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تراوین - Misc
شنبه 23 بهمن 1389

Misc

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Misc


Here gathered two most complicated parts of combat mechanics: catapults and rams.

3.a. Catapults

There's a formula, which determines amount of catapults, enough to completely destroy any building of certain level:

X = round{(morale · (lvl^2 + lvl + 1) / (8 · U / D)) + 0.5} (8)

U – catapult's upgrade, U = round(200 · 1.0205^{upgrade_level})/200;
Yes, it is common upgrade level made in blacksmith, except offense points, destruction capability of catapult is also affected by this upgrade level.
D – durability multiplier, combined effect of stonemason and artifacts. If none of them present, then D = 1
lvl – level of building;
morale – (attacker's population / defender's population)^0.3, also 100% ≤ morale ≤ 300%. And maximum is reached, when attacker's populations is 40 times larger than defender's population or more.
Х is amount of catapults came into action (sic!).

In the heat of battle while slow catapults go to their firing position, part of them could be damaged and negated before discharge. Of course, attacker's troops are protecting their siege machines, but the more advantage defending troops have, the less catapults reach their firing position and will fire. Percent of catapults came into action is determined by next formulaes:

X = (offense points / defense points)^1.5 (9)
if X > 1, then this part will be = 1 – 0.5 / X
if X < 1, then this part will be = 0.5 · X
Amount of catapults isn't rounded.

In simple terms this formula could be described as follows:
If there's no defense, catapults will work at almost 100% of their potential.
In case of almost balanced forces only half of catapults will work.
If defense has overwhelming majority, only half of catapults alive as if it was raid, would work.

If amount of worked catapults is less than sufficient (8), then building will be demolished only partially or will not destroyed at all. Due to quadratic dependence higher levels are harder to destroy.
E.g., to destroy building from 99th to 98th level 25 (worked) catapults are required.
To destroy building from 19th to 18th level 5 (worked) catapults are required, or 5 times less.
However, if village is affected by unique durability artifact, making buildings 5x more durable, it will be wiser to attack WW with catapults as long as WW buildings itself isn't affected by durability artifact.

When you set 2 targets for catapults, their force is divided between two targets equally.
When you target some kind of building and there're several such buildings in destination village (e.g.: cropland, warehouse, etc.), catapults will always hit building of certain type with highest level.


3.b. Rams
When there's no defense rams destroy walls almost as well as catapults destroy buildings, but when there's some defense things become much more complicated since wall gives bonus in combat. Rams' destruction capability is unaffected by morale, and durability multiplier has one additional part, which depends on wall's tribe. Racial durability is listed below:

Roman city wall: 1

Gallic palisade: 2

Teutonic earth wall: 5


Firstly, rams virtually "demolish" wall to some intermediate level, which is used in later calculations.
This value is always and integer between initial and final wall level inclusive. Formula is very complicated and consists of two parabolas so I will provide only total "virtual durability":

DDR = DC · { L·(L+1)/8 + 5 + (24.875 + 0.625·L2)·L2/2 } (10)
L2 = round{ (L – 1) / 2 }


L — starting level of wall.
DDR — Demolition Damage of Rams, equals percent of worked rams (9).
DC — Durability coefficient, depends on tribe, stonemason, rams' upgrades and durability artifact.

Again, this is not explicit value you can see in combat report. However you could find out this value by log. I'll show how to obtain this intermediate value later.

There's a chart with 3 series below. Each series have corresponding start wall level (see legend) and depict dependency between amount of worked rams and our intermediate level of wall.
Roman city wall with no stonemason and artifacts assumed.


After calculating this intermediate level, defense points are recalculated (another wall level => another wall bonus) and final result of battle, all losses are calculated using this new values.
Consider next battle:
20,000 clubswingers, 5000 Teutonic knight and 100 rams attacks
15,000 praetorians behind 20th level roman wall.
No upgrades and other boni are assumed for the sake of simplicity. Try it.
Wall was demolished completely, what else do we need?

Let's replace rams with some other infantry troops and find out, which wall level should be set to get the same losses. Who said "zero"? Try it yourself firstly!
100 rams = 108 axemen + 2 spearmen in offense points.
A-ha! 9th level of wall. That's how we could find this implicit value.

Destruction capability of rams is affected by upgrade level as well as for catapults (8).


3.c. Espionage

Finally, I describe simulation for scouts (I mean recon.troops for all tribes). Formula for "combat" between scouts is the same as for common attack (3), except defender's losses. It is always 0%, also there're no immense battles, i.e. 1.5 is used in power for any battle.
Instead of offense and defense points scouting and counter-scouting points are used. Base values are 35 and 20 respectively for any tribe. This attributes are also affected by common formula for upgrades in blacksmith and armory (7). As could be saw from formula, Romans and Gallic spies receive greater bonus from upgrades. Combine it with horse drinking trough, and Romans Equites Legatti are the best. For classic servers Teutonic scouts are considered the best, since speed isn't a great deal for recon.operations.
Possible results of recon.operation:
All "attackers" die. They would know nothing, and "defender" would know who came.
None of "attackers" die. "Defender" won't know he/she was scouted.
Note: This could happen even if "defender" have some small amount of scouts.
In all other cases both sides will receive reports with corresponding info.


 
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