Attacking & Defending

Military Efficiency

Base Military Efficiency

Base Military Efficiency = ( 60 + 40 * ( Effective Wage Rate / 100 ) ^0.25 ) * Gangbang Protection * Science Bonus

Rounded to one decimal point, it should return the most accurate values. Effective Wage Rate lies between 50 to 200.
While wages can be changed instantly, the effective wage rate used for base military efficiency changes slowly per tick. The formula for change in effective wage rate is:

Change in Effective Wage Rate =  0.05 * (Wage Rate Paid - Effective Wage Rate)

If wages were not fully paid in the previous tick, Wage Rate Paid will be set at 50 regardless of the amount of wages actually paid.

Condition	Modifier
Gangbang Protection	Varies, see GBP

Offensive Military Efficiency

OME = (Base Military Efficiency + Training Ground Bonus + Honor Bonus) * Fanaticism Bonus

Defensive Military Efficiency

DME = (Base Military Efficiency + Forts Bonus) * Minor/Greater Protection * Fanaticism * Plague

Attacking

Raw Offense

Raw Off = Soldiers + (Offensive Specs * Offspec value) + (Elites * Elite Attack value) + Horses + [(Mercs + Prisoners) * 3]

Modified Offense

Mod Off = Raw Offense * (OME + General Bonus + Personality Bonus) * Race Bonus

Condition	Modifier
OME	check your Military Advisor
General Bonus	+3% per additional general over 1

Attack Times

Attack Time = Base Attack Time * Race Bonus * Personality Bonus * Barracks Bonus * Quick Feet * Stance * Attack Type * War * NW Mod

Note: War attack speed is -10% immediately on war declaration, and phases in to a maximum of -20% after 12 hours of war have passed
There is a networth value adjustment for attack times. This adjustment compares your networth to the networth of the province you are planning to attack. If these are close to each other the base attack times as given below are used. If the networth differs, then the base attack time is multiplied, so your attack time is longer. This does not affect intra-KD attacks or in war.

Base Attack Time

The base attack time is 16 hours. This is the value all calculations are based upon.

Location	*Intra KD*	*Same Island*	*Diff Island*
Attack Times	12.6	14.4	16

Minimum Offense to Win

Random factor is +-3.5% for offense and defense. Off/def ratio needed to win is 0.97. Thus in the worst case (-3.5% offense, +3.5% defense) the borderline winning situation is:

Condition to Win = (Mod Off * 0.965) / (Mod Def * 1.035) ≥ 0.97

Which simplifies to:

Mod Off = Mod Def * 0.97 * 1.035 / 0.965

Mod Off = Mod Def * 1.040362694

Therefore, to guarantee a win, you must send a Mod Off that is ~4.04% greater than the defenders Mod Def.

On Conquest attacks, the minimum offense to win is 51% of the opponents defense.

Attack Gains

 Gains = Target Resource * Attack Type * PNF * KNF * GBP * GS * Race * Stance * Relations * Target Stance * Attack time modifier * Anonymity

Province Networth Factor

 Relative Province Networth (rpnw) = Targets Networth / Self Networth
 
 Province Networth Factor = DEPEND ( rpnw ) :
                                     rpnw < 0.567   = 0
                             0.567 < rpnw < 0.9     = 3 * rpnw - 1.7
                             0.9   < rpnw < 1.1     = 1
                             1.1   < rpnw < 1.6     = -2 * rpnw + 3.2
                                     rpnw > 1.6     = 0

Kingdom Networth Factor

 Relative Kingdom Networth (rknw) = Target Kingdom Networth / Self Kingdom Networth
 
 Kingdom Networth Factor = DEPEND ( rknw ) :
                                    rknw < 0.4      = 0.6666
                              0.4 < rknw < 0.9      = rknw * 2/3 + 0.4
                                    rknw > 0.9      = 1

Attack time adjustment factor

Attack time adjustment (with reduced time):

 Attack time adjustment factor = 1 - 1.5 (Hours reduced / base attack time)

Attack Type

Traditional March

Base gains are 12% and Traditional March gains are capped at 20% of your or your opponent's land, whichever is smaller.

Plunder

Base gains are 50% gold, 60% food and 60% runes. Max gains is 1.35x base (67.5% gold, 81% runes/food).

Raze

Destroys a portion of the targets land. In war this attack only destroys buildings

Learn

Base gains are 9.375% of each category of science.

Conquest

Base gains are 6.8% land for a full hit, gains are decreased in proportion to the relative offense sent vs. targets defence.

Massacre

Base gains are 9.5% peasants, 8.5% thieves and 5% wizards

Defending

Raw Defense = (Defense Specs * Def Spec Points) + (Elites at Home * Elite's Defense) + (Soldiers * Def Points Sold * Aggression) + Townwatch

Mod Defense = MAX ( Raw Defense * Defensive Military Efficiency , Land )

Modifier Type	Active	Otherwise
Def Spec Points	5 (+1 bonus to def spec, check races)	4
Elite Defense	Variable
Aggression	0	1
Townwatch	Peasants / 4	0

Minimum Defense

All land is protected by a minimum of 1 defense per acre. That is, if you should send every single elite and general out, and release your defense specialists, an opponent would still need to send 1 offence point per acre to conduct a successful attack against you.