Difference between revisions of "Sacred 2:Ancient Magic - formulas and tables"

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Line 45: Line 45:
 
The formula for Damage +X% is:
 
The formula for Damage +X% is:
 
<blockquote>ValueOfBonus = SkillValue</blockquote>
 
<blockquote>ValueOfBonus = SkillValue</blockquote>
<blockquote>TooltipValue = ValueOfBonus * 0.1</blockquote>
+
<blockquote>TooltipValue = 0.1 * ValueOfBonus</blockquote>
 
This TooltipValue is then subject to precision loss from 32-bit floats, and is rounded down to one decimal place. In short, the resulting value may end up being lower by 0.1.
 
This TooltipValue is then subject to precision loss from 32-bit floats, and is rounded down to one decimal place. In short, the resulting value may end up being lower by 0.1.
  
Line 51: Line 51:
  
 
The formula for Opponents' Immunities -X% is:
 
The formula for Opponents' Immunities -X% is:
<blockquote>ValueOfBonus = 1000 * SkillValue / (1000 + SkillValue)</blockquote>
+
<blockquote>ValueOfBonus = SkillValue</blockquote>
<blockquote>TooltipValue = -1 * ValueOfBonus * 0.1</blockquote>
+
<blockquote>DiminishedValue = 1000 * ValueOfBonus / (1000 + ValueOfBonus)</blockquote>
 +
<blockquote>TooltipValue = -0.1 * DiminishedValue</blockquote>
 
This TooltipValue is then rounded down to one decimal place.
 
This TooltipValue is then rounded down to one decimal place.
  
Line 61: Line 62:
 
Where:
 
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.
 
* 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.
+
* OpponentsImmunities - The DiminishedValue for the opponents' immunities bonus.
  
  
Line 89: Line 90:
  
 
And now, by using these formulas, we can fill in the following table:
 
And now, by using these formulas, we can fill in the following table:
 
+
* Note: The values for Damage +X% are without precision loss, because that happens only in the tooltip.
Note: The listed values for Damage +X% are before applying precision loss. And the listed values for Opponents' Immunities +X% are before rounding down. The reason is these operations affect only the tooltips and not the actual damage calculations.
+
* Note: The values for Opponents' Immunities +X% are not rounded down, because that happens only in the tooltip.
  
 
{| class="skills"
 
{| class="skills"

Latest revision as of 14:45, 29 November 2024

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 = 0.1 * ValueOfBonus

This TooltipValue is then subject to precision loss from 32-bit floats, and is rounded down to one decimal place. In short, the resulting value may end up being lower by 0.1.


The formula for Opponents' Immunities -X% is:

ValueOfBonus = SkillValue

DiminishedValue = 1000 * ValueOfBonus / (1000 + ValueOfBonus)

TooltipValue = -0.1 * DiminishedValue

This TooltipValue is then 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 DiminishedValue 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, because that happens only in the tooltip.
  • Note: The values for Opponents' Immunities +X% are not rounded down, because that happens only in the tooltip.
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%
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References