WEBVTT

1
00:00:05.770 --> 00:00:09.841
Game Advanced
Combat System Formulas in MORPGs

2
00:00:09.841 --> 00:00:12.281
GCC Academy

3
00:00:27.144 --> 00:00:28.800
Hello everyone

4
00:00:28.800 --> 00:00:31.719
This is Park Hyung-seon, in charge
of Action RPG Balance Game Design

5
00:00:32.359 --> 00:00:38.120
In this session, we will discuss the combat system formulas
used in MORPG games

6
00:00:38.480 --> 00:00:40.880
I will explain the most common combat formulas

7
00:00:40.880 --> 00:00:43.040
and the method of converting defense values

8
00:00:43.040 --> 00:00:46.040
into defense rates for calculations

9
00:00:46.040 --> 00:00:48.560
Additionally, to achieve balanced gameplay,

10
00:00:48.560 --> 00:00:50.840
it is crucial to convert defense

11
00:00:50.840 --> 00:00:52.680
into health points

12
00:00:52.680 --> 00:00:54.400
using combat formulas

13
00:00:54.400 --> 00:00:57.200
I will introduce this method in detail

14
00:00:57.200 --> 00:00:58.919
The foundation of combat balance

15
00:00:58.919 --> 00:01:01.480
lies in organizing values for attack factors

16
00:01:01.480 --> 00:01:03.480
and defense factors

17
00:01:03.480 --> 00:01:05.800
to ensure equilibrium between the two

18
00:01:05.800 --> 00:01:09.480
I will explain the methodology for achieving this balance

19
00:01:09.936 --> 00:01:14.116
Combat Formulas and Converting Defense into Defense Rate

20
00:01:14.800 --> 00:01:19.620
This is the first step in organizing values
and standards related to combat balance

21
00:01:21.000 --> 00:01:24.039
Today, we will examine combat formulas

22
00:01:24.599 --> 00:01:30.620
and the formulas for calculating defense values
and defense rates

23
00:01:32.160 --> 00:01:36.160
A basic attack consists of four hits over two seconds

24
00:01:36.160 --> 00:01:37.820
A mob has 100 HP

25
00:01:38.400 --> 00:01:41.000
It takes four hits

26
00:01:41.000 --> 00:01:45.379
from the player to defeat a mob

27
00:01:45.879 --> 00:01:51.299
Since the basic attack executes four hits
in two seconds,

28
00:01:51.879 --> 00:01:53.640
each hit deals 25 damage,

29
00:01:54.301 --> 00:01:58.641
resulting in a damage output of 50 per second

30
00:02:00.000 --> 00:02:04.060
A skill attack can be used once every 20 seconds

31
00:02:04.480 --> 00:02:09.639
Each use of the skill deals 100 damage to three enemies

32
00:02:10.399 --> 00:02:12.599
This results in a total skill damage output of 300 per use,

33
00:02:12.979 --> 00:02:16.319
so for one second, the skill attack is 15

34
00:02:16.919 --> 00:02:19.059
So, in the end,

35
00:02:19.759 --> 00:02:26.339
The basic attack DPS of 50 +

36
00:02:26.859 --> 00:02:31.479
the skill attack DPS 15

37
00:02:31.479 --> 00:02:37.140
results in 65 damage per second

38
00:02:38.420 --> 00:02:45.199
The duration of a single combat session is
three minutes, which equals 180 seconds

39
00:02:45.819 --> 00:02:51.899
180 x 65

40
00:02:52.559 --> 00:02:58.599
means the maximum damage for three minutes
is 11,700

41
00:03:00.219 --> 00:03:07.040
Now, let’s break this down in a more intuitive way

42
00:03:08.240 --> 00:03:12.080
Suppose each mob has 100 HP

43
00:03:13.600 --> 00:03:18.139
The fact that a basic attack consists
of four hits executed over two seconds

44
00:03:18.679 --> 00:03:22.240
means that an attack sequence consists of

45
00:03:22.240 --> 00:03:25.599
slash, slash, slash, and boom

46
00:03:26.759 --> 00:03:29.800
The total execution time of two seconds

47
00:03:30.360 --> 00:03:35.119
also includes average movement time

48
00:03:35.119 --> 00:03:39.000
If we count only the animation frames,

49
00:03:39.000 --> 00:03:42.260
it would be slightly shorter than two seconds

50
00:03:42.600 --> 00:03:47.700
However, considering movement animation
and other factors,

51
00:03:48.240 --> 00:03:51.639
we round this to two seconds

52
00:03:51.639 --> 00:03:57.079
Each hit deals 25 damage

53
00:03:57.839 --> 00:04:00.240
After four hits, the total damage reaches 100

54
00:04:00.240 --> 00:04:04.220
And this includes the time for movement

55
00:04:04.720 --> 00:04:07.580
So that's two seconds

56
00:04:08.520 --> 00:04:12.539
So it is 50 for a minute

57
00:04:12.839 --> 00:04:18.840
So the basic attack's DPS is 50

58
00:04:19.320 --> 00:04:25.520
DPS, again, refers to damage per second

59
00:04:25.520 --> 00:04:33.439
So the DPS, the damage per second, for basic attack
is 50

60
00:04:34.559 --> 00:04:38.180
So that concludes the basic attack damage

61
00:04:38.880 --> 00:04:42.140
Now, we move on to the skill damage

62
00:04:42.920 --> 00:04:45.160
Since a skill attack is used every 20 seconds

63
00:04:45.160 --> 00:04:51.939
and deals 100 damage to each of three mobs,

64
00:04:52.679 --> 00:04:55.140
the damage per use is 300

65
00:04:55.140 --> 00:04:58.000
dividing by 20, the cooldown time,

66
00:04:59.579 --> 00:05:03.559
gives a DPS of 15

67
00:05:03.559 --> 00:05:06.379
That's the calculation

68
00:05:07.959 --> 00:05:16.620
Because the player can use skill and basic attacks,

69
00:05:18.040 --> 00:05:19.799
we add the values

70
00:05:19.799 --> 00:05:23.279
The basic attack DPS of 50,

71
00:05:24.199 --> 00:05:26.200
with the skill attack DPS of 15,

72
00:05:26.200 --> 00:05:29.579
these are the DPS values we add up

73
00:05:29.579 --> 00:05:34.359
We are assuming that the player could

74
00:05:34.359 --> 00:05:36.159
use the skills along with the basic attacks

75
00:05:36.799 --> 00:05:40.079
So the total DPS is 65

76
00:05:40.959 --> 00:05:45.180
One combat lasts three minutes, or 180 seconds,

77
00:05:46.000 --> 00:05:50.320
because that's the optimal duration for player engagement

78
00:05:50.320 --> 00:05:52.299
That's the reason

79
00:05:53.559 --> 00:05:57.140
So DPS here is 65,

80
00:05:57.140 --> 00:06:01.699
adding the DPS values of basic and skill attacks

81
00:06:01.699 --> 00:06:04.059
So it is 50 + 15 = 65

82
00:06:04.419 --> 00:06:10.960
And multiplying it by 180 gives us 11,700

83
00:06:11.720 --> 00:06:16.279
So the DPS values for the player, for basic and skill attacks,

84
00:06:16.279 --> 00:06:19.959
are multiplied by three minutes, which gives us 11,700

85
00:06:21.359 --> 00:06:29.160
So, the player can inflict 11,700 damage for three minutes

86
00:06:30.720 --> 00:06:32.279
Now, the enemies should withstand

87
00:06:32.279 --> 00:06:36.200
this much damage, of 11,700, for three minutes

88
00:06:37.000 --> 00:06:38.959
Now, I'm talking about all enemies

89
00:06:38.959 --> 00:06:43.500
This does not separate boss monsters

90
00:06:45.900 --> 00:06:47.720
from regular mobs

91
00:06:48.060 --> 00:06:50.119
We combine the two,

92
00:06:50.119 --> 00:06:57.680
or even three, including the little boss mobs,
to get the value 11,700

93
00:06:58.600 --> 00:07:01.440
So here is the formula for it

94
00:07:03.160 --> 00:07:08.419
We have the HP for one mob,

95
00:07:09.559 --> 00:07:10.980
which is 100

96
00:07:12.700 --> 00:07:18.019
Now, we divide the HP for boss and mob

97
00:07:19.519 --> 00:07:24.979
Let's say the boss gets half of 11,700

98
00:07:26.059 --> 00:07:29.720
The reason is, we want the player

99
00:07:31.040 --> 00:07:38.960
to be fighting the boss for around 1.5 minutes

100
00:07:39.720 --> 00:07:47.399
And fight the mobs for the other 1.5 minutes

101
00:07:47.879 --> 00:07:50.519
So first, halve the value

102
00:07:51.199 --> 00:07:55.519
So the mobs get 5850

103
00:07:55.519 --> 00:07:58.459
And we rounded this value

104
00:07:58.756 --> 00:07:59.756
to have 5900 for boss HP

105
00:08:00.039 --> 00:08:03.560
and 5800 for the total mobs HP

106
00:08:03.560 --> 00:08:06.280
One mob gets 100 HP

107
00:08:06.920 --> 00:08:12.800
So 5800 divided by that will give us 58 mobs

108
00:08:13.480 --> 00:08:16.319
This is how we can fine-tune the details

109
00:08:17.239 --> 00:08:21.140
So, here is the summary of our values from lastt class

110
00:08:22.120 --> 00:08:29.159
The player can inflict 50 damage with basic attack
per second

111
00:08:29.679 --> 00:08:34.239
With skill attacks, the damage is 15 per second

112
00:08:34.559 --> 00:08:38.200
We have four basic attacks in two seconds
and one skill in 20 seconds

113
00:08:39.100 --> 00:08:41.860
The total play time is 3 minutes,

114
00:08:41.861 --> 00:08:45.221
so the player can inflict the total of 11,700 damage

115
00:08:45.840 --> 00:08:49.919
And this equates the total mobs HP for one stage

116
00:08:50.419 --> 00:08:53.999
Each mob gets 100 HP,

117
00:08:54.544 --> 00:08:56.324
and there are 58 of it

118
00:08:56.639 --> 00:09:01.440
There is one boss with the HP of 5900

119
00:09:01.440 --> 00:09:06.439
So the sum of the mobs HP becomes 11,700

120
00:09:08.639 --> 00:09:13.479
So this is the most foundational criteria

121
00:09:13.479 --> 00:09:17.940
So the player total attack damage
equates the enemies total HP

122
00:09:18.880 --> 00:09:22.139
The total DPS that the player can deal over three minutes

123
00:09:22.679 --> 00:09:26.880
must be absorbed by the enemy over the same period,

124
00:09:26.880 --> 00:09:28.239
so that's the total HP

125
00:09:28.239 --> 00:09:35.140
Please keep in mind this fundamental concept

126
00:09:37.540 --> 00:09:44.039
Key Elements to Adjust in Combat Balance

127
00:09:46.239 --> 00:09:50.519
First, we have damage formulas
and the conversion of defense into defense rate

128
00:09:51.119 --> 00:09:59.539
Next are standard stats for enemies across 100 stages

129
00:10:01.339 --> 00:10:06.200
Understanding how to calculate the damage dealt
to enemies,

130
00:10:07.040 --> 00:10:12.600
along with concepts like defense and defense rate,
is crucial

131
00:10:13.480 --> 00:10:15.380
The amount of damage dealt per hit

132
00:10:16.280 --> 00:10:21.840
Next, converting defense into HP to simplify balancing

133
00:10:22.760 --> 00:10:27.280
I will explain the detailed formulas for this later

134
00:10:27.880 --> 00:10:32.880
Additionally, I will go over the standard stats
for enemies across 100 stages

135
00:10:34.080 --> 00:10:37.900
Each stage contains mobs

136
00:10:38.820 --> 00:10:45.280
that have specific values for HP, defense, and attack power

137
00:10:47.320 --> 00:10:52.479
If we assume that there are 100 stages,

138
00:10:52.479 --> 00:10:54.180
we need to establish

139
00:10:54.784 --> 00:10:56.724
baseline values for attack power, defense,

140
00:10:57.260 --> 00:11:01.860
and HP per second for the mobs in each stage

141
00:11:03.640 --> 00:11:08.339
Typically, we create base stat values using formulas

142
00:11:09.179 --> 00:11:13.719
We start with these base stats,

143
00:11:13.719 --> 00:11:16.259
which are then adjusted

144
00:11:16.919 --> 00:11:22.300
with modifiers and fine-tuned for balance

145
00:11:23.760 --> 00:11:27.260
This is essential for combat balance

146
00:11:27.700 --> 00:11:33.200
Matching the total HP and attack power of players
and enemies

147
00:11:34.400 --> 00:11:38.220
For example, if we are currently designing Stage 10,

148
00:11:39.200 --> 00:11:43.400
the player's stats like attack power and HP will reflect

149
00:11:43.400 --> 00:11:48.473
their equipped gear and character progression

150
00:11:49.000 --> 00:11:52.679
Similarly, enemies will have predefined

151
00:11:53.640 --> 00:11:56.120
attack power and HP values

152
00:11:57.599 --> 00:12:00.499
Adjustments can be made

153
00:12:01.052 --> 00:12:04.232
through gear and experience rewards

154
00:12:05.119 --> 00:12:09.039
After determining the enemy attack power,

155
00:12:09.500 --> 00:12:15.220
the player's attack power and HP must be set accordingly

156
00:12:16.340 --> 00:12:21.139
This is done by adjusting gear rewards

157
00:12:21.759 --> 00:12:23.720
and ensuring that

158
00:12:24.292 --> 00:12:30.392
the player's stats align with the enemy's attack level

159
00:12:30.980 --> 00:12:34.340
Let's break this down further

160
00:12:35.420 --> 00:12:39.300
First, we determined

161
00:12:40.221 --> 00:12:44.601
how much damage the player can deal over three minutes

162
00:12:44.960 --> 00:12:50.799
Next, we calculated how much total HP enemies
must have to endure this damage

163
00:12:50.799 --> 00:12:56.019
Now, we must also determine how much damage

164
00:12:56.286 --> 00:13:00.226
the enemy should deal to the player over the same duration

165
00:13:00.859 --> 00:13:02.400
Based on that information,

166
00:13:02.791 --> 00:13:08.551
we adjust the player's HP accordingly

167
00:13:08.551 --> 00:13:16.000
The key concept here is symmetry
between player and enemy stats

168
00:13:16.300 --> 00:13:21.520
The player’s total attack power
must match the enemy’s total HP

169
00:13:21.900 --> 00:13:28.460
The enemy’s total attack power
must match the player’s total HP

170
00:13:28.560 --> 00:13:31.939
This calculation must be time-based

171
00:13:32.559 --> 00:13:36.159
If we set the standard combat duration to three minutes,
we must:

172
00:13:36.579 --> 00:13:42.359
Determine the total damage
the player can deal in three minutes

173
00:13:42.359 --> 00:13:45.719
Playtest to determine how much damage

174
00:13:46.679 --> 00:13:52.300
the enemy should deal to the player in three minutes

175
00:13:52.300 --> 00:13:57.179
Use this data to set the player’s HP accordingly

176
00:13:59.159 --> 00:14:02.279
Establishing the Balancing Goals

177
00:14:03.219 --> 00:14:12.500
In an action MORPG, let’s assume
we have 100 stages of standard battles

178
00:14:13.420 --> 00:14:22.500
We must set enemy attack power, HP,
and defense across these stages

179
00:14:23.080 --> 00:14:25.120
Accordingly, we then adjust

180
00:14:25.852 --> 00:14:28.272
the player’s attack power, HP,

181
00:14:29.000 --> 00:14:34.400
and defense to maintain difficulty balance

182
00:14:34.635 --> 00:14:38.815
The goal is to maintain this equilibrium

183
00:14:40.320 --> 00:14:43.699
When the game begins,

184
00:14:43.700 --> 00:14:48.446
there are many stages unfolding,

185
00:14:49.479 --> 00:14:53.379
like stage 1, 2, 3, 4, and on

186
00:14:54.799 --> 00:14:57.519
Each stage must have a set playtime

187
00:14:58.439 --> 00:15:00.519
So ensuring that

188
00:15:01.008 --> 00:15:05.168
player and enemy stats remain balanced
throughout the progression

189
00:15:05.828 --> 00:15:07.368
is crucial for balance

190
00:15:08.239 --> 00:15:12.099
The stage should be clearable within the set playtime

191
00:15:12.899 --> 00:15:17.920
So, we first define the stages we will release

192
00:15:17.921 --> 00:15:23.640
and adjust the balance for each stage accordingly

193
00:15:25.000 --> 00:15:31.739
Each stage must be individually fine-tuned
to ensure the proper difficulty curve

194
00:15:32.479 --> 00:15:37.780
To achieve this, we need to study
how defense affects incoming damage

195
00:15:38.520 --> 00:15:42.320
through combat and damage formulas

196
00:15:43.280 --> 00:15:47.040
The reason we balance stage-by-stage

197
00:15:47.940 --> 00:15:54.340
is that the game’s service model is stage-based

198
00:15:54.940 --> 00:15:58.479
While we’ve used 100 stages as an example,

199
00:15:58.479 --> 00:16:02.760
in a real open beta scenario,

200
00:16:03.320 --> 00:16:05.459
we might launch with 300+ stages

201
00:16:05.460 --> 00:16:09.297
Each of these must be carefully balanced before release

202
00:16:09.619 --> 00:16:12.040
To simplify, think of it this way

203
00:16:12.716 --> 00:16:18.296
Player and enemy strength
must scale appropriately for each stage

204
00:16:19.080 --> 00:16:21.820
we delve into it, it gets more complex

205
00:16:22.480 --> 00:16:25.620
because we have to consider player equipment

206
00:16:26.080 --> 00:16:30.400
Unlike static enemy stats,

207
00:16:31.360 --> 00:16:35.400
players gain stronger gear as they progress

208
00:16:35.960 --> 00:16:41.079
This means stats are always improving, affecting
the balance curve

209
00:16:41.559 --> 00:16:46.280
Because of this, we must adjust not only combat balance

210
00:16:46.280 --> 00:16:51.099
but also reward balance and economic balance

211
00:16:51.100 --> 00:16:54.260
to that progress

212
00:16:54.260 --> 00:16:58.059
to create a smooth progression

213
00:16:59.719 --> 00:17:03.659
Let's now discuss the combat formula

214
00:17:05.239 --> 00:17:11.640
Assuming the defense absorbs part of incoming damage,

215
00:17:12.560 --> 00:17:18.640
we can express it through different formulas

216
00:17:20.000 --> 00:17:27.720
Let's set example values for the defense

217
00:17:28.500 --> 00:17:31.539
Let's say the attack power is 100,

218
00:17:32.568 --> 00:17:34.048
the defense 50,

219
00:17:34.649 --> 00:17:36.929
and HP 100

220
00:17:38.119 --> 00:17:44.619
Let's use simple subtraction method

221
00:17:45.799 --> 00:17:49.620
So the allies attack damage is 100,

222
00:17:50.720 --> 00:17:55.440
and the enemies defense 50

223
00:17:56.020 --> 00:17:58.860
100 - 50 = 50

224
00:17:59.780 --> 00:18:06.100
We can just use simple addition and subtraction

225
00:18:07.900 --> 00:18:14.899
So one allies attack will result in 100-50 for the enemy HP

226
00:18:15.319 --> 00:18:21.580
But the problem is, this isn't always the case

227
00:18:22.900 --> 00:18:26.559
Let's consider this instead

228
00:18:27.219 --> 00:18:30.979
If attack power equates to defense,

229
00:18:32.359 --> 00:18:36.599
with defense of 100 and HP 100,

230
00:18:38.680 --> 00:18:41.640
Attack - Defense = 0

231
00:18:41.641 --> 00:18:44.821
It's a subtraction method

232
00:18:46.140 --> 00:18:51.319
So 100 attack damage with the 100 defense

233
00:18:52.199 --> 00:18:56.320
will result in a 100% defense,

234
00:18:57.140 --> 00:18:59.820
or 0 damage inflicted

235
00:18:59.920 --> 00:19:02.020
There is no damage

236
00:19:03.116 --> 00:19:05.676
So with this simple subtraction method,

237
00:19:07.140 --> 00:19:12.019
a major flaw appears

238
00:19:12.704 --> 00:19:14.884
when defense exceeds attack

239
00:19:15.419 --> 00:19:19.280
Even after a lot of attack, the HP is not affected

240
00:19:19.956 --> 00:19:23.276
This will make a very boring game

241
00:19:23.599 --> 00:19:29.180
So this combat formula is not what we want

242
00:19:29.480 --> 00:19:34.560
Some indie games have mistakenly used this formula,

243
00:19:34.561 --> 00:19:39.401
but players tend to find these games unfun

244
00:19:40.801 --> 00:19:47.140
Because of these major flaws, most modern games

245
00:19:48.240 --> 00:19:51.639
do not use subtraction-based defense

246
00:19:53.379 --> 00:19:57.940
Instead, most games use
a proportional damage absorption formula

247
00:19:59.028 --> 00:20:01.868
The standard formula

248
00:20:03.140 --> 00:20:09.999
that converts defense into a percentage-based reduction

249
00:20:11.219 --> 00:20:19.520
is Damage Absorption
= Defense / (Defense + Defense Constant)

250
00:20:20.200 --> 00:20:26.080
Damage absorption is the same as defense

251
00:20:26.081 --> 00:20:27.401
It's the same term

252
00:20:28.400 --> 00:20:33.240
And defense constant is a variable

253
00:20:33.640 --> 00:20:37.779
Here, we use 1000 for defense constant

254
00:20:38.799 --> 00:20:44.940
Let me demonstrate how the value changes

255
00:20:44.940 --> 00:20:47.860
as the defense constant changes

256
00:20:48.696 --> 00:20:52.216
Let's say the attack power is 100

257
00:20:52.760 --> 00:20:56.000
and defense absorption, 0.8

258
00:20:57.148 --> 00:21:00.868
0.8 equates to 80%

259
00:21:01.660 --> 00:21:09.220
It means that 80% of the attack damage is absorbed

260
00:21:09.860 --> 00:21:13.012
So 0.8 means 80%

261
00:21:14.056 --> 00:21:18.896
It should never exceed 1

262
00:21:20.160 --> 00:21:22.960
100 x 0.8 is 20

263
00:21:23.476 --> 00:21:25.936
So 20 is the damage that gets through,

264
00:21:26.157 --> 00:21:29.717
while 80 is being blocked

265
00:21:30.857 --> 00:21:32.819
To remember it,

266
00:21:34.800 --> 00:21:39.379
0.8 of damage absorption

267
00:21:39.848 --> 00:21:42.368
is like a shield

268
00:21:42.839 --> 00:21:45.019
0.8 of it is shielded,

269
00:21:45.940 --> 00:21:48.940
while 0.8 means 80%

270
00:21:49.899 --> 00:21:55.619
So we get 80% of the damage being shielded

271
00:21:56.479 --> 00:21:59.610
But let's say that the conditions change

272
00:21:59.908 --> 00:22:04.508
For example, 0.8 with the attack power of 100

273
00:22:06.160 --> 00:22:08.280
means it's a 80% shield

274
00:22:08.547 --> 00:22:11.947
So it blocks 80 and receives only 20 damage

275
00:22:12.294 --> 00:22:15.394
But the attack power can change

276
00:22:16.154 --> 00:22:19.339
What if the attack power is not 100 but 1000?

277
00:22:19.339 --> 00:22:24.467
We have 0.8 damage absorption, or 80% shield

278
00:22:25.347 --> 00:22:30.840
So 800 is being blocked and 200 inflicted

279
00:22:31.900 --> 00:22:39.239
Damage absorption means the amount
of damage or attack power absorbed

280
00:22:40.920 --> 00:22:44.559
Defense literally means the defense rate

281
00:22:45.208 --> 00:22:47.488
By adding a number,

282
00:22:47.759 --> 00:22:52.360
this defense formula will give you
the damage absorption rate

283
00:22:52.897 --> 00:22:56.157
Let's go over the formula once again

284
00:22:56.760 --> 00:23:01.579
Damage absorption is defense divided
by defense plus defense constant,

285
00:23:02.508 --> 00:23:06.348
for which we'll use 1000

286
00:23:06.999 --> 00:23:11.700
Then the damage absorption
is defense plus defense divided by 1000

287
00:23:12.580 --> 00:23:14.440
So let's say that damage absorption

288
00:23:14.948 --> 00:23:18.148
or the final value is the y value

289
00:23:19.020 --> 00:23:22.820
Then the defense is the input value, or the x value

290
00:23:22.820 --> 00:23:29.559
So y = x + x / 1000

291
00:23:31.299 --> 00:23:37.280
Next, the Formula for Damage Taken Ratio

292
00:23:39.640 --> 00:23:45.659
The defense constant is
a freely adjustable value in the formula

293
00:23:46.519 --> 00:23:51.460
Its value affects the graph’s sensitivity

294
00:23:52.700 --> 00:23:58.680
With defense constants of 100, 1000, and 5000,

295
00:23:59.560 --> 00:24:05.039
I will show how defense and damage absorption change

296
00:24:07.559 --> 00:24:12.220
Defense rate is the same as damage absorption

297
00:24:12.220 --> 00:24:15.120
The formula for both is:

298
00:24:15.688 --> 00:24:19.588
Defense / (Defense + Defense Constant)

299
00:24:20.880 --> 00:24:24.199
The x value is the input

300
00:24:24.539 --> 00:24:28.679
that represents defense

301
00:24:28.679 --> 00:24:43.360
For example, values like 0, 100,
1000, 5000, and 30,000 are set

302
00:24:43.760 --> 00:24:46.259
It equals defense

303
00:24:47.464 --> 00:24:50.344
Since x is the input, it equals defense

304
00:24:51.240 --> 00:24:55.110
The defense constant varies,

305
00:24:55.550 --> 00:25:00.850
so we’ll test different values

306
00:25:01.960 --> 00:25:04.160
I will provide three examples,

307
00:25:05.124 --> 00:25:07.044
when defense constant is 5000,

308
00:25:08.120 --> 00:25:15.100
1000, and 100, in that order

309
00:25:15.900 --> 00:25:19.500
Any formula can be customized,

310
00:25:21.319 --> 00:25:25.299
but let’s start with 5000

311
00:25:26.322 --> 00:25:35.222
With defense 100 and constant 5000, the result is 0.021

312
00:25:35.222 --> 00:25:42.757
With defense 1000 and constant 5000, it’s 0.167

313
00:25:42.897 --> 00:25:50.667
It also equates to 16.7% damage blocked

314
00:25:51.160 --> 00:25:53.259
Damage absorption, defense rate,

315
00:25:53.260 --> 00:25:57.700
and shield all mean the same

316
00:25:58.699 --> 00:26:00.519
A defense rate,

317
00:26:00.840 --> 00:26:03.920
meaning the damage blocked,

318
00:26:04.501 --> 00:26:07.641
is 16.7%

319
00:26:09.259 --> 00:26:14.699
Now, with a defense constant of 1000:

320
00:26:15.499 --> 00:26:17.940
At defense 1000,

321
00:26:18.504 --> 00:26:21.944
the rate jumps from 16.7%

322
00:26:23.020 --> 00:26:28.319
to 50% with the defense constant becoming 1000

323
00:26:28.320 --> 00:26:30.000
It's a huge difference

324
00:26:30.072 --> 00:26:35.132
At defense 1000, the rate jumps from 16.7% to 50%

325
00:26:35.612 --> 00:26:39.259
With a constant of 100,

326
00:26:40.520 --> 00:26:43.719
a defense value of 1000 blocks .909

327
00:26:44.440 --> 00:26:51.179
or 90.9% of damage

328
00:26:52.299 --> 00:26:57.160
So if the x value is 1000

329
00:26:57.455 --> 00:26:59.855
with the defense constant 1000,

330
00:27:00.176 --> 00:27:03.651
it is excessively high

331
00:27:04.580 --> 00:27:07.719
Blocking 90.9%

332
00:27:08.472 --> 00:27:11.199
means almost no damage is taken

333
00:27:11.199 --> 00:27:14.839
If defense grows beyond 1000,

334
00:27:14.840 --> 00:27:18.085
there arises a big problem

335
00:27:18.712 --> 00:27:21.452
Balance becomes difficult

336
00:27:22.199 --> 00:27:26.140
with defense over 1000

337
00:27:26.141 --> 00:27:33.203
With a defense constant of 100,
a defense of 1000 already blocks 90.9%

338
00:27:33.483 --> 00:27:36.700
So everything is already used out

339
00:27:37.348 --> 00:27:39.128
Thus, in practice,

340
00:27:39.568 --> 00:27:43.908
small defense constants like 100 should not be used

341
00:27:43.908 --> 00:27:49.180
In real applications, 1000 or higher
is used for defense constants

342
00:27:49.465 --> 00:27:50.705
So, in practice,

343
00:27:51.412 --> 00:27:52.992
this damage formula,

344
00:27:53.680 --> 00:27:58.040
or this conversion formula uses

345
00:27:59.120 --> 00:28:00.900
values over 1000

346
00:28:01.620 --> 00:28:08.500
and typically between 1000 and 5000
for the defense constant

347
00:28:08.800 --> 00:28:11.121
If you look at the graph on the right,

348
00:28:11.576 --> 00:28:13.626
when using a defense constant of 100,

349
00:28:14.343 --> 00:28:19.103
the curve rises too steeply

350
00:28:19.520 --> 00:28:23.821
With a defense constant of 1000, it rises evenly

351
00:28:23.975 --> 00:28:28.935
And with 5000, the increase is gradual

352
00:28:29.480 --> 00:28:34.581
If you want to use large defense values in your game,

353
00:28:35.457 --> 00:28:39.976
a defense constant of 5000 is suitable

354
00:28:40.880 --> 00:28:46.319
For a general game, a defense constant
of 1000 is appropriate

355
00:28:46.319 --> 00:28:52.651
To prevent setting excessively small defense values,

356
00:28:52.879 --> 00:28:56.679
it is best not to use a defense constant below 1000

357
00:28:56.800 --> 00:28:59.320
By comparing the graphs,

358
00:28:59.731 --> 00:29:02.481
you can clearly see how defense rate changes

359
00:29:02.881 --> 00:29:07.080
depending on the input defense value

360
00:29:08.719 --> 00:29:17.630
Now, let’s look at various derived formulas
based on the defense rate formula

361
00:29:17.880 --> 00:29:23.050
This part is quite complex, so it may be difficult

362
00:29:23.243 --> 00:29:27.792
I will explain it slowly

363
00:29:29.599 --> 00:29:39.569
First, damage absorption is calculated as
Defense / (Defense + Defense Constant)

364
00:29:40.719 --> 00:29:44.361
Now, let’s consider the reverse concept

365
00:29:45.185 --> 00:29:48.135
This leads to the idea of the damage taken ratio

366
00:29:48.760 --> 00:29:52.960
The formula for damage taken ratio is
1 - Damage Absorption

367
00:29:54.280 --> 00:29:56.160
This is the inverse concept

368
00:29:57.024 --> 00:29:59.274
We defined damage absorption as a shield

369
00:29:59.560 --> 00:30:05.609
If the absorption rate is 0.8,
it means the shield blocks 80% of the damage

370
00:30:06.059 --> 00:30:10.309
The damage taken ratio is simply 1 - 0.8 = 0.2

371
00:30:10.815 --> 00:30:13.555
Thus, 20% of the damage penetrates the shield

372
00:30:14.359 --> 00:30:17.820
In other words, 0.2,

373
00:30:17.821 --> 00:30:21.446
or 20% of the attack is actually received

374
00:30:21.738 --> 00:30:24.878
The damage taken ratio represents
this remaining percentage

375
00:30:26.079 --> 00:30:29.291
For deriving the defense values,

376
00:30:30.177 --> 00:30:32.197
by extending this formula,

377
00:30:32.336 --> 00:30:35.356
we can define a new equation as follows

378
00:30:36.640 --> 00:30:43.751
The formula for damage taken ratio is this

379
00:30:44.890 --> 00:30:52.180
Defense Constant / (Defense + Defense Constant)

380
00:30:52.181 --> 00:30:54.321
For Defense + Defense Constant,

381
00:30:55.040 --> 00:30:57.400
we need to make the value 1

382
00:30:58.287 --> 00:31:04.066
So the numerator and denominator have the same values

383
00:31:04.239 --> 00:31:12.380
(Defense + Defense Constant)
/ (Defense + Defense Constant) = 1

384
00:31:12.500 --> 00:31:18.620
We can rewrite it as
1 - (Defense / (Defense + Defense Constant))

385
00:31:19.120 --> 00:31:22.701
It subtracts the damage absorption,

386
00:31:22.702 --> 00:31:25.302
and we already defined damage absorption

387
00:31:25.943 --> 00:31:28.822
Defense / (Defense + Defense Constant)

388
00:31:29.400 --> 00:31:35.540
So, the damage taken ratio has been newly
formulated into a rather complex equation

389
00:31:35.541 --> 00:31:37.621
Once again,

390
00:31:38.760 --> 00:31:43.187
(Defense + Defense Constant)

391
00:31:43.187 --> 00:31:46.687
/ (Defense + Defense Constant)

392
00:31:46.688 --> 00:31:50.871
It subtracts the second part from the first

393
00:31:52.239 --> 00:31:56.360
We can simplify this equation further

394
00:31:58.160 --> 00:31:58.975
Since

395
00:31:59.336 --> 00:32:02.675
the denominator remains the same,

396
00:32:02.675 --> 00:32:04.381
the denominator across

397
00:32:04.963 --> 00:32:07.583
this complex equation is consistently
Defense + Defense Constant

398
00:32:11.260 --> 00:32:13.359
So, we can simply subtract the numerators

399
00:32:13.622 --> 00:32:14.902
Since the denominator remains the same,

400
00:32:15.679 --> 00:32:19.540
the left side retains Defense + Defense Constant,

401
00:32:19.540 --> 00:32:21.819
and the right side retains Defense

402
00:32:21.819 --> 00:32:26.191
Subtracting these leaves only Defense Constant
in the numerator

403
00:32:26.447 --> 00:32:30.267
Thus, the final equation for the damage taken ratio is:

404
00:32:30.998 --> 00:32:35.837
Defense Constant / (Defense + Defense Constant)

405
00:32:37.640 --> 00:32:39.660
Now, we've gone through three steps of calculation

406
00:32:39.661 --> 00:32:41.993
Next, we substitute values

407
00:32:42.760 --> 00:32:48.430
Multiplying both sides by the denominator:

408
00:32:49.386 --> 00:32:54.605
(Damage Taken Ratio) × (Defense + Defense Constant)
= Defense Constant

409
00:32:55.079 --> 00:32:58.301
The reason for repeated adjustments

410
00:32:58.453 --> 00:33:00.994
is ultimately to derive a formula for Defense itself

411
00:33:00.994 --> 00:33:02.871
That is the purpose of this calculation

412
00:33:04.279 --> 00:33:11.359
In step four, we have:
(Damage Taken Ratio) × (Defense + Defense Constant)

413
00:33:11.360 --> 00:33:14.080
Now, we move this term to the right-hand side

414
00:33:14.419 --> 00:33:20.080
On the left remains Defense + Defense Constant,

415
00:33:20.080 --> 00:33:25.680
and on the right remains
Defense Constant / Damage Taken Ratio

416
00:33:26.220 --> 00:33:31.710
This makes it easier to isolate Defense

417
00:33:32.542 --> 00:33:35.502
The final equation for Defense is:

418
00:33:36.272 --> 00:33:40.251
(Defense Constant / Damage Taken Ratio)
- Defense Constant

419
00:33:41.079 --> 00:33:43.120
By performing these calculations,

420
00:33:43.899 --> 00:33:46.139
and using these formulae,

421
00:33:46.620 --> 00:33:49.200
we derive a formula for Defense

422
00:33:49.839 --> 00:33:53.900
Now, an important new concept appears

423
00:33:54.692 --> 00:33:57.512
Effective Health

424
00:33:57.512 --> 00:33:59.881
We will discuss this next

425
00:34:00.120 --> 00:34:04.900
Effective health is defined as
Health / Damage Taken Ratio

426
00:34:05.160 --> 00:34:09.579
We will explain why this is the case later

427
00:34:11.479 --> 00:34:16.679
Let’s review the Damage Taken Ratio concept

428
00:34:18.219 --> 00:34:22.459
If Damage Absorption is 0.8,
then Damage Taken Ratio =

429
00:34:23.599 --> 00:34:24.680
1 - 0.8 = 0.2

430
00:34:25.278 --> 00:34:28.138
The Damage Taken Ratio is
the inverse of Damage Absorption

431
00:34:30.199 --> 00:34:33.400
Subtracting the shield portion,

432
00:34:33.400 --> 00:34:36.300
this is the remaining damage taken

433
00:34:38.720 --> 00:34:45.139
Let’s summarize the Defense
and Defense Rate formulas again

434
00:34:45.719 --> 00:34:48.059
Since we already calculated these above,

435
00:34:48.328 --> 00:34:50.288
you just need to review them

436
00:34:52.120 --> 00:34:56.059
Damage Absorption
= Defense / (Defense + Defense Constant)

437
00:34:56.060 --> 00:34:58.800
Damage Taken Ratio = 1 - Damage Absorption

438
00:34:58.800 --> 00:35:01.639
And as explained earlier,

439
00:35:01.640 --> 00:35:04.520
after intermediate calculations,

440
00:35:04.919 --> 00:35:12.540
Defense is (Defense Constant / Damage Taken Ratio)
- Defense Constant

441
00:35:12.840 --> 00:35:15.723
The blue text is the key equation

442
00:35:16.237 --> 00:35:18.297
Another key concept is

443
00:35:18.836 --> 00:35:20.876
Effective Health

444
00:35:21.170 --> 00:35:25.500
Effective Health = Health / Damage Taken Ratio

445
00:35:25.834 --> 00:35:29.873
Connverting Defense into Health

446
00:35:30.280 --> 00:35:37.879
Here’s a more detailed explanation of Effective Health

447
00:35:38.679 --> 00:35:43.961
If the Damage Taken Ratio is 0.1,

448
00:35:43.961 --> 00:35:47.401
meaning only 10% of the damage is taken,

449
00:35:48.320 --> 00:35:54.559
this means the actual health is effectively 10 times higher

450
00:35:56.239 --> 00:35:57.100
For example,

451
00:35:59.480 --> 00:36:01.821
let’s consider a case with an ally and an enemy

452
00:36:02.719 --> 00:36:03.959
Ally health: 100

453
00:36:03.959 --> 00:36:05.180
Enemy attack power: 100

454
00:36:06.460 --> 00:36:09.680
A single hit depletes all 100 HP

455
00:36:10.104 --> 00:36:14.364
This is assuming the ally has no damage absorption

456
00:36:15.179 --> 00:36:18.200
Now, let’s consider the opposite case

457
00:36:19.637 --> 00:36:21.117
Ally health: 100

458
00:36:21.458 --> 00:36:23.498
Damage absorption: 0.9

459
00:36:23.879 --> 00:36:25.860
Damage taken ratio: 0.1

460
00:36:26.372 --> 00:36:29.892
If the enemy attack power is 100,

461
00:36:31.840 --> 00:36:35.081
90% is blocked by the shield

462
00:36:35.770 --> 00:36:39.889
The damage taken ratio is 0.1

463
00:36:40.360 --> 00:36:44.861
So, out of 100 attack power, only 10 damage is received

464
00:36:44.861 --> 00:36:45.861
Only 10 damage

465
00:36:46.320 --> 00:36:50.360
Since each hit only does 10 damage,

466
00:36:50.521 --> 00:36:52.241
the ally must be hit 10 times

467
00:36:52.626 --> 00:36:58.546
This effectively makes their health 10 times higher,
meaning 1000 HP

468
00:36:58.966 --> 00:37:02.659
This is when the ally has damage absorption

469
00:37:03.439 --> 00:37:09.699
Comparing with the previous case
where there was no defense,

470
00:37:10.499 --> 00:37:14.800
taking 100 damage would immediately
reduce HP from 100 to 0

471
00:37:15.962 --> 00:37:18.462
With 90% damage absorption, or 0.9,

472
00:37:18.563 --> 00:37:21.343
and 10% damage taken ratio, or 0.1,

473
00:37:21.945 --> 00:37:23.340
only 10%

474
00:37:23.624 --> 00:37:25.784
or 10 of the attack is received

475
00:37:25.954 --> 00:37:28.934
This is the same as having 1000 HP

476
00:37:29.719 --> 00:37:33.521
Since the ally can endure 10 extra hits,

477
00:37:33.522 --> 00:37:39.141
it effectively has 1000 HP

478
00:37:39.141 --> 00:37:41.841
This is the concept of Effective Health

479
00:37:41.901 --> 00:37:43.501
Effective health is the true HP,

480
00:37:43.502 --> 00:37:45.273
sometimes called the real HP

481
00:37:47.199 --> 00:37:53.319
Effective Health = Health / Damage Taken Ratio

482
00:37:54.399 --> 00:37:58.930
If Damage Constant = 1000,
and Health = 1000,

483
00:37:59.930 --> 00:38:06.729
The key concept is that Defense can
be converted into Health

484
00:38:07.679 --> 00:38:11.790
Defense can be expressed as Health

485
00:38:11.978 --> 00:38:16.338
That's the basic concept, that defense can be health

486
00:38:17.739 --> 00:38:29.059
As the Damage Taken Ratio changes from 1 →
0.95 → 0.9 → 0.85 → 0.8 → 0.75 → 0.7 → 0.65 → 0.6,

487
00:38:30.299 --> 00:38:35.079
if the Damage Taken Ratio is 1, it means no shield exists

488
00:38:35.519 --> 00:38:39.781
Since Damage Taken Ratio = (1 - Shield),

489
00:38:40.960 --> 00:38:45.100
if the Damage Taken Ratio is 0.9,

490
00:38:45.101 --> 00:38:48.280
the shield is 0.1

491
00:38:48.679 --> 00:38:49.721
To put it simply,

492
00:38:50.553 --> 00:38:57.032
if Damage Taken Ratio = 0.5,
then half of the damage is blocked

493
00:38:57.032 --> 00:38:58.421
And Defense = 1000

494
00:38:58.558 --> 00:39:01.338
With Defense = 1000 and Defense Constant = 100,

495
00:39:02.115 --> 00:39:04.015
the Damage Taken Ratio becomes 0.5

496
00:39:04.016 --> 00:39:05.851
Since half the damage is blocked,

497
00:39:05.851 --> 00:39:08.071
Effective Health = 200

498
00:39:08.250 --> 00:39:11.260
This means the effective HP is doubled

499
00:39:12.385 --> 00:39:16.145
Now, why do we convert Defense into Health?

500
00:39:17.439 --> 00:39:22.580
Without this conversion, balancing involves three variables:

501
00:39:22.997 --> 00:39:26.177
Defense, Health, and Attack Power

502
00:39:27.080 --> 00:39:32.059
Balancing both ally and enemy defense is complicated

503
00:39:32.719 --> 00:39:39.340
But if we reduce balancing to only two variables,
it's much easier

504
00:39:39.800 --> 00:39:44.500
If we only consider Health and Attack Power,

505
00:39:44.967 --> 00:39:48.327
we simply match Enemy HP to Ally Attack Power

506
00:39:48.507 --> 00:39:52.087
and Ally HP to Enemy Attack Power

507
00:39:52.307 --> 00:39:56.280
So, by converting Defense into Effective Health,

508
00:39:56.281 --> 00:40:01.560
balancing requires only two factors,

509
00:40:02.042 --> 00:40:03.042
making it easier

510
00:40:03.679 --> 00:40:07.700
The core of combat balance is adjusting

511
00:40:08.035 --> 00:40:12.334
Attack factors and defense factors

512
00:40:12.719 --> 00:40:16.381
So, if everything is converted to Attack Power and Health,

513
00:40:16.381 --> 00:40:19.821
balancing becomes simple

514
00:40:20.760 --> 00:40:23.540
For attack power,

515
00:40:23.541 --> 00:40:29.312
attack-related things like critical hits are converted to DPS

516
00:40:29.719 --> 00:40:33.001
And Defense is converted into Health,

517
00:40:33.432 --> 00:40:36.232
so by comparing the attack power and health,

518
00:40:36.233 --> 00:40:38.826
you can efficiently balance combat

519
00:40:40.820 --> 00:40:42.479
This concludes today's lecture

520
00:40:42.818 --> 00:40:44.498
Great job, everyone

521
00:40:44.498 --> 00:40:45.300
Thank you

522
00:40:45.741 --> 00:40:47.301
Combat Mechanics & Balance Factors
Key elements of combat balance:
Damage formula, defense, and defense ratio
Enemy stats for 100 stages
HP and attack

523
00:40:47.301 --> 00:40:48.642
Damage absorption = Defense ratio
Defense / (Defense + Defense Constant)
Determines how much damage is blocked when attacked

524
00:40:48.642 --> 00:40:50.403
If damage absorption = 0.8 (80%),
an enemy attack of 100 deals only 20 damage

525
00:40:50.403 --> 00:40:51.624
Defense value:
Direct stat representing a character's defense
Used in the defense ratio formula
to calculate damage absorption

526
00:40:51.625 --> 00:40:53.345
Formulas for Defense & Damage Taken
Damage Absorption
= Defense / (Defense + Defense Constant
Damage Taken Ratio = 1 - Damage Absorption

527
00:40:53.345 --> 00:40:55.445
Damage Taken Ratio
= (Defense Constant / (Defense + Defense Constant))
(Damage Taken Ratio) × (Defense + Defense Constant)
= Defense Constant

528
00:40:55.445 --> 00:40:57.666
Defense = (Defense Constant / Damage Taken Ratio)
- Defense Constant
Effective Health = HP / Damage Taken Ratio

529
00:40:57.666 --> 00:40:58.908
If Damage Taken Ratio = 0.1 (taking only 10% of damage),

530
00:40:58.908 --> 00:41:00.368
the character effectively has 10x HP
Defense can be converted into HP equivalent

531
00:41:00.368 --> 00:41:01.269
Why Convert Defense to HP?
Without conversion, too many variables to balance

532
00:41:01.269 --> 00:41:02.030
With conversion, only two factors to balance
(HP & Attack Power), simplifying calculations

533
00:41:02.030 --> 00:41:02.891
Combat Balance Basics
Key principle: Adjust attack factors and defense factors
to maintain balance

534
00:41:02.891 --> 00:41:03.723
Convert all stats into Attack Power (DPS)
and Effective Health (EHP) for simplified combat balancing