Ability Range: Difference between revisions

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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 ==