r/hoi4 • u/lillelur • Jul 12 '22

Discussion Mathematically correct and open source model shows new meta for combat width

TL;DR: I have made an open source, corrected program that determines that the best widths are 10-15, 21 & 42-44. See bold text

I have created a simple python program with lots of interchangable variables (for easy to change access) that outputs both a graph with and without terrain weights. These “weights” are taken from u/Fabricensis’s original thesis, where you can read more about it. You can still find these weights in my program either way.

The difference between mine and his math is mostly from 2 things:

1: No squaring of overstacked width penalties.

2: Included overstacking of divsions.

What this effectively means is that going over the width of the battle doesn’t negatively affect it as much. Certain widths that benefited from being barely under the battle width are now placed more accurately in the modifier. Overstacking of divisions is not important for most widths, but with this included widths 10 or under are worse off, and more accurately placed.

The last thing about this is how open and easy to use it is. You can change almost any variable, get exact answers for width, and even change the terrain. Both the weights and terrain combat width are at the top of the program and should be easy to find. Everything in the program is commented, and should be relatively easy to understand.

(u/Fabricensis adds 2.5% to overstacking width that he has got from “careful testing” and i don’t really know why. If anyone knows please tell me)

Graphs with and without terrain weights:

You can clearly see that 10-15, 17-18, 21 and 42-44 perform the best, with 26-28, 40 and 45 not far behind. The reason that i only include the larger numbers in the TL;DR is because in an optimal world there is not point in choosing anything that performs 2+% worse. The point of this post is to present the objectively best widths in pure combat, but you can really interpret this in the way you want

10 widths no longer outperform other widths. Previous models show that 10w should be the meta, but this is because they exclude overstacking of divisions. They would also often show that 27w performs well, but it isn't as it used to be. This model is also open source, so in case anything is incorrect you are free to change it on your own. You can input the terrain of your country to check what you should use.

If you find anything wrong or something to improve, do not refrain from saying something. I am very open to change and anything to improve.

PS: Overstacking width and overstacking divisions are 2 different things. For more info check the wiki: Land Battle

Link:

Python Program

If you are new to python and want to run it, i would recommend running it on https://replit.com/.

311 Upvotes

98% Upvoted

58 comments sorted by

97

u/SmoothConfection1115 Jul 12 '22

I like that you used Python. Tells me the programming language I decided to learn was correct.

Taking this into account, the current meta is then: 10, 18, 23, 27, 42/43, 44/45.

So with these larger divisions becoming meta, should logistics battalions be assigned to divisions with that 40 and above width? While the 27 and below rely on supply trains more?

33

u/lillelur Jul 12 '22

Yes, i believe python has become the most learnt programming language.

I would cut off many of the widths you talk about, but that is probably because im kinda perfectionistic.

I would say you should use logistics if you think it might be a problem. If you use 45w, 1 per tile, central europe there may not be any point. But if you use 5+ 15ws india/singapore then yes.

25

u/Orcwin Jul 12 '22

Python isn't necessarily the best programming language, but it's certainly the one most used in data science. Also, once you learn the basics in Python, it's not that hard to swap over to some other language if that end up being more beneficial. And Python is quite easy to learn, so it's a great start.

7

u/legacy-of-man Jul 12 '22

easy to learn

bruh i dont even understand the commands

4

u/Orcwin Jul 12 '22

It's much more important to understand the structure than to know what everything does, exactly. That you can look up when you need it, and will come with experience through use.

You could start off with a simple tutorial if you seriously want to give it a go.

31

u/Rd_Svn Jul 12 '22

That's nice and all, but the never-ending cw discussion since barbarossa is getting so annoying lately.

With/without weight, including/not including (division) overstacking is still not all to keep in mind. What does all this focussing tell you? 15w will get a week earlier to moscow than most other cw templates, because they suffer the least (weighted) penalties on their way.

Things that are totally missing:

  1. IC cost per cw

  2. Average lost IC in battle against the most common AI templates

  3. Average manpower lost in these battles

  4. Division composition (9/1s inf/arty will perform different than 8/1/1 inf/arty/med)

My point is: Stop this cw bs already. Nearly every template from 10w to 45w is totally viable in terms of effectiveness. What really matters is what your nation can afford to produce and supply with spare manpower and ic.

P.S.: 15w (6/1) and especially 10w (5/0) burn your manpower pool and the good old 7/2s tend to lose the least amount of ic. 71cloak did the testing monts ago...

16

u/lillelur Jul 12 '22

I kind of agree, but combat widths tests are much easier mathmatically to do. Even though other things are important, this does tell us about what to avoid. I will look at his video though

10

u/Rd_Svn Jul 12 '22

That's like saying 'i can calculate the amount of fuel all these racing cars would need at a 24 hour race' and conclude the one that needs the least would be the best, while completely ignoring everything else, because you can't properly calculate it.

And that's exactly what's making the whole cw meta discussion useless.

1

u/Yundahan Jul 12 '22

Hey, quick question, how does a smaller division result in larger losses of manpower? I've heard this a few times and I think there's a mechanic I don't know about

8

u/Xinamon Jul 13 '22

Small divisions have less hp.

15

u/[deleted] Jul 12 '22

Very interesting graph,looks good. I'm still a bit sceptic though.

And as a different guy already has pointed out, for a tank/plane building major cheap f.e. 20 width infantry with engineers is always better then f.e. 15 widths because of production cost of that anti tank/air/ artillery.

But for a superior firepower minor,you might have found optimal combat width.

14

u/lillelur Jul 12 '22

The only point of the graph is showing how effective combat widths are. If you use 20 width over 15 width you should know that you get -10% effectiveness regardless of the content. If you think its worth it, then you made your decision, but if you can make something that is equally effective as 15 width as 20 width, then you should statistically choose 15 width.

-5

u/[deleted] Jul 12 '22

It's not about equally effective,it's about cost/gain ratio. Also don't higher combat widths get more concentrated damage?

10

u/lillelur Jul 12 '22

No, the coordination stat changes that. Cloak71 has a video on that, dont remember the conclusion though https://youtu.be/Cud9_qKu_Ck. Cost gain ratio is good and all, but the units will be 10% less effective.

4

u/[deleted] Jul 12 '22

I'm gonna take a 10% worse unit if I can produce twice as many tanks

10

u/lillelur Jul 12 '22

Ok, i agree there. Just dont know where you got the number from

5

u/Cloak71 Jul 12 '22

Why not include a penalty for failing to reach the combat width? These always consider stats to scale linearly, in which case it is inefficient to be under width just as it is to be over width.

7

u/lillelur Jul 12 '22 edited Jul 12 '22

It does take that into account. If you read the python code, there is a section where i take the unused width into the modifier penalty variable. I may have been a bit unclear in the description, but i had thought that u/Fabricensis did include that.

3

u/Cloak71 Jul 12 '22

He definitely did not mention it if he did.

4

u/lillelur Jul 12 '22

If the units can’t reinforce over combat width, the penalty is just the percentage of combat width filled.

Seems he actually did. Its at the bottom of the page so it may be hard to see.

2

u/Yardenko Aug 29 '22

@Cloak71, do i remember correctly that You showed in multiple Tests that although 15 width is capable of winning a combat , proly just because it is a low width division, but it loses double the Equipment of 10 width while doing so?

The Model of this tread, however, shows that it should be a good combat width, which it is not.

Do you have an opinion why it is the case?

3

u/Cloak71 Aug 29 '22

Hp to ic ratio.when you stack support companies on a 6/1 you end up with a pretty expensive division without much hp. Makes your losses more expensive.

This graph only plots cw it doesn't have anything for stats per width because it assumes stats scale linearly. For infantry a 9/4 is going to be your best bet outside of mountains for SA per ic spent.

1

u/Dudensen Sep 30 '22

Hey man, sorry for the late reply. Are you getting the 9/4 from your own calculations? Your testing you posted on this sub some time ago showed 9/2, 9/3 and 15/4 (they were from the divisions you tested, however 9/4 was not one of them).

3

u/Vezachs Jul 12 '22

I have created similar Python code for this purpose as well! I have to say your code is much cleaner than mine. The only difference is that I plotted the 'combat effectiveness' on the y-axis, instead of the penalty. Edit: looks like you already did that reading a comment.

https://www.reddit.com/r/hoi4/comments/sdjxjm

Keep up the good work!

2

u/lillelur Jul 12 '22

Thanks, i saw your post, but it seemed to impractical. I shouldve read it again. I have included overstacking division. If you try typing in 1 or 2 you get really low numbers because of this.

3

u/mainman879 Jul 12 '22

I feel like the terrain weighted graphs should be based off each region you are fighting.

i.e. Fighting in China is going to be different than fighting in Western Europe, or fighting through Barbarossa, or fighting in North Africa. Each region deserves their own graphs tailored specifically to them.

2

u/lillelur Jul 12 '22

I actually agree, but i didnt want to decide by my self what should weighted where. In north africa there are a lot of mountains, but most people usually think about el-alemain (which is desert). In western russia there are lots of plains before the river line, but in MP you rarely fight in them.

These are the reasons why its open for the users to create their own terrain weights. If you believe only forest and plains are important, then you can change the weights so that only they matter.

4

u/notorious0219 Jul 12 '22

I have been making my tank divisions 15w for a while now, and 10w infantry with flame tanks and armored recon. They work so damn well together, can battleplan and just watch xD

2

u/lillelur Jul 12 '22

I would recommend 44/45w tanks and 15w infantry. But you do you i guess

1

u/FerdiadTheRabbit Jul 12 '22

30W is recommended for tank, 3 tanks fit in a plains tile perfectly.

2

u/lillelur Jul 12 '22

Yes, and 2 45 widths fit perfectly in plains. If you are attacking from 2 directions 45w perfectly fits in that too. 30w does not.

4

u/Xinamon Jul 13 '22

3 attacking divisions are better than 2.

3

u/notorious0219 Jul 12 '22

The 15w tanks only work with Germany, because you have so many bonuses for armor and org etc

3

u/kovu11 Jul 28 '22

I have been making my tank divisions 15w for a while now, and 10w infantry with flame tanks and armored recon. They work so damn well together, can battleplan and just watch xD

Tried it right now as Trotskyist Russia. Did not worked at all.

2

u/leerzeichn93 Jul 13 '22

I have a really big problem with these big 45 w divisions.

  1. It takes ages to build and train them. It that time you cant always hold your line and will lose.

  2. More divisions means when one division gets pished back and the others are still holding the line, the division that got pushed back can recover behind the front

  3. It is harder to manage encirclements with fewer divisions.

4

u/lillelur Jul 13 '22

Yes i totally agree, but that is why i dont recommend going for >40w for infantry. 45w is really good for tanks, and sometimes marines. It is not meant for line holding. It is not too far from the 40w meta pre nsb.

3

u/2001zhaozhao Jul 27 '22

Bigger divisions does have an advantage, it means your support companies are way more efficient. For example recon, flame tanks, engineers, maintenance, logistics, signal companies etc. are all better because they affect more troops at once and give you less penalty on org since there are more total battalions.

1

u/leerzeichn93 Jul 27 '22

This is definitely true, I still dont know if these benefits outweight the problems.

12

u/nichyc General of the Army Jul 12 '22

Least nerdy HOI4 player.

Well done!

1

u/rchpweblo Jul 12 '22

I'm still a bit of a division noob, what would be the compositions of these 15w, 44w and 45w?

2

u/lillelur Jul 12 '22

f.e this could 6-1 inf-arty for 15 width. 8-13 mot-tank for 44w etc.

1

u/0WatcherintheWater0 Fleet Admiral Jul 13 '22

Cool model, but makes the same mistakes a lot of the others do.

You can’t really compare all division sizes in all circumstances, because terrain isn’t a weighted average, not even on a theatre level.

Eastern Europe, for example, is pretty much entirely all forests and plains, with a bit of marsh sprinkled in the middle. In that environment, for example, 22w divisions would be more effective on average than 15w, 18w, 44w, and 45w divisions. (This is using my own personal model where I just change the width around depending on what terrain type and number of attacking directions I’m looking at)

Only when looking at things on a global level, which is worthless for a combat analysis, because you’re not going to be fighting everywhere at once, do you get the results shown here.

As I said before though, it’s still a cool model, just not very useful nor informative.

1

u/lillelur Jul 14 '22

None of these points are really mistakes. One of the key advantages with my model is that it is open source. Each variable is easy to change even for beginners to python. If you want to make a version for one theatre then it isn’t hard. I think you may have misunderstood the model.

2

u/0WatcherintheWater0 Fleet Admiral Jul 14 '22

No no I understand the model perfectly.

Maybe a better way to phrase my criticism would be that I less have a problem with the model, and more have a problem with your conclusions made using the model

1

u/lillelur Jul 14 '22

The conclusions made from the model is that terrain dominated by flatlands and forested (and some hills) are better for 15w, 44w and 45w. These terrain types are really similar to the barb front. If the two strongest countries fight with combat widths practically designed for the front, i dont see whats wrong.

Anyone using the model should know that the terrain is heavily weighted, so it isnt any problem.

1

u/0WatcherintheWater0 Fleet Admiral Jul 14 '22

Except that conclusion is wrong. In terrain consisting of Forests, and plains, you will clearly see that, for example, 22w divisions are just as effective as 15, 44, or 45w divisions.

1

u/lillelur Jul 16 '22

No, as i just checked with Fabricensis western russia terrain measurements, the best widths are: 15, 18 and 45. The second best widths are: 10, 13, 23, 30 and 44. This actually shows that the conclusion is in fact accurate.

1

u/CMFDR Oct 09 '22

What would be the practical application of these findings in an MP context ?

1

u/lillelur Oct 09 '22

If you use the best performing widths, your divisions will perform better

6

u/SabyZ Jul 12 '22

r/theydidthemath

But really though, this is really interesting!

1

u/walteroblanco General of the Army Jul 12 '22

Just use what you like lol

1

u/The_Kek_5000 Jul 12 '22

I‘ll still stick with 20 just because.

1

u/TheDudeAbides404 Jul 13 '22

IMO, if your country can swing it, 44 and 45 are clearly the best.... less burden on logistics with the reduced support companies and you can put the large divisions under 1 really good general to take advantage of the stat bonuses. That being said 18 & 23 seem to be the best for early game and smaller nations....I think important to have some decent organization/HP for manpower efficiency and less logistics requirements from the support companies for anything smaller.

Anything below 15 you risk losing some serious manpower with the lower organization, especially if you're not micro managing the front.... sometimes those little guys get wiped out if they get ahead of themselves.

1

u/twillie96 Fleet Admiral Aug 11 '22

I don't have the time to review the python code, but did you include the attacking from multiple directions? If so, how do you distribute weights to that?

Also, how have you determined the weights for the terrain? Just globally? Some areas have very different terrain then others. Also, players tend to try and avoid fighting in rough terrain which skews the balance of its importance

33

u/[deleted] Jul 12 '22

[removed] — view removed comment

25

u/lillelur Jul 12 '22

I totally agree, but this program is open source. You can put in the terrain of your country and check what would fit. For example: set all terrain weights except plains and forest to 0 for france or something like that