can you post an example, your calculation's result and the "correct" result? I think formula is quite right, but I never checked it
Yes, granted this will be done in Death and Taxes 9.0, which I don't think will have any affect on the combat formula.
I will attempt to follow the formula given in the wiki for my calculations to the best of my ability to understand it, ask questions where I don't understand it, and point out where I believe it to be incomplete or incorrect.
For reference, here is an excerpt of the Military article of the EU3 Wiki, which addresses land combat:
Combat
Combat consists of a series of combat resolutions. A single combat resolution lasts for a 5-day period, beginning with a 5-day shock combat resolution, followed by a 5-day fire combat resolution. This alternating process completes until one army runs out of morale. This system means that shock combat resolutions are slightly more common, and that combat against defeated or retreating forces will be resolved entirely in the shock combat resolution.
Actual combat is resolved using the following formula. The process is the same for shock combat resolutions as it is for fire, simply using fire attack/defense rating instead of shock attack/defense ratings. On each day of combat the game evaluates how many casualties each side inflicts on the other by the following formula:
Casualties
Modified roll = (Attack + Dice) - (Defense + Terrain) + (Leader Differential)
Final Casualties: Base Roll * Tech Level Modifier * Discipline * 6
If the Modified roll is 13 or greater, then use 12 as the modified roll.
If the Modified roll is less than 13 but greater than 1, then subtract 1 from the modified roll.
If the Modified roll is 1, then use the modified roll.
If the Modified roll is less than 1, then the use 2^(modified roll).
Definitions:
Attack: the attack rating (shock or fire rating depending on the combat resolution).
Dice: A random number (in the range 0-9) representing luck for the combat resolution
Terrain: Terrain modifiers are applied to both the attacker and defender's offensive roll - it subtracts from the attacker and adds to the defender. Cavalry takes double penalties (but does not get double benefit on defense).
Forest/Marsh/Hills: -1 for the attacker, +1 for the defender
Mountains: -2 for the attacker, +2 for the defender
River Crossing: -1 for the attacker, +1 for the defender
Defense: the defense rating (shock or fire rating depending on the combat resolution).
In IN, if there an artillery unit in the back row, it gives half its defense rating to the infantry unit in front of it as a bonus.
Leader Differential: The difference in capability between the opposing leaders.
Tech Level Modifier: The Shock or Fire multiplier based on the tech level of the army's nation.
Discipline: A damage modifier. So discipline of 125% increases the damage done by the unit by 25%, discipline 90% reduces the damage done by 10%. The National Idea Napoleonic Warfare increases Discipline by 25%, but requires a Land Tech level of ≥53.
In IN, if an artillery unit is in the back row, its damage is halved.
Military tactics is a concept introduced in Heir to the Throne. It is a value that increases with some Land Tech levels and it makes a big difference in combat. As the vlaue of Military tactics increases the amount of damage taken decreases. The amount of damage done is modified by the military tactics value by the follwing formula: Damage = Base damage / (1 + Military Tactics)
Morale
Modified roll = Morale Offense - Morale Defense
Final Morale Damage = Modified roll * Tech Level Modifier * 0.08
If the Modified roll is 13 or greater, then use 12 as the modified roll.
If the Modified roll is less than 13 but greater than 2, then subtract 1 from the modified roll.
If the Modified roll is less than 2, then use 1 for the modified roll.
http://www.paradoxian.org/eu3wiki/Military
I have decided to play a random scenario for this example. I will be in command of the Polish against the Russians in the Livonian War.
Here is the battle of Smolensk
An assumption that I am going to make is that the result of the final losses in moral and casualties for both armies per day is the sum of that for all of their units, where this formula, and thus the real 'combat' applies to individual units fighting each other, and not entire armies. But, the results of the combat among these individual units are added together to determine the damage done to the entire army. I do need to apologize if this didn't make sense. Sometimes I have difficulty formulating my thoughts into words.
And, going off of that assumption, I will observe the combat between Vladimir's 1st Regiment of infantry, and Mazovia's 1st Regiment of infantry for all calculations.
Before I attempt to calculate anything, I must ask, (and this was not mentioned in the wiki), is the effectiveness of a unit in combat directly proportionate to its percentage of men? For instance, would a unit of 900 men be 90% as effective as it would be with 1,000 men? This would definitely make sense, but it was not mentioned anywhere in the wiki.
Regardless, here I begin. Please point out any inaccuracies or errors that I commit.
To Determine Casualties
"Modified roll = (Attack + Dice) - (Defense + Terrain) + (Leader Differential)"
So, I will posit this: "Modified Role = (3 + 6) - (0 + (-2)) + (1)" - Modified Role = 12 (originally 13)
Now, when it says "defense" this is obviously the defense of the enemy unit, right?
Since Russia is the defender, and the terrain modifier is 2 in this case, would I posit -2 to my modified role, since I would subtract it for +2 to my modified role?
The wiki mentions that terrain "subtracts from the attacker and adds to the defender" as it concerns the offensive role. I added it in the second set of parentheses to be subtracted from the first, but that is all that I need to do with it, right?
Now, for casualties, the wiki says "base role". Is this the same as the modified role? I really wish it was consistent with its terms here. Nonetheless, I will assume that it means the modified role. In that case:
"Final Casualties: Base Roll * Tech Level Modifier * Discipline * 6"
"Final Casualties = 12 * 2 * .88 * 6 = 126.72" (I will round this to 127)"
'Tech Level Modifier' is Military Tactics, I presume?
Thus, on this day, Vladimir's 1st Regiment should inflict 127 casualties upon Mazovia's 1st Regiment, if my calculations were correct. They had 986 men at the beginning of the day, so they obviously should have 859 men by tomorrow.
However, they only were reduced to 972 men! What am I doing wrong here? Please, please help me to understand this. I don't have time to do this whole process again for morale. I'll try that another day. In the meantime, thank you very much for your help.
