Healing: Difference between revisions

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m replace * with middots in math formulas; middots formally denotes multiplication
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'''Healing''' is the act of recovering a unit's current [[health]], which includes various methods such as lifesteal, health regen, and item effects.
'''Healing''' is the act of recovering a unit's current [[health]], which includes various methods such as lifesteal, health regen, and item effects.
== Math ==
The formula for healing is:
<math>\text{healing}_f = \text{healing}_i \cdot \prod(1 - \text{healing}_{red} \cdot b) \cdot (1 + \text{healing}_{amp})</math><br/>
where <math>\text{healing}_f</math> is final healing, <math>\text{healing}_i</math> is initial healing, <math>\text{healing}_{red}</math> is healing reduction amount, <math>b</math> is (1 - healing reduction resistance), and <math>\text{healing}_{amp}</math> is healing amp. 


== Healing Amp ==
== Healing Amp ==
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== Healing Reduction ==
== Healing Reduction ==
Health reduction is a negative effect which reduces the effectiveness of healing on the unit it is applied to.
Healing Reduction is a negative effect which reduces the effectiveness of healing on the unit it is applied to.
 
Healing Reduction is represented as a percentage and stacks multiplicatively, meaning each additional source has diminishing returns.
 
If a player is hit by the same source of Healing Reduction before its effect has worn off (e.g. two or more enemy players with Healbane), only the first source is applied.
 
== Calculation ==
 
=== Calculating Healing Reduction ===
Multiple sources of Healing Reduction stack '''multiplicatively''':
 
<math>\text{Total Reduction} = 1 - (1 - R_1) \times (1 - R_2) \dots</math>
 
'''Example:'''
If two sources of Healing Reduction are applied, one providing '''40%''' and another providing '''40%''':
# Convert percentages to decimals: 0.40 and 0.40.
# Subtract from 1: (1 - 0.40) = '''0.60''' and (1 - 0.40) = '''0.60'''.
# Multiply the remainders: 0.60 × 0.60 = '''0.36'''.
# Subtract from 1: 1 - 0.36 = '''0.64'''.
# Total Healing Reduction is '''64%''', not 80%.
 
=== Calculating Final Healing ===


Healing reduction is represented as a percentage and stacks multiplicatively. For example, two different sources of 40% healing reduction would result in a total reduction of 64% to incoming heals.
<math>\text{Final Healing} = \text{Initial Healing} \times (1 - \text{Total Reduction}) \times (1 + \text{Healing Amp})</math>


If a player is hit by the same source of healing reduction before its effect has worn off (e.g. two or more enemy players with Healbane), only the first source is applied.
'''Example:'''
A heal of '''200 HP''' is applied to a target with '''64%''' Total Healing Reduction. The healer has '''25%''' Healing Amp.
# Apply Reduction: 200 × (1 - 0.64) = 200 × 0.36 = '''72 HP'''.
# Apply Amp: 72 × (1 + 0.25) = 72 × 1.25 = '''90 HP'''.
# Final Healing received is '''90 HP'''.


== Sources of direct healing ==
== Sources of direct healing ==