Ability Range - Revision history

~2026-LaneFireUrn1085: /* Calculating Ability Range */ cleanup #replace itemdata -> DataProp

2026-09-12T16:02:46Z

Calculating Ability Range: cleanup #replace itemdata -> DataProp

← Older revision		Revision as of 16:02, 12 September 2026
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	'''Example:'''		'''Example:'''
	With '''{{~~ItemData~~\|{{#vardefineecho: Item1\|Greater Expansion}}\|TechRangeMultiplier}}''' from {{ItemIcon\|~~Greater Expansion~~}} and '''{{~~ItemData~~\|{{#vardefineecho: Item2\|Divine Barrier}}\|TechRangeMultiplier}}''' from {{ItemIcon\|~~Divine Barrier~~}}:		With '''{{DataProp\|{{#vardefineecho: Item1\|Greater Expansion}}\|TechRangeMultiplier}}%''' from {{ItemIcon\|{{#var: Item1}}}} and '''{{DataProp\|{{#vardefineecho: Item2\|Divine Barrier}}\|TechRangeMultiplier}}%''' from {{ItemIcon\|{{#var: Item2}}}}:
	# 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}}}}.		# Convert percentages to decimals: {{DataProp\|{{#var: Item1}}\|TechRangeMultiplier}}% to {{#vardefineecho: Item1Range\|{{#expr: {{DataProp\|{{#var: Item1}}\|TechRangeMultiplier}} / 100}}}} and {{DataProp\|{{#var: Item2}}\|TechRangeMultiplier}}% to {{#vardefineecho: Item2Range\|{{#expr: {{DataProp\|{{#var: Item2}}\|TechRangeMultiplier}} / 100}}}}.
	# Subtract from 1: (1 - {{#var: Item1Range}}) = '''{{#expr: 1 - {{#var: Item1Range}}}}''' and (1 - {{#var: Item2Range}}) = '''{{#expr: 1 - {{#var: Item2Range}}}}'''.		# Subtract from 1: (1 - {{#var: Item1Range}}) = '''{{#expr: 1 - {{#var: Item1Range}}}}''' and (1 - {{#var: Item2Range}}) = '''{{#expr: 1 - {{#var: Item2Range}}}}'''.
	# Multiply the differences: {{#expr: 1 - {{#var: Item1Range}}}} × {{#expr: 1 - {{#var: Item2Range}}}} = '''{{#vardefineecho: CombinedItemRange\|{{#expr: (1 - {{#var: Item1Range}}) * (1 - {{#var: Item2Range}}) round 4}}}}'''.		# Multiply the differences: {{#expr: 1 - {{#var: Item1Range}}}} × {{#expr: 1 - {{#var: Item2Range}}}} = '''{{#vardefineecho: CombinedItemRange\|{{#expr: (1 - {{#var: Item1Range}}) * (1 - {{#var: Item2Range}}) round 4}}}}'''.

~2026-LaneFireUrn1085: /* Calculation */ rewrite to use https://www.mediawiki.org/wiki/Extension:Variables

2026-09-10T17:01:33Z

Calculation: rewrite to use https://www.mediawiki.org/wiki/Extension:Variables

← Older revision		Revision as of 17:01, 10 September 2026
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	'''Example:'''		'''Example:'''
	With '''{{ItemData\|Greater Expansion\|TechRangeMultiplier}}''' from {{ItemIcon\|Greater Expansion}} and '''{{ItemData\|Divine Barrier\|TechRangeMultiplier}}''' 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: {{ItemData\|~~Greater Expansion~~\|TechRangeMultiplier}} to {{#expr: {{#replace: {{ItemData\|~~Greater Expansion~~\|TechRangeMultiplier}}\|%\|}} / 100}} and {{ItemData\|~~Divine Barrier~~\|TechRangeMultiplier}} to {{#expr: {{#replace: {{ItemData\|~~Divine Barrier~~\|TechRangeMultiplier}}\|%\|}} / 100}}.		# 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}}}}.
	# Subtract from 1: (1 - {{#~~expr~~: ~~{{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100~~}}) = '''{{#expr: 1 - {{#~~replace~~: ~~{{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|~~}} ~~/ 100~~}}''' and (1 - {{#~~expr~~: ~~{{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100~~}}) = '''{{#expr: 1 - {{#~~replace~~: ~~{{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|~~}} ~~/ 100~~}}'''.		# Subtract from 1: (1 - {{#var: Item1Range}}) = '''{{#expr: 1 - {{#var: Item1Range}}}}''' and (1 - {{#var: Item2Range}}) = '''{{#expr: 1 - {{#var: Item2Range}}}}'''.
	# Multiply the differences: {{#expr: 1 - {{#~~replace~~: ~~{{ItemData\|Greater Expansion\|TechRangeMultiplier~~}}~~\|%\|}} / 100~~}} × {{#expr: 1 - {{#~~replace~~: ~~{{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|~~}} ~~/ 100~~}} = '''{{#expr: (1 - {{#~~replace~~: ~~{{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|~~}} ~~/ 100~~) * (1 - {{#~~replace~~: ~~{{ItemData\|Divine Barrier\|TechRangeMultiplier~~}}~~\|%\|}} / 100~~) round 4}}'''.		# Multiply the differences: {{#expr: 1 - {{#var: Item1Range}}}} × {{#expr: 1 - {{#var: Item2Range}}}} = '''{{#vardefineecho: CombinedItemRange\|{{#expr: (1 - {{#var: Item1Range}}) * (1 - {{#var: Item2Range}}) round 4}}}}'''.
	# Subtract from 1: 1 - {{#~~expr: (1 - {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100) * (1 - {{#replace~~: ~~{{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100) round 4~~}} = '''{{#expr: ~~1 - (~~1 - {{#~~replace~~: ~~{{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|~~}} ~~/ 100) * (1 - {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100)~~ round 4}}'''.		# Subtract from 1: 1 - {{#var: CombinedItemRange}} = '''{{#expr: 1 - {{#var: CombinedItemRange}} round 4}}'''.
	# Total Ability Range bonus is '''{{#expr: ~~(1 -~~ (1 - {{#~~replace~~: ~~{{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|~~}} ~~/ 100) * (1 - {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100)~~) * 100}}%''', not {{#expr: {{#~~replace~~: ~~{{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|~~}} + {{#~~replace~~: ~~{{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|~~}} round 1}}%.		# Total Ability Range bonus is '''{{#expr: (1 - {{#var: CombinedItemRange}}) * 100}}%''', not {{#expr: ({{#var: Item1Range}} + {{#var: Item2Range}}) * 100 round 1}}%.

	== Sources of Ability Range ==		== Sources of Ability Range ==

~2026-LaneFireUrn1085: /* Calculation */ change calculation section to dynamically pull from ItemData. this was already out of date so I'm trying this out, feel free to undo it if it's causing performance issues

2026-09-10T16:37:46Z

Calculation: change calculation section to dynamically pull from ItemData. this was already out of date so I'm trying this out, feel free to undo it if it's causing performance issues

← Older revision		Revision as of 16:37, 10 September 2026
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	'''Example:'''		'''Example:'''
	With '''~~35%~~''' from {{ItemIcon\|Greater Expansion}} and '''~~10%~~''' from {{ItemIcon\|Divine Barrier}}:		With '''{{ItemData\|Greater Expansion\|TechRangeMultiplier}}''' from {{ItemIcon\|Greater Expansion}} and '''{{ItemData\|Divine Barrier\|TechRangeMultiplier}}''' from {{ItemIcon\|Divine Barrier}}:
	# Convert percentages to decimals: ~~0.35~~ and ~~0.10~~.		# Convert percentages to decimals: {{ItemData\|Greater Expansion\|TechRangeMultiplier}} to {{#expr: {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100}} and {{ItemData\|Divine Barrier\|TechRangeMultiplier}} to {{#expr: {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100}}.
	# Subtract from 1: (1 - ~~0.35~~) = '''~~0.65~~''' and (1 - ~~0.10~~) = '''~~0.90~~'''.		# Subtract from 1: (1 - {{#expr: {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100}}) = '''{{#expr: 1 - {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100}}''' and (1 - {{#expr: {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100}}) = '''{{#expr: 1 - {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100}}'''.
	# Multiply the differences: ~~0.65~~ × ~~0.90~~ = '''~~0.585~~'''.		# Multiply the differences: {{#expr: 1 - {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100}} × {{#expr: 1 - {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100}} = '''{{#expr: (1 - {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100) * (1 - {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100) round 4}}'''.
	# Subtract from 1: 1 - ~~0.585~~ = '''~~0.415~~'''.		# Subtract from 1: 1 - {{#expr: (1 - {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100) * (1 - {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100) round 4}} = '''{{#expr: 1 - (1 - {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100) * (1 - {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100) round 4}}'''.
	# Total Ability Range bonus is ~~approximately~~ '''~~41.5~~%''', not 45%.		# Total Ability Range bonus is '''{{#expr: (1 - (1 - {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} / 100) * (1 - {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} / 100)) * 100}}%''', not {{#expr: {{#replace: {{ItemData\|Greater Expansion\|TechRangeMultiplier}}\|%\|}} + {{#replace: {{ItemData\|Divine Barrier\|TechRangeMultiplier}}\|%\|}} round 1}}%.

	== Sources of Ability Range ==		== Sources of Ability Range ==

~2026-LaneFireUrn1085: add note about items having cylindrical ability range

2026-09-10T16:00:22Z

add note about items having cylindrical ability range

← Older revision		Revision as of 16:00, 10 September 2026
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	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'''.		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 ==		== Calculation ==

~2026-LaneFireUrn1085: clarify that ability range affects items (I think this is worth mentioning since Ability Range/Duration affect items but not Ability Cooldown)

2026-09-10T15:52:35Z

clarify that ability range affects items (I think this is worth mentioning since Ability Range/Duration affect items but not Ability Cooldown)

← Older revision		Revision as of 15:52, 10 September 2026
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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]]		[[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'''.		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'''.

Monster Domosed: Reverted edits by ~2026-RegenHideBebop921 (talk) to last revision by Rem

2026-08-16T21:11:02Z

Reverted edits by ~2026-RegenHideBebop921 (talk) to last revision by Rem

← Older revision		Revision as of 21:11, 16 August 2026
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	== Calculation ==		== 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:'''		'''Example:'''
	With '''35%''' from {{ItemIcon\|Greater Expansion}} and '''10%''' from {{ItemIcon\|Divine Barrier}}:		With '''35%''' from {{ItemIcon\|Greater Expansion}} and '''10%''' from {{ItemIcon\|Divine Barrier}}:
	# Convert percentages to decimals: 0.35 and 0.10.		# Convert percentages to decimals: 0.35 and 0.10.
	# ~~Take the complement with~~ 1: (1 - 0.35) = '''0.65''' and (1 - 0.10) = '''0.90'''.		# Subtract from 1: (1 - 0.35) = '''0.65''' and (1 - 0.10) = '''0.90'''.
	# Multiply the ~~complements~~: 0.65 × 0.90 = '''0.585'''.		# Multiply the differences: 0.65 × 0.90 = '''0.585'''.
	# ~~Take the complement with~~ 1: 1 - 0.585 = '''0.415'''.		# Subtract from 1: 1 - 0.585 = '''0.415'''.
	# ~~Effective~~ Ability Range bonus is approximately '''41.5%''', not 45%.		# Total Ability Range bonus is approximately '''41.5%''', not 45%.

	== Sources of Ability Range ==		== Sources of Ability Range ==

~2026-RegenHideBebop921: Remove unfinished sentence

2026-08-16T21:04:28Z

Remove unfinished sentence

← Older revision		Revision as of 21:04, 16 August 2026
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	# Take the complement with 1: 1 - 0.585 = '''0.415'''.		# Take the complement with 1: 1 - 0.585 = '''0.415'''.
	# Effective Ability Range bonus is approximately '''41.5%''', not 45%.		# Effective Ability Range bonus is approximately '''41.5%''', not 45%.
	~~Of note is that~~

	== Sources of Ability Range ==		== Sources of Ability Range ==

~2026-RegenHideBebop921: Rephrase calculation section to call it 'diminishing returns' instead of 'multiplicative' and to clarify the way it diminishes

2026-08-16T20:44:23Z

Rephrase calculation section to call it 'diminishing returns' instead of 'multiplicative' and to clarify the way it diminishes

← Older revision		Revision as of 20:44, 16 August 2026
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	== Calculation ==		== 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%.

	~~=== Calculating Ability Range ===~~		<math>\text{Effective Ability Range bonus} = 1 - (1 - R_1) \times (1 - R_2) \dots</math>
	~~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:'''		'''Example:'''
	With '''35%''' from {{ItemIcon\|Greater Expansion}} and '''10%''' from {{ItemIcon\|Divine Barrier}}:		With '''35%''' from {{ItemIcon\|Greater Expansion}} and '''10%''' from {{ItemIcon\|Divine Barrier}}:
	# Convert percentages to decimals: 0.35 and 0.10.		# Convert percentages to decimals: 0.35 and 0.10.
	# ~~Subtract from~~ 1: (1 - 0.35) = '''0.65''' and (1 - 0.10) = '''0.90'''.		# Take the complement with 1: (1 - 0.35) = '''0.65''' and (1 - 0.10) = '''0.90'''.
	# Multiply the ~~differences~~: 0.65 × 0.90 = '''0.585'''.		# Multiply the complements: 0.65 × 0.90 = '''0.585'''.
	# ~~Subtract from~~ 1: 1 - 0.585 = '''0.415'''.		# Take the complement with 1: 1 - 0.585 = '''0.415'''.
	# ~~Total~~ Ability Range bonus is approximately '''41.5%''', not 45%.		# Effective Ability Range bonus is approximately '''41.5%''', not 45%.
			Of note is that

	== Sources of Ability Range ==		== Sources of Ability Range ==

Rem: The wording was not correct, it stated to Multiply the remainders, when it should be differences. Remainders is for division problems and would mean a totally different equation.

2026-06-20T16:53:49Z

The wording was not correct, it stated to Multiply the remainders, when it should be differences. Remainders is for division problems and would mean a totally different equation.

← Older revision		Revision as of 16:53, 20 June 2026
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	# Convert percentages to decimals: 0.35 and 0.10.		# Convert percentages to decimals: 0.35 and 0.10.
	# Subtract from 1: (1 - 0.35) = '''0.65''' and (1 - 0.10) = '''0.90'''.		# Subtract from 1: (1 - 0.35) = '''0.65''' and (1 - 0.10) = '''0.90'''.
	# Multiply the ~~remainders~~: 0.65 × 0.90 = '''0.585'''.		# Multiply the differences: 0.65 × 0.90 = '''0.585'''.
	# Subtract from 1: 1 - 0.585 = '''0.415'''.		# Subtract from 1: 1 - 0.585 = '''0.415'''.
	# Total Ability Range bonus is approximately '''41.5%''', not 45%.		# Total Ability Range bonus is approximately '''41.5%''', not 45%.

~2026-BoundlessHeavyBlue204: /* Calculation */ change of item from guardian ward to divine barrier to match current balance and maintain current formula

2026-05-17T19:34:19Z

Calculation: change of item from guardian ward to divine barrier to match current balance and maintain current formula

← Older revision		Revision as of 19:34, 17 May 2026
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	'''Example:'''		'''Example:'''
	With '''35%''' from {{ItemIcon\|Greater Expansion}} and '''10%''' from {{ItemIcon\|~~Guardian Ward~~}}:		With '''35%''' from {{ItemIcon\|Greater Expansion}} and '''10%''' from {{ItemIcon\|Divine Barrier}}:
	# Convert percentages to decimals: 0.35 and 0.10.		# Convert percentages to decimals: 0.35 and 0.10.
	# Subtract from 1: (1 - 0.35) = '''0.65''' and (1 - 0.10) = '''0.90'''.		# Subtract from 1: (1 - 0.35) = '''0.65''' and (1 - 0.10) = '''0.90'''.