Quantitative Division Design

[dhelmet99]

I've put together a number of comparisons to help us quantitatively assess different division designs. I'm using the data for the base unit statistics as presented in the wiki. This ignores the effect of technology on the stats and practical knowledge on cost and time. To start with I will also be only looking at individual divisions, although stacks will be analyzed a bit later.

The baseline for comparison of all division designs is the classic triangular division of three infantry brigades. I will also limit the number of brigades to four.

We'll start with different configurations of infantry and artillery. The addition of one artillery brigade seems to be pretty cost-effective. We can't really evaluate the reduced number of infantry without taking the stacking penalty into account.

Now we can look at the various special forces type divisions. None of the tradeoffs here should be surprising to HOI2 veterans. Increased manpower and IC, with reduced attack stats, particularly hard attack.

Now we'll look at different configurations of garrison and militia units. The garrison unit is a reasonably effective defensive unit. The combination of three militia and one artillery could also make a decent cheap defensive unit. The others will be better evaluated in a stack.

I split out the anti-tank and tank destroyer to reduce the massive size. The low hard attack is one of the critical deficiencies of the militia unit (on top of low toughness and speed). The two TD version has a softness of 65% and therefore the CA bonus (assumed to be 30%) was applied to the attack and defense values for that division.

The next post will look at stacking infantry-artillery and militia-artillery.

 

[Athalian]

Nice one, mind posting the xls file?

 

[dhelmet99]

To evaluate full stacks of divisions we need to apply the stacking penalty. In the manual it states that the stacking penalty is approximately 1% per brigade. I've done some testing to assess this, and it looks fairly close most of the time.

I've run tests of leaderless units all the way up the chain of command in an attempt to eliminate the effect of leader bonuses. Keeping track of only the number of brigades attacking from a single province gave me inconsistent results so there may be something else affecting the stacking penalty. If anyone has a better way to calculate it than I'm presenting then please let me know.

The approximation I came up with was that:

Penalty = 1.8 * (# of brigades - 10)

The penalty should only be applied for 13 or more brigades as there appears to be no penalty at 12. This is at least close to the actual penalty even if it is not exact.

Applying the stacking penalty to a range of infantry-artillery based designs gives us some interesting results. All of the combat statistics are reduced according to the equation listed above. Not every possible combination of infantry and artillery possible in a 10 wide front is shown, but the excluded ones are all worse than the included ones. Note that the stats always increase with more brigades, but not nearly as fast as the costs. So we can cram more firepower using more brigades, but it isn't very cost effective.

It is perhaps more illuminating to extract out a few of the combinations and compare it to the full stack of three infantry brigade divisions. The three infantry and one artillery brigade combo performs fairly well from a cost-effectiveness standpoint. This is the type of stack I was leaning toward using anyway, but it is nice to have some quantitative justification for it.

We can do the same analysis with militia brigades to see if these can be paired with artillery brigades to make a super-stack. They can't. The cost effectiveness of this combo is not as good as the infantry version. That shouldn't be a big surprise.

We'll finish up with some of the same individual stacks compared to the three infantry brigade stack.

 

[dhelmet99]

Nice one, mind posting the xls file?

The xls I'm using is below. In the main sheet there is a note with some simple instructions. I use a shorthand to type in the different brigade names and automatically calculate the statistics. There is a lot of clutter of saved comparisons. Everyone should feel free to play around with it and post here (always nice to share).

http://www.mediafire.com/?sharekey=fd2447d9e8f5a04c8ef1259ff1b60e81e04e75f6e8ebb871

I don't have all the permutations figured out yet, but one other interesting observation is that one armoured and two motorized brigades makes for 66.7% softness and is therefore ineligible for the combined arms bonus. That was surprising.

 

[danoh]

A very cool and useful post, thanks.

It's nice to see what makes intuitive sense to me, like 3 infantry plus one arty brigade, stacks up so well. Playing as the Americans with the 5th brigade option I wanted to add an AA brigade for both AA and some hard attack, but I am not getting the combined arms bonus so I may need to put in TDs.

That the classic combo of one armored and two motorized brigades does not get the combined arms bonus is surprising. I've been trying to adjust the 5th brigade in my Ami divisions to get this bonus but a normal arty plus TD was still out of the sweet spot.

Off topic: May I ask if the combined arms bonus is calculated for each division, or for the total units in each attack?

 

[PanzerMan7]

That the classic combo of one armored and two motorized brigades does not get the combined arms bonus is surprising. I've been trying to adjust the 5th brigade in my Ami divisions to get this bonus but a normal arty plus TD was still out of the sweet spot.

Off topic: May I ask if the combined arms bonus is calculated for each division, or for the total units in each attack?

ur kidding right? so i have to put armor in with leg inf...

do mechs get CA with armor?

wut about 1 armor, 2 mots, 1 spart

 

[EntropyAvatar]

I don't have all the permutations figured out yet, but one other interesting observation is that one armoured and two motorized brigades makes for 66.7% softness and is therefore ineligible for the combined arms bonus.

1 armour plus 2 motorized shows up as 65% softness in the game, and definitely gets the combined arms bonus. You can even squeeze in a SP-ART and just squeak-in under the limit. If you are using light armour, however, you need two armoured brigades per division.

 

[unmerged(83949)]

Thanks, dhelmet. Is this the WW2 buff's equivalent of 'playing with your dolls again?'

 

[Athalian]

The xls I'm using is below. In the main sheet there is a note with some simple instructions. I use a shorthand to type in the different brigade names and automatically calculate the statistics. There is a lot of clutter of saved comparisons. Everyone should feel free to play around with it and post here (always nice to share).

http://www.mediafire.com/?sharekey=fd2447d9e8f5a04c8ef1259ff1b60e81e04e75f6e8ebb871

I don't have all the permutations figured out yet, but one other interesting observation is that one armoured and two motorized brigades makes for 66.7% softness and is therefore ineligible for the combined arms bonus. That was surprising.

2 medium armor, 1 sp art and one motorized has combined arms, soooo

 

[EnderV]

1 armour plus 2 motorized shows up as 65% softness in the game, and definitely gets the combined arms bonus. You can even squeeze in a SP-ART and just squeak-in under the limit. If you are using light armour, however, you need two armoured brigades per division.

That depends, as say L-ARM armour technologies lower the softness of mot. So you could increase the overal hardness to the point where it doesn't get the CA bonus.

 

[dhelmet99]

Thanks, dhelmet. Is this the WW2 buff's equivalent of 'playing with your dolls again?'

Knock on my door! Knock next time!

1 armour plus 2 motorized shows up as 65% softness in the game, and definitely gets the combined arms bonus. You can even squeeze in a SP-ART and just squeak-in under the limit. If you are using light armour, however, you need two armoured brigades per division.

That is because each technology level reduces the softness of motorized by 1%. Germany at the 1939 start has three levels of motorized technology, reducing the motorized softness to 87%, and therefore the overall division softness to 65%.

One of the major disadvantages to ignoring the effect of technology is missing things like that. Certain units only become available at certain technology levels and that can also distort the view when looking only at base statistics. There used to be a table on the wiki showing the change in unit statistics for each tech level, but it disappeared in the last couple of days. Does anyone know if that was because it was wrong?

 

[conanthelibrari]

And combined arms bonus is between 33-66% right?

 

[notger.heinz]

Another disadvantage of not looking at techs is that you miss out on the halved combat front of militia, which greatly increases the number of units you can put into battle.

Still, a good read.

3xInf+Art was my choice after my own analysis and will be.

 

[Darkrenown]

And combined arms bonus is between 33-66% right?

Yes.

 

[EnderV]

Does combat in general work the same way as it used in HOI2? I implemented combat the way manual suggests it should work (as a python script, for monte-carlo like testing ), but I'm pretty sure it doesn't work that way (or that I misunderstood).
If it did, two divisions, each with 1 INF brigade (same stats, for simplicity), with no efficiency bonuses/maluses would slog it out without end, as their SA is lower than D/T (which are the same, initially).
Of course, I have no idea how much difference the randomness aluded to in the manual makes.

V.

 

[EntropyAvatar]

Having defensiveness or toughness available only gives you a (high) chance to avoid damage from a hit, it doesn't guarantee it.

 

[TheLand]

Does combat in general work the same way as it used in HOI2? I implemented combat the way manual suggests it should work (as a python script, for monte-carlo like testing ), but I'm pretty sure it doesn't work that way (or that I misunderstood).
If it did, two divisions, each with 1 INF brigade (same stats, for simplicity), with no efficiency bonuses/maluses would slog it out without end, as their SA is lower than D/T (which are the same, initially).
Of course, I have no idea how much difference the randomness aluded to in the manual makes.

Defensiveness and toughness are only a partial defence. A number of attacks equal to the effective defence value do less damage than any further attacks.

I imagine the Manual simplifies combat a bit, the underlying algorithms are complicated.

 

[EnderV]

I know this was the case in HOI2, what I want to know is how much (if at all) are the formulas in HOI3 different.

 

[dhelmet99]

I know this was the case in HOI2, what I want to know is how much (if at all) are the formulas in HOI3 different.

It's difficult to tell. I have noticed that the modifiers (which are listed as percentages) are additive and not multiplicative. This means that if there is a 5% stacking penalty and the 50% night malus then the net effectiveness is 45% (100 - 5 - 50), for example.

Another disadvantage of not looking at techs is that you miss out on the halved combat front of militia, which greatly increases the number of units you can put into battle.

Still, a good read.

3xInf+Art was my choice after my own analysis and will be.

The reduced front for the militia really doesn't matter. The idea behind militia is that you can use them to replace infantry as the front unit very cheaply, while getting the power from the support brigades. My stacking analysis shows that this is not that cost effective. So yes it would be possible to cram 20 Mil and 60 Art into one space, and while that would give you more firepower (I think, I haven't checked stacking penalties for that high a number of brigades), the cost in IC, manpower, and officers would not justify using such a stack. There could be exceptions where you really need to power a breakthrough in a limited formation, but at that point you should probably use armour.

 

[dhelmet99]

I thought it might be useful to do some more general cost effectiveness studies of the various brigade types individually, and not just combined in divisions or stacks.

First, I took the base statistics and calculated the soft and hard attack values per thousand IC-days of cost. To combine these into a single metric I then took a weighted sum of the two, with 80% of the value coming from soft attack and the rest from hard. The assumption here is that most of the opposing units will be soft and therefore that value is more important. The result is below. The most cost effective unit is the garrison, and all the armored type units are bringing up the rear.

Obviously cost-effectiveness is not everything, as manpower, speed, softness, defensive values, and stacking penalties are important too. I think this does provide some useful information, just not in isolation.

To add to this I thought it might be useful to look at manpower effectiveness as well. The results are quite different.

The super heavy armored brigade is much better than any other on this metric. Not too surprising since it has beefy stats and little manpower usage.

Comparing the two lists it appears that the different kinds of artillery perform pretty well on both, as well as the armored car.

I know that this kind of analysis has its limitations. I am tempted to apply some more hardcore multi-attribute decision making techniques, but to do that I would have to apply subjective weightings to each of the brigade attributes, and that subjectiveness would kind of defeat the purpose.

Coming soon I will be looking at the different combos to make armored divisions. Then I hope to explore armored stacks, and compare those to the infantry-artillery stacks above.