Summation chart

Bonus (n)	Ranks Needed (r)
	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

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" ($\mathrm {\sigma }$). 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.

Example

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%

Calculation

$\mathrm {Bonus}$	$\quad n=\left\lfloor 1-\sigma +{\sqrt {(\sigma -1)^{2}+2r}}\right\rfloor \quad$
$\mathrm {Skill\ Ranks\ Needed}$	$\quad r={\frac {n^{2}-n}{2}}+n\sigma$
$\mathrm {Seed}$	$\quad \sigma ={\frac {1-n}{2}}+{\frac {r}{n}}$

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