Difference between revisions of "Sacred 2:Tactics Lore - formulas and tables"

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(Remove FLOOR operation as precision loss is not observed.)
 
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 52: Line 52:
 
The formula for Chance for Critical Hits Increased by +X% is:
 
The formula for Chance for Critical Hits Increased by +X% is:
 
<blockquote>ValueOfBonus = SkillValue / (10 + CharacterLevel / 20)</blockquote>
 
<blockquote>ValueOfBonus = SkillValue / (10 + CharacterLevel / 20)</blockquote>
<blockquote>TooltipValue = ValueOfBonus * 0.1</blockquote>
+
<blockquote>TooltipValue = 0.1 * ValueOfBonus</blockquote>
 
This TooltipValue is then rounded down to one decimal place.
 
This TooltipValue is then rounded down to one decimal place.
  
Line 81: Line 81:
  
 
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. The reason is this operation affects only the tooltip and not the actual damage calculations.
 
  
 
{| class="skills"
 
{| class="skills"

Latest revision as of 15:01, 29 November 2024

The skill definition can be found in creatures.txt.

mgr.createSkill {
	skill_name = "skill_tactics_lore",
	advance_level = 75,
	min_level = 0,
	mean_value = 200,
	advance_mean_value = 300,
	skillgroup = "SKG_ATTACK",
	adv_skill_name = "skill_tactics_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. Tactics Lore provides two bonuses: Damage +X% and Chance for Critical Hits Increased by +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 Chance for Critical Hits Increased by +X% is:

ValueOfBonus = SkillValue / (10 + CharacterLevel / 20)

TooltipValue = 0.1 * ValueOfBonus

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 * 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 values for Damage +X% are without precision loss, because that happens only in the tooltip.
Skill level Pre-mastery Post-mastery
Damage +X% Chance for Critical Hits Increased by +X% Damage +X% Chance for Critical Hits Increased by +X%
Character level 1 Character level 200 Character level 1 Character level 200
1 +9.9% +0.9% +0.4%
2 +13.7% +1.3% +0.6%
3 +17.4% +1.7% +0.8%
4 +21.1% +2% +1%
5 +24.7% +2.4% +1.2%
6 +28.3% +2.8% +1.4%
7 +31.7% +3.1% +1.5%
8 +35.1% +3.4% +1.7%
9 +38.5% +3.8% +1.9%
10 +41.8% +4.1% +2%
11 +45% +4.4% +2.2%
12 +48.2% +4.7% +2.4%
13 +51.3% +5.1% +2.5%
14 +54.3% +5.4% +2.7%
15 +57.3% +5.7% +2.8%
16 +60.3% +6% +3%
17 +63.2% +6.2% +3.1%
18 +66.1% +6.5% +3.3%
19 +68.9% +6.8% +3.4%
20 +71.6% +7.1% +3.5%
21 +74.3% +7.3% +3.7%
22 +77% +7.6% +3.8%
23 +79.6% +7.9% +3.9%
24 +82.2% +8.1% +4.1%
25 +84.8% +8.4% +4.2%
26 +87.3% +8.6% +4.3%
27 +89.7% +8.9% +4.4%
28 +92.1% +9.1% +4.6%
29 +94.5% +9.4% +4.7%
30 +96.9% +9.6% +4.8%
31 +99.2% +9.8% +4.9%
32 +101.5% +10% +5%
33 +103.7% +10.3% +5.1%
34 +105.9% +10.5% +5.2%
35 +108.1% +10.7% +5.4%
36 +110.2% +10.9% +5.5%
37 +112.4% +11.1% +5.6%
38 +114.4% +11.3% +5.7%
39 +116.5% +11.5% +5.8%
40 +118.5% +11.7% +5.9%
41 +120.5% +11.9% +6%
42 +122.5% +12.1% +6.1%
43 +124.4% +12.3% +6.2%
44 +126.3% +12.5% +6.3%
45 +128.2% +12.7% +6.4%
46 +130.1% +12.9% +6.5%
47 +131.9% +13.1% +6.5%
48 +133.7% +13.3% +6.6%
49 +135.5% +13.4% +6.7%
50 +137.3% +13.6% +6.8%
51 +139% +13.8% +6.9%
52 +140.7% +14% +7%
53 +142.4% +14.1% +7.1%
54 +144.1% +14.3% +7.2%
55 +145.8% +14.5% +7.2%
56 +147.4% +14.6% +7.3%
57 +149% +14.8% +7.4%
58 +150.6% +14.9% +7.5%
59 +152.2% +15.1% +7.6%
60 +153.7% +15.2% +7.6%
61 +155.2% +15.4% +7.7%
62 +156.7% +15.5% +7.8%
63 +158.2% +15.7% +7.9%
64 +159.7% +15.8% +7.9%
65 +161.2% +16% +8%
66 +162.6% +16.1% +8.1%
67 +164% +16.3% +8.2%
68 +165.4% +16.4% +8.2%
69 +166.8% +16.5% +8.3%
70 +168.2% +16.7% +8.4%
71 +169.5% +16.8% +8.4%
72 +170.9% +17% +8.5%
73 +172.2% +17.1% +8.6%
74 +173.5% +17.2% +8.6%
75 +174.8% +17.3% +8.7% +180.8% +17.9% +9%
76 +176.1% +17.5% +8.8% +183.8% +18.2% +9.1%
77 +177.4% +17.6% +8.8% +186.7% +18.5% +9.3%
78 +178.6% +17.7% +8.9% +189.5% +18.8% +9.4%
79 +179.8% +17.8% +8.9% +192.4% +19.1% +9.6%
80 +181.1% +18% +9% +195.2% +19.4% +9.7%
81 +182.3% +18.1% +9.1% +197.9% +19.6% +9.8%
82 +183.5% +18.2% +9.1% +200.6% +19.9% +10%
83 +184.6% +18.3% +9.2% +203.3% +20.2% +10.1%
84 +185.8% +18.4% +9.2% +206% +20.4% +10.3%
85 +187% +18.6% +9.3% +208.6% +20.7% +10.4%
86 +188.1% +18.7% +9.4% +211.1% +21% +10.5%
87 +189.3% +18.8% +9.4% +213.7% +21.2% +10.6%
88 +190.4% +18.9% +9.5% +216.2% +21.5% +10.8%
89 +191.5% +19% +9.5% +218.7% +21.7% +10.9%
90 +192.6% +19.1% +9.6% +221.1% +22% +11%
91 +193.7% +19.2% +9.6% +223.5% +22.2% +11.1%
92 +194.7% +19.3% +9.7% +225.9% +22.4% +11.2%
93 +195.8% +19.4% +9.7% +228.3% +22.7% +11.4%
94 +196.9% +19.5% +9.8% +230.6% +22.9% +11.5%
95 +197.9% +19.6% +9.8% +232.9% +23.1% +11.6%
96 +198.9% +19.7% +9.9% +235.1% +23.3% +11.7%
97 +200% +19.9% +10% +237.4% +23.6% +11.8%
98 +201% +20% +10% +239.6% +23.8% +11.9%
99 +202% +20% +10.1% +241.8% +24% +12%
100 +203% +20.1% +10.1% +243.9% +24.2% +12.1%
101 +203.9% +20.2% +10.1% +246.1% +24.4% +12.3%
102 +204.9% +20.3% +10.2% +248.2% +24.6% +12.4%
103 +205.9% +20.4% +10.2% +250.2% +24.8% +12.5%
104 +206.8% +20.5% +10.3% +252.3% +25.1% +12.6%
105 +207.8% +20.6% +10.3% +254.3% +25.3% +12.7%
106 +208.7% +20.7% +10.4% +256.3% +25.5% +12.8%
107 +209.6% +20.8% +10.4% +258.3% +25.7% +12.9%
108 +210.5% +20.9% +10.5% +260.3% +25.9% +13%
109 +211.4% +21% +10.5% +262.2% +26% +13.1%
110 +212.3% +21.1% +10.6% +264.2% +26.2% +13.2%
111 +213.2% +21.2% +10.6% +266.1% +26.4% +13.3%
112 +214.1% +21.3% +10.7% +267.9% +26.6% +13.3%
113 +215% +21.3% +10.7% +269.8% +26.8% +13.4%
114 +215.8% +21.4% +10.7% +271.6% +27% +13.5%
115 +216.7% +21.5% +10.8% +273.4% +27.2% +13.6%
116 +217.5% +21.6% +10.8% +275.2% +27.3% +13.7%
117 +218.4% +21.7% +10.9% +277% +27.5% +13.8%
118 +219.2% +21.8% +10.9% +278.8% +27.7% +13.9%
119 +220% +21.8% +11% +280.5% +27.9% +14%
120 +220.9% +21.9% +11% +282.2% +28% +14.1%
121 +221.7% +22% +11% +283.9% +28.2% +14.1%
122 +222.5% +22.1% +11.1% +285.6% +28.4% +14.2%
123 +223.3% +22.2% +11.1% +287.3% +28.5% +14.3%
124 +224.1% +22.2% +11.2% +288.9% +28.7% +14.4%
125 +224.8% +22.3% +11.2% +290.5% +28.9% +14.5%
126 +225.6% +22.4% +11.2% +292.1% +29% +14.6%
127 +226.4% +22.5% +11.3% +293.7% +29.2% +14.6%
128 +227.1% +22.5% +11.3% +295.3% +29.3% +14.7%
129 +227.9% +22.6% +11.3% +296.9% +29.5% +14.8%
130 +228.6% +22.7% +11.4% +298.4% +29.6% +14.9%
131 +229.4% +22.8% +11.4% +300% +29.8% +15%
132 +230.1% +22.8% +11.5% +301.5% +30% +15%
133 +230.9% +22.9% +11.5% +303% +30.1% +15.1%
134 +231.6% +23% +11.5% +304.5% +30.2% +15.2%
135 +232.3% +23.1% +11.6% +305.9% +30.4% +15.2%
136 +233% +23.1% +11.6% +307.4% +30.5% +15.3%
137 +233.7% +23.2% +11.6% +308.8% +30.7% +15.4%
138 +234.4% +23.3% +11.7% +310.2% +30.8% +15.5%
139 +235.1% +23.3% +11.7% +311.7% +31% +15.5%
140 +235.8% +23.4% +11.7% +313.1% +31.1% +15.6%
141 +236.5% +23.5% +11.8% +314.4% +31.2% +15.7%
142 +237.1% +23.5% +11.8% +315.8% +31.4% +15.7%
143 +237.8% +23.6% +11.8% +317.2% +31.5% +15.8%
144 +238.5% +23.7% +11.9% +318.5% +31.6% +15.9%
145 +239.1% +23.7% +11.9% +319.9% +31.8% +15.9%
146 +239.8% +23.8% +11.9% +321.2% +31.9% +16%
147 +240.4% +23.9% +12% +322.5% +32% +16.1%
148 +241.1% +23.9% +12% +323.8% +32.2% +16.1%
149 +241.7% +24% +12% +325.1% +32.3% +16.2%
150 +242.4% +24.1% +12.1% +326.3% +32.4% +16.3%
151 +243% +24.1% +12.1% +327.6% +32.5% +16.3%
152 +243.6% +24.2% +12.1% +328.8% +32.7% +16.4%
153 +244.2% +24.2% +12.2% +330.1% +32.8% +16.5%
154 +244.8% +24.3% +12.2% +331.3% +32.9% +16.5%
155 +245.4% +24.4% +12.2% +332.5% +33% +16.6%
156 +246% +24.4% +12.3% +333.7% +33.2% +16.6%
157 +246.6% +24.5% +12.3% +334.9% +33.3% +16.7%
158 +247.2% +24.5% +12.3% +336.1% +33.4% +16.8%
159 +247.8% +24.6% +12.3% +337.3% +33.5% +16.8%
160 +248.4% +24.7% +12.4% +338.4% +33.6% +16.9%
161 +249% +24.7% +12.4% +339.6% +33.7% +16.9%
162 +249.6% +24.8% +12.4% +340.7% +33.9% +17%
163 +250.1% +24.8% +12.5% +341.9% +34% +17%
164 +250.7% +24.9% +12.5% +343% +34.1% +17.1%
165 +251.3% +25% +12.5% +344.1% +34.2% +17.2%
166 +251.8% +25% +12.5% +345.2% +34.3% +17.2%
167 +252.4% +25.1% +12.6% +346.3% +34.4% +17.3%
168 +252.9% +25.1% +12.6% +347.4% +34.5% +17.3%
169 +253.5% +25.2% +12.6% +348.5% +34.6% +17.4%
170 +254% +25.2% +12.7% +349.5% +34.7% +17.4%
171 +254.6% +25.3% +12.7% +350.6% +34.8% +17.5%
172 +255.1% +25.3% +12.7% +351.6% +34.9% +17.5%
173 +255.6% +25.4% +12.7% +352.7% +35% +17.6%
174 +256.2% +25.4% +12.8% +353.7% +35.1% +17.6%
175 +256.7% +25.5% +12.8% +354.7% +35.2% +17.7%
176 +257.2% +25.5% +12.8% +355.7% +35.3% +17.7%
177 +257.7% +25.6% +12.8% +356.7% +35.4% +17.8%
178 +258.2% +25.6% +12.9% +357.7% +35.5% +17.8%
179 +258.7% +25.7% +12.9% +358.7% +35.6% +17.9%
180 +259.2% +25.7% +12.9% +359.7% +35.7% +17.9%
181 +259.7% +25.8% +12.9% +360.7% +35.8% +18%
182 +260.2% +25.8% +13% +361.6% +35.9% +18%
183 +260.7% +25.9% +13% +362.6% +36% +18.1%
184 +261.2% +25.9% +13% +363.6% +36.1% +18.1%
185 +261.7% +26% +13% +364.5% +36.2% +18.2%
186 +262.2% +26% +13.1% +365.4% +36.3% +18.2%
187 +262.7% +26.1% +13.1% +366.4% +36.4% +18.3%
188 +263.1% +26.1% +13.1% +367.3% +36.5% +18.3%
189 +263.6% +26.2% +13.1% +368.2% +36.6% +18.4%
190 +264.1% +26.2% +13.2% +369.1% +36.7% +18.4%
191 +264.6% +26.3% +13.2% +370% +36.8% +18.5%
192 +265% +26.3% +13.2% +370.9% +36.9% +18.5%
193 +265.5% +26.4% +13.2% +371.8% +36.9% +18.5%
194 +265.9% +26.4% +13.2% +372.6% +37% +18.6%
195 +266.4% +26.5% +13.3% +373.5% +37.1% +18.6%
196 +266.8% +26.5% +13.3% +374.4% +37.2% +18.7%
197 +267.3% +26.5% +13.3% +375.2% +37.3% +18.7%
198 +267.7% +26.6% +13.3% +376.1% +37.4% +18.8%
199 +268.2% +26.6% +13.4% +376.9% +37.5% +18.8%
200 +268.6% +26.7% +13.4% +377.8% +37.5% +18.8%
201 +269.1% +26.7% +13.4% +378.6% +37.6% +18.9%
202 +269.5% +26.8% +13.4% +379.4% +37.7% +18.9%
203 +269.9% +26.8% +13.4% +380.2% +37.8% +19%
204 +270.3% +26.8% +13.5% +381.1% +37.9% +19%
205 +270.8% +26.9% +13.5% +381.9% +38% +19%
206 +271.2% +26.9% +13.5% +382.7% +38% +19.1%
207 +271.6% +27% +13.5% +383.5% +38.1% +19.1%
208 +272% +27% +13.6% +384.3% +38.2% +19.2%
209 +272.4% +27.1% +13.6% +385% +38.3% +19.2%
210 +272.9% +27.1% +13.6% +385.8% +38.3% +19.2%
211 +273.3% +27.1% +13.6% +386.6% +38.4% +19.3%
212 +273.7% +27.2% +13.6% +387.4% +38.5% +19.3%
213 +274.1% +27.2% +13.7% +388.1% +38.6% +19.4%
214 +274.5% +27.3% +13.7% +388.9% +38.6% +19.4%
215 +274.9% +27.3% +13.7% +389.6% +38.7% +19.4%
216 +275.3% +27.3% +13.7% +390.4% +38.8% +19.5%
217 +275.7% +27.4% +13.7% +391.1% +38.9% +19.5%
218 +276.1% +27.4% +13.8% +391.9% +38.9% +19.5%
219 +276.4% +27.5% +13.8% +392.6% +39% +19.6%
220 +276.8% +27.5% +13.8% +393.3% +39.1% +19.6%
221 +277.2% +27.5% +13.8% +394% +39.2% +19.7%
222 +277.6% +27.6% +13.8% +394.7% +39.2% +19.7%
223 +278% +27.6% +13.9% +395.5% +39.3% +19.7%
224 +278.3% +27.6% +13.9% +396.2% +39.4% +19.8%
225 +278.7% +27.7% +13.9% +396.9% +39.4% +19.8%
226 +279.1% +27.7% +13.9% +397.6% +39.5% +19.8%
227 +279.5% +27.8% +13.9% +398.2% +39.6% +19.9%
228 +279.8% +27.8% +13.9% +398.9% +39.6% +19.9%
229 +280.2% +27.8% +14% +399.6% +39.7% +19.9%
230 +280.6% +27.9% +14% +400.3% +39.8% +20%
231 +280.9% +27.9% +14% +401% +39.9% +20%
232 +281.3% +27.9% +14% +401.6% +39.9% +20%
233 +281.6% +28% +14% +402.3% +40% +20.1%
234 +282% +28% +14.1% +403% +40% +20.1%
235 +282.3% +28% +14.1% +403.6% +40.1% +20.1%
236 +282.7% +28.1% +14.1% +404.3% +40.2% +20.2%
237 +283% +28.1% +14.1% +404.9% +40.2% +20.2%
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References