Sacred 2:Ancient Magic - formulas and tables

The skill definition can be found in creatures.txt.

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

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. Ancient Magic provides two bonuses: Damage +X% and Opponents' Immunities -X%.

The formula for Damage +X% is:

ValueOfBonus = SkillValue

TooltipValue = ValueOfBonus * 0.1

The TooltipValue is subject to precision loss from 32-bit floats! This means that the shown value could be 0.1 less than the real value.

The formula for Opponents' Immunities -X% is:

ValueOfBonus = 1000 * SkillValue / (1000 + SkillValue)

TooltipValue = -1 * ValueOfBonus * 0.1

The TooltipValue is also rounded down to one decimal place.

Opponents' Immunities -X% reduces the damage mitigation in the following way:

NewDamageMitigation = FLOOR(DamageMitigation * (1 - OpponentsImmunities / 1000))

Where:

• DamageMitigation - The ValueOfBonus for the damage mitigation bonus. If the percentage is 51.6%, then the ValueOfBonus is 516. Note to self: Test if all-channel and single-channel damage mitigation are reduced separately.
• OpponentsImmunities - The ValueOfBonus for the opponents' immunities bonus.

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:

Note: The values for Damage +X% are without precision loss, and the values for Opponents' Immunities +X% are not rounded down, because these operations affect only the tooltips and not actual combat.

Skill level	Pre-mastery	Post-mastery
	Damage +X%	Damage +X%	Opponents' Immunities -X%
1	+4.9%
2	+6.8%
3	+8.7%
4	+10.5%
5	+12.3%
6	+14.1%
7	+15.8%
8	+17.5%
9	+19.2%
10	+20.9%
11	+22.5%
12	+24.1%
13	+25.6%
14	+27.1%
15	+28.6%
16	+30.1%
17	+31.6%
18	+33%
19	+34.4%
20	+35.8%
21	+37.1%
22	+38.5%
23	+39.8%
24	+41.1%
25	+42.4%
26	+43.6%
27	+44.8%
28	+46%
29	+47.2%
30	+48.4%
31	+49.6%
32	+50.7%
33	+51.8%
34	+52.9%
35	+54%
36	+55.1%
37	+56.2%
38	+57.2%
39	+58.2%
40	+59.2%
41	+60.2%
42	+61.2%
43	+62.2%
44	+63.1%
45	+64.1%
46	+65%
47	+65.9%
48	+66.8%
49	+67.7%
50	+68.6%
51	+69.5%
52	+70.3%
53	+71.2%
54	+72%
55	+72.9%
56	+73.7%
57	+74.5%
58	+75.3%
59	+76.1%
60	+76.8%
61	+77.6%
62	+78.3%
63	+79.1%
64	+79.8%
65	+80.6%
66	+81.3%
67	+82%
68	+82.7%
69	+83.4%
70	+84.1%
71	+84.7%
72	+85.4%
73	+86.1%
74	+86.7%
75	+87.4%	+90.4%	-47.4789915966387%
76	+88%	+91.9%	-47.8895257946847%
77	+88.7%	+93.3%	-48.2669425763063%
78	+89.3%	+94.7%	-48.6389316897792%
79	+89.9%	+96.2%	-49.0316004077472%
80	+90.5%	+97.6%	-49.3927125506073%
81	+91.1%	+98.9%	-49.7234791352438%
82	+91.7%	+100.3%	-50.0748876684973%
83	+92.3%	+101.6%	-50.3968253968254%
84	+92.9%	+103%	-50.7389162561576%
85	+93.5%	+104.3%	-51.052373959863%
86	+94%	+105.5%	-51.338199513382%
87	+94.6%	+106.8%	-51.6441005802708%
88	+95.2%	+108.1%	-51.9461797212878%
89	+95.7%	+109.3%	-52.2216913521261%
90	+96.3%	+110.5%	-52.4940617577197%
91	+96.8%	+111.7%	-52.7633443552197%
92	+97.3%	+112.9%	-53.0295913574448%
93	+97.9%	+114.1%	-53.2928538066324%
94	+98.4%	+115.3%	-53.5531816070599%
95	+98.9%	+116.4%	-53.7892791127542%
96	+99.4%	+117.5%	-54.0229885057471%
97	+100%	+118.7%	-54.2752629172382%
98	+100.5%	+119.8%	-54.5040946314832%
99	+101%	+120.9%	-54.7306473517429%
100	+101.5%	+121.9%	-54.9346552501127%
101	+101.9%	+123%	-55.1569506726457%
102	+102.4%	+124.1%	-55.3770638107988%
103	+102.9%	+125.1%	-55.5752998667259%
104	+103.4%	+126.1%	-55.7717823971694%
105	+103.9%	+127.1%	-55.9665345662704%
106	+104.3%	+128.1%	-56.1595791319597%
107	+104.8%	+129.1%	-56.3509384548232%
108	+105.2%	+130.1%	-56.5406345067362%
109	+105.7%	+131.1%	-56.728688879273%
110	+106.1%	+132.1%	-56.9151227919001%
111	+106.6%	+133%	-57.0815450643777%
112	+107%	+133.9%	-57.2466866182129%
113	+107.5%	+134.9%	-57.428693060877%
114	+107.9%	+135.8%	-57.5911789652248%
115	+108.3%	+136.7%	-57.752429235319%
116	+108.7%	+137.6%	-57.9124579124579%
117	+109.2%	+138.5%	-58.0712788259958%
118	+109.6%	+139.4%	-58.2289055973267%
119	+110%	+140.2%	-58.368026644463%
120	+110.4%	+141.1%	-58.5234342596433%
121	+110.8%	+141.9%	-58.6606035551881%
122	+111.2%	+142.8%	-58.8138385502471%
123	+111.6%	+143.6%	-58.9490968801314%
124	+112%	+144.4%	-59.0834697217676%
125	+112.4%	+145.2%	-59.2169657422512%
126	+112.8%	+146%	-59.349593495935%
127	+113.2%	+146.8%	-59.4813614262561%
128	+113.5%	+147.6%	-59.6122778675283%
129	+113.9%	+148.4%	-59.7423510466989%
130	+114.3%	+149.2%	-59.8715890850722%
131	+114.7%	+150%	-60%
132	+115%	+150.7%	-60.1116872756282%
133	+115.4%	+151.5%	-60.2385685884692%
134	+115.8%	+152.2%	-60.3489294210944%
135	+116.1%	+152.9%	-60.4586793198893%
136	+116.5%	+153.7%	-60.5833661805282%
137	+116.8%	+154.4%	-60.6918238993711%
138	+117.2%	+155.1%	-60.7996863974912%
139	+117.5%	+155.8%	-60.9069585613761%
140	+117.9%	+156.5%	-61.0136452241715%
141	+118.2%	+157.2%	-61.1197511664075%
142	+118.5%	+157.9%	-61.2252811167119%
143	+118.9%	+158.6%	-61.3302397525135%
144	+119.2%	+159.2%	-61.4197530864198%
145	+119.5%	+159.9%	-61.5236629472874%
146	+119.9%	+160.6%	-61.6270145817345%
147	+120.2%	+161.2%	-61.7151607963247%
148	+120.5%	+161.9%	-61.8174875906835%
149	+120.8%	+162.5%	-61.9047619047619%
150	+121.2%	+163.1%	-61.9916381603953%
151	+121.5%	+163.8%	-62.0924943138741%
152	+121.8%	+164.4%	-62.178517397882%
153	+122.1%	+165%	-62.2641509433962%
154	+122.4%	+165.6%	-62.3493975903615%
155	+122.7%	+166.2%	-62.4342599549211%
156	+123%	+166.8%	-62.5187406296852%
157	+123.3%	+167.4%	-62.602842183994%
158	+123.6%	+168%	-62.6865671641791%
159	+123.9%	+168.6%	-62.7699180938198%
160	+124.2%	+169.2%	-62.852897473997%
161	+124.5%	+169.8%	-62.9355077835434%
162	+124.8%	+170.3%	-63.0040695523492%
163	+125%	+170.9%	-63.0860095976375%
164	+125.3%	+171.5%	-63.1675874769797%
165	+125.6%	+172%	-63.2352941176471%
166	+125.9%	+172.6%	-63.3162142333089%
167	+126.2%	+173.1%	-63.3833760527279%
168	+126.4%	+173.7%	-63.4636463280965%
169	+126.7%	+174.2%	-63.5302698760029%
170	+127%	+174.7%	-63.5966508918821%
171	+127.3%	+175.3%	-63.6759898292772%
172	+127.5%	+175.8%	-63.7418419144307%
173	+127.8%	+176.3%	-63.8074556641332%
174	+128.1%	+176.8%	-63.8728323699422%
175	+128.3%	+177.3%	-63.9379733141003%
176	+128.6%	+177.8%	-64.0028797696184%
177	+128.8%	+178.3%	-64.0675530003593%
178	+129.1%	+178.8%	-64.1319942611191%
179	+129.3%	+179.3%	-64.1962047977086%
180	+129.6%	+179.8%	-64.2601858470336%
181	+129.8%	+180.3%	-64.3239386371745%
182	+130.1%	+180.8%	-64.3874643874644%
183	+130.3%	+181.3%	-64.4507643085674%
184	+130.6%	+181.8%	-64.513839602555%
185	+130.8%	+182.2%	-64.5641389085755%
186	+131.1%	+182.7%	-64.6268128758401%
187	+131.3%	+183.2%	-64.6892655367232%
188	+131.5%	+183.6%	-64.7390691114245%
189	+131.8%	+184.1%	-64.8011263639564%
190	+132%	+184.5%	-64.8506151142355%
191	+132.3%	+185%	-64.9122807017544%
192	+132.5%	+185.4%	-64.9614576033637%
193	+132.7%	+185.9%	-65.0227352221056%
194	+132.9%	+186.3%	-65.0716032134125%
195	+133.2%	+186.7%	-65.1203348447855%
196	+133.4%	+187.2%	-65.1810584958217%
197	+133.6%	+187.6%	-65.2294853963839%
198	+133.8%	+188%	-65.2777777777778%
199	+134.1%	+188.4%	-65.3259361997226%
200	+134.3%	+188.9%	-65.3859466943579%
201	+134.5%	+189.3%	-65.4338057379883%
202	+134.7%	+189.7%	-65.4815326199517%
203	+134.9%	+190.1%	-65.5291278869355%
204	+135.1%	+190.5%	-65.5765920826162%
205	+135.4%	+190.9%	-65.6239257476796%
206	+135.6%	+191.3%	-65.6711294198421%
207	+135.8%	+191.7%	-65.7182036338704%
208	+136%	+192.1%	-65.7651489216022%
209	+136.2%	+192.5%	-65.8119658119658%
210	+136.4%	+192.9%	-65.8586548310003%
211	+136.6%	+193.3%	-65.9052165018752%
212	+136.8%	+193.7%	-65.9516513449098%
213	+137%	+194%	-65.9863945578231%
214	+137.2%	+194.4%	-66.0326086956522%
215	+137.4%	+194.8%	-66.078697421981%
216	+137.6%	+195.2%	-66.1246612466125%
217	+137.8%	+195.5%	-66.1590524534687%
218	+138%	+195.9%	-66.2047989185536%
219	+138.2%	+196.3%	-66.2504218697266%
220	+138.4%	+196.6%	-66.2845583277141%
221	+138.6%	+197%	-66.3299663299663%
222	+138.8%	+197.3%	-66.3639421459805%
223	+139%	+197.7%	-66.4091367148136%
224	+139.1%	+198.1%	-66.4542099966454%
225	+139.3%	+198.4%	-66.4879356568365%
226	+139.5%	+198.8%	-66.5327978580991%
227	+139.7%	+199.1%	-66.5663657639585%
228	+139.9%	+199.4%	-66.5998663994656%
229	+140.1%	+199.8%	-66.6444296197465%
230	+140.3%	+200.1%	-66.6777740753082%
231	+140.4%	+200.5%	-66.7221297836938%
232	+140.6%	+200.8%	-66.7553191489362%
233	+140.8%	+201.1%	-66.7884423779475%
234	+141%	+201.5%	-66.832504145937%
235	+141.1%	+201.8%	-66.8654738237243%
236	+141.3%	+202.1%	-66.898378020523%
237	+141.5%	+202.4%	-66.9312169312169%
238	+141.7%	+202.7%	-66.9639907499174%
239	+141.8%	+203.1%	-67.0075882547014%
240	+142%	+203.4%	-67.04021094265%
241	+142.2%	+203.7%	-67.0727691801119%
242	+142.3%	+204%	-67.1052631578947%
243	+142.5%	+204.3%	-67.1376930660532%
244	+142.7%	+204.6%	-67.1700590938936%
245	+142.8%	+204.9%	-67.202361429977%
246	+143%	+205.2%	-67.2346002621232%
247	+143.2%	+205.5%	-67.2667757774141%
248	+143.3%	+205.8%	-67.2988881621975%
249	+143.5%	+206.1%	-67.3309376020908%
250	+143.7%	+206.4%	-67.3629242819843%
251	+143.8%	+206.7%	-67.394848386045%
252	+144%	+207%	-67.4267100977199%
253	+144.1%	+207.3%	-67.4585095997397%
254	+144.3%	+207.6%	-67.4902470741222%
255	+144.5%	+207.9%	-67.521922702176%
256	+144.6%	+208.2%	-67.5535366645036%
257	+144.8%	+208.5%	-67.5850891410049%
258	+144.9%	+208.7%	-67.6060900550696%
259	+145.1%	+209%	-67.6375404530744%
260	+145.2%	+209.3%	-67.6689298415778%
261	+145.4%	+209.6%	-67.7002583979328%
262	+145.5%	+209.9%	-67.7315262988061%
263	+145.7%	+210.1%	-67.7523379554982%
264	+145.8%	+210.4%	-67.7835051546392%
265	+146%	+210.7%	-67.8146121660766%
266	+146.1%	+210.9%	-67.8353168221293%
267	+146.3%	+211.2%	-67.866323907455%
268	+146.4%	+211.5%	-67.8972712680578%
269	+146.6%	+211.7%	-67.9178697465512%
270	+146.7%	+212%	-67.9487179487179%
271	+146.9%	+212.3%	-67.979506884406%
272	+147%	+212.5%	-68%
273	+147.1%	+212.8%	-68.0306905370844%
274	+147.3%	+213%	-68.0511182108626%
275	+147.4%	+213.3%	-68.0817108203%
276	+147.6%	+213.5%	-68.1020733652313%
277	+147.7%	+213.8%	-68.1325685149777%
278	+147.8%	+214%	-68.1528662420382%
279	+148%	+214.3%	-68.1832643970729%
280	+148.1%	+214.5%	-68.2034976152623%
281	+148.2%	+214.8%	-68.2337992376112%
282	+148.4%	+215%	-68.2539682539683%
283	+148.5%	+215.3%	-68.2841738027276%
284	+148.6%	+215.5%	-68.3042789223455%
285	+148.8%	+215.8%	-68.3343888537049%
286	+148.9%	+216%	-68.3544303797468%
287	+149%	+216.2%	-68.3744465528147%
288	+149.2%	+216.5%	-68.4044233807267%
289	+149.3%	+216.7%	-68.4243763814335%
290	+149.4%	+216.9%	-68.4443041969075%
291	+149.6%	+217.2%	-68.4741488020177%
292	+149.7%	+217.4%	-68.4940138626339%
293	+149.8%	+217.6%	-68.5138539042821%
294	+150%	+217.9%	-68.5435671594841%
295	+150.1%	+218.1%	-68.5633448601069%
296	+150.2%	+218.3%	-68.5830977065661%
297	+150.3%	+218.5%	-68.6028257456829%
298	+150.5%	+218.8%	-68.6323713927227%
299	+150.6%	+219%	-68.6520376175549%
300	+150.7%	+219.2%	-68.671679197995%
301	+150.8%	+219.4%	-68.6912961803381%
302	+150.9%	+219.7%	-68.7206756334063%
303	+151.1%	+219.9%	-68.7402313222882%
304	+151.2%	+220.1%	-68.7597625741956%
305	+151.3%	+220.3%	-68.7792694349048%
306	+151.4%	+220.5%	-68.798751950078%
307	+151.5%	+220.7%	-68.8182101652635%
308	+151.7%	+220.9%	-68.8376441258959%
309	+151.8%	+221.2%	-68.8667496886675%
310	+151.9%	+221.4%	-68.8861232109521%
311	+152%	+221.6%	-68.9054726368159%
312	+152.1%	+221.8%	-68.9247980111871%
313	+152.3%	+222%	-68.944099378882%
314	+152.4%	+222.2%	-68.9633767846058%
315	+152.5%	+222.4%	-68.9826302729529%
316	+152.6%	+222.6%	-69.0018598884067%
317	+152.7%	+222.8%	-69.0210656753408%
318	+152.8%	+223%	-69.0402476780186%
319	+152.9%	+223.2%	-69.0594059405941%
320	+153%	+223.4%	-69.0785405071119%
321	+153.2%	+223.6%	-69.097651421508%
322	+153.3%	+223.8%	-69.1167387276096%
323	+153.4%	+224%	-69.1358024691358%
324	+153.5%	+224.2%	-69.1548426896977%
325	+153.6%	+224.4%	-69.173859432799%
326	+153.7%	+224.6%	-69.1928527418361%
327	+153.8%	+224.8%	-69.2118226600985%
328	+153.9%	+225%	-69.2307692307692%
329	+154%	+225.1%	-69.2402337742233%
330	+154.1%	+225.3%	-69.2591454042422%
331	+154.2%	+225.5%	-69.2780337941628%
332	+154.3%	+225.7%	-69.2968989867977%
333	+154.5%	+225.9%	-69.3157410248543%
334	+154.6%	+226.1%	-69.3345599509353%
335	+154.7%	+226.3%	-69.3533558075391%
336	+154.8%	+226.4%	-69.3627450980392%
337	+154.9%	+226.6%	-69.3815064298836%
338	+155%	+226.8%	-69.4002447980416%
339	+155.1%	+227%	-69.4189602446483%
340	+155.2%	+227.2%	-69.4376528117359%
341	+155.3%	+227.3%	-69.4469905285671%
342	+155.4%	+227.5%	-69.4656488549618%
343	+155.5%	+227.7%	-69.4842844064693%
344	+155.6%	+227.9%	-69.5028972247637%
345	+155.7%	+228.1%	-69.5214873514172%
346	+155.8%	+228.2%	-69.5307739183425%
347	+155.9%	+228.4%	-69.5493300852619%
348	+156%	+228.6%	-69.5678636640292%
349	+156.1%	+228.7%	-69.5771219957408%
350	+156.2%	+228.9%	-69.5956217695348%
351	+156.3%	+229.1%	-69.6140990580371%
352	+156.4%	+229.3%	-69.6325539022168%
353	+156.5%	+229.4%	-69.6417729204615%
354	+156.6%	+229.6%	-69.6601941747573%
355	+156.7%	+229.8%	-69.6785930867192%
356	+156.7%	+229.9%	-69.6877841770233%
357	+156.8%	+230.1%	-69.7061496516207%
358	+156.9%	+230.3%	-69.7244928852558%
359	+157%	+230.4%	-69.7336561743341%
360	+157.1%	+230.6%	-69.7519661222021%
361	+157.2%	+230.7%	-69.7611127910493%
362	+157.3%	+230.9%	-69.7793895436688%
363	+157.4%	+231.1%	-69.7976442162489%
364	+157.5%	+231.2%	-69.8067632850242%
365	+157.6%	+231.4%	-69.8249849124925%
366	+157.7%	+231.5%	-69.8340874811463%
367	+157.8%	+231.7%	-69.8522761531504%
368	+157.9%	+231.9%	-69.8704429044893%
369	+157.9%	+232%	-69.8795180722892%
370	+158%	+232.2%	-69.8976520168573%
371	+158.1%	+232.3%	-69.9067108034908%
372	+158.2%	+232.5%	-69.9248120300752%
373	+158.3%	+232.6%	-69.9338544798557%
374	+158.4%	+232.8%	-69.9519230769231%
375	+158.5%	+232.9%	-69.9609492340042%
376	+158.6%	+233.1%	-69.9789852897028%
377	+158.7%	+233.2%	-69.9879951980792%
378	+158.7%	+233.4%	-70.00599880024%
379	+158.8%	+233.5%	-70.0149925037481%
380	+158.9%	+233.7%	-70.0329637398861%
381	+159%	+233.8%	-70.0419412822049%
382	+159.1%	+234%	-70.059880239521%
383	+159.2%	+234.1%	-70.0688416641724%
384	+159.2%	+234.3%	-70.0867484295543%
385	+159.3%	+234.4%	-70.0956937799043%
386	+159.4%	+234.6%	-70.1135684399283%
387	+159.5%	+234.7%	-70.1224977591873%
388	+159.6%	+234.9%	-70.1403404001194%
389	+159.7%	+235%	-70.1492537313433%
390	+159.7%	+235.1%	-70.1581617427634%
391	+159.8%	+235.3%	-70.1759618252311%
392	+159.9%	+235.4%	-70.1848539057841%
393	+160%	+235.6%	-70.2026221692491%
394	+160.1%	+235.7%	-70.2114983616324%
395	+160.2%	+235.9%	-70.2292348913367%
396	+160.2%	+236%	-70.2380952380952%
397	+160.3%	+236.1%	-70.246950312407%
398	+160.4%	+236.3%	-70.2646446625037%
399	+160.5%	+236.4%	-70.2734839476813%
400	+160.6%	+236.5%	-70.2823179791976%

References

• https://darkmatters.org/forums/index.php?/topic/18511-how-is-sacred-2-weapon-damage-calculated/&do=findComment&comment=7146451
• https://darkmatters.org/forums/index.php?/topic/18511-how-is-sacred-2-weapon-damage-calculated/&do=findComment&comment=7146939