 30000
| 16875
| 22500
| 44%
| 19%
|-
| 20%
| 30000
| 18000
| 24000
| 40%
| 20%
|-
| 15%
| 30000
| 19125
| 25500
| 36%
| 21%
|-
| 10%
| 30000
| 20250
| 27000
| 33%
| 23%
|-
| 5%
| 30000
| 21375
| 28500
| 29%
| 24%
|-
| 0%
| 30000
| 22500
| 30000
| 25%
| 25%
|}

For characters with less than 76% Chaos Resistance, '''Incandescent Heart''' acts as an elemental damage taken multiplier, increasing the total amount of elemental damage taken as illustrated in the following table:

{| class="wikitable"
! Elemental Resistances
! Chaos Resistance
! Elemental Damage Taken
! NET Damage taken w/ IH
! NET Damage Taken w/o IH
! (Percent of) Elemental Damage Taken
|-
| 75%
| -60%
| 30000
| 17625
| 7500
| 235%
|-
| 75%
| -40%
| 30000
| 16125
| 7500
| 215%
|-
| 75%
| -20%
| 30000
| 14625
| 7500
| 195%
|-
| 75%
| 0%
| 30000
| 13125
| 7500
| 175%
|-
| 75%
| 20%
| 30000
| 11625
| 7500
| 155%
|-
| 75%
| 40%
| 30000
| 10125
| 7500
| 135%
|-
| 75%
| 60%
| 30000
| 8625
| 7500
| 115%
|-
| 75%
| 75%
| 30000
| 7500
| 7500
| 100%
|-
| 75%
| 100%
| 30000
| 5625
| 7500
| 75%
|}
</div></div>

----

;Main
{{Collapse top|Example}}
* A player is wielding a bow that deals 100 Physical Damage,
* a {{il|Blackgleam}} quiver that has {{c|mod|50% of Physical Damage '''converted''' to Fire Damage}},
* and {{il|Hrimsorrow}} gloves that have {{c|mod|25% of Physical Damage '''converted''' to Cold Damage}}.
* The player is using the skill {{il|Lightning Arrow}}, which has {{c|mod|50% of Physical Damage '''converted''' to Lightning Damage}}
::The total in this is example is 125% of Physical Damage, and must be scaled. Since it comes from a skill gem, Lightning Arrow's modifier takes priority and is not scaled. The other two are scaled proportionally to convert the remaining 50% of physical damage.
:::50 * (50/75) = 33.33% Converted to Fire Damage by Blackgleam
:::25 * (50/75) = 16.67% Converted to Cold Damage by Hrimsorrow
::In summary, the resulting converted damage would be 50 Lightning Damage, 33 Fire Damage, and 17 Cold Damage, and 0 Physical Damage, a total of 100 Damage.
{{cob}}

;Sandbox
{{Collapse top/sandbox|Example}}
* A player is wielding a bow that deals 100 Physical Damage,
* a {{il|Blackgleam}} quiver that has {{c|mod|50% of Physical Damage '''converted''' to Fire Damage}},
* and {{il|Hrimsorrow}} gloves that have {{c|mod|25% of Physical Damage '''converted''' to Cold Damage}}.
* The player is using the skill {{il|Lightning Arrow}}, which has {{c|mod|50% of Physical Damage '''converted''' to Lightning Damage}}
::The total in this is example is 125% of Physical Damage, and must be scaled. Since it comes from a skill gem, Lightning Arrow's modifier takes priority and is not scaled. The other two are scaled proportionally to convert the remaining 50% of physical damage.
:::50 * (50/75) = 33.33% Converted to Fire Damage by Blackgleam
:::25 * (50/75) = 16.67% Converted to Cold Damage by Hrimsorrow
::In summary, the resulting converted damage would be 50 Lightning Damage, 33 Fire Damage, and 17 Cold Damage, and 0 Physical Damage, a total of 100 Damage.
</div></div>