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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 | [[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. | ||
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'''. | ||
== 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> | |||
<math>\text{ | |||
'''Example:''' | '''Example:''' | ||
With ''' | With '''35%''' from {{ItemIcon|Greater Expansion}} and '''10%''' from {{ItemIcon|Divine Barrier}}: | ||
# Convert percentages to decimals: | # 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'''. | ||
# Multiply the | # Multiply the complements: 0.65 × 0.90 = '''0.585'''. | ||
# | # Take the complement with 1: 1 - 0.585 = '''0.415'''. | ||
# | # Effective Ability Range bonus is approximately '''41.5%''', not 45%. | ||
Of note is that | |||
== Sources of Ability Range == | == Sources of Ability Range == | ||