Sacred 2:Toughness - formulas and tables

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The skill definition can be found in creatures.txt.

mgr.createSkill {
	skill_name = "skill_toughness",
	advance_level = 75,
	min_level = 1,
	mean_value = 200,
	advance_mean_value = 300,
	skillgroup = "SKG_DEFENCE",
	adv_skill_name = "skill_advanced_toughness",
}


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. Toughness provides two bonuses: Armor per Damage Type +X and Opponent's Damage -X%.


The formula for Armor per Damage Type +X is:

For pre-mastery skill levels:

ValueOfBonus = FLOOR(SkillValue / 20)

For post-mastery skill levels:

ValueOfBonus = FLOOR(SkillValue / 15)

Then:

TooltipValue = ValueOfBonus


The formula for Opponent's Damage -X% is:

For pre-mastery skill levels:

ValueOfBonus = FLOOR(SkillValue / 20)

For post-mastery skill levels:

ValueOfBonus = FLOOR(SkillValue / 15)

Then:

TooltipValue = -1 * ValueOfBonus * 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.


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 * 200 * (SkillLevel + 100 * 0.015) / (SkillLevel + 100))

SkillValue = FLOOR(4000 * (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 * 300 * (SkillLevel - 34 + 100 * 0.015) / (SkillLevel - 34 + 100))

SkillValue = FLOOR(6000 * (SkillLevel - 34 + 1.5) / (SkillLevel + 66))

SkillValue = FLOOR(6000 * (SkillLevel - 32.5) / (SkillLevel + 66))


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

Note: The listed values for Opponent's Damage -X% are before applying precision loss. The reason is this operation affects only the tooltip and not the actual damage calculations.

Skill level Pre-mastery Post-mastery
Armor per Damage Type +X Opponent's Damage -X% Armor per Damage Type +X Opponent's Damage -X%
1 +4 -0.4%
2 +6 -0.6%
3 +8 -0.8%
4 +10 -1%
5 +12 -1.2%
6 +14 -1.4%
7 +15 -1.5%
8 +17 -1.7%
9 +19 -1.9%
10 +20 -2%
11 +22 -2.2%
12 +24 -2.4%
13 +25 -2.5%
14 +27 -2.7%
15 +28 -2.8%
16 +30 -3%
17 +31 -3.1%
18 +33 -3.3%
19 +34 -3.4%
20 +35 -3.5%
21 +37 -3.7%
22 +38 -3.8%
23 +39 -3.9%
24 +41 -4.1%
25 +42 -4.2%
26 +43 -4.3%
27 +44 -4.4%
28 +46 -4.6%
29 +47 -4.7%
30 +48 -4.8%
31 +49 -4.9%
32 +50 -5%
33 +51 -5.1%
34 +52 -5.2%
35 +54 -5.4%
36 +55 -5.5%
37 +56 -5.6%
38 +57 -5.7%
39 +58 -5.8%
40 +59 -5.9%
41 +60 -6%
42 +61 -6.1%
43 +62 -6.2%
44 +63 -6.3%
45 +64 -6.4%
46 +65 -6.5%
47 +65 -6.5%
48 +66 -6.6%
49 +67 -6.7%
50 +68 -6.8%
51 +69 -6.9%
52 +70 -7%
53 +71 -7.1%
54 +72 -7.2%
55 +72 -7.2%
56 +73 -7.3%
57 +74 -7.4%
58 +75 -7.5%
59 +76 -7.6%
60 +76 -7.6%
61 +77 -7.7%
62 +78 -7.8%
63 +79 -7.9%
64 +79 -7.9%
65 +80 -8%
66 +81 -8.1%
67 +82 -8.2%
68 +82 -8.2%
69 +83 -8.3%
70 +84 -8.4%
71 +84 -8.4%
72 +85 -8.5%
73 +86 -8.6%
74 +86 -8.6%
75 +87 -8.7% +120 -12%
76 +88 -8.8% +122 -12.2%
77 +88 -8.8% +124 -12.4%
78 +89 -8.9% +126 -12.6%
79 +89 -8.9% +128 -12.8%
80 +90 -9% +130 -13%
81 +91 -9.1% +131 -13.1%
82 +91 -9.1% +133 -13.3%
83 +92 -9.2% +135 -13.5%
84 +92 -9.2% +137 -13.7%
85 +93 -9.3% +139 -13.9%
86 +94 -9.4% +140 -14%
87 +94 -9.4% +142 -14.2%
88 +95 -9.5% +144 -14.4%
89 +95 -9.5% +145 -14.5%
90 +96 -9.6% +147 -14.7%
91 +96 -9.6% +149 -14.9%
92 +97 -9.7% +150 -15%
93 +97 -9.7% +152 -15.2%
94 +98 -9.8% +153 -15.3%
95 +98 -9.8% +155 -15.5%
96 +99 -9.9% +156 -15.6%
97 +100 -10% +158 -15.8%
98 +100 -10% +159 -15.9%
99 +101 -10.1% +161 -16.1%
100 +101 -10.1% +162 -16.2%
101 +101 -10.1% +164 -16.4%
102 +102 -10.2% +165 -16.5%
103 +102 -10.2% +166 -16.6%
104 +103 -10.3% +168 -16.8%
105 +103 -10.3% +169 -16.9%
106 +104 -10.4% +170 -17%
107 +104 -10.4% +172 -17.2%
108 +105 -10.5% +173 -17.3%
109 +105 -10.5% +174 -17.4%
110 +106 -10.6% +176 -17.6%
111 +106 -10.6% +177 -17.7%
112 +107 -10.7% +178 -17.8%
113 +107 -10.7% +179 -17.9%
114 +107 -10.7% +181 -18.1%
115 +108 -10.8% +182 -18.2%
116 +108 -10.8% +183 -18.3%
117 +109 -10.9% +184 -18.4%
118 +109 -10.9% +185 -18.5%
119 +110 -11% +187 -18.7%
120 +110 -11% +188 -18.8%
121 +110 -11% +189 -18.9%
122 +111 -11.1% +190 -19%
123 +111 -11.1% +191 -19.1%
124 +112 -11.2% +192 -19.2%
125 +112 -11.2% +193 -19.3%
126 +112 -11.2% +194 -19.4%
127 +113 -11.3% +195 -19.5%
128 +113 -11.3% +196 -19.6%
129 +113 -11.3% +197 -19.7%
130 +114 -11.4% +198 -19.8%
131 +114 -11.4% +200 -20%
132 +115 -11.5% +201 -20.1%
133 +115 -11.5% +202 -20.2%
134 +115 -11.5% +203 -20.3%
135 +116 -11.6% +203 -20.3%
136 +116 -11.6% +204 -20.4%
137 +116 -11.6% +205 -20.5%
138 +117 -11.7% +206 -20.6%
139 +117 -11.7% +207 -20.7%
140 +117 -11.7% +208 -20.8%
141 +118 -11.8% +209 -20.9%
142 +118 -11.8% +210 -21%
143 +118 -11.8% +211 -21.1%
144 +119 -11.9% +212 -21.2%
145 +119 -11.9% +213 -21.3%
146 +119 -11.9% +214 -21.4%
147 +120 -12% +215 -21.5%
148 +120 -12% +215 -21.5%
149 +120 -12% +216 -21.6%
150 +121 -12.1% +217 -21.7%
151 +121 -12.1% +218 -21.8%
152 +121 -12.1% +219 -21.9%
153 +122 -12.2% +220 -22%
154 +122 -12.2% +220 -22%
155 +122 -12.2% +221 -22.1%
156 +123 -12.3% +222 -22.2%
157 +123 -12.3% +223 -22.3%
158 +123 -12.3% +224 -22.4%
159 +123 -12.3% +224 -22.4%
160 +124 -12.4% +225 -22.5%
161 +124 -12.4% +226 -22.6%
162 +124 -12.4% +227 -22.7%
163 +125 -12.5% +227 -22.7%
164 +125 -12.5% +228 -22.8%
165 +125 -12.5% +229 -22.9%
166 +125 -12.5% +230 -23%
167 +126 -12.6% +230 -23%
168 +126 -12.6% +231 -23.1%
169 +126 -12.6% +232 -23.2%
170 +127 -12.7% +233 -23.3%
171 +127 -12.7% +233 -23.3%
172 +127 -12.7% +234 -23.4%
173 +127 -12.7% +235 -23.5%
174 +128 -12.8% +235 -23.5%
175 +128 -12.8% +236 -23.6%
176 +128 -12.8% +237 -23.7%
177 +128 -12.8% +237 -23.7%
178 +129 -12.9% +238 -23.8%
179 +129 -12.9% +239 -23.9%
180 +129 -12.9% +239 -23.9%
181 +129 -12.9% +240 -24%
182 +130 -13% +241 -24.1%
183 +130 -13% +241 -24.1%
184 +130 -13% +242 -24.2%
185 +130 -13% +243 -24.3%
186 +131 -13.1% +243 -24.3%
187 +131 -13.1% +244 -24.4%
188 +131 -13.1% +244 -24.4%
189 +131 -13.1% +245 -24.5%
190 +132 -13.2% +246 -24.6%
191 +132 -13.2% +246 -24.6%
192 +132 -13.2% +247 -24.7%
193 +132 -13.2% +247 -24.7%
194 +132 -13.2% +248 -24.8%
195 +133 -13.3% +249 -24.9%
196 +133 -13.3% +249 -24.9%
197 +133 -13.3% +250 -25%
198 +133 -13.3% +250 -25%
199 +134 -13.4% +251 -25.1%
200 +134 -13.4% +251 -25.1%
201 +134 -13.4% +252 -25.2%
202 +134 -13.4% +252 -25.2%
203 +134 -13.4% +253 -25.3%
204 +135 -13.5% +254 -25.4%
205 +135 -13.5% +254 -25.4%
206 +135 -13.5% +255 -25.5%
207 +135 -13.5% +255 -25.5%
208 +136 -13.6% +256 -25.6%
209 +136 -13.6% +256 -25.6%
210 +136 -13.6% +257 -25.7%
211 +136 -13.6% +257 -25.7%
212 +136 -13.6% +258 -25.8%
213 +137 -13.7% +258 -25.8%
214 +137 -13.7% +259 -25.9%
215 +137 -13.7% +259 -25.9%
216 +137 -13.7% +260 -26%
217 +137 -13.7% +260 -26%
218 +138 -13.8% +261 -26.1%
219 +138 -13.8% +261 -26.1%
220 +138 -13.8% +262 -26.2%
221 +138 -13.8% +262 -26.2%
222 +138 -13.8% +263 -26.3%
223 +139 -13.9% +263 -26.3%
224 +139 -13.9% +264 -26.4%
225 +139 -13.9% +264 -26.4%
226 +139 -13.9% +265 -26.5%
227 +139 -13.9% +265 -26.5%
228 +139 -13.9% +265 -26.5%
229 +140 -14% +266 -26.6%
230 +140 -14% +266 -26.6%
231 +140 -14% +267 -26.7%
232 +140 -14% +267 -26.7%
233 +140 -14% +268 -26.8%
234 +141 -14.1% +268 -26.8%
235 +141 -14.1% +269 -26.9%
236 +141 -14.1% +269 -26.9%
237 +141 -14.1% +269 -26.9%
238 +141 -14.1% +270 -27%
239 +141 -14.1% +270 -27%
240 +142 -14.2% +271 -27.1%
241 +142 -14.2% +271 -27.1%
242 +142 -14.2% +272 -27.2%
243 +142 -14.2% +272 -27.2%
244 +142 -14.2% +272 -27.2%
245 +142 -14.2% +273 -27.3%
246 +143 -14.3% +273 -27.3%
247 +143 -14.3% +274 -27.4%
248 +143 -14.3% +274 -27.4%
249 +143 -14.3% +274 -27.4%
250 +143 -14.3% +275 -27.5%
251 +143 -14.3% +275 -27.5%
252 +144 -14.4% +276 -27.6%
253 +144 -14.4% +276 -27.6%
254 +144 -14.4% +276 -27.6%
255 +144 -14.4% +277 -27.7%
256 +144 -14.4% +277 -27.7%
257 +144 -14.4% +278 -27.8%
258 +144 -14.4% +278 -27.8%
259 +145 -14.5% +278 -27.8%
260 +145 -14.5% +279 -27.9%
261 +145 -14.5% +279 -27.9%
262 +145 -14.5% +279 -27.9%
263 +145 -14.5% +280 -28%
264 +145 -14.5% +280 -28%
265 +146 -14.6% +280 -28%
266 +146 -14.6% +281 -28.1%
267 +146 -14.6% +281 -28.1%
268 +146 -14.6% +282 -28.2%
269 +146 -14.6% +282 -28.2%
270 +146 -14.6% +282 -28.2%
271 +146 -14.6% +283 -28.3%
272 +147 -14.7% +283 -28.3%
273 +147 -14.7% +283 -28.3%
274 +147 -14.7% +284 -28.4%
275 +147 -14.7% +284 -28.4%
276 +147 -14.7% +284 -28.4%
277 +147 -14.7% +285 -28.5%
278 +147 -14.7% +285 -28.5%
279 +148 -14.8% +285 -28.5%
280 +148 -14.8% +286 -28.6%
281 +148 -14.8% +286 -28.6%
282 +148 -14.8% +286 -28.6%
283 +148 -14.8% +287 -28.7%
284 +148 -14.8% +287 -28.7%
285 +148 -14.8% +287 -28.7%
286 +148 -14.8% +288 -28.8%
287 +149 -14.9% +288 -28.8%
288 +149 -14.9% +288 -28.8%
289 +149 -14.9% +289 -28.9%
290 +149 -14.9% +289 -28.9%
291 +149 -14.9% +289 -28.9%
292 +149 -14.9% +289 -28.9%
293 +149 -14.9% +290 -29%
294 +150 -15% +290 -29%
295 +150 -15% +290 -29%
296 +150 -15% +291 -29.1%
297 +150 -15% +291 -29.1%
298 +150 -15% +291 -29.1%
299 +150 -15% +292 -29.2%
300 +150 -15% +292 -29.2%
301 +150 -15% +292 -29.2%
302 +150 -15% +292 -29.2%
303 +151 -15.1% +293 -29.3%
304 +151 -15.1% +293 -29.3%
305 +151 -15.1% +293 -29.3%
306 +151 -15.1% +294 -29.4%
307 +151 -15.1% +294 -29.4%
308 +151 -15.1% +294 -29.4%
309 +151 -15.1% +294 -29.4%
310 +151 -15.1% +295 -29.5%
311 +152 -15.2% +295 -29.5%
312 +152 -15.2% +295 -29.5%
313 +152 -15.2% +296 -29.6%
314 +152 -15.2% +296 -29.6%
315 +152 -15.2% +296 -29.6%
316 +152 -15.2% +296 -29.6%
317 +152 -15.2% +297 -29.7%
318 +152 -15.2% +297 -29.7%
319 +152 -15.2% +297 -29.7%
320 +153 -15.3% +297 -29.7%
321 +153 -15.3% +298 -29.8%
322 +153 -15.3% +298 -29.8%
323 +153 -15.3% +298 -29.8%
324 +153 -15.3% +298 -29.8%
325 +153 -15.3% +299 -29.9%
326 +153 -15.3% +299 -29.9%
327 +153 -15.3% +299 -29.9%
328 +153 -15.3% +300 -30%
329 +154 -15.4% +300 -30%
330 +154 -15.4% +300 -30%
331 +154 -15.4% +300 -30%
332 +154 -15.4% +301 -30.1%
333 +154 -15.4% +301 -30.1%
334 +154 -15.4% +301 -30.1%
335 +154 -15.4% +301 -30.1%
336 +154 -15.4% +301 -30.1%
337 +154 -15.4% +302 -30.2%
338 +155 -15.5% +302 -30.2%
339 +155 -15.5% +302 -30.2%
340 +155 -15.5% +302 -30.2%
341 +155 -15.5% +303 -30.3%
342 +155 -15.5% +303 -30.3%
343 +155 -15.5% +303 -30.3%
344 +155 -15.5% +303 -30.3%
345 +155 -15.5% +304 -30.4%
346 +155 -15.5% +304 -30.4%
347 +155 -15.5% +304 -30.4%
348 +156 -15.6% +304 -30.4%
349 +156 -15.6% +305 -30.5%
350 +156 -15.6% +305 -30.5%
351 +156 -15.6% +305 -30.5%
352 +156 -15.6% +305 -30.5%
353 +156 -15.6% +305 -30.5%
354 +156 -15.6% +306 -30.6%
355 +156 -15.6% +306 -30.6%
356 +156 -15.6% +306 -30.6%
357 +156 -15.6% +306 -30.6%
358 +156 -15.6% +307 -30.7%
359 +157 -15.7% +307 -30.7%
360 +157 -15.7% +307 -30.7%
361 +157 -15.7% +307 -30.7%
362 +157 -15.7% +307 -30.7%
363 +157 -15.7% +308 -30.8%
364 +157 -15.7% +308 -30.8%
365 +157 -15.7% +308 -30.8%
366 +157 -15.7% +308 -30.8%
367 +157 -15.7% +309 -30.9%
368 +157 -15.7% +309 -30.9%
369 +157 -15.7% +309 -30.9%
370 +158 -15.8% +309 -30.9%
371 +158 -15.8% +309 -30.9%
372 +158 -15.8% +310 -31%
373 +158 -15.8% +310 -31%
374 +158 -15.8% +310 -31%
375 +158 -15.8% +310 -31%
376 +158 -15.8% +310 -31%
377 +158 -15.8% +311 -31.1%
378 +158 -15.8% +311 -31.1%
379 +158 -15.8% +311 -31.1%
380 +158 -15.8% +311 -31.1%
381 +159 -15.9% +311 -31.1%
382 +159 -15.9% +312 -31.2%
383 +159 -15.9% +312 -31.2%
384 +159 -15.9% +312 -31.2%
385 +159 -15.9% +312 -31.2%
386 +159 -15.9% +312 -31.2%
387 +159 -15.9% +313 -31.3%
388 +159 -15.9% +313 -31.3%
389 +159 -15.9% +313 -31.3%
390 +159 -15.9% +313 -31.3%
391 +159 -15.9% +313 -31.3%
392 +159 -15.9% +313 -31.3%
393 +160 -16% +314 -31.4%
394 +160 -16% +314 -31.4%
395 +160 -16% +314 -31.4%
396 +160 -16% +314 -31.4%
397 +160 -16% +314 -31.4%
398 +160 -16% +315 -31.5%
399 +160 -16% +315 -31.5%
400 +160 -16% +315 -31.5%

References