Sacred 2:Concentration - formulas and tables

The skill definition can be found in creatures.txt.

mgr.createSkill {
	skill_name = "skill_concentration",
	advance_level = 75,
	min_level = 0,
	mean_value = 100,
	advance_mean_value = 150,
	skillgroup = "SKG_ASPECTS",
	adv_skill_name = "skill_advanced_concentration",
}

Almost all skills (including this one) use the following method to determine a single "SkillValue":

For pre-mastery skill levels:

MeanValue = mean_value

AdjustedSkillLevel = SkillLevel

For post-mastery skill levels:

MeanValue = advance_mean_value

AdjustedSkillLevel = SkillLevel - FLOOR((advance_level + 1) / 2.222)

Then:

SkillValue = FLOOR(20 * MeanValue * (AdjustedSkillLevel + SkillPivotPoint * 0.015) / (AdjustedSkillLevel + SkillPivotPoint))

Where:

• SkillLevel - total skill points in the skill.
• SkillPivotPoint - from balance.txt. Default value is 100.
• mean_value - from the skill definition in creatures.txt.
• advance_level - from the skill definition in creatures.txt.
• advance_mean_value - from the skill definition in creatures.txt.

This "SkillValue" is then used to determine the value of each bonus that the skill provides. Concentration provides only one scalable bonus: Regeneration Time -X%.

The formula for Regeneration Time -X% is:

ValueOfBonus = SkillValue

DiminishedValue = 1000 * ValueOfBonus / (1000 + ValueOfBonus)

TooltipValue = -0.1 * DiminishedValue

This TooltipValue is then rounded down to one decimal place.

Since most of the parameters are known in advance, we can simplify the formulas:

For pre-mastery skill levels:

SkillValue = FLOOR(20 * MeanValue * (AdjustedSkillLevel + SkillPivotPoint * 0.015) / (AdjustedSkillLevel + SkillPivotPoint))

SkillValue = FLOOR(20 * 100 * (SkillLevel + 100 * 0.015) / (SkillLevel + 100))

SkillValue = FLOOR(2000 * (SkillLevel + 1.5) / (SkillLevel + 100))

For post-mastery skill levels:

AdjustedSkillLevel = SkillLevel - FLOOR((advance_level + 1) / 2.222)

AdjustedSkillLevel = SkillLevel - FLOOR((75 + 1) / 2.222)

AdjustedSkillLevel = SkillLevel - FLOOR(76 / 2.222)

AdjustedSkillLevel = SkillLevel - FLOOR(34.2034203420342)

AdjustedSkillLevel = SkillLevel - 34

SkillValue = FLOOR(20 * MeanValue * (AdjustedSkillLevel + SkillPivotPoint * 0.015) / (AdjustedSkillLevel + SkillPivotPoint))

SkillValue = FLOOR(20 * 150 * (SkillLevel - 34 + 100 * 0.015) / (SkillLevel - 34 + 100))

SkillValue = FLOOR(3000 * (SkillLevel - 34 + 1.5) / (SkillLevel + 66))

SkillValue = FLOOR(3000 * (SkillLevel - 32.5) / (SkillLevel + 66))

And now, by using these formulas, we can fill in the following table:

Skill level	Pre-mastery	Post-mastery
	Regeneration Time -X%	Regeneration Time -X%
1	-4.6%
2	-6.3%
3	-8%
4	-9.5%
5	-10.9%
6	-12.3%
7	-13.6%
8	-14.8%
9	-16.1%
10	-17.2%
11	-18.3%
12	-19.4%
13	-20.3%
14	-21.3%
15	-22.2%
16	-23.1%
17	-24%
18	-24.8%
19	-25.5%
20	-26.3%
21	-27%
22	-27.7%
23	-28.4%
24	-29.1%
25	-29.7%
26	-30.3%
27	-30.9%
28	-31.5%
29	-32%
30	-32.6%
31	-33.1%
32	-33.6%
33	-34.1%
34	-34.5%
35	-35%
36	-35.5%
37	-35.9%
38	-36.3%
39	-36.7%
40	-37.1%
41	-37.5%
42	-37.9%
43	-38.3%
44	-38.6%
45	-39%
46	-39.3%
47	-39.7%
48	-40%
49	-40.3%
50	-40.6%
51	-41%
52	-41.2%
53	-41.5%
54	-41.8%
55	-42.1%
56	-42.4%
57	-42.6%
58	-42.9%
59	-43.2%
60	-43.4%
61	-43.6%
62	-43.9%
63	-44.1%
64	-44.3%
65	-44.6%
66	-44.8%
67	-45%
68	-45.2%
69	-45.4%
70	-45.6%
71	-45.8%
72	-46%
73	-46.2%
74	-46.4%
75	-46.6%	-47.4%
76	-46.8%	-47.8%
77	-47%	-48.2%
78	-47.1%	-48.6%
79	-47.3%	-49%
80	-47.5%	-49.3%
81	-47.6%	-49.7%
82	-47.8%	-50%
83	-47.9%	-50.3%
84	-48.1%	-50.7%
85	-48.3%	-51%
86	-48.4%	-51.3%
87	-48.6%	-51.6%
88	-48.7%	-51.9%
89	-48.9%	-52.2%
90	-49%	-52.4%
91	-49.1%	-52.7%
92	-49.3%	-53%
93	-49.4%	-53.2%
94	-49.5%	-53.5%
95	-49.7%	-53.7%
96	-49.8%	-54%
97	-50%	-54.2%
98	-50.1%	-54.5%
99	-50.2%	-54.7%
100	-50.3%	-54.9%
101	-50.4%	-55.1%
102	-50.5%	-55.3%
103	-50.7%	-55.5%
104	-50.8%	-55.7%
105	-50.9%	-55.9%
106	-51%	-56.1%
107	-51.1%	-56.3%
108	-51.2%	-56.5%
109	-51.3%	-56.7%
110	-51.4%	-56.9%
111	-51.5%	-57%
112	-51.6%	-57.2%
113	-51.8%	-57.4%
114	-51.8%	-57.5%
115	-51.9%	-57.7%
116	-52%	-57.9%
117	-52.1%	-58%
118	-52.2%	-58.2%
119	-52.3%	-58.3%
120	-52.4%	-58.5%
121	-52.5%	-58.6%
122	-52.6%	-58.8%
123	-52.7%	-58.9%
124	-52.8%	-59%
125	-52.9%	-59.2%
126	-53%	-59.3%
127	-53%	-59.4%
128	-53.1%	-59.6%
129	-53.2%	-59.7%
130	-53.3%	-59.8%
131	-53.4%	-60%
132	-53.4%	-60.1%
133	-53.5%	-60.2%
134	-53.6%	-60.3%
135	-53.7%	-60.4%
136	-53.8%	-60.5%
137	-53.8%	-60.6%
138	-53.9%	-60.7%
139	-54%	-60.9%
140	-54.1%	-61%
141	-54.1%	-61.1%
142	-54.2%	-61.2%
143	-54.3%	-61.3%
144	-54.3%	-61.4%
145	-54.4%	-61.5%
146	-54.5%	-61.6%
147	-54.5%	-61.7%
148	-54.6%	-61.8%
149	-54.7%	-61.9%
150	-54.7%	-61.9%
151	-54.8%	-62%
152	-54.9%	-62.1%
153	-54.9%	-62.2%
154	-55%	-62.3%
155	-55%	-62.4%
156	-55.1%	-62.5%
157	-55.2%	-62.6%
158	-55.2%	-62.6%
159	-55.3%	-62.7%
160	-55.3%	-62.8%
161	-55.4%	-62.9%
162	-55.5%	-63%
163	-55.5%	-63%
164	-55.6%	-63.1%
165	-55.6%	-63.2%
166	-55.7%	-63.3%
167	-55.7%	-63.3%
168	-55.8%	-63.4%
169	-55.8%	-63.5%
170	-55.9%	-63.5%
171	-56%	-63.6%
172	-56%	-63.7%
173	-56.1%	-63.8%
174	-56.1%	-63.8%
175	-56.1%	-63.9%
176	-56.2%	-64%
177	-56.2%	-64%
178	-56.3%	-64.1%
179	-56.3%	-64.1%
180	-56.4%	-64.2%
181	-56.4%	-64.3%
182	-56.5%	-64.3%
183	-56.5%	-64.4%
184	-56.6%	-64.5%
185	-56.6%	-64.5%
186	-56.7%	-64.6%
187	-56.7%	-64.6%
188	-56.8%	-64.7%
189	-56.8%	-64.8%
190	-56.8%	-64.8%
191	-56.9%	-64.9%
192	-56.9%	-64.9%
193	-57%	-65%
194	-57%	-65%
195	-57.1%	-65.1%
196	-57.1%	-65.1%
197	-57.1%	-65.2%
198	-57.2%	-65.2%
199	-57.2%	-65.3%
200	-57.3%	-65.3%
201	-57.3%	-65.4%
202	-57.3%	-65.4%
203	-57.4%	-65.5%
204	-57.4%	-65.5%
205	-57.5%	-65.6%
206	-57.5%	-65.6%
207	-57.5%	-65.7%
208	-57.6%	-65.7%
209	-57.6%	-65.8%
210	-57.6%	-65.8%
211	-57.7%	-65.9%
212	-57.7%	-65.9%
213	-57.8%	-65.9%
214	-57.8%	-66%
215	-57.8%	-66%
216	-57.9%	-66.1%
217	-57.9%	-66.1%
218	-57.9%	-66.2%
219	-58%	-66.2%
220	-58%	-66.2%
221	-58%	-66.3%
222	-58.1%	-66.3%
223	-58.1%	-66.4%
224	-58.1%	-66.4%
225	-58.2%	-66.4%
226	-58.2%	-66.5%
227	-58.2%	-66.5%
228	-58.3%	-66.5%
229	-58.3%	-66.6%
230	-58.3%	-66.6%
231	-58.4%	-66.7%
232	-58.4%	-66.7%
233	-58.4%	-66.7%
234	-58.5%	-66.8%
235	-58.5%	-66.8%
236	-58.5%	-66.8%
237	-58.5%	-66.9%
238	-58.6%	-66.9%
239	-58.6%	-67%
240	-58.6%	-67%
241	-58.7%	-67%
242	-58.7%	-67.1%
243	-58.7%	-67.1%
244	-58.7%	-67.1%
245	-58.8%	-67.2%
246	-58.8%	-67.2%
247	-58.8%	-67.2%
248	-58.8%	-67.2%
249	-58.9%	-67.3%
250	-58.9%	-67.3%
251	-58.9%	-67.3%
252	-59%	-67.4%
253	-59%	-67.4%
254	-59%	-67.4%
255	-59.1%	-67.5%
256	-59.1%	-67.5%
257	-59.1%	-67.5%
258	-59.1%	-67.6%
259	-59.2%	-67.6%
260	-59.2%	-67.6%
261	-59.2%	-67.7%
262	-59.2%	-67.7%
263	-59.2%	-67.7%
264	-59.3%	-67.7%
265	-59.3%	-67.8%
266	-59.3%	-67.8%
267	-59.3%	-67.8%
268	-59.4%	-67.8%
269	-59.4%	-67.9%
270	-59.4%	-67.9%
271	-59.4%	-67.9%
272	-59.5%	-68%
273	-59.5%	-68%
274	-59.5%	-68%
275	-59.5%	-68%
276	-59.6%	-68.1%
277	-59.6%	-68.1%
278	-59.6%	-68.1%
279	-59.6%	-68.1%
280	-59.6%	-68.2%
281	-59.7%	-68.2%
282	-59.7%	-68.2%
283	-59.7%	-68.2%
284	-59.7%	-68.3%
285	-59.8%	-68.3%
286	-59.8%	-68.3%
287	-59.8%	-68.3%
288	-59.8%	-68.4%
289	-59.8%	-68.4%
290	-59.9%	-68.4%
291	-59.9%	-68.4%
292	-59.9%	-68.4%
293	-59.9%	-68.5%
294	-60%	-68.5%
295	-60%	-68.5%
296	-60%	-68.5%
297	-60%	-68.6%
298	-60%	-68.6%
299	-60%	-68.6%
300	-60.1%	-68.6%
301	-60.1%	-68.6%
302	-60.1%	-68.7%
303	-60.1%	-68.7%
304	-60.1%	-68.7%
305	-60.2%	-68.7%
306	-60.2%	-68.7%
307	-60.2%	-68.8%
308	-60.2%	-68.8%
309	-60.2%	-68.8%
310	-60.3%	-68.8%
311	-60.3%	-68.9%
312	-60.3%	-68.9%
313	-60.3%	-68.9%
314	-60.3%	-68.9%
315	-60.3%	-68.9%
316	-60.4%	-69%
317	-60.4%	-69%
318	-60.4%	-69%
319	-60.4%	-69%
320	-60.4%	-69%
321	-60.5%	-69%
322	-60.5%	-69.1%
323	-60.5%	-69.1%
324	-60.5%	-69.1%
325	-60.5%	-69.1%
326	-60.5%	-69.1%
327	-60.5%	-69.2%
328	-60.6%	-69.2%
329	-60.6%	-69.2%
330	-60.6%	-69.2%
331	-60.6%	-69.2%
332	-60.6%	-69.2%
333	-60.7%	-69.3%
334	-60.7%	-69.3%
335	-60.7%	-69.3%
336	-60.7%	-69.3%
337	-60.7%	-69.3%
338	-60.7%	-69.4%
339	-60.7%	-69.4%
340	-60.8%	-69.4%
341	-60.8%	-69.4%
342	-60.8%	-69.4%
343	-60.8%	-69.4%
344	-60.8%	-69.5%
345	-60.8%	-69.5%
346	-60.9%	-69.5%
347	-60.9%	-69.5%
348	-60.9%	-69.5%
349	-60.9%	-69.5%
350	-60.9%	-69.5%
351	-60.9%	-69.6%
352	-60.9%	-69.6%
353	-61%	-69.6%
354	-61%	-69.6%
355	-61%	-69.6%
356	-61%	-69.6%
357	-61%	-69.7%
358	-61%	-69.7%
359	-61%	-69.7%
360	-61.1%	-69.7%
361	-61.1%	-69.7%
362	-61.1%	-69.7%
363	-61.1%	-69.7%
364	-61.1%	-69.8%
365	-61.1%	-69.8%
366	-61.1%	-69.8%
367	-61.2%	-69.8%
368	-61.2%	-69.8%
369	-61.2%	-69.8%
370	-61.2%	-69.8%
371	-61.2%	-69.9%
372	-61.2%	-69.9%
373	-61.2%	-69.9%
374	-61.3%	-69.9%
375	-61.3%	-69.9%
376	-61.3%	-69.9%
377	-61.3%	-69.9%
378	-61.3%	-70%
379	-61.3%	-70%
380	-61.3%	-70%
381	-61.3%	-70%
382	-61.4%	-70%
383	-61.4%	-70%
384	-61.4%	-70%
385	-61.4%	-70%
386	-61.4%	-70.1%
387	-61.4%	-70.1%
388	-61.4%	-70.1%
389	-61.4%	-70.1%
390	-61.4%	-70.1%
391	-61.5%	-70.1%
392	-61.5%	-70.1%
393	-61.5%	-70.2%
394	-61.5%	-70.2%
395	-61.5%	-70.2%
396	-61.5%	-70.2%
397	-61.5%	-70.2%
398	-61.5%	-70.2%
399	-61.6%	-70.2%
400	-61.6%	-70.2%

References

• https://darkmatters.org/forums/index.php?/topic/18511-how-is-sacred-2-weapon-damage-calculated/&do=findComment&comment=7146451