Summation chart: Difference between revisions

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(linked some other useful information from a saved post)
m (Formulas were wrong. Did some coloring in the table. Sorry I don't know how to color it neatly. Maybe someone can clean up my mess.)
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{| {{prettytable}}
{| {{prettytable}}
|-
|-
| X
| n
| Bonus
| Bonus
|-
|-
| Y
| σ
| Seed
| Seed
|-
|-
| Z
| r
| Skill Ranks Needed
| Skill Ranks Needed
|}
|}


X = (sqrt(4Y^2 - 4Y + 8Z + 1) - 2Y + 1) / 2
n = trunc[ 1-σ + sqrt[(σ-1)^2+2r] ]


Y = -(X^2 - X - 2Z) / 2X
r = (n/2)(n+2σ-1)


Z = (X^2 - X) / 2 + XY
σ = (1/2)(1+2r/n-n)


== Summation Chart ==
== Summation Chart ==
{| {{prettytable|text-align:center;}}
{| {{prettytable|text-align:center;}}
! colspan=11 bgcolor = #ddd | Ranks Needed (Z)
! colspan=11 bgcolor = #ddd | Ranks Needed (r)
|-
|-
! Bonus (X)
! Bonus (n)
! colspan="10" | Seed (Y)
! colspan=10 style="color:#ff0000" | Seed (σ)
|-
|-
! 1
! 1
| 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10
|style="color:#ff0000"| 1 ||style="color:#ff0000"| 2 ||style="color:#ff0000"| 3 ||style="color:#ff0000"| 4 ||style="color:#ff0000"| 5 ||style="color:#ff0000"| 6 ||style="color:#ff0000"| 7 ||style="color:#ff0000"| 8 ||style="color:#ff0000"| 9 ||style="color:#ff0000"| 10
|-
|-
! 2
! 2

Revision as of 04:14, 17 August 2009

A chart used to determine the number of ranks required to attain a bonus, based on an incremental additive scale. It is used particularly for Lore bonuses in certain spells. To use the chart all you need to know is the number of skill ranks (not skill bonus) needed to first see a bonus. This value is known as the Seed.


Calculation

n Bonus
σ Seed
r Skill Ranks Needed 
 n = trunc[ 1-σ + sqrt[(σ-1)^2+2r] ]

 r = (n/2)(n+2σ-1)

 σ = (1/2)(1+2r/n-n)

Summation Chart

Ranks Needed (r)
Bonus (n) Seed (σ)
1 1 2 3 4 5 6 7 8 9 10
2 3 5 7 9 11 13 15 17 19 21
3 6 9 12 15 18 21 24 27 30 33
4 10 14 18 22 26 30 34 38 42 46
5 15 20 25 30 35 40 45 50 55 60
6 21 27 33 39 45 51 57 63 69 75
7 28 35 42 49 56 63 70 77 84 91
8 36 44 52 60 68 76 84 92 100 108
9 45 54 63 72 81 90 99 108 117 126
10 55 65 75 85 95 105 115 125 135 145
11 66 77 88 99 110 121 132 143 154 165
12 78 90 102 114 126 138 150 162 174 186
13 91 104 117 130 143 156 169 182 195 208
14 105 119 133 147 161 175 189 203 217 231
15 120 135 150 165 180 195 210 225 240 255
16 136 152 168 184 200 216 232 248 264 280
17 153 170 187 204 221 238 255 272 289
18 171 189 207 225 243 261 279 297
19 190 209 228 247 266 285
20 210 230 250 270 290
21 231 252 273 294
22 253 275 297
23 276 299
24 300

See Also:

Resources

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