imported>ZHOUY1: fix math display

2018-01-22T21:01:38Z

fix math display

New page

{| {{prettytable|text-align:center;float:left;}}
|- bgcolor = #ddd
! rowspan=2 valign=bottom | Bonus (n)
! colspan=10 bgcolor = #ddd | Ranks Needed (r)
|-
! colspan=10 style="color:#ff0000" | Seed (σ)
|-
! 1
|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
| 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 || colspan=2 |
|-
! 19
|190 ||209 ||228 ||247 ||266 ||285 || colspan=4 |
|-
! 20
|210 ||230 ||250 ||270 ||290 || colspan=5 |
|-
! 21
|231 ||252 ||273 ||294 || colspan=6 |
|-
! 22
|253 ||275 ||297 || colspan=7 |
|-
! 23
|276 ||299 || colspan=8 |
|-
! 24
|300 || colspan=9 |
|}

The '''summation chart''' is used to determine the number of ranks required to attain a bonus, based on an incremental additive. It is used particularly for [[Lore]] bonuses in certain spells.

For spells that provide a summation bonus, the first step to determine the progression at which you will gain further benefits is to find the first rank at which you gain a bonus. This is commonly called the "seed" (σ). Find this rank number in the red row underneath the red Seed heading. Since the seed is also the first rank at which you gain a bonus, it corresponds with '1' under the Bonus column.

Now, reading downward from the seed will tell you the next rank at which the next bonus can be achieved. Each of these milestones corresponds to their respective numbers in the Bonus column.

The method is based on [https://en.wikipedia.org/wiki/Triangular_number triangular numbers] and allows for a relatively straight forward manner to set the skill required corresponding to a given bonus threshold simultaneously to the degree with which the returns diminish.
__NOTOC__
===Example===
The Lore Benefits section of the spell page for [[Spirit Warding II (107)]] reads as follows:

:'''{{#section:Spirit Warding II (107)|lore}}'''

The Seed in this case is 10, which corresponds to a Bonus of 1 in the chart, or a 1% chance for activation. Tracing downward from the seed shows that the next bonus is at 21 ranks, or 2% chance for activation. The progression continues in this manner until it maximizes at 186 ranks for [[pure]]s (12% chance for activation) under normal training ability, or 14% chance for activation with 231 ranks made possible using [[enhancive item]]s. Bonuses occurring at seed 10 are intended by design to be relatively rare occurrences.

Lore charts have been added to spell pages to illustrate bonuses.
{{#section:Spirit Warding II (107)|chart}}
== Calculation ==
{| {{prettytable}}
|-
| align=right| Bonus
| {{math|n {{=}} &lfloor;1 - σ + {{sqrt|(σ - 1)<sup>2</sup> + 2r}}&rfloor;}}
|-
| align=right|Skill Ranks Needed
| {{math|r {{=}} (n<sup>2</sup> - n)/2 + nσ}}
|-
| align=right|Seed
| {{math|σ {{=}} (1 - n)/2 + r/n}}
|}
{{clear}}
== Resources ==
* [[/saved posts|Saved posts]]

[[category:Magic]][[category:Lores]][[category:Skills]]

Summation chart - Revision history

imported>ZHOUY1: fix math display