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Chapter 3: Abilities
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Skill
Modifiers per Overall Ability
Sub-ability
score
Skill Modifie r
1-6
- 99
7-12
- 74
13-18
- 64
19-24
- 56
25-30
- 50
31-36
- 44
37-42
- 38
43-48
- 34
49-54
- 29
55-60
- 25
61-66
- 21
67-72
- 17
73-78
- 13
79-84
- 10
85-90
- 6
91-96
- 3
97-102
-
103-108
+ 3
109-114
+ 6
115-120
+ 9
121-126
+ 12
127-132
+ 14
133-138
+ 17
139-144
+ 20
145-150
+ 22
151-156
+ 25
157-162
+ 27
163-168
+ 30
169-174
+ 32
175-180
+ 34
181-186
+ 37
187-192
+ 39
193-198
+ 41
199-204
+ 43
205-210
+ 45
211-216
+ 47
217-222
+ 49
223-228
+ 52
229-234
+ 54
235-240
+ 56
241-246
+ 58
247-252
+ 59
253-258
+ 61
259-264
+ 63
265-270
+ 65
271-276
+ 67
277-282
+ 69
283-288
+ 71
289-294
+ 72
295-300
+ 74
1. Although the relationships between many variables in the
tables for sub-abilities are linear, such as Strength and Damage,
many are also curvilinear, such as sub-ability scores and skill
modifiers. Most curvilinear relationships are calculated as
parabolas. The parabolic formula that opens to the right is: (y
- y c
) 2 = 4a(x - x d
). The variable ‘c’ is the vertical distance from
the vertex to y=0, and ‘d’ is the horizontal distance from the
vertex to x=0. Finally, ‘a’ is the distance from the vertex to
the focus of the parabola. For example, skill modifiers are
considered to range from -99 to +250 over 200 categories
(such as 1-6, 7-12, etc.) of sub-ability scores. Only Strength
has 200 categories; other sub-abilities have 50. Therefore, the
vertex is (1, -99), so consider the vertex in the equation: (y +
99) 2 = 4a(x - 1). Now, solve for ‘a’ by inputting any other
known point, such as the apex (17, 0), and: (0 + 99) 2 = 4a(17
- 1). Hence: 99 2 = 4a(16). Therefore: 9801 = 64a. Finally,
a=153.14. Consequently, 4a=612.56. Now, any point may be
plotted along the curve: (y + 99) 2 = 612.56(x - 1). For example,
the highest Strength category (1,195-1,200, the 200 th category)
is: (y + 99) 2 = 612.56(200 - 1). Next: (y + 99) 2 = 612.56(199).
Next: (y + 99) 2 = 121899.44, and is equivalent to: y + 99 =
121899.44 0.5 . And: y + 99 = 349. Finally: y=250. All
curvilinear relationships were calculated in Microsoft Excel.
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