A question that returns now and again is how to compose armies. How many cavalry regiments should I use? Is artillery useful? When should I start using artillery in battle?
To better answer these questions, I did some analysis on the damage the various regiments do for all the tech levels. So I took the data from the files of my DW copy, copied them into a spreadsheet and started doing some calculations.
Besides inf, cav and art, I consider artillery firing from behind infantry and its supported infantry regiment as one "unit", which I call inf+art. The reason for this is that during combat the inf and art units basically fight as one unit as long as the inf has morale, after which the unit "transforms" into a regular art unit.
Total modifier comparison
First, I charted the fire and shock modifiers:
This graphs show for each of the four different unit types the sum of their shock and fire modifiers. For the inf+art unit I added the total modifier of the inf unit plus half of the art unit, as artillery firing from the second row does half damage.
I have divided the chart into four areas, one for each increase in the "Military Tactics" parameter, to give you a feel with which years the tech level correspond. I must remind you that the blue and green areas cover about 75% of the Grand Campaign, so while the orange and red areas cover more than half the graph, the period covered by those techs is only a century in total, with the red area even covering only about 20 years.
As you can see, cavalry will have double the total modifier infantry has pretty much the entire game until about tech level 55 (year 1790), after which the difference decreases.
Frontline artillery (yellow line) does not become significantly stronger than infantry until tech level 35 (year 1709) and only become as strong as cavalry around tech level 40 (year 1727). After tech level 52 (year 1775) artillery becomes stronger than cavalry.
Inf+art is during Era 2 a unit which strength lies halfway between cavalry and infantry and becomes as strong as frontline artillery around tech level 40 (yer 1727), after which inf+art and frontline artillery remain equally strong.
So in conclusion, cavalry is the strongest unit by far until 1700 and only begins to be outclassed by frontline artillery and inf+art after 1775.
Calculating casualties
However, the above analysis only takes the fire and shock modifiers into account, but there are more factors. So in the next step I take into account the "pips" units have, the offensive/defensive shock/fire pips. I will only look at casualties caused: I leave out morale damage.
I calculate casualties based on the formula from the wiki: http://www.paradoxian.org/eu3wiki/Military#Casualties
What I did is that for each tech level I selected one infantry, cavalry and artillery unit from the Western tech group, based on the following criteria:
I then calculate the casualties the four different unit type do against infantry with the formula:
Y = (4,5 + OF - DF) * FM +(4,5 + OS - DS) * SM
where
Y is casualties
OF is offensive fire of the unit
DF is defensive fire of the infantry unit
FM is the fire modifier
OS is offensive shock of the unit
DS is defensive shock of the infantry unit
SM is the shock modifier
The 4,5 is the average result of a 0-9 die roll. Note that I have made the following assumptions:
As artillery from the second row does half damage, the damage done by the inf+art unit is calculated by taking the inf damage as calculated by the above formula and add half of artillery damage, likewise calculated.
So in the next sections I will show the results of these casualty calculations of all four unit types against infantry.
Damage vs infantry
This graph shows how much damage each of the four units do againt infantry of the same tech level (all units are from the Western tech group). As you can see, the graph is quite different than the total modifier graph. Let me walk your through the graph era by era.
Era 1
All units' damage drop at tech level 11. That's because at that level Condotta Infantry become available, which has defensive shock 3, a great upgrade compared to the Longbow's defensive shock 1. Artillery at the end of the age is quite strong against infantry because of its many pips (8 in total vs 4 for inf and 1 for cav).
Also note that while cav shock modifier rises in this period, cav damage versus infantry remains level, as infantry gets more pips while cavalry remains the same.
Era 2
While at the start cavalry and artillery are equally damaging, cavalry makes a huge jump at tech level 22 as Latin Caracole Cavalry is available. The introduction of Highlanders Infantry hugely increase inf vs inf damage at tech level 28 (year 1636).
Cavalry is by far the most deadly unit versus infantry until tech level 35 (year 1700), where inf+art becomes as deadly as cavalry because of the introduction of both Caroline Infantry and Coehorn Mortars. Note that inf+art is much stronger than frontline art, due to that most of its damage comes from the inf part.
Era 3
Until tech level 43 (year 1735), cavalry and inf+art are equally dominating. With tech level 43 comes the Redcoat infantry, who has 4 more fire defense pips and 2 more shock defensie pips than its predecessor, Caroline Infantry. This means that all damage against infantry is drastically reduced, especially artillery.
Artillery becomes again very lethal with the introduction of Royal Mortars at tech level 47 (year 1750). Cavalry makes a huge jump at tech level 52 (year 1780) with Latin Cuirassiers (4 more offensive shock than before).
Square Infantry at tech level 55 (year 1790) again greatly reduces infantry casualties. Artillery becomes immensely deadly after that drop due to increasing fire modifier and the introduction of Flying Battery (+2 offensive fire compared to Royal Mortars).
Era 4
Surprisingly, from tech level 59 (year 1798) until the end, cavalry is much more deadly to infantry than inf+art or frontline artillery, even with the much higher fire modifier for artillery. That is because
Even with its fire modifier twice as high as cavalry's shock modifier, the balance is heavily in favour of cavalry.
Preliminary conclusion
To my surprise, the pips are much more important than I thought. While units from the same tech level differ very little from each other (Redcoats are not that much stronger than Bluecoats, for example), the pips do significantly determine casualties, having maybe even more influence than fire and shock modifiers.
In short, cavalry remains king of the battlefield until 1700, after which it's equal to inf+art. After 1798 cavalry again becomes the strongest unit by far.
Based on this, I cautiously conclude that on featureless terrain without leaders, artillery (in the form of inf+art) is never really worth its cost against infantry as cavalry always does more or equal damage and costs much less in both manpower and maintenance. Armies should have as much cavalry as possible with enough infantry to provide the Military Tactics bonus.
However, I need to do more analysis to back up this conclusion and maybe find out some new conclusion. As this takes a lot of time, I would like to know if there is any interest in doing so. If nobody cares about this, I'll just let it rest.
Any comments or questions?
To better answer these questions, I did some analysis on the damage the various regiments do for all the tech levels. So I took the data from the files of my DW copy, copied them into a spreadsheet and started doing some calculations.
Besides inf, cav and art, I consider artillery firing from behind infantry and its supported infantry regiment as one "unit", which I call inf+art. The reason for this is that during combat the inf and art units basically fight as one unit as long as the inf has morale, after which the unit "transforms" into a regular art unit.
Total modifier comparison
First, I charted the fire and shock modifiers:
This graphs show for each of the four different unit types the sum of their shock and fire modifiers. For the inf+art unit I added the total modifier of the inf unit plus half of the art unit, as artillery firing from the second row does half damage.
I have divided the chart into four areas, one for each increase in the "Military Tactics" parameter, to give you a feel with which years the tech level correspond. I must remind you that the blue and green areas cover about 75% of the Grand Campaign, so while the orange and red areas cover more than half the graph, the period covered by those techs is only a century in total, with the red area even covering only about 20 years.
As you can see, cavalry will have double the total modifier infantry has pretty much the entire game until about tech level 55 (year 1790), after which the difference decreases.
Frontline artillery (yellow line) does not become significantly stronger than infantry until tech level 35 (year 1709) and only become as strong as cavalry around tech level 40 (year 1727). After tech level 52 (year 1775) artillery becomes stronger than cavalry.
Inf+art is during Era 2 a unit which strength lies halfway between cavalry and infantry and becomes as strong as frontline artillery around tech level 40 (yer 1727), after which inf+art and frontline artillery remain equally strong.
So in conclusion, cavalry is the strongest unit by far until 1700 and only begins to be outclassed by frontline artillery and inf+art after 1775.
Calculating casualties
However, the above analysis only takes the fire and shock modifiers into account, but there are more factors. So in the next step I take into account the "pips" units have, the offensive/defensive shock/fire pips. I will only look at casualties caused: I leave out morale damage.
I calculate casualties based on the formula from the wiki: http://www.paradoxian.org/eu3wiki/Military#Casualties
What I did is that for each tech level I selected one infantry, cavalry and artillery unit from the Western tech group, based on the following criteria:
- Infantry: the unit with the most pips, if equal the unit with the most defensive shock pips.
- Cavalry: the unit with the most offensive shock pips, if equal the unit with the most pips.
- Artillery: the unit with the most offensive fire pips, if equal the unit with the most pips.
I then calculate the casualties the four different unit type do against infantry with the formula:
Y = (4,5 + OF - DF) * FM +(4,5 + OS - DS) * SM
where
Y is casualties
OF is offensive fire of the unit
DF is defensive fire of the infantry unit
FM is the fire modifier
OS is offensive shock of the unit
DS is defensive shock of the infantry unit
SM is the shock modifier
The 4,5 is the average result of a 0-9 die roll. Note that I have made the following assumptions:
- There are an equal number of fire and shock phases
- No terrain modifiers
- Both side have no leaders / have equal leaders
As artillery from the second row does half damage, the damage done by the inf+art unit is calculated by taking the inf damage as calculated by the above formula and add half of artillery damage, likewise calculated.
So in the next sections I will show the results of these casualty calculations of all four unit types against infantry.
Damage vs infantry
This graph shows how much damage each of the four units do againt infantry of the same tech level (all units are from the Western tech group). As you can see, the graph is quite different than the total modifier graph. Let me walk your through the graph era by era.
Era 1
All units' damage drop at tech level 11. That's because at that level Condotta Infantry become available, which has defensive shock 3, a great upgrade compared to the Longbow's defensive shock 1. Artillery at the end of the age is quite strong against infantry because of its many pips (8 in total vs 4 for inf and 1 for cav).
Also note that while cav shock modifier rises in this period, cav damage versus infantry remains level, as infantry gets more pips while cavalry remains the same.
Era 2
While at the start cavalry and artillery are equally damaging, cavalry makes a huge jump at tech level 22 as Latin Caracole Cavalry is available. The introduction of Highlanders Infantry hugely increase inf vs inf damage at tech level 28 (year 1636).
Cavalry is by far the most deadly unit versus infantry until tech level 35 (year 1700), where inf+art becomes as deadly as cavalry because of the introduction of both Caroline Infantry and Coehorn Mortars. Note that inf+art is much stronger than frontline art, due to that most of its damage comes from the inf part.
Era 3
Until tech level 43 (year 1735), cavalry and inf+art are equally dominating. With tech level 43 comes the Redcoat infantry, who has 4 more fire defense pips and 2 more shock defensie pips than its predecessor, Caroline Infantry. This means that all damage against infantry is drastically reduced, especially artillery.
Artillery becomes again very lethal with the introduction of Royal Mortars at tech level 47 (year 1750). Cavalry makes a huge jump at tech level 52 (year 1780) with Latin Cuirassiers (4 more offensive shock than before).
Square Infantry at tech level 55 (year 1790) again greatly reduces infantry casualties. Artillery becomes immensely deadly after that drop due to increasing fire modifier and the introduction of Flying Battery (+2 offensive fire compared to Royal Mortars).
Era 4
Surprisingly, from tech level 59 (year 1798) until the end, cavalry is much more deadly to infantry than inf+art or frontline artillery, even with the much higher fire modifier for artillery. That is because
- Napoleonic Square infantry has defensive fire 11 and defensive shock 9, meaning that it can defend itself much better against artillery than against cavalry
- Napoleonic Lancers have offensive shock 11, while Flying Battery has offensive fire 8.
Even with its fire modifier twice as high as cavalry's shock modifier, the balance is heavily in favour of cavalry.
Preliminary conclusion
To my surprise, the pips are much more important than I thought. While units from the same tech level differ very little from each other (Redcoats are not that much stronger than Bluecoats, for example), the pips do significantly determine casualties, having maybe even more influence than fire and shock modifiers.
In short, cavalry remains king of the battlefield until 1700, after which it's equal to inf+art. After 1798 cavalry again becomes the strongest unit by far.
Based on this, I cautiously conclude that on featureless terrain without leaders, artillery (in the form of inf+art) is never really worth its cost against infantry as cavalry always does more or equal damage and costs much less in both manpower and maintenance. Armies should have as much cavalry as possible with enough infantry to provide the Military Tactics bonus.
However, I need to do more analysis to back up this conclusion and maybe find out some new conclusion. As this takes a lot of time, I would like to know if there is any interest in doing so. If nobody cares about this, I'll just let it rest.
Any comments or questions?
Last edited:
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