Sacred 2:Concentration - formulas and tables

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Revision as of 15:15, 29 November 2024 by Maneus (talk | contribs) (Update the table data)
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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
ValueOfBonus Regeneration Time -X% ValueOfBonus Regeneration Time -X%
1 49 -4.67111534795043%
2 68 -6.36704119850187%
3 87 -8.00367985280589%
4 105 -9.50226244343891%
5 123 -10.9528049866429%
6 141 -12.3575810692375%
7 158 -13.6442141623489%
8 175 -14.8936170212766%
9 192 -16.1073825503356%
10 209 -17.2870140612076%
11 225 -18.3673469387755%
12 241 -19.41982272361%
13 256 -20.3821656050955%
14 271 -21.3217938630999%
15 286 -22.2395023328149%
16 301 -23.1360491929285%
17 316 -24.0121580547112%
18 330 -24.812030075188%
19 344 -25.5952380952381%
20 358 -26.3622974963181%
21 371 -27.0605397520058%
22 385 -27.797833935018%
23 398 -28.4692417739628%
24 411 -29.128277817151%
25 424 -29.7752808988764%
26 436 -30.3621169916435%
27 448 -30.939226519337%
28 460 -31.5068493150685%
29 472 -32.0652173913043%
30 484 -32.6145552560647%
31 496 -33.1550802139037%
32 507 -33.64299933643%
33 518 -34.1238471673254%
34 529 -34.597776324395%
35 540 -35.0649350649351%
36 551 -35.5254674403611%
37 562 -35.9795134443022%
38 572 -36.3867684478371%
39 582 -36.7888748419722%
40 592 -37.1859296482412%
41 602 -37.5780274656679%
42 612 -37.9652605459057%
43 622 -38.347718865598%
44 631 -38.6879215205395%
45 641 -39.061547836685%
46 650 -39.3939393939394%
47 659 -39.7227245328511%
48 668 -40.0479616306954%
49 677 -40.3697078115683%
50 686 -40.6880189798339%
51 695 -41.0029498525074%
52 703 -41.2800939518497%
53 712 -41.588785046729%
54 720 -41.8604651162791%
55 729 -42.1631000578369%
56 737 -42.4294761082326%
57 745 -42.6934097421203%
58 753 -42.9549343981746%
59 761 -43.214082907439%
60 768 -43.4389140271493%
61 776 -43.6936936936937%
62 783 -43.9147504206394%
63 791 -44.1652707984366%
64 798 -44.3826473859844%
65 806 -44.6290143964563%
66 813 -44.8428019856591%
67 820 -45.0549450549451%
68 827 -45.2654625068418%
69 834 -45.474372955289%
70 841 -45.6816947311244%
71 847 -45.8581483486735%
72 854 -46.0625674217907%
73 861 -46.2654486835035%
74 867 -46.4381360471344%
75 874 -46.6382070437567% 904 -47.4789915966387%
76 880 -46.8085106382979% 919 -47.8895257946847%
77 887 -47.0058293587705% 933 -48.2669425763063%
78 893 -47.1737982039091% 947 -48.6389316897792%
79 899 -47.3407056345445% 962 -49.0316004077472%
80 905 -47.50656167979% 976 -49.3927125506073%
81 911 -47.6713762428048% 989 -49.7234791352438%
82 917 -47.8351591027647% 1003 -50.0748876684973%
83 923 -47.9979199167967% 1016 -50.3968253968254%
84 929 -48.1596682218766% 1030 -50.7389162561576%
85 935 -48.3204134366925% 1043 -51.052373959863%
86 940 -48.4536082474227% 1055 -51.338199513382%
87 946 -48.6125385405961% 1068 -51.6441005802708%
88 952 -48.7704918032787% 1081 -51.9461797212878%
89 957 -48.9013796627491% 1093 -52.2216913521261%
90 963 -49.0575649516047% 1105 -52.4940617577197%
91 968 -49.1869918699187% 1117 -52.7633443552197%
92 973 -49.3157627977699% 1129 -53.0295913574448%
93 979 -49.4694290045478% 1141 -53.2928538066324%
94 984 -49.5967741935484% 1153 -53.5531816070599%
95 989 -49.7234791352438% 1164 -53.7892791127542%
96 994 -49.8495486459378% 1175 -54.0229885057471%
97 1000 -50% 1187 -54.2752629172382%
98 1005 -50.1246882793017% 1198 -54.5040946314832%
99 1010 -50.2487562189055% 1209 -54.7306473517429%
100 1015 -50.3722084367246% 1219 -54.9346552501127%
101 1019 -50.4705299653294% 1230 -55.1569506726457%
102 1024 -50.5928853754941% 1241 -55.3770638107988%
103 1029 -50.7146377525875% 1251 -55.5752998667259%
104 1034 -50.8357915437562% 1261 -55.7717823971694%
105 1039 -50.9563511525258% 1271 -55.9665345662704%
106 1043 -51.052373959863% 1281 -56.1595791319597%
107 1048 -51.171875% 1291 -56.3509384548232%
108 1052 -51.2670565302144% 1301 -56.5406345067362%
109 1057 -51.3855128828391% 1311 -56.728688879273%
110 1061 -51.4798641436196% 1321 -56.9151227919001%
111 1066 -51.5972894482091% 1330 -57.0815450643777%
112 1070 -51.6908212560386% 1339 -57.2466866182129%
113 1075 -51.8072289156626% 1349 -57.428693060877%
114 1079 -51.8999518999519% 1358 -57.5911789652248%
115 1083 -51.9923187710034% 1367 -57.752429235319%
116 1087 -52.0843315764255% 1376 -57.9124579124579%
117 1092 -52.1988527724665% 1385 -58.0712788259958%
118 1096 -52.2900763358779% 1394 -58.2289055973267%
119 1100 -52.3809523809524% 1402 -58.368026644463%
120 1104 -52.4714828897338% 1411 -58.5234342596433%
121 1108 -52.561669829222% 1419 -58.6606035551881%
122 1112 -52.6515151515152% 1428 -58.8138385502471%
123 1116 -52.7410207939509% 1436 -58.9490968801314%
124 1120 -52.8301886792453% 1444 -59.0834697217676%
125 1124 -52.9190207156309% 1452 -59.2169657422512%
126 1128 -53.0075187969925% 1460 -59.349593495935%
127 1132 -53.0956848030019% 1468 -59.4813614262561%
128 1135 -53.1615925058548% 1476 -59.6122778675283%
129 1139 -53.2491818606826% 1484 -59.7423510466989%
130 1143 -53.3364442370509% 1492 -59.8715890850722%
131 1147 -53.4233814625058% 1500 -60%
132 1150 -53.4883720930233% 1507 -60.1116872756282%
133 1154 -53.5747446610956% 1515 -60.2385685884692%
134 1158 -53.660797034291% 1522 -60.3489294210944%
135 1161 -53.7251272559% 1529 -60.4586793198893%
136 1165 -53.810623556582% 1537 -60.5833661805282%
137 1168 -53.8745387453875% 1544 -60.6918238993711%
138 1172 -53.9594843462247% 1551 -60.7996863974912%
139 1175 -54.0229885057471% 1558 -60.9069585613761%
140 1179 -54.1073887104176% 1565 -61.0136452241715%
141 1182 -54.1704857928506% 1572 -61.1197511664075%
142 1185 -54.233409610984% 1579 -61.2252811167119%
143 1189 -54.3170397441754% 1586 -61.3302397525135%
144 1192 -54.3795620437956% 1592 -61.4197530864198%
145 1195 -54.4419134396355% 1599 -61.5236629472874%
146 1199 -54.524783992724% 1606 -61.6270145817345%
147 1202 -54.5867393278837% 1612 -61.7151607963247%
148 1205 -54.6485260770975% 1619 -61.8174875906835%
149 1208 -54.7101449275362% 1625 -61.9047619047619%
150 1212 -54.7920433996383% 1631 -61.9916381603953%
151 1215 -54.8532731376975% 1638 -62.0924943138741%
152 1218 -54.9143372407574% 1644 -62.178517397882%
153 1221 -54.975236380009% 1650 -62.2641509433962%
154 1224 -55.0359712230216% 1656 -62.3493975903615%
155 1227 -55.0965424337674% 1662 -62.4342599549211%
156 1230 -55.1569506726457% 1668 -62.5187406296852%
157 1233 -55.2171965965069% 1674 -62.602842183994%
158 1236 -55.2772808586762% 1680 -62.6865671641791%
159 1239 -55.3372041089772% 1686 -62.7699180938198%
160 1242 -55.3969669937556% 1692 -62.852897473997%
161 1245 -55.456570155902% 1698 -62.9355077835434%
162 1248 -55.5160142348754% 1703 -63.0040695523492%
163 1250 -55.5555555555556% 1709 -63.0860095976375%
164 1253 -55.6147359076787% 1715 -63.1675874769797%
165 1256 -55.6737588652482% 1720 -63.2352941176471%
166 1259 -55.7326250553342% 1726 -63.3162142333089%
167 1262 -55.7913351016799% 1731 -63.3833760527279%
168 1264 -55.8303886925795% 1737 -63.4636463280965%
169 1267 -55.8888398764888% 1742 -63.5302698760029%
170 1270 -55.9471365638767% 1747 -63.5966508918821%
171 1273 -56.005279366476% 1753 -63.6759898292772%
172 1275 -56.043956043956% 1758 -63.7418419144307%
173 1278 -56.1018437225637% 1763 -63.8074556641332%
174 1281 -56.1595791319597% 1768 -63.8728323699422%
175 1283 -56.1979851073149% 1773 -63.9379733141003%
176 1286 -56.2554680664917% 1778 -64.0028797696184%
177 1288 -56.2937062937063% 1783 -64.0675530003593%
178 1291 -56.3509384548232% 1788 -64.1319942611191%
179 1293 -56.3890100305277% 1793 -64.1962047977086%
180 1296 -56.4459930313589% 1798 -64.2601858470336%
181 1298 -56.4838990426458% 1803 -64.3239386371745%
182 1301 -56.5406345067362% 1808 -64.3874643874644%
183 1303 -56.5783760312636% 1813 -64.4507643085674%
184 1306 -56.6348655680833% 1818 -64.513839602555%
185 1308 -56.6724436741768% 1822 -64.5641389085755%
186 1311 -56.728688879273% 1827 -64.6268128758401%
187 1313 -56.7661046260268% 1832 -64.6892655367232%
188 1315 -56.8034557235421% 1836 -64.7390691114245%
189 1318 -56.8593615185505% 1841 -64.8011263639564%
190 1320 -56.8965517241379% 1845 -64.8506151142355%
191 1323 -56.9522169608265% 1850 -64.9122807017544%
192 1325 -56.989247311828% 1854 -64.9614576033637%
193 1327 -57.0262140094542% 1859 -65.0227352221056%
194 1329 -57.06311721769% 1863 -65.0716032134125%
195 1332 -57.1183533447684% 1867 -65.1203348447855%
196 1334 -57.1550985432734% 1872 -65.1810584958217%
197 1336 -57.1917808219178% 1876 -65.2294853963839%
198 1338 -57.2284003421728% 1880 -65.2777777777778%
199 1341 -57.2832123024349% 1884 -65.3259361997226%
200 1343 -57.3196756295348% 1889 -65.3859466943579%
201 1345 -57.3560767590618% 1893 -65.4338057379883%
202 1347 -57.3924158500213% 1897 -65.4815326199517%
203 1349 -57.428693060877% 1901 -65.5291278869355%
204 1351 -57.4649085495534% 1905 -65.5765920826162%
205 1354 -57.5191163976211% 1909 -65.6239257476796%
206 1356 -57.5551782682513% 1913 -65.6711294198421%
207 1358 -57.5911789652248% 1917 -65.7182036338704%
208 1360 -57.6271186440678% 1921 -65.7651489216022%
209 1362 -57.6629974597798% 1925 -65.8119658119658%
210 1364 -57.6988155668359% 1929 -65.8586548310003%
211 1366 -57.7345731191885% 1933 -65.9052165018752%
212 1368 -57.7702702702703% 1937 -65.9516513449098%
213 1370 -57.8059071729958% 1940 -65.9863945578231%
214 1372 -57.8414839797639% 1944 -66.0326086956522%
215 1374 -57.87700084246% 1948 -66.078697421981%
216 1376 -57.9124579124579% 1952 -66.1246612466125%
217 1378 -57.9478553406224% 1955 -66.1590524534687%
218 1380 -57.9831932773109% 1959 -66.2047989185536%
219 1382 -58.0184718723762% 1963 -66.2504218697266%
220 1384 -58.0536912751678% 1966 -66.2845583277141%
221 1386 -58.0888516345348% 1970 -66.3299663299663%
222 1388 -58.1239530988275% 1973 -66.3639421459805%
223 1390 -58.1589958158996% 1977 -66.4091367148136%
224 1391 -58.176495190297% 1981 -66.4542099966454%
225 1393 -58.2114500626828% 1984 -66.4879356568365%
226 1395 -58.2463465553236% 1988 -66.5327978580991%
227 1397 -58.2811848143513% 1991 -66.5663657639585%
228 1399 -58.3159649854106% 1994 -66.5998663994656%
229 1401 -58.350687213661% 1998 -66.6444296197465%
230 1403 -58.3853516437786% 2001 -66.6777740753082%
231 1404 -58.4026622296173% 2005 -66.7221297836938%
232 1406 -58.4372402327515% 2008 -66.7553191489362%
233 1408 -58.4717607973422% 2011 -66.7884423779475%
234 1410 -58.50622406639% 2015 -66.832504145937%
235 1411 -58.5234342596433% 2018 -66.8654738237243%
236 1413 -58.5578118524658% 2021 -66.898378020523%
237 1415 -58.592132505176% 2024 -66.9312169312169%
238 1417 -58.6263963591229% 2027 -66.9639907499174%
239 1418 -58.6435070306038% 2031 -67.0075882547014%
240 1420 -58.6776859504132% 2034 -67.04021094265%
241 1422 -58.7118084227911% 2037 -67.0727691801119%
242 1423 -58.7288485348741% 2040 -67.1052631578947%
243 1425 -58.7628865979381% 2043 -67.1376930660532%
244 1427 -58.7968685620107% 2046 -67.1700590938936%
245 1428 -58.8138385502471% 2049 -67.202361429977%
246 1430 -58.8477366255144% 2052 -67.2346002621232%
247 1432 -58.8815789473684% 2055 -67.2667757774141%
248 1433 -58.898479243732% 2058 -67.2988881621975%
249 1435 -58.9322381930185% 2061 -67.3309376020908%
250 1437 -58.9659417316373% 2064 -67.3629242819843%
251 1438 -58.9827727645611% 2067 -67.394848386045%
252 1440 -59.0163934426229% 2070 -67.4267100977199%
253 1441 -59.0331831216715% 2073 -67.4585095997397%
254 1443 -59.0667212443717% 2076 -67.4902470741222%
255 1445 -59.1002044989775% 2079 -67.521922702176%
256 1446 -59.1169255928046% 2082 -67.5535366645036%
257 1448 -59.1503267973856% 2085 -67.5850891410049%
258 1449 -59.1670069416088% 2087 -67.6060900550696%
259 1451 -59.2003263973888% 2090 -67.6375404530744%
260 1452 -59.2169657422512% 2093 -67.6689298415778%
261 1454 -59.2502037489813% 2096 -67.7002583979328%
262 1455 -59.2668024439919% 2099 -67.7315262988061%
263 1457 -59.2999592999593% 2101 -67.7523379554982%
264 1458 -59.3165174938975% 2104 -67.7835051546392%
265 1460 -59.349593495935% 2107 -67.8146121660766%
266 1461 -59.3661113368549% 2109 -67.8353168221293%
267 1463 -59.3991067803492% 2112 -67.866323907455%
268 1464 -59.4155844155844% 2115 -67.8972712680578%
269 1466 -59.448499594485% 2117 -67.9178697465512%
270 1467 -59.4649371706526% 2120 -67.9487179487179%
271 1469 -59.4977723774808% 2123 -67.979506884406%
272 1470 -59.5141700404858% 2125 -68%
273 1471 -59.5305544314043% 2128 -68.0306905370844%
274 1473 -59.5632834613829% 2130 -68.0511182108626%
275 1474 -59.5796281325788% 2133 -68.0817108203%
276 1476 -59.6122778675283% 2135 -68.1020733652313%
277 1477 -59.628582963262% 2138 -68.1325685149777%
278 1478 -59.6448748991122% 2140 -68.1528662420382%
279 1480 -59.6774193548387% 2143 -68.1832643970729%
280 1481 -59.6936719064893% 2145 -68.2034976152623%
281 1482 -59.709911361805% 2148 -68.2337992376112%
282 1484 -59.7423510466989% 2150 -68.2539682539683%
283 1485 -59.7585513078471% 2153 -68.2841738027276%
284 1486 -59.7747385358005% 2155 -68.3042789223455%
285 1488 -59.8070739549839% 2158 -68.3343888537049%
286 1489 -59.8232221775814% 2160 -68.3544303797468%
287 1490 -59.8393574297189% 2162 -68.3744465528147%
288 1492 -59.8715890850722% 2165 -68.4044233807267%
289 1493 -59.8876855194545% 2167 -68.4243763814335%
290 1494 -59.9037690457097% 2169 -68.4443041969075%
291 1496 -59.9358974358974% 2172 -68.4741488020177%
292 1497 -59.951942330797% 2174 -68.4940138626339%
293 1498 -59.9679743795036% 2176 -68.5138539042821%
294 1500 -60% 2179 -68.5435671594841%
295 1501 -60.015993602559% 2181 -68.5633448601069%
296 1502 -60.0319744204636% 2183 -68.5830977065661%
297 1503 -60.0479424690372% 2185 -68.6028257456829%
298 1505 -60.0798403193613% 2188 -68.6323713927227%
299 1506 -60.0957701516361% 2190 -68.6520376175549%
300 1507 -60.1116872756282% 2192 -68.671679197995%
301 1508 -60.1275917065391% 2194 -68.6912961803381%
302 1509 -60.1434834595456% 2197 -68.7206756334063%
303 1511 -60.1752289924333% 2199 -68.7402313222882%
304 1512 -60.1910828025478% 2201 -68.7597625741956%
305 1513 -60.2069239952248% 2203 -68.7792694349048%
306 1514 -60.2227525855211% 2205 -68.798751950078%
307 1515 -60.2385685884692% 2207 -68.8182101652635%
308 1517 -60.2701628923321% 2209 -68.8376441258959%
309 1518 -60.285941223193% 2212 -68.8667496886675%
310 1519 -60.3017070265979% 2214 -68.8861232109521%
311 1520 -60.3174603174603% 2216 -68.9054726368159%
312 1521 -60.3332011106704% 2218 -68.9247980111871%
313 1523 -60.3646452635751% 2220 -68.944099378882%
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376 1586 -61.3302397525135% 2331 -69.9789852897028%
377 1587 -61.3451874758407% 2332 -69.9879951980792%
378 1587 -61.3451874758407% 2334 -70.00599880024%
379 1588 -61.3601236476043% 2335 -70.0149925037481%
380 1589 -61.3750482811897% 2337 -70.0329637398861%
381 1590 -61.3899613899614% 2338 -70.0419412822049%
382 1591 -61.4048629872636% 2340 -70.059880239521%
383 1592 -61.4197530864198% 2341 -70.0688416641724%
384 1592 -61.4197530864198% 2343 -70.0867484295543%
385 1593 -61.4346317007327% 2344 -70.0956937799043%
386 1594 -61.449498843485% 2346 -70.1135684399283%
387 1595 -61.4643545279383% 2347 -70.1224977591873%
388 1596 -61.4791987673344% 2349 -70.1403404001194%
389 1597 -61.4940315748941% 2350 -70.1492537313433%
390 1597 -61.4940315748941% 2351 -70.1581617427634%
391 1598 -61.5088529638183% 2353 -70.1759618252311%
392 1599 -61.5236629472874% 2354 -70.1848539057841%
393 1600 -61.5384615384615% 2356 -70.2026221692491%
394 1601 -61.5532487504806% 2357 -70.2114983616324%
395 1602 -61.5680245964643% 2359 -70.2292348913367%
396 1602 -61.5680245964643% 2360 -70.2380952380952%
397 1603 -61.5827890895121% 2361 -70.246950312407%
398 1604 -61.5975422427035% 2363 -70.2646446625037%
399 1605 -61.6122840690979% 2364 -70.2734839476813%
400 1606 -61.6270145817345% 2365 -70.2823179791976%

References