Ability Range: Difference between revisions

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[[File:Ability Range.png|thumb|[[Shiv]]'s Slice and Dice ability, improved by bonus [[Ability Range]] and [[Spirit Power]] stats.|class=notpageimage]]

[[Ability Range]] determines the effective distance and cast range of hero abilities. It is measured in a distance of meters, and stat gains are measured in percentages.

[[Ability Range]] determines the effective distance and cast range of hero abilities and items. It is measured in a distance of meters, and stat gains are measured in percentages.

For example, [[Shiv]]'s '''Slice and Dice''' ability has a dash range of '''12 meters'''. Purchasing [[Mystic Expansion]] improves this by '''35%''', making the new effective dash range of the ability '''16.2 meters'''.

The range of [[Active Items]] does not consider height and their cast range is shaped like a cylinder. This means their range can be greater than expected when targeting heroes above or below the player.

== Calculation ==

Multiple sources of Ability Range stack with diminishing returns, rather than multiplicatively or additively. Additional sources of Ability Range contribute less the closer the effective bonus gets to 100%, and the effective bonus can never actually reach 100%.

<math>\text{~~Effective~~ Ability Range ~~bonus~~} = 1 - (1 - R_1) \times (1 - R_2) \dots</math>

=== Calculating Ability Range ===

Multiple sources of Ability Range stack '''multiplicatively''', not additively:

<math>\text{Total Ability Range} = 1 - (1 - R_1) \times (1 - R_2) \dots</math>

'''Example:'''

With '''~~35%~~''' from {{ItemIcon|Greater Expansion}} and '''~~10%~~''' from {{ItemIcon|Divine Barrier}}:

With '''{{ItemData|{{#vardefineecho: Item1|Greater Expansion}}|TechRangeMultiplier}}''' from {{ItemIcon|Greater Expansion}} and '''{{ItemData|{{#vardefineecho: Item2|Divine Barrier}}|TechRangeMultiplier}}''' from {{ItemIcon|Divine Barrier}}:

# Convert percentages to decimals: ~~0.35~~ and ~~0.10~~.

# Convert percentages to decimals: {{ItemData|{{#var: Item1}}|TechRangeMultiplier}} to {{#vardefineecho: Item1Range|{{#expr: {{#replace: {{ItemData|{{#var: Item1}}|TechRangeMultiplier}}|%|}} / 100}}}} and {{ItemData|{{#var: Item2}}|TechRangeMultiplier}} to {{#vardefineecho: Item2Range|{{#expr: {{#replace: {{ItemData|{{#var: Item2}}|TechRangeMultiplier}}|%|}} / 100}}}}.

# ~~Take the complement with~~ 1: (1 - ~~0.35~~) = '''~~0.65~~''' and (1 - ~~0.10~~) = '''~~0.90~~'''.

# Subtract from 1: (1 - {{#var: Item1Range}}) = '''{{#expr: 1 - {{#var: Item1Range}}}}''' and (1 - {{#var: Item2Range}}) = '''{{#expr: 1 - {{#var: Item2Range}}}}'''.

# Multiply the ~~complements~~: ~~0.65~~ × ~~0.90~~ = '''~~0.585~~'''.

# Multiply the differences: {{#expr: 1 - {{#var: Item1Range}}}} × {{#expr: 1 - {{#var: Item2Range}}}} = '''{{#vardefineecho: CombinedItemRange|{{#expr: (1 - {{#var: Item1Range}}) * (1 - {{#var: Item2Range}}) round 4}}}}'''.

# ~~Take the complement with~~ 1: 1 - ~~0.585~~ = '''~~0.415~~'''.

# Subtract from 1: 1 - {{#var: CombinedItemRange}} = '''{{#expr: 1 - {{#var: CombinedItemRange}} round 4}}'''.

# ~~Effective~~ Ability Range bonus is ~~approximately~~ '''~~41.5~~%''', not 45%.

# Total Ability Range bonus is '''{{#expr: (1 - {{#var: CombinedItemRange}}) * 100}}%''', not {{#expr: ({{#var: Item1Range}} + {{#var: Item2Range}}) * 100 round 1}}%.

~~Of note is that~~

== Sources of Ability Range ==

Ability Range: Difference between revisionsGive feedback

~2026-LaneFireUrn1085 (talk)

@@ Line 1: / Line 1: @@
 [[File:Ability Range.png|thumb|[[Shiv]]'s Slice and Dice ability, improved by bonus [[Ability Range]] and [[Spirit Power]] stats.|class=notpageimage]]
-[[Ability Range]] determines the effective distance and cast range of hero abilities. It is measured in a distance of meters, and stat gains are measured in percentages.
+[[Ability Range]] determines the effective distance and cast range of hero abilities and items. It is measured in a distance of meters, and stat gains are measured in percentages.
 For example, [[Shiv]]'s '''Slice and Dice''' ability has a dash range of '''12 meters'''. Purchasing [[Mystic Expansion]] improves this by '''35%''', making the new effective dash range of the ability '''16.2 meters'''.
+The range of [[Active Items]] does not consider height and their cast range is shaped like a cylinder. This means their range can be greater than expected when targeting heroes above or below the player.
 == Calculation ==
-Multiple sources of Ability Range stack with diminishing returns, rather than multiplicatively or additively. Additional sources of Ability Range contribute less the closer the effective bonus gets to 100%, and the effective bonus can never actually reach 100%.
-<math>\text{Effective Ability Range bonus} = 1 - (1 - R_1) \times (1 - R_2) \dots</math>
+=== Calculating Ability Range ===
+Multiple sources of Ability Range stack '''multiplicatively''', not additively:
+<math>\text{Total Ability Range} = 1 - (1 - R_1) \times (1 - R_2) \dots</math>
 '''Example:'''
-With '''35%''' from {{ItemIcon|Greater Expansion}} and '''10%''' from {{ItemIcon|Divine Barrier}}:
+With '''{{ItemData|{{#vardefineecho: Item1|Greater Expansion}}|TechRangeMultiplier}}''' from {{ItemIcon|Greater Expansion}} and '''{{ItemData|{{#vardefineecho: Item2|Divine Barrier}}|TechRangeMultiplier}}''' from {{ItemIcon|Divine Barrier}}:
-# Convert percentages to decimals: 0.35 and 0.10.
+# Convert percentages to decimals: {{ItemData|{{#var: Item1}}|TechRangeMultiplier}} to {{#vardefineecho: Item1Range|{{#expr: {{#replace: {{ItemData|{{#var: Item1}}|TechRangeMultiplier}}|%|}} / 100}}}} and {{ItemData|{{#var: Item2}}|TechRangeMultiplier}} to {{#vardefineecho: Item2Range|{{#expr: {{#replace: {{ItemData|{{#var: Item2}}|TechRangeMultiplier}}|%|}} / 100}}}}.
-# Take the complement with 1: (1 - 0.35) = '''0.65''' and (1 - 0.10) = '''0.90'''.
+# Subtract from 1: (1 - {{#var: Item1Range}}) = '''{{#expr: 1 - {{#var: Item1Range}}}}''' and (1 - {{#var: Item2Range}}) = '''{{#expr: 1 - {{#var: Item2Range}}}}'''.
-# Multiply the complements: 0.65 × 0.90 = '''0.585'''.
+# Multiply the differences: {{#expr: 1 - {{#var: Item1Range}}}} × {{#expr: 1 - {{#var: Item2Range}}}} = '''{{#vardefineecho: CombinedItemRange|{{#expr: (1 - {{#var: Item1Range}}) * (1 - {{#var: Item2Range}}) round 4}}}}'''.
-# Take the complement with 1: 1 - 0.585 = '''0.415'''.
+# Subtract from 1: 1 - {{#var: CombinedItemRange}} = '''{{#expr: 1 - {{#var: CombinedItemRange}} round 4}}'''.
-# Effective Ability Range bonus is approximately '''41.5%''', not 45%.
+# Total Ability Range bonus is '''{{#expr: (1 - {{#var: CombinedItemRange}}) * 100}}%''', not {{#expr: ({{#var: Item1Range}} + {{#var: Item2Range}}) * 100 round 1}}%.
-Of note is that
 == Sources of Ability Range ==