Sacred 2:Concentration - formulas and tables

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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:

  • Note: The values for Regeneration Time -X% are not rounded down, because that happens only in the tooltip.
Skill level Pre-mastery Post-mastery
Regeneration Time -X% (ValueOfBonus) Regeneration Time -X% (ValueOfBonus)
1 -4.67111534795043% (49)
2 -6.36704119850187% (68)
3 -8.00367985280589% (87)
4 -9.50226244343891% (105)
5 -10.9528049866429% (123)
6 -12.3575810692375% (141)
7 -13.6442141623489% (158)
8 -14.8936170212766% (175)
9 -16.1073825503356% (192)
10 -17.2870140612076% (209)
11 -18.3673469387755% (225)
12 -19.41982272361% (241)
13 -20.3821656050955% (256)
14 -21.3217938630999% (271)
15 -22.2395023328149% (286)
16 -23.1360491929285% (301)
17 -24.0121580547112% (316)
18 -24.812030075188% (330)
19 -25.5952380952381% (344)
20 -26.3622974963181% (358)
21 -27.0605397520058% (371)
22 -27.797833935018% (385)
23 -28.4692417739628% (398)
24 -29.128277817151% (411)
25 -29.7752808988764% (424)
26 -30.3621169916435% (436)
27 -30.939226519337% (448)
28 -31.5068493150685% (460)
29 -32.0652173913043% (472)
30 -32.6145552560647% (484)
31 -33.1550802139037% (496)
32 -33.64299933643% (507)
33 -34.1238471673254% (518)
34 -34.597776324395% (529)
35 -35.0649350649351% (540)
36 -35.5254674403611% (551)
37 -35.9795134443022% (562)
38 -36.3867684478371% (572)
39 -36.7888748419722% (582)
40 -37.1859296482412% (592)
41 -37.5780274656679% (602)
42 -37.9652605459057% (612)
43 -38.347718865598% (622)
44 -38.6879215205395% (631)
45 -39.061547836685% (641)
46 -39.3939393939394% (650)
47 -39.7227245328511% (659)
48 -40.0479616306954% (668)
49 -40.3697078115683% (677)
50 -40.6880189798339% (686)
51 -41.0029498525074% (695)
52 -41.2800939518497% (703)
53 -41.588785046729% (712)
54 -41.8604651162791% (720)
55 -42.1631000578369% (729)
56 -42.4294761082326% (737)
57 -42.6934097421203% (745)
58 -42.9549343981746% (753)
59 -43.214082907439% (761)
60 -43.4389140271493% (768)
61 -43.6936936936937% (776)
62 -43.9147504206394% (783)
63 -44.1652707984366% (791)
64 -44.3826473859844% (798)
65 -44.6290143964563% (806)
66 -44.8428019856591% (813)
67 -45.0549450549451% (820)
68 -45.2654625068418% (827)
69 -45.474372955289% (834)
70 -45.6816947311244% (841)
71 -45.8581483486735% (847)
72 -46.0625674217907% (854)
73 -46.2654486835035% (861)
74 -46.4381360471344% (867)
75 -46.6382070437567% (874) -47.4789915966387% (904)
76 -46.8085106382979% (880) -47.8895257946847% (919)
77 -47.0058293587705% (887) -48.2669425763063% (933)
78 -47.1737982039091% (893) -48.6389316897792% (947)
79 -47.3407056345445% (899) -49.0316004077472% (962)
80 -47.50656167979% (905) -49.3927125506073% (976)
81 -47.6713762428048% (911) -49.7234791352438% (989)
82 -47.8351591027647% (917) -50.0748876684973% (1003)
83 -47.9979199167967% (923) -50.3968253968254% (1016)
84 -48.1596682218766% (929) -50.7389162561576% (1030)
85 -48.3204134366925% (935) -51.052373959863% (1043)
86 -48.4536082474227% (940) -51.338199513382% (1055)
87 -48.6125385405961% (946) -51.6441005802708% (1068)
88 -48.7704918032787% (952) -51.9461797212878% (1081)
89 -48.9013796627491% (957) -52.2216913521261% (1093)
90 -49.0575649516047% (963) -52.4940617577197% (1105)
91 -49.1869918699187% (968) -52.7633443552197% (1117)
92 -49.3157627977699% (973) -53.0295913574448% (1129)
93 -49.4694290045478% (979) -53.2928538066324% (1141)
94 -49.5967741935484% (984) -53.5531816070599% (1153)
95 -49.7234791352438% (989) -53.7892791127542% (1164)
96 -49.8495486459378% (994) -54.0229885057471% (1175)
97 -50% (1000) -54.2752629172382% (1187)
98 -50.1246882793017% (1005) -54.5040946314832% (1198)
99 -50.2487562189055% (1010) -54.7306473517429% (1209)
100 -50.3722084367246% (1015) -54.9346552501127% (1219)
101 -50.4705299653294% (1019) -55.1569506726457% (1230)
102 -50.5928853754941% (1024) -55.3770638107988% (1241)
103 -50.7146377525875% (1029) -55.5752998667259% (1251)
104 -50.8357915437562% (1034) -55.7717823971694% (1261)
105 -50.9563511525258% (1039) -55.9665345662704% (1271)
106 -51.052373959863% (1043) -56.1595791319597% (1281)
107 -51.171875% (1048) -56.3509384548232% (1291)
108 -51.2670565302144% (1052) -56.5406345067362% (1301)
109 -51.3855128828391% (1057) -56.728688879273% (1311)
110 -51.4798641436196% (1061) -56.9151227919001% (1321)
111 -51.5972894482091% (1066) -57.0815450643777% (1330)
112 -51.6908212560386% (1070) -57.2466866182129% (1339)
113 -51.8072289156626% (1075) -57.428693060877% (1349)
114 -51.8999518999519% (1079) -57.5911789652248% (1358)
115 -51.9923187710034% (1083) -57.752429235319% (1367)
116 -52.0843315764255% (1087) -57.9124579124579% (1376)
117 -52.1988527724665% (1092) -58.0712788259958% (1385)
118 -52.2900763358779% (1096) -58.2289055973267% (1394)
119 -52.3809523809524% (1100) -58.368026644463% (1402)
120 -52.4714828897338% (1104) -58.5234342596433% (1411)
121 -52.561669829222% (1108) -58.6606035551881% (1419)
122 -52.6515151515152% (1112) -58.8138385502471% (1428)
123 -52.7410207939509% (1116) -58.9490968801314% (1436)
124 -52.8301886792453% (1120) -59.0834697217676% (1444)
125 -52.9190207156309% (1124) -59.2169657422512% (1452)
126 -53.0075187969925% (1128) -59.349593495935% (1460)
127 -53.0956848030019% (1132) -59.4813614262561% (1468)
128 -53.1615925058548% (1135) -59.6122778675283% (1476)
129 -53.2491818606826% (1139) -59.7423510466989% (1484)
130 -53.3364442370509% (1143) -59.8715890850722% (1492)
131 -53.4233814625058% (1147) -60% (1500)
132 -53.4883720930233% (1150) -60.1116872756282% (1507)
133 -53.5747446610956% (1154) -60.2385685884692% (1515)
134 -53.660797034291% (1158) -60.3489294210944% (1522)
135 -53.7251272559% (1161) -60.4586793198893% (1529)
136 -53.810623556582% (1165) -60.5833661805282% (1537)
137 -53.8745387453875% (1168) -60.6918238993711% (1544)
138 -53.9594843462247% (1172) -60.7996863974912% (1551)
139 -54.0229885057471% (1175) -60.9069585613761% (1558)
140 -54.1073887104176% (1179) -61.0136452241715% (1565)
141 -54.1704857928506% (1182) -61.1197511664075% (1572)
142 -54.233409610984% (1185) -61.2252811167119% (1579)
143 -54.3170397441754% (1189) -61.3302397525135% (1586)
144 -54.3795620437956% (1192) -61.4197530864198% (1592)
145 -54.4419134396355% (1195) -61.5236629472874% (1599)
146 -54.524783992724% (1199) -61.6270145817345% (1606)
147 -54.5867393278837% (1202) -61.7151607963247% (1612)
148 -54.6485260770975% (1205) -61.8174875906835% (1619)
149 -54.7101449275362% (1208) -61.9047619047619% (1625)
150 -54.7920433996383% (1212) -61.9916381603953% (1631)
151 -54.8532731376975% (1215) -62.0924943138741% (1638)
152 -54.9143372407574% (1218) -62.178517397882% (1644)
153 -54.975236380009% (1221) -62.2641509433962% (1650)
154 -55.0359712230216% (1224) -62.3493975903615% (1656)
155 -55.0965424337674% (1227) -62.4342599549211% (1662)
156 -55.1569506726457% (1230) -62.5187406296852% (1668)
157 -55.2171965965069% (1233) -62.602842183994% (1674)
158 -55.2772808586762% (1236) -62.6865671641791% (1680)
159 -55.3372041089772% (1239) -62.7699180938198% (1686)
160 -55.3969669937556% (1242) -62.852897473997% (1692)
161 -55.456570155902% (1245) -62.9355077835434% (1698)
162 -55.5160142348754% (1248) -63.0040695523492% (1703)
163 -55.5555555555556% (1250) -63.0860095976375% (1709)
164 -55.6147359076787% (1253) -63.1675874769797% (1715)
165 -55.6737588652482% (1256) -63.2352941176471% (1720)
166 -55.7326250553342% (1259) -63.3162142333089% (1726)
167 -55.7913351016799% (1262) -63.3833760527279% (1731)
168 -55.8303886925795% (1264) -63.4636463280965% (1737)
169 -55.8888398764888% (1267) -63.5302698760029% (1742)
170 -55.9471365638767% (1270) -63.5966508918821% (1747)
171 -56.005279366476% (1273) -63.6759898292772% (1753)
172 -56.043956043956% (1275) -63.7418419144307% (1758)
173 -56.1018437225637% (1278) -63.8074556641332% (1763)
174 -56.1595791319597% (1281) -63.8728323699422% (1768)
175 -56.1979851073149% (1283) -63.9379733141003% (1773)
176 -56.2554680664917% (1286) -64.0028797696184% (1778)
177 -56.2937062937063% (1288) -64.0675530003593% (1783)
178 -56.3509384548232% (1291) -64.1319942611191% (1788)
179 -56.3890100305277% (1293) -64.1962047977086% (1793)
180 -56.4459930313589% (1296) -64.2601858470336% (1798)
181 -56.4838990426458% (1298) -64.3239386371745% (1803)
182 -56.5406345067362% (1301) -64.3874643874644% (1808)
183 -56.5783760312636% (1303) -64.4507643085674% (1813)
184 -56.6348655680833% (1306) -64.513839602555% (1818)
185 -56.6724436741768% (1308) -64.5641389085755% (1822)
186 -56.728688879273% (1311) -64.6268128758401% (1827)
187 -56.7661046260268% (1313) -64.6892655367232% (1832)
188 -56.8034557235421% (1315) -64.7390691114245% (1836)
189 -56.8593615185505% (1318) -64.8011263639564% (1841)
190 -56.8965517241379% (1320) -64.8506151142355% (1845)
191 -56.9522169608265% (1323) -64.9122807017544% (1850)
192 -56.989247311828% (1325) -64.9614576033637% (1854)
193 -57.0262140094542% (1327) -65.0227352221056% (1859)
194 -57.06311721769% (1329) -65.0716032134125% (1863)
195 -57.1183533447684% (1332) -65.1203348447855% (1867)
196 -57.1550985432734% (1334) -65.1810584958217% (1872)
197 -57.1917808219178% (1336) -65.2294853963839% (1876)
198 -57.2284003421728% (1338) -65.2777777777778% (1880)
199 -57.2832123024349% (1341) -65.3259361997226% (1884)
200 -57.3196756295348% (1343) -65.3859466943579% (1889)
201 -57.3560767590618% (1345) -65.4338057379883% (1893)
202 -57.3924158500213% (1347) -65.4815326199517% (1897)
203 -57.428693060877% (1349) -65.5291278869355% (1901)
204 -57.4649085495534% (1351) -65.5765920826162% (1905)
205 -57.5191163976211% (1354) -65.6239257476796% (1909)
206 -57.5551782682513% (1356) -65.6711294198421% (1913)
207 -57.5911789652248% (1358) -65.7182036338704% (1917)
208 -57.6271186440678% (1360) -65.7651489216022% (1921)
209 -57.6629974597798% (1362) -65.8119658119658% (1925)
210 -57.6988155668359% (1364) -65.8586548310003% (1929)
211 -57.7345731191885% (1366) -65.9052165018752% (1933)
212 -57.7702702702703% (1368) -65.9516513449098% (1937)
213 -57.8059071729958% (1370) -65.9863945578231% (1940)
214 -57.8414839797639% (1372) -66.0326086956522% (1944)
215 -57.87700084246% (1374) -66.078697421981% (1948)
216 -57.9124579124579% (1376) -66.1246612466125% (1952)
217 -57.9478553406224% (1378) -66.1590524534687% (1955)
218 -57.9831932773109% (1380) -66.2047989185536% (1959)
219 -58.0184718723762% (1382) -66.2504218697266% (1963)
220 -58.0536912751678% (1384) -66.2845583277141% (1966)
221 -58.0888516345348% (1386) -66.3299663299663% (1970)
222 -58.1239530988275% (1388) -66.3639421459805% (1973)
223 -58.1589958158996% (1390) -66.4091367148136% (1977)
224 -58.176495190297% (1391) -66.4542099966454% (1981)
225 -58.2114500626828% (1393) -66.4879356568365% (1984)
226 -58.2463465553236% (1395) -66.5327978580991% (1988)
227 -58.2811848143513% (1397) -66.5663657639585% (1991)
228 -58.3159649854106% (1399) -66.5998663994656% (1994)
229 -58.350687213661% (1401) -66.6444296197465% (1998)
230 -58.3853516437786% (1403) -66.6777740753082% (2001)
231 -58.4026622296173% (1404) -66.7221297836938% (2005)
232 -58.4372402327515% (1406) -66.7553191489362% (2008)
233 -58.4717607973422% (1408) -66.7884423779475% (2011)
234 -58.50622406639% (1410) -66.832504145937% (2015)
235 -58.5234342596433% (1411) -66.8654738237243% (2018)
236 -58.5578118524658% (1413) -66.898378020523% (2021)
237 -58.592132505176% (1415) -66.9312169312169% (2024)
238 -58.6263963591229% (1417) -66.9639907499174% (2027)
239 -58.6435070306038% (1418) -67.0075882547014% (2031)
240 -58.6776859504132% (1420) -67.04021094265% (2034)
241 -58.7118084227911% (1422) -67.0727691801119% (2037)
242 -58.7288485348741% (1423) -67.1052631578947% (2040)
243 -58.7628865979381% (1425) -67.1376930660532% (2043)
244 -58.7968685620107% (1427) -67.1700590938936% (2046)
245 -58.8138385502471% (1428) -67.202361429977% (2049)
246 -58.8477366255144% (1430) -67.2346002621232% (2052)
247 -58.8815789473684% (1432) -67.2667757774141% (2055)
248 -58.898479243732% (1433) -67.2988881621975% (2058)
249 -58.9322381930185% (1435) -67.3309376020908% (2061)
250 -58.9659417316373% (1437) -67.3629242819843% (2064)
251 -58.9827727645611% (1438) -67.394848386045% (2067)
252 -59.0163934426229% (1440) -67.4267100977199% (2070)
253 -59.0331831216715% (1441) -67.4585095997397% (2073)
254 -59.0667212443717% (1443) -67.4902470741222% (2076)
255 -59.1002044989775% (1445) -67.521922702176% (2079)
256 -59.1169255928046% (1446) -67.5535366645036% (2082)
257 -59.1503267973856% (1448) -67.5850891410049% (2085)
258 -59.1670069416088% (1449) -67.6060900550696% (2087)
259 -59.2003263973888% (1451) -67.6375404530744% (2090)
260 -59.2169657422512% (1452) -67.6689298415778% (2093)
261 -59.2502037489813% (1454) -67.7002583979328% (2096)
262 -59.2668024439919% (1455) -67.7315262988061% (2099)
263 -59.2999592999593% (1457) -67.7523379554982% (2101)
264 -59.3165174938975% (1458) -67.7835051546392% (2104)
265 -59.349593495935% (1460) -67.8146121660766% (2107)
266 -59.3661113368549% (1461) -67.8353168221293% (2109)
267 -59.3991067803492% (1463) -67.866323907455% (2112)
268 -59.4155844155844% (1464) -67.8972712680578% (2115)
269 -59.448499594485% (1466) -67.9178697465512% (2117)
270 -59.4649371706526% (1467) -67.9487179487179% (2120)
271 -59.4977723774808% (1469) -67.979506884406% (2123)
272 -59.5141700404858% (1470) -68% (2125)
273 -59.5305544314043% (1471) -68.0306905370844% (2128)
274 -59.5632834613829% (1473) -68.0511182108626% (2130)
275 -59.5796281325788% (1474) -68.0817108203% (2133)
276 -59.6122778675283% (1476) -68.1020733652313% (2135)
277 -59.628582963262% (1477) -68.1325685149777% (2138)
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399 -61.6122840690979% (1605) -70.2734839476813% (2364)
400 -61.6270145817345% (1606) -70.2823179791976% (2365)

References