Points

Casus Belli

(Only counts for the first attack.)

Backstabbing -10 to attacker (Attacking allies without having a conflict (if you were allies in the last three turns))
None -5 to attacker (ur lazy)
Fake/staged event -3 to attacker (at least you did something to justify the war)
Provoked -2 to attacker (people don't care who started first, they don't like war)
Helping allies -1 to attacker (y don't ya help'em with supplies instead of sending us to die?)
Political casus belli 0 (so that island is your? How'dya like my spear in yo head)
Defending your people +2 to attacker (did you just kill a bunch of my people? Come here mothe....)

Motives

(Only one can be selected, "fake motives" is applied for certain reasons)

Life or Death of a country +5 to defender (fear of losing all territory makes your men fight harder)
Independence +3 to defender (Nations don't usually want to lose freedom, land, religion, traditions or live in vassal/puppet state)
Religion +3 to attacker (Crusade, Jihad and stuff) (triggers independence)
Social or moral +2 to attacker (Other culture is making human sacrifices, and you don't like that, so you go and kill'em)(triggers independence)
Economical +1 to attacker (You want iron or gold, dontchya?)(triggers independence)
Expansion and gaining influence +0 to the attacker
Fake motives -5 to attacker.
1. If you fight Carthage for Sicily because you were provoked there, you must conquer Sicily, not some distant region. Of course you can keep small portion of other conquered lands, but not too much.
2. Religious wars are only for religion, keeping big chunks of lands

Landscape and fortification

Landscape
Plains: 0.5 to defender*
(Arctic/Hot) Desert: 1 to defender (yes it is hard landscape but not only for attacker, also no resources for making field defenses)
Forests/swamps/hills: +2 to defender*
Landing on beach: +3 to defender*
Island: +3.5 to defender*
Mountain: +4 to defender*
Mountainous island: +5 to defender*

[*value is doubled if there is no fortification and defending army had one turn to prepare. Applied only to landscapes marked with asterisks]

Fortifications

Fortress:+7 to defender (+landscape factor)
- To fortify something, you need to have Economy at 3 or higher and it takes two turns.
Great Walls: +15 to defender (+landscape factor)
- To build a wall you need to have Economy at 3 or higher. You can build particular number of px every three turns.
- The number of px you can build: (Economy * n) + military
  - If your economy is from 3 to 5, n = 3.
  - If your economy is from 5 to 7, n = 4.
  - If your economy is higher than 7, n = 5.

[Both, Forts and Walls will be marked on the political map.]

Battlefield and army factor

Superior tactics and rested army with high morale is also a important thing if you want to defeat your enemy.

Homeland +3 to defender.
Enough of that c**p! -3 to army that has been fighting for 3 turns in a row.
Bad memories -3 to army that lost last turn (All the crazy stuff they did last turn, those would not be the best memories.)
If you fight on two or more fronts, your armies will be split equally on all of them, unless you mention how many you send to fight on each.
If you leave a front unguarded (no soldiers), no matter what bonuses you have, they don't count and enemy takes the amount of land equal to his expansion limit.
Army score army size divided by 1000.
Army score multiplier (army score * army score multiplier)
- If superior army is 1,5 - 2 times bigger: 1,1
- If superior army is 2 - 3 times bigger: 1,25
- If superior army is 3 - 4 times bigger: 1,5
- If superior army is 4 - 5 times bigger: 1,75
- If superior army is 6-7 times bigger: 2
- If superior army is 7-9 times bigger: 3
- If superior army is 10+ times bigger: 4

Economy and Military

Economical categories:

Collapsing/Recovering/Growing
Struggling
Weak
Fragile
Developing
Reasonable
Fair
Good
Strong
Stronk
Thriving
Powerhouse
All-Consuming
Frightening

Military categories:

Local Garrison
Defensive Power
Insignificant Power
Local Power
Moderate Power
Regional Power
Great Power
Continental Power
World Superpower

Both participants get points for military category, defender (if there is one) also gets +ep as a bonus for local support and supply lines.

Multipliers

Fortune

There are always some factors that cannot be defined properly but can really influence the battle, for example, half of your army ate bad berries and right when the battle starts they get really sick. To represent that small chance of luck for one or another army there is Random Org, the system is kinda complicated but eh, sometimes Tyche has really incredible things to offer.

So the thing goes as follows:

Step 1: Two RNG's are made from 1 to 101, one for each fighting side. This determines a small chance of Epic WIN/FAIL. 1 represents win, 101 represents fail and other 99 numbers show that no miracle happened that day.

Step 1.1: If somehow someone was so unlucky to get 101, another RNG is made from 50 to 100, number that you get, divided by 100, represents multiplier for the final score of that side.

Step 1.2: If somehow someone was so lucky to get 1, another RNG is made from 100 to 150, number that you get, divided by 100, represents multiplier for the final score of that side.

Step 2: If no epicness took place in that battle, two other RNG's are made from 95 to 105, number that you get for each side, divided by 100, represents multiplier for the final score of that side.

Results

Count the scores for both sides.

Multiply the scores by Fortune coefficient.

Find winning coefficient (losing score/winning score)

Take portion* of losing army. (represents losing side casualties)

That number depends on what role do you play in battle:

Defender wins (if any of the sides is defending) - 40% of losing army total and 0.5 battle role multip.
Attacker wins (if any of the sides is defending) - 60% of losing army total and 1 battle role multip.
Face to face battle (no defence bonuses) - 80% of losing army total and 1.5 battle role multip.

Multiply losing army casualties by winning coefficient (casualties*coef.), this represents winning side casualties.

[Very important] Even if you have better score, you can not lose all of your soldiers, otherwise you will be the losing side. i.e. Sparta has 0.5 winning coef. in the face to face battle and 1000 men, Athens have 3000 men. If we count by the algorithm, Sparta will lose 1,500 men, so it will be declared the losing side. Real Athenian casualties will be: Full size of spartan troops/coef.

Winning side can take (expansion limit/coef*battle role multiplier) px of land.