# Thread: The Mathematics of Combat

1. Could someone with a high degree of understanding (Yuuki? KocMoc?) explain briefly (or not so) the Mathematics of Combat?

I.e. or e.g., how can one calculate the result of a combat between an H4,W1,A2 Monk and an H5,W2,A3 Nagicav, where the monks are standing and the cav is charging?

And if that is not complicated enough, when in gods name do the Hvy cav get their +8 defensive bonus?

Thanks to those selfless and illuminated souls who can answer these questions!

2. At best, it helps you to understand the strength and weakness of the unit you have and the unit you are facing, and whether your whatever decision have a chance to do good. The base stats are given in the troopstat.txt if you do not yet know. The resolution of H2H combat that most know is just a skeleton of how the game engine works, surely there are more beyond what we know.

Visit my STW site. Hope it helps.

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tootee the goldfish,
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3. Let's see,

charge/melee/defense
NC is 11/4/1, H5 makes it 11/9/6, W2 makes it 11/11/6 and A3 makes it 11/11/9

WM is 4/5/2, H4 makes it 4/9/6, W1 makes it 4/10/6 and A2 makes it 4/10/8

df (difference factor) = melee - defense + bonus
bonus = 0
NC strikes at WM, df = 11 - 8 = 3
WM strikes at NC, df = 10 - 9 = 1

chance to kill = 19% * 1.2 ** df
for NC, 19% * 1.2 ** 3 = 33%
for WM, 19% * 1.2 ** 1 = 23%

The NC is 1.44x [33%/23%] better than the WM without considering charge. The NC can probably drop about 8 WM upon initial contact with it's charge. That would give it an additional advantage. With 60 man units, I estimate that 6 points of charge is roughly equivalent to 1 point of melee. That would make the NC about 100% or 2x better than the WM if it can charge into a standing WM. Keep in mind that as combat progresses the unit with more men gets double and possibly triple attacks on the men in the smaller unit. This is another factor that increases the number of men the NC wins by, and it could win by more than 2 to 1 casualties.

For online play:
The H5/W2/A3 NC costs 3060 koku
The H4/W1/A2 WM costs 2156 koku

The formula for chance to kill was given to us by longjohn2 who programmed this part of the game.

MizuYuuki ~~~
Clan Takiyama ~~~

[This message has been edited by Puzz3D (edited 04-18-2002).]

4. Quote Originally posted by Puzz3D:

for NC, 19% * 1.2 ** 3 = 33%
for WM, 19% * 1.2 ** 1 = 23%
[/QUOTE]

For simplicity assume no charge bonus, except NC hits first. Everyone can attack everyone else up to a 3 to 1 advantage.

NC WM
60 60
51 40
45 23
43 8

WM hit first
WM NC
60 60
45 46
33 36
24 28
16 23
10 19
4 17

That is the difference in a two point spread!

Factor in relative costs and let them all go head to head;

NC first;
NC WM
60 85
45 65
33 51
24 40
17 32
11 26
6 22

WM first;
WM NC
85 60
72 40
64 24
61 9

So numbers really do make a difference.

So stall your enemy with a hard wearing force and use a lot of 'little' units to gangbang others and get the morale bonuses as well

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Victory First, Battle Last

[This message has been edited by Papewaio (edited 04-18-2002).]

5. if i am not mistaken there is also a random factor

6. Right Magyar! The 44% advantage gained by 2 combat points is not enough to guarantee victory with all other factors being equal. You'll win probably 8 times out of 10, and suffer a lot of casualties in 2 or 3 of the wins. You need 4 combat points which gives a 100% or 2x advantage to guarantee victory which is the equivalent of +2 honor.

MizuYuuki ~~~

7. Quote Originally posted by MagyarKhans Cham:
if i am not mistaken there is also a random factor[/QUOTE]

Definitly. That is just a statistical average, using some very broad assumptions. But it is what you can expect on average if two lines converge and all individuals can hit each other.

My next computation would be for two units 4 deep and only the first 15 being able to combat each other (essentially it would multiple the time by 4). Also I could add the standard deviation using the size of the units as they get depleted.

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Victory First, Battle Last

8. Don't count on numbers. Use the force!
With it a h2 ashi can beat a h2 warrior monk!

*ashis must be top of a 89 degree hill

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Don't use only honour, use theforce, too.

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