How to compare unit builds

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I've seen a number of threads over time discussing the best design of individual units and nobody posting any proper build up of how to compare them. I suspect there is good reason for this as comparing units via mathematics rather than trying them in game is nearly impossible due to the impacts of breakthrough/defence and the concentrated attack effect from unit width. These things make it impossible to compare in a general sense but it is possible to compare on a more limited basis giving genuine insight into the expected consequences of different unit designs.

The basic thing to understand is that if you are comparing two units, imagining that they are fighting each other, then if neither breakthrough nor defence is exceeded the formula is a simple application of Lanchester's Square Law. Even this isn't easy to apply but ...
  • If you are interested in relative %age loss then the formula is Attack x Hit Points
  • If you are interested in 'winning' a battle then the formula is Attack x Organisation
This is therefore very simple and immediately reveals one important aspect of unit capability which is that attack strength applies both to optimising casualties and battle winning whereas HP and Org only apply to one or the other. [On the other hand once you bring tanks into it then the fact that HP and org apply irrespective of enemy hardness is relevant]

The above calculations are pretty useless on their own and require a bit more thought to derive something useful. For the purposes of further analysis I'm going to simply look at 2 infantry units, made of purely infantry and artillery, fighting each other with a fixed width (ie same width units rather than same IC or same manpower). I won't bother showing the spreadsheet but we can analyse a number of things for a fixed width division
  • Firepower (soft attack for inf vs inf)
  • HP
  • Manpower requirements
  • Industrial cost
  • Relative casualties for a combat - formula is SA x HP / MP
  • Relative material losses for a combat - formula is SA x HP / IC
This leads rapidly to some simple conclusions
  • For minimising casualties a 7/2 division is close to optimal. In actual fact a 4/4 is very slightly better but the actual optimum is a mix you can't construct but 7/2 gets us most of the reduced casualty benefit of adding artillery
  • For minimising material losses pure infantry wins hands down
  • For org there is a similar trade off BUT the conclusion is massively affected by doctrine bonuses
  • More artillery is more firepower and more chances of defeating enemy breakthrough / defence. Divisions with artillery are particularly effective against inferior tech / build enemy units.
  • The relative value of artillery declines through the war BUT only with modern equipment
The upshot of this is that by looking at the analysis you can establish why a particular unit is good or bad for a particular purpose. You quickly get some things you can say as global statements
  • The only real reasons for mixing artillery into your infantry divisions is to reduce manpower requirements and losses. You need to ask yourself whether this is more useful than building more tanks and/or aircraft. If you have plenty of manpower than why bother.
Not much of a bullet list but that seems to be it. Same as people are saying in the "is 7/2 no longer good" threads but without them mentioning about minimising casualties.

There are other interesting things that turn up when you do this sort of analysis such as replacing infantry weapons with better ones is far more important that manufacturing newer artillery. 1936 artillery is far from useless even late in the war whereas 1936 infantry weapons are well obsolete (1936 -> 1942 36% improvement in artillery, 100% improvement for infantry weapons)

It is worth considering that my analysis was for a fixed width, in a combat situation where there is scope for stacking more units the material advantage becomes more significant and it would be valid to compare units based on identical material cost. This pushes even more in favour of pure infantry.
 
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I'd like to see the spreadsheet.

I don't think the "Saves manpower" aspect actually applies. There are 2 parts to various costs, 'sink', and 'bleed'. The 7/2 (or a 4/4) will have a worse MP/HP ratio than the 10/0, so it will bleed more manpower. But the 7/2 costs less manpower up front, so it will 'sink' less. Your example also seem to assume that all attacks are defended either way, so the lowered defense of the 7/2 and 4/4 (and massively reduced breakthrough of attacker) doesn't seem them taking the amplified damage they most likely would in a live scenario. Which is fine, we'll slowly iterate towards a better system to try to quantify a division.

Sunk manpower can more or less be recovered whenever you want it. Delete or change the template, that manpower has been repurposed. 'Bled' manpower on the other hand is forever lost. There will be a point of total HP lost where the 7/2 is going to have sunk and bled a combined total of more manpower than what the 10/0 would have in combination of sunk and bled manpower for the same HP. At that point either one will have had the same impact on what remains in your pool, suffering more damage is going to mean the 7/2 has been worse for your pool.
 
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I'd like to see the spreadsheet as well.

Interested in the effects if Artillery had ORG and Inf Equip stats reflect a more historical value.
 

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"is 7/2 no longer good" threads but without them mentioning about minimising casualties.
not sure if you're just saying this in the context of 20w infantry or not, but 7/2s (and smaller, org-heaver divisions in general) tend to take more losses in combat in general.
 

Kanitatlan

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... so it will bleed more manpower. ...

To be clear, analysis (and experience) shows that the 7/2 division doesn't bleed more manpower. The combination of increased firepower and reduced manpower investment (ignoring defence) results in a 690/845 reduction in manpower losses as long as the division still has enough defence. This is a distinct difference and if combined with using 40 width division (14/4) can easily result in an approximate 33% reduction in casualties. I have verified this through multiple play throughs of "victory by attrition" using defensive positions to bleed the enemy dry. The downside is having to construct a defence that has enough org to hold the position which is far, far easier with a 10/0. Also, given the loss ratio you tend to achieve with that strategy the improvement is quite modest.

The real story of the analysis is that this is all you get from using a 7/2 infantry division.

not sure if you're just saying this in the context of 20w infantry or not, but 7/2s (and smaller, org-heaver divisions in general) tend to take more losses in combat in general.

The use of 40 width divisions makes a further difference but the main reason for posting the thread is to highlight that there are tools for analysis and they can lead to fairly clear conclusions in some cases - as in, all you really get from a 7/2 division is slightly reduced casualties and this is unlikely to compensate for the shifts in other aspects of the division.

To expand on the casualty ratio above - the material loss ratio (based on an arbitrary time selection) is 725/519 - ie 7/2 divisions cost significantly more IC to reinforce after battle even if the manpower loss is reduced.

By the way, the reason I haven't posted the spreadsheet is that I'm using a fairly dynamic excel spreadsheet where you can easily adjust parameters to compare different things and single snapshots aren't particularly informative.
 
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To be clear, analysis (and experience) shows that the 7/2 division doesn't bleed more manpower.
Without supports, a 10-0 loses 40 manpower for each 1 HP of damage it suffers. A 7-2 will lose 45.4. A 4/4 is 58.5. Against a constant stream of equal HP loss, the arty mixes bleed more manpower. Two key parts of that is constant, and equal HP loss.

In an "infinite combat" where both sides have enough reserves to be constantly cycling in an out, or if there are fixed intervals of combat and non-combat, the constant applies. In a more practical sense though, the arty mixes have more attacks and will end a combat sooner by kicking the enemy out. Our theoretical enemy would presumably take the same span of time outside of the combat to re-org and then attack again against any pattern of our divisions, so the trend of the arty mixes is that they will be spending comparatively less of the time inside of combats, and so will avoid taking some damage.

Equal HP loss is assumed as long as either side has enough defense/breakthrough to minimize enemy hit rates. But the arty mixes having less defense, and with later techs and certain doctrines possibly less breakthrough as well, against enemies that have particular levels of firepower they can be suffering additional damage.
I have verified this through multiple play throughs of "victory by attrition" using defensive positions to bleed the enemy dry.
This relies on a couple of things.

It relies on the AI being the AI and doing stupid AI stuff. Endlessly attacking with infantry and grinding away all of their manpower and production is absolutely stupid and is specifically not the sort of things we should expect a competent rival power to be interested in doing.

We should also be comparing the percentage of the remaining manpower pool that is being lost on either side. The side that is losing a greater percentage of its pool is going to run out first. It doesn't matter if you're killing them 40:1 if they have 50x the pool (and can sustain the production loss), you're going to run out of manpower first.

It also relies on the attacker in this case actually suffering more damage/manpower losses than they are inflicting. This is really an extension of the first point, AI mindlessly grinding away their infantry. Infantry specifically don't have much breakthrough, hardness, or armour. If you're attacking with them, they will tend to suffer a lot of damage. But if they attacked with a high-armour, high-hardness division with enough breakthrough and more attack than the particular arty-mix can defend against (like a mek/MRA), I'm sure the defender would actually be suffering more manpower losses than the attacker would.

The real story of the analysis is that this is all you get from using a 7/2 infantry division.
Which I think means that this sort of analysis is inappropriate. Of the different factors that limit the force you can apply (manpower, production, supply, width, research), manpower is often the least limiting. It also practically ignores the operations layer, where breakthroughs, overruns, and encirclement will often be able to achieve massive kill/death ratios, because you're destroying the entire division/army without having to repeatedly fight against them. These sorts of alpha changes to the balance of force on the front can lead to destabilization where the enemy may be capitulated sooner and without having to "bleed the enemy dry".
 
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Kanitatlan

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The analytical balance of 7/2 vs 10/0 is the trade off between the increased firepower of the 7/2 versus the higher hit points of the 10/0. The 7/2 takes casualties slightly faster than a 10/0 would be inflicts casualties even faster so that it ends up ahead. The combat time is shortened for both divisions due to what amounts to an increased combat intensity.

The main point I was making about the specific division type 7 inf + 2 art is that the only real benefit it brings in the "I've got enough defence" comparison is reduced casualties (and less use of manpower). This doesn't really compensate for the other characteristics such as increased material cost and losses along with the impact on defence and org. In many cases the role of the infantry division may simply be staying power and oddly enough if the task is "hold the enemy for 24 hours" the 10/0 takes fewer casualties.

As you can see, every time you go back and look at it the 7/2 looks less good and this reflects my point, which is that the only thing it does for you is potentially reduce casualties.
 

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As you can see, every time you go back and look at it the 7/2 looks less good and this reflects my point, which is that the only thing it does for you is potentially reduce casualties.
I think you're ignoring the benefits of concentration of force. As an example, by concentrating attacks:combat width 4 7/2s could beat 2 entrenched 10/0s in a combat, whereas 4 10/0 might not, even if neither side is critting. And being able to take provinces at all, regardless of how bad the trade is, is key to getting encirclements, and also obviously necessary for winning wars.
 

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I think you're ignoring the benefits of concentration of force. As an example, by concentrating attacks:combat width 4 7/2s could beat 2 entrenched 10/0s in a combat, whereas 4 10/0 might not, even if neither side is critting. And being able to take provinces at all, regardless of how bad the trade is, is key to getting encirclements, and also obviously necessary for winning wars.
You are perfectly correct that I am ignoring concentration of force. If you are going to attack with infantry than 7:2 is not a bad choice but it does require some significant force superiority. Using 14/4 divisions is better because it expands the concentration of force. If the enemy is basically rubbish units it is possible to get enough breakthrough for infantry attacks to be decently effective and the mixed inf/art division is the best tool for that job.

The real problem is I'm just trying to provide some hints on force analysis and in actual fact the full story requires a massive essay.
 

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Using 14/4 divisions is better because it expands the concentration of force.
You actually would have more attacks/combat width with 7/2s due to support companies, but I get what you mean (even though I was referring to attacks/width)
The real problem is I'm just trying to provide some hints on force analysis and in actual fact the full story requires a massive essay.
You have repeatedly said that the only reason to use arty in your infantry is to minimize casualties, despite it having the opposite effect in some cases (when you consider the opportunity cost - build tanks instead). You have also said that, conversely, pure infantry is better if you care about materiel losses, despite the opposite being true in many cases (when 10/0s can't break and 7/2s or 14/4s or 11/6s can).

While I think your math itself is very helpful for lending perspective to interactions between different templates, I don't think that your conclusions are helpful at all.
 

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You have repeatedly said that the only reason to use arty in your infantry is to minimize casualties, despite it having the opposite effect in some cases

The conclusion from analysis is that for a 20 width inf/art division the combination of firepower and manpower present in a 7/2 division results in lower manpower losses to the unit per hit point of damage inflicted on the enemy. However, it does this by having higher firepower which increases the rate of combat. If your objective is to hold for a fixed time whilst other operations take place then a 10/0 has advantages as it generates a slower rate of combat and suffers losses at a slower rate.

In the case of material losses the divisions with artillery always take more losses due to the expense of the artillery losses.

This sort of thing reveals just how complicated unit analysis can be. The simplistic analysis in the first post is intended to provide some guidance on how to start analysing units. Whilst I would quite like to write a 50 page essay on the full details of unit analysis, I am finding the prospect more than a little daunting.