Ability Range: Difference between revisions

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== 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}}:

# 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 ==

Ability Range: Difference between revisionsGive feedback

Monster Domosed (talk | contribs)

@@ Line 6: / Line 6: @@
 == 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}}:
 # 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 ==