A limited analysis of EU3 units

[Maginor]

Without more analysis, your prediction that pure cav will beat a mix of inf and art is just as much speculation as thinking that resistance to damage does play a larger role. At least you should not give advice on what to build based on these preliminary data.

Good effort, though. I would love it if you actually made the full analysis.

 

[knul]

Bad news everybody. It looks like my analysis is fatally flawed. Take a look at this:

In this graph you can see the damage cavalry does against infantry of equal tech level (red line) and the damage the infantry does against the same cavalry (blue line). Again, all Western units.

According to this, between tech 11 and 21 infantry does more damage to cavalry than vice versa. The same for level 34-35 and 43-51. And up until tech level 22, they do roughly the same amounts of damage to each other.

That can't be right. Remember, this is without terrain modifiers, the optimal situation for cavalry. This is ridiculous.

So basically it's back to the drawing board . Personally I think the culprit is reducing the die roll to its average value, because of the floor and ceiling effects in the casualties formula. But perhaps I made a mistake with the other assumptions, or the combat formula isn't correct in some way, or something else...

 

[Adam Smith]

Without more analysis, your prediction that pure cav will beat a mix of inf and art is just as much speculation as thinking that resistance to damage does play a larger role. At least you should not give advice on what to build based on these preliminary data.

Seriously? He has already made the stipulation that it was a "limited analysis," "I need to do more analysis" to verify this conclusion, etc. How many more times does he need to say that it is not a complete analysis of the units before he'll stop being badgered for it not being a complete analysis? The disclaimer is pretty obvious here...

Nice job, knul! Hope to see the "limited analysis" turned into a complete analysis someday!

 

[knul]

One other consideration, at least in the very early game, is cost-benefit. Infantry may look inferior but are 2-3 infantry units worse than one cavalry unit, assuming force limits and other factors are not barriers?

Cost-benefit is indeed yet another factor that complicates things. Basically I leave that to the reader: if I can show what units are powerful at what times and with which ratio, I think I would have accomplished quite a lot already.

Without more analysis, your prediction that pure cav will beat a mix of inf and art is just as much speculation as thinking that resistance to damage does play a larger role. At least you should not give advice on what to build based on these preliminary data.

Good effort, though. I would love it if you actually made the full analysis.

You're right, it was indeed speculation by me, I'm sorry if I made it appear otherwise.

As for the advise in the conclusion, I do state that it is all very preliminary and limited to flat terrain. No matter, as it appears the analysis was wrong all the time anytime.

 

[Maginor]

Seriously? He has already made the stipulation that it was a "limited analysis," "I need to do more analysis" to verify this conclusion, etc. How many more times does he need to say that it is not a complete analysis of the units before he'll stop being badgered for it not being a complete analysis? The disclaimer is pretty obvious here...

Nice job, knul! Hope to see the "limited analysis" turned into a complete analysis someday!

He still claimed that one could draw conclusions from it, which is what I addressed.

Edit: good job with the followup, knul!

 

[Gpeterse]

This reminds me of a dissertation proposal meeting I observed. There seems to be a lot of good ideas behind what you are trying to do, the statistics are much more complex than they first appear, and everyone (myself included) has an opinion that they are willing to voice.


I would like to point out that maybe your analysis isn't too flawed. It probably should contain four lines though;

Inf -> Inf
Cal -> Cal
Inf -> Cal
Cal -> Inf

Then when you consider artillery;

Inf -> Inf
Cal -> Cal
Inf -> Cal
Cal -> Inf
Inf + Art -> Cal
Inf + Art -> Inf
Inf + Art -> Inf + Art
Cal -> Inf + Art

To get a true sense of the value you would then need to decide how many times each of these situations arises and weight them accordingly. You would also need to be open to the idea that it may be more complex then it changing at one point from a certain type of unit(s) being the best to another type. It may switch back and forth repeatedly. Other factors such as cost may be relevant, complicated by the difference between initial costs, upkeep costs, and manpower costs. That doesn't even include the different tech groups and different units involved in each tech group or the random die roll(s) that can influence them.

Actually, this is more complex than the dissertation proposal. I like what you are trying to do and hope to see you progress further but it does seem you are tackling quite a task.

 

[Jazerus]

Perhaps you should also analyze inf-cav armies? In practice, most players tend to use those most of the time, and it would be interesting to see how much of a difference the combined arms makes - that is, mathematically, is there any situation in DW where having to have those extra infantry for the bonus actually reduces the overall capability of the stack because they're so much less effective than cavalry?

 

[knul]

He still claimed that one could draw conclusions from it, which is what I addressed.

Edit: good job with the followup, knul!

Point taken. I will be more cautious with my conclusions.

This reminds me of a dissertation proposal meeting I observed. There seems to be a lot of good ideas behind what you are trying to do, the statistics are much more complex than they first appear, and everyone (myself included) has an opinion that they are willing to voice.


I would like to point out that maybe your analysis isn't too flawed. It probably should contain four lines though;

Inf -> Inf
Cal -> Cal
Inf -> Cal
Cal -> Inf

Then when you consider artillery;

Inf -> Inf
Cal -> Cal
Inf -> Cal
Cal -> Inf
Inf + Art -> Cal
Inf + Art -> Inf
Inf + Art -> Inf + Art
Cal -> Inf + Art

To get a true sense of the value you would then need to decide how many times each of these situations arises and weight them accordingly. You would also need to be open to the idea that it may be more complex then it changing at one point from a certain type of unit(s) being the best to another type. It may switch back and forth repeatedly. Other factors such as cost may be relevant, complicated by the difference between initial costs, upkeep costs, and manpower costs. That doesn't even include the different tech groups and different units involved in each tech group or the random die roll(s) that can influence them.

Actually, this is more complex than the dissertation proposal. I like what you are trying to do and hope to see you progress further but it does seem you are tackling quite a task.

Isn't inf -> cav and cav -> inf the same deal?

It does seem the problem is even more complicated than I thought!

Perhaps you should also analyze inf-cav armies? In practice, most players tend to use those most of the time, and it would be interesting to see how much of a difference the combined arms makes - that is, mathematically, is there any situation in DW where having to have those extra infantry for the bonus actually reduces the overall capability of the stack because they're so much less effective than cavalry?

Well, the analysis was basically about 1 regiment vs another regiment (with inf-art considered to be a regiment, as it takes the same battlefront space as inf, art or cav), with the unspoken assumptions (yet another one!) that both sides have the combined arms bonus or both sides lack the bonus. So I dont analyze armies but units. Analyzing armies would increase the complexity even more, as there are quite a lot plausible armies to consider. And then I also should analyze smaller armies vs bigger...

Remember guys, I'm just doing this for fun, I'm not looking for a PhD project!

 

[StephenT]

It's a good analysis - especially once you work out the problem (if any) with your third graph.

However, I do note that when you simplified the calculations, the factors you left out are exactly those which help infantry more than cavalry. First, terrain, as many others have noted. Cavalry work well in the flat open steppe, but less well in the hills and forests of Western Europe. Second, though, you left out morale. Consider the following units, from the same period:

Caracolle cavalry versus Maurician infantry
Cavalry attack 2 versus infantry defence 4.
Infanty attack 6 versus cavalry defence 2.

Galoop cavalry versus Gustavian infantry
Cavalry attack 4 versus infantry defence 5.
Infantry attack 7 versus cavalry defence 2.

Arme Blanche Cavalry versus Redcoats
Cavalry attack 5 versus infantry defence 10.
Infantry attack 8 versus cavalry defence 3.

In other words, most of the time the cavalry will have its morale destroyed and flee the battlefield while the infantry are still standing. They'll do more damage while they're around, as your analysis shows - but that won't help them when they retreat with zero morale and get insta-killed by a stack of 1,000 men in the next province. In other words, it seems that the best army is a balance of cavalry to do the killing and infantry to soak up the losses and make sure the army still holds the field at the end of the day.

 

[knul]

It's a good analysis - especially once you work out the problem (if any) with your third graph.

The problem is not contained: the fact the cav-vs-inf graph shows such errors means that the everything-vs-inf graph is flawed as well, as both are based on the same calculations. There is apparantly something wrong with my model.

However, I do note that when you simplified the calculations, the factors you left out are exactly those which help infantry more than cavalry. First, terrain, as many others have noted. Cavalry work well in the flat open steppe, but less well in the hills and forests of Western Europe.

But leaving out terrain (i.e. assuming that we fight on plains) means that the situation is optimal for cavalry, not for infantry. If infantry does so well already on plains without rivers, then it should be downright devastating in any other situation. Basically, in almost all battles infantry would annihilate cavalry up to tech level 22. This does not line up with our observations in the game, so the model is flawed.

Second, though, you left out morale. Consider the following units, from the same period:

Caracolle cavalry versus Maurician infantry
Cavalry attack 2 versus infantry defence 4.
Infanty attack 6 versus cavalry defence 2.

Galoop cavalry versus Gustavian infantry
Cavalry attack 4 versus infantry defence 5.
Infantry attack 7 versus cavalry defence 2.

Arme Blanche Cavalry versus Redcoats
Cavalry attack 5 versus infantry defence 10.
Infantry attack 8 versus cavalry defence 3.

In other words, most of the time the cavalry will have its morale destroyed and flee the battlefield while the infantry are still standing. They'll do more damage while they're around, as your analysis shows - but that won't help them when they retreat with zero morale and get insta-killed by a stack of 1,000 men in the next province. In other words, it seems that the best army is a balance of cavalry to do the killing and infantry to soak up the losses and make sure the army still holds the field at the end of the day.

But now you make the simplification of leaving out fire and shock modifiers

I would love to take moral into account, but the formula in the wiki is a bit unclear (does morale use the result of the same die as the shock/fire roll? If not, is a separte 0-9 die rolled for morale damge? Or even another die altogether? Does terrain influence this?). Also, another thing that is a bit unclear to me is the exact way terrain modifiers work. Apparantly according to the wiki it is applied to both attacker and defender, yet in the game I always only see a penalty to the attacker.

Can anyone shine some light on these issues?

 

[Gpeterse]

"Isn't inf -> cav and cav -> inf the same deal?"

If you are measuring damage then Inf -> Cal would be how much damage infantry does to cavalry while Cal -> Inf would be how much damage cavalry does to infantry.

"Remember guys, I'm just doing this for fun, I'm not looking for a PhD project!"

Definitely not. It is interesting to figure this out but I think you can only accurately do this with Hierarchical Linear Modelling and Structural Equation Modelling. You can probably get close with some less complex forms of regression. There may be other ways but those are the methods I can think of.

 

[knul]

"Isn't inf -> cav and cav -> inf the same deal?"

If you are measuring damage then Inf -> Cal would be how much damage infantry does to cavalry while Cal -> Inf would be how much damage cavalry does to infantry.

Ahh. Then graph three combines inf -> cav (blue line) and cav -> inf (red line).

"Remember guys, I'm just doing this for fun, I'm not looking for a PhD project!"

Definitely not. It is interesting to figure this out but I think you can only accurately do this with Hierarchical Linear Modelling and Structural Equation Modelling. You can probably get close with some less complex forms of regression. There may be other ways but those are the methods I can think of.[/QUOTE]

Problem is that I have absolutely no knowledge or experience iwth these kinds of analysis. I'm considering just running simulations instead, with say a million battles between any two units. Should be good enough for our purposes and a lot easier to do.

 

[BootOnFace]

Woohoo! I was right all along with my Inf and Art-heavy armies! I always thought that the bonus from back-row artillery and the terrain modifiers would overcome the shock modifier of cavalry.

 

[Gpeterse]

"Problem is that I have absolutely no knowledge or experience iwth these kinds of analysis. I'm considering just running simulations instead, with say a million battles between any two units. Should be good enough for our purposes and a lot easier to do."

That would probably give you a rough estimate which would be be close to accurate. You probably don't need 1,000,000 simulations though. About 10,000 would probably get rid of any chance of randomly getting inaccurate results. :rofl:

Edit: 10,000 per upgrade level. Sorry.

 

[Neblogai]

One other consideration, at least in the very early game, is cost-benefit. Infantry may look inferior but are 2-3 infantry units worse than one cavalry unit, assuming force limits and other factors are not barriers?

True. But if you field an army similar in price- 30 regiments of infantry vs say 14 regiments of cavalry- the actual battle will be only 16 regiments of infantry vs 14 regiments of cavalry, with the rest of infantry waiting. So 2 regiments of cavalry at the sides will be flanked and damaged by 2 regiments of infantry, however, the rest of cavalry in the middle will have an easy day fighting weaker enemy. I will not go into details right now, but the end result is contravercial:
A) Army of infantry will suffer way more losses, so, more WE, and this will hurt manpower. Also, more WE from attrition.
B) Army of cavalry will lose both to morale damage and number of enemy troops- so unless safe retreat is possible, army risks annihilation.

 

[Blastaz]

True. But if you field an army similar in price- 30 regiments of infantry vs say 14 regiments of cavalry- the actual battle will be only 16 regiments of infantry vs 14 regiments of cavalry, with the rest of infantry waiting. So 2 regiments of cavalry at the sides will be flanked and damaged by 2 regiments of infantry, however, the rest of cavalry in the middle will have an easy day fighting weaker enemy. I will not go into details right now, but the end result is contravercial:
A) Army of infantry will suffer way more losses, so, more WE, and this will hurt manpower. Also, more WE from attrition.
B) Army of cavalry will lose both to morale damage and number of enemy troops- so unless safe retreat is possible, army risks annihilation.

Morale is king, and if you fielded that 30 inf as two stacks of 15k, or 5 of 6k you could use swaping tactics tactics to refit them as the battle, and pursuit, went on. and you could always make the inf stack 26 inf 2 cav, to double up your flanking advantage.

Of course as soon as you started worrying about cost you would have to take sliders (like aristocracy) into account as well...

 

[Neblogai]

Damn, didn't think of that. Still, I have no idea how much attack power is lost with losses (is it linear?). Besides, it would be too complicated for me to factor that in.
I guess we have to accept that this analysis is indeed quite limited and that any conclusions drawn from it must be watched with some suspicion.

I did not sum up the pips: I used the casualty formula from the wiki, as descirbed in the "calculating casualties" section. I even mention that I assume an equal amount of fire and shock phases, which is not structly true in almost all situations but was a necessary simplification.

AFAIK, losses reduce combat effectiveness of a regiment in linear way. Except, of course, the case of Inf+Art, as in this case Artillery would keep the damage, with only infantry suffering loss of combat effectiveness.

However, the problem with your chart is the value of Average roll. Basically, there are damage modifiers depending on roll and many modifiers affecting ability of cavalry to deal damage like terrain, unit defense, general. Most of them are or tend to be negative- such as high shock defense of infantry lowering the damage potential of cavalry. So, as you calculate this, you use shock defense of infantry, add an Average roll of +4.5 and get the damage potential. But all those modifiers make damage not linear to roll values, so I believe you are not using the real average of damage potential.

 

[unmerged(18418)]

Too much math for me. Can I just go with enough infantry to fill the front row, enough cavalry for a flank, and some art for back row damage?

 

[Gpeterse]

Too much math for me. Can I just go with enough infantry to fill the front row, enough cavalry for a flank, and some art for back row damage?

You could and that would be absolutely valid but only to the point of how often that occurs in actual play. Of course if it gets so complex that you decide not to do anything then nothing is learned.

If you really are interested in figuring something out about this subject narrow it down to the time period in EU3 that you like the best and test common scenarios you encounter when you play. It would be interesting to everyone else and helpful for you.

 

[Elcyion]

usualy its not 15k Cav versus 30k Inf cost wise u also have to apply Forcelimits and the cost to have 15 Inf over forcelimits i think u will find its cheaper to have 15cav then.