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Kanitatlan

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Mar 13, 2003
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If you can contribute information about morale rules then please see this thread.
I am going to make a number of posts in this thread that I hope will together form an effective military FAQ covering all the aspects of land operations. I have done no proper naval analysis as yet and therefore that area will be left uncovered. As I add FAQ posts I will add them to and index here. As forum members post corrections/suggestions I will update the main posts – each main post will end with a statement of the form “modified for all posts up to #nnn”. If you feel that a FAQ has not adequately reflected posts I claim to have reviewed then feel free to comment again but please try to keep down the repetition on subjects I haven’t yet reviewed. I will try to keep a record of reviewing in this first post so viewers can keep track of what is going on. I am hoping that this may ultimately end up reposting in the FAQ section and/or be transferred to the EU III wiki

At various places in the posts I will flag certain items with “Sneaky” to introduce clever techniques for exploiting the system to achieve better results.

Please not that FAQ sections may be initially posted incomplete and out of order

FAQ1 – Casualties – Post #2
FAQ2 – Morale (winning battles)
FAQ3 – Units
FAQ4 – Battlefield deployment
FAQ5 – Examples

Status – initial post
 
Military FAQ Part 1 - Casualties

Introduction

This post is concerned with the mechanism whereby units take casualties and how to understand the likely casualties your units will cause or take. The FAQ assumes that you have read the relevant section of the manual. The manual gives the raw statement about how combat work but this will leave most players with little appreciation of what this means in practice.

Combat consists of a series of combat resolutions extending over a significant period in days. There is a single combat resolution for each 5 day period which is then applied in each successive days. Sneaky This has some interesting implications as it means that after day one you know what will happen in the next 4 days so you can actually break off from battle if the first day shows bad results.

The combat types are currently 5 days shock action followed by 5 days fire action and repeat. This has some important implications for battle analysis. In particular

. The number of fire days in a complete battle will almost always be less then the number of shock days and will certainly never be more

. Combat against defeated and retreating enemies will always be shock days only as they are pushed into new retreats before the first fire day occurs

How it works

Be cautious in reading and understanding this section. Inflicting casualties is not the only issue in battles and you need to be conscious of winning the battle as well. That is covered by the morale section and results in some significantly different conclusions.

Actual combat is resolved using the following formulae. The process is the same for fire days as it is for shock days, simply using fire factors instead of shock factors, so I will provide just the one general illustration.

On each day the game evaluates how many casualties each side inflicts on the other by the following

Attack+Dice+Terrain+Leader-Defence = score

Where
Attack = the attack rating of your unit
Dice = the periods dice roll (in the range 0-9)
Terrain = any terrain adjustments, these are applied to one side adjusting both attack and defence (see below)
Leader = a positive or negative adjustment reflecting the difference in capability between your leader and the enemy’s leader
Defence = the enemy target unit’s defence score.​
One of the most important issues to understand in this formula is which parts affect both attack and defence and which only effect one of them. This is because anything affecting both can be considered as twice as significant.

Terrain, for example, affects both and therefore a –1 for terrain is worth 2 points and should be considered like a –2 on the dice rather than –1. (In actual fact it matches –1 on your dice roll PLUS +1 on the enemy dice roll).

Attack factors, Defence factors and the Dice roll only have a singular effect and therefore they only count for one point per point. Leader values and terrain effects are applied to both attack and defence and therefore their factors apply twice and should be evaluated as worth 2 points each. This makes high grade leaders extremely powerful.

Having calculated a score this is then looked up on the following tables to obtain the number of casualties inflicted on the enemy. The process is…

1) Look up the casualties per 10,000 on the casualty table
2) Multiply by the relative strength of the attacking unit
3) Multiply by the tech level modifier for unit class and combat type (see below)
4) Subtract casualties​
Note: I have used casualties per 10,000 so that the results are in whole numbers rather than fractions.

4d371ab.jpg
This table is at least very close to correct but I cannot be certain of exactness. The formula is

(score-1) x 3.5 for scores of 2 and above (the figure 3.5 proven correct within about 2%)
3.5 for a score of 1
2^(score-1) x 3.5 for scores below 1 (this amounts to halving the casualties for each point below one)

40pe3vd.jpg
The figures in this table can be looked up in the game files but are not visible in game. The table is incomplete and only covers tech levels up to 35 (year 1735). Actual tech levels in the game extend to level 59 BUT this is dated 1825 and hence not typically reachable.

Worked examples

This is all a bit complex for most players so here are a few worked examples simply designed to illustrate the workings of these formulae. This are not intended to provide insight into particular combat situations.

1.
1 Latin Knight fighting 1 Latin Medieval Infantry, both at full strength at tech level 0
2 examples with different dice rolls

Knights: 1 attack + 5 dice = 6 => 5 x 3.5 x (Tech modifier) 4 = 70
Infantry: 0 attack + 5 dice = 5 => 4 x 3.5 x 0.5 = 7

Ouch

Knights: 1 attack + 0 dice = 1 => 1 x 3.5 x (Tech modifier) 4 = 14
Infantry: 0 attack + 9 dice = 9 => 8 x 3.5 x 0.5 = 14

Best possible result its same casualties

This nicely illustrates the situation at low tech-levels. The tech level modifier gives the cavalry an 8:1 advantage in causing casualties and this easily overwhelms all other factors.

1 Caroline infantry (5/4) fighting 1 Grenzer infantry (2/6), shock action

Caroline: 5 attack + 6 dice – 6 defence = 5 => 4 x 3.5 x 1 (Tech) = 14
Grenzer: 2 attack + 6 dice – 4 defence = 4 => 3 x 3.5 x 1 (Tech) = 10.5

Difference is quite limited and easily overwhelmed by the dice roll.

Now trying both of the above against 1 Latin Knight

Caroline: 5 attack + 7 dice – 0 defence = 12 => 11 x 3.5 x 1 (Tech) = 38.5
Knights: 1 attack + 7 dice – 4 defence = 4 => 3 x 3.5 x 4 = 42
Grenzer: 2 attack + 7 dice – 0 defence = 9 => 8 x 3.5 x 1 (Tech) = 28
Knights: 1 attack + 7 dice – 6 defence = 2 => 1 x 3.5 x 4 = 14

(dice roll of 7 chosen to keep on the linear part of the casualty tree)

The purpose of this example was to show that defence factors become more prominent when infantry fights cavalry than when they fight each other. See unit evaluation section for more details

Repeating the above with lower dice rolls allows us to look at calculations below the linear section of the table. Using 1 Knight versus 1 Grenzer

Knights: 1 attack + 9 dice – 4 defence = 6 => 5 x 3.5 x 4 = 70
Knights: 1 attack + 8 dice – 4 defence = 5 => 4 x 3.5 x 4 = 56
Knights: 1 attack + 7 dice – 4 defence = 4 => 3 x 3.5 x 4 = 42
Knights: 1 attack + 6dice – 4 defence = 3 => 2 x 3.5 x 4 = 28
Knights: 1 attack + 5 dice – 4 defence = 2 => 1 x 3.5 x 4 = 14
Knights: 1 attack + 4 dice – 4 defence = 1 => 1 x 3.5 x 4 = 14
Knights: 1 attack + 3 dice – 4 defence = 0 => 0.5 x 3.5 x 4 = 7
Knights: 1 attack + 2 dice – 4 defence = -1 => 0.25 x 3.5 x 4 = 3.5
Knights: 1 attack + 1 dice – 4 defence = -2 => 0.125 x 3.5 x 4 = 1.75
Knights: 1 attack + 0 dice – 4 defence = -3 => 0.0625 x 3.5 x 4 = 0.875

Grenzer: 2 attack + 9 dice – 0 defence = 11 => 10 x 3.5 x 1 (Tech) = 35
Grenzer: 2 attack + 7 dice – 0 defence = 9 => 8 x 3.5 x 1 (Tech) = 28
Grenzer: 2 attack + 3dice – 0 defence = 5 => 4 x 3.5 x 1 (Tech) = 14
Grenzer: 2 attack + 0dice – 0 defence = 2 => 1 x 3.5 x 1 (Tech) = 3.5

Notice how the more linear and closer spread of the Grenzer means that this combat is very strongly dependent on the cavalry dice role. An interesting side issue is that this combat can be dramatically affected by leadership. Give the infantry a level 6 leader against none for the cavalry and they are completely protected from the higher combat results. The cavalry will vary from ineffective to very moderate whilst the infantry will always achieve reasonable results.

Do it the other way round and the cavalry are shifted to spectacular results as against modest for the infantry.

This illustrates nicely that leadership is more significant for an effective tech level disadvantage in unit scores. It is not an illustration that leaders are more significant for cavalry.
 
Last edited:
Nice. But your multiplier graph is a bit messed up (multipliers should be the vertical line, not the horizontal one)
 
Mork said:
Nice. But your multiplier graph is a bit messed up (multipliers should be the vertical line, not the horizontal one)
My apologies to everyone, it is the axis labels that are messed up. I will correct this.

Corrected.
 
Morale

Unit Morale is an extremely important characteristic and a major influence on whether you win or lose a battle. If you go to your country tabs (click on the shield at the top left of the user interface) and select military you have a display of preferred unit types and other information. Hover your cursor over the stars for land units and you get a unit Morale tool tip as illustrated below. This will show you what your maximum morale is and how it is made up.

33pgfb5.jpg


One of the most important things to understand from this is what all those percentages mean. They are very misleading as what they mean is a simple additive bonus to your morale level. +50% means that 0.5 is added to total morale. This makes some of those available bonuses rather less attractive than you might first think, especially the +50% for selecting military drill as a national idea.

I think this display shows examples of all the possible sources of morale increases breaking down as follows.

  • Technology – ranges from 0 to 3.5
  • Current Ruler – I think this is 0.1 x military rating
  • Sliders, +/-0.1 Offensive, +0/0.1 Land Naval, +/-0.05 Serfdom
  • +0.5 for military drill
  • +0.5 Defender of the faith
  • +0 to +2.0 for land maintenance
  • + Half of prestige (+0 to +0.5)

In my view one of the most revealing aspects of this is the poor showing of the military drill national idea and the tiny effects from slider settings. After viewing this I would seriously consider ignoring the morale issue when considering slider settings. If you want extra morale then it is worth considering defender of the faith rather than military drill especially if you are a large country. You can achieve the effect of military drill for 1,000 ducats, admittedly a lot of money but national ideas are quite precious.

A very important issue is the rising significance of the technology contribution, which will slowly reduce the importance of all the others. Also, rather obviously, maintenance has a profound affect on morale especially at low technology.

Morale recovery rates are currently quite unclear and some player experimental data would be gratefully received. Morale increases on the 1st of each month the same as reinforcements are received. This occurs whether the unit is retreating or not and is therefore received every month no matter what. Some brief experiments suggest that the recovery rate is variable but may be something around 15-20% per month in enemy territory and twice that in friendly territory (not sure what the definition of enemy and friendly is in this context). I will update this post when proper information is available.

IF YOU CAN DO SOME EXPERIMENTS OR SIMPLY COLLECT DATA AROUND THE TURN OF THE MONTH IN A GAME YOU ARE PLAYING THEN PLEASE POST IN THIS THREAD. If you do collect data then please provide
Morale before/Morale after/Max Morale/Status (moving, stationary, sieging)/Province status (owned, allied, controlled, enemy)/Army maintenance level
 
Test worked example

This worked example based on the first few days of the Battle of Alexandria is intended to demonstrate the accuracy of the casualty rules worked out so far and perhaps provide some insight into other factors. The battle is between a French cavalry army, tech level 25 galoop cavalry, under an excellent general fighting against a Kara Koyonlu mixed army of tech level 10.

4i6ov20.jpg


After 1 day of battle

3zrj0v5.jpg


After 2 days of battle​

By inspecting individual units I can tell that the overlapping Qara Koyonlu end units have not been attacked and all units have attacked the enemy unit opposite to them or nearest at the ends except both the right hand French cavalry have been attacked by a Kara cavalry. The red lines on the display illustrate the apparent Kara lines of attack. This gives no immediate insight into the battle AI’s operation but does suggest that in normal battles nothing very weird is going on.

Qara tech level 10, French tech level 25. Oddly enough these have no impact on shock modifiers. Infantry have 1.0 and cavalry have 4.0 for both sides. Qara units are cavalry 2/2/2/0 [morale a/d shock a/d] and infantry 3/2/1/0 whilst the French have 4/2/4/2.

The dice roll appears to have compensated for the leader but the two are not actually equivalent. Our leadership increases the casualties that we inflict and decreases the casualties that the enemy inflicts whereas the enemy’s superior dice roll only improves the casualties that they inflict.

Working out the battle we get…

Casualties
French Cav versus Kara Any = 4+3+2-0 = 9 -> 8x3.5x4 -> 112
For the whole force 112 x 7 x 6,845/7,000 = 767 casualties when, in fact, 762 were reported. This is assumed to be the result of rounding errors with casualties being evaluated separately for each unit.

Kara Inf versus French Cav = 1+5-(2+2) = 2 -> 3.5
In fact, in the middle of the line the French cavalry took 3 casualties each on the first day and 2 on the second day. This clearly shows a casualty rate of 2.5 rather than 3.5 so there is a slight discrepancy here indicating that the FAQ is not entirely correct.

Kara Cav versus French Cav = 2+5-(2+2) = 3 -> 2x3.5x4 -> 28
At the left flank this should be 80.8 casualties scaled for day 1 losses (all the exposed units in the Kara line are at 888 men). The actual losses by this end unit are 80 so we have as good as an exact match there. At the other end we have a similar match (worked out separately but seems correct).

Over all losses are a reasonably good match for the FAQ going as 155/784 on day one and then 142/762 on day 2. The declining rate simply reflecting the shrinking size of the two armies.

Moving on I want to have a look at morale losses and the analysis plus facts are as follows

Either Kara Inf versus French Cav 3+5-(2+2) = 4 -> lose .25, .25 actual = {6.21 -> 5.96 -> 5.71}
Or Kara Inf versus French Cav 3+5-(2) = 6 -> lose .25, .25 actual = {6.21 -> 5.96 -> 5.71} (no leader)

Either French Cav versus Kara Inf 4+3+2-2 = 7 -> lose .8, .8 actual = {4.06, 3.26, 2.46}
Or French Cav versus Kara Inf 4+3-2 = 5 ->

Either 3 Kara Cav 2+5-(2+2) = 3 -> lose 2.4, 2.4
Or 3 Kara Cav 2+5-(2) = 5 -> lose 2.4, 2.4

If leaders don’t count but tech modifiers do and the formula is 0.05x(score-1) then we get values of – 5x.05=.25, 4x0.05x4=.8, 4x.05x4x3=2.4 which are the right answers. This seems to suggest that this is the right idea.

Looking at the other end of the line we have 1 Kara Cav causing 0.8 morale loss to the end unit and 1 Kara Cav + 1 Inf causing 1.05 morale loss to the second one in. The formulae all add up again!!

Next round a score of 4 for the Kara infantry has knocked 0.2 off a cavalry unit. This still matches my formula so, for the time being I am going to consider this correct.

So the morale rules are the same as for casualties except that the multiplier is 0.05 instead of 3.5, leaders don’t count and unit strength doesn't count. Note that I have not managed to obtain a battle with terrain effects so I will be coming back to this issue.
 
Kanitatlan said:
If leaders don’t count but tech modifiers do and the formula is 0.05x(score-1) then we get values of – 5x.05=.25, 4x0.05x4=.8, 4x.05x4x3=2.4 which are the right answers. This seems to suggest that this is the right idea.

Looking at the other end of the line we have 1 Kara Cav causing 0.8 morale loss to the end unit and 1 Kara Cav + 1 Inf causing 1.05 morale loss to the second one in. The formulae all add up again!!

Next round a score of 4 for the Kara infantry has knocked 0.2 off a cavalry unit. This still matches my formula so, for the time being I am going to consider this correct.

So the morale rules are the same as for casualties except that the multiplier is 0.05 instead of 3.5, leaders don’t count and unit strength doesn't count. Note that I have not managed to obtain a battle with terrain effects so I will be coming back to this issue.

Very good analysis. IMHO, the entire combat system is bass-ackwards. Tech-levels and unit superiority should be the determinant factor in casualties taken and received, not leader stats. Leaders should add a *small * bonus but primarily help with morale. For example you could have the shiny new units but with bad leaders they won't stay in the battle very long on a bad die roll. That and the far too overpowered cavalry are really stretching the suspension of disbelief.
 
Attrition (Interim statement)

This is an interim statement on attrition since the game clearly has a number of existing faults around this area. This FAQ section should at least give you some clues about the level of attrition and support capacity of various provinces. Investigation has shown the following facts.

Attrition rates are as follows based on province and prevailing weather/climate conditions

Base 5%
mild winter +2%
normal winter +5%
severe winter +10%
tropical +5%

I can detect no other factors affecting attrition rate.

Support capacity seems to consist of the following

Base capacity = N
Army camp gives +2 (unknown if this counts for non-controller of the province)
If you control the province then + base tax rate x 0.2 (unknown if this counts for non-controller)
If you are an owner occupier then x5
If you are the controller then x3
If stationary (besieging) then x2
Otherwise x1
+ leadership effect (see below)

Attrition occurs on the first day of every month and is evaluated based on the total number of units present as against your capacity. This means that quite a large enemy army can be present with no attrition whilst your army is being affected. If you exceed the capacity then you suffer attrition, there are no gradations, it is all or nothing.

Leadership seems to be something of the order of +1.4 to +1.7 capacity per point of manoeuvre ability of the leader. This has only been evaluated in a single high capacity province so this may be rather inaccurate.

Attrition is a highly important subject so I will be revisiting it later in the context of discussing strategy and tactics.
 
Lord Vader said:
Very good analysis. IMHO, the entire combat system is bass-ackwards. Tech-levels and unit superiority should be the determinant factor in casualties taken and received, not leader stats. Leaders should add a *small * bonus but primarily help with morale. For example you could have the shiny new units but with bad leaders they won't stay in the battle very long on a bad die roll. That and the far too overpowered cavalry are really stretching the suspension of disbelief.
As I have said elsewhere, my feeling is that the combat results are in fact too variable. This has been caused by the leadership and dice roll modifiers having too prominent a role. This could be cured by significantly increasing all unit values and scaling back the tech modifiers to maintain the casualty levels. Unfortunately this would also scale down the impact of terrain modifiers which is not what is intended.

As with any simple model the game is unable to reflect properly the characteristics of combat in this period. In particular it does not reflect the rock/paper/scissors effect of pitting one unit type against another and hence there is little coercion to go for mixed armies.
 
29m1110.jpg


I've been doing some investigation of battle deployments to see if I can work out exactly what the battle AI does. The above battle images rather tellingly indicate that the reality of the situation is that only very litmited superior force in terms of more regiments can be applied against the enemy. It looks very much like the larger force fills its front line to a 4 or 5 regiment overlap and then places units in the second line. The cavalry is always given priority on the flanks and, I suspect, priority in the frontline. The ultimate verdict from this is that the larger force will be able to apply up to 2 more infantry regiments than the enemy and 2 cavalry. This means that numbers of regiments is a very weak strategy for defeating an enemy force. I haven't done enough tests of this yet but my current game should sooner or later see Chinese hordes trying to defeat European armies which should reveal the sordid truth.

If this really is the situation then this will be very serious for the low tech countries in the world and, of course, a happy hunting ground for sneaky strategies.
 
Sorry Kanitatlan, but I really hope you have to do this great work again. Because in the alternate history of EU3, cavalry is a doomsday device, but at the same time, the ones that really used cavalry en masse, the khanates, seem to have misplaced all their bows.

1.2 soon?
 
Your analysis of number of regiments/strength of regiments confirms my suspicions. It indicates that when conducting "The Great Cavalry Sweep of Eastern Europe" you should reorganize your most damaged cavalry regiments and put them on siege duty while the main body continues to pursue and destroy. Of course, you should only do this if the sieging force is not threatened.

I am, however, unclear on what is happening with cavalry versus infantry. I understand that a brilliant leader is the most decisive factor, but what I am not understanding is how effective shock defense values on infantry are versus offensive shock values. I know that for any given unit type, you must multiply the shock or fire value listed on the unit type by the shock or fire value listed in the ledger. Is that the same for shock defense and fire defense? If not, then what possible value do Tercio and other defensive infantry formations have, when offensive infantry formations, like Free Shooter or the late game fire-based infantry formations whose names I cannot remember at the moment, will inflict more damage per day?
 
Given the tech level multipliers for infantry fire, what is the point of early fire-based infantry like Longbowmen? By the time you can do any damage at all in the fire phase, the Longbowmen and even Condotta Infantry are obsolete.
 
As far as I can tell, there isn't any point. They are, in fact, more worthless than other infantry.

When this excellent analysis of military stuff is complete, and thus we fully understand what in the hell is going on in battles, I will be modding my game to give these early fire-based infantry some relevance, even if they will still suck compared to cavalry.

I also would like to give cavalry archers their due, since the lack of a fire phase makes cavalry archers just as worthless as longbowmen.
 
Namm said:
Sorry Kanitatlan, but I really hope you have to do this great work again. Because in the alternate history of EU3, cavalry is a doomsday device, but at the same time, the ones that really used cavalry en masse, the khanates, seem to have misplaced all their bows.

1.2 soon?
I must admit I tend to agree with you. I haven't published the analysis but relatively early on one cavalry is equal to two infantry in terms of winning battles (infantry gain from being able to absorb more casualties and more morale loss because there are two of them). Unfortuantely the battlefield deployment issue makes things even worse for the infantry since even a mixed cavalry/infantry force has great difficulty applying their superior numbers.

To some extent I am doing the analysis now to perhaps illustrate to Paradox exactly what the consequences of the current algorithms are and so that I have a solid foundation for re-analysis under later patches. I generally try to be restrained about publishing opinion and stick to trying to present the facts. This doesn't mean I think it works how it should.
Secret Master said:
Your analysis of number of regiments/strength of regiments confirms my suspicions. It indicates that when conducting "The Great Cavalry Sweep of Eastern Europe" you should reorganize your most damaged cavalry regiments and put them on siege duty while the main body continues to pursue and destroy. Of course, you should only do this if the sieging force is not threatened.

I am, however, unclear on what is happening with cavalry versus infantry. I understand that a brilliant leader is the most decisive factor, but what I am not understanding is how effective shock defense values on infantry are versus offensive shock values. I know that for any given unit type, you must multiply the shock or fire value listed on the unit type by the shock or fire value listed in the ledger. Is that the same for shock defense and fire defense? If not, then what possible value do Tercio and other defensive infantry formations have, when offensive infantry formations, like Free Shooter or the late game fire-based infantry formations whose names I cannot remember at the moment, will inflict more damage per day?
The key issue is the ratio of friendly casualties to enemy casualties. Since the friendly defence is subtracted from the enemy offense you have a situation where +1 on the enemy offense has exactly the same value as +1 on the friendly defence (they cancel out). This makes attack and defence factors generally of equal value.

BUT

If the attacking unit has a higher casualty multiplier then defence will reduce your casualties by more than offense would increase the enemies. This may of course be moot since the enemy having a higher multiplier will mean they are going to beat you (afraid so).

The main issue is that whilst the fire effect multiplier is low relative to the shock effect multiplier the fire factors of a unit are close to irrelevant.
Ungor said:
Given the tech level multipliers for infantry fire, what is the point of early fire-based infantry like Longbowmen? By the time you can do any damage at all in the fire phase, the Longbowmen and even Condotta Infantry are obsolete.
And the answer is, absolutely no point whatsoever.