|Bonus (n)||Ranks Needed (r)|
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 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.
The Lore Benefits section of the spell page for Spirit Warding II (107) reads as follows:
- Spiritual Lore, Blessings provides a chance to temporarily experience a +25 boost in a warding attempt based on a seed 10 summation of ranks.
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 pures (12% chance for activation) under normal training ability, or 14% chance for activation with 231 ranks made possible using enhancive items. 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.
Spiritual Lore, Blessings ranks 10 21 33 46 60 75 91 108 126 145 165 186 208 231 Chance for activation 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14%
|Bonus||n = ⌊1 - σ + √ ⌋|
|Skill Ranks Needed||r = (n2 - n)/2 + nσ|
|Seed||σ = (1 - n)/2 + r/n|