I have a dumb question for both
@GAGA Extrem and
@jju_57 :
The number of support (non width/frontage) battalions is fixed. Bigger and smaller divisions can only each have one support version of ART, AA, AT, REC, and so on no matter how big they are.
The actual number of divisions does not seem to matter in combat; only width does. So, given the value of non-width battalions like ART and AT, why wouldn't I build a bunch of 5 width infantry divisions (say, 2xINF/1xAT + [ART/AT/whatever]) to maximize firepower per width? Obviously, their ORG is lower, but I am also going to put 4 times as many 5 width divisions into combat as 20 width divisions.
Back of the envelope calculations with the Soviet Union at 1944 (maxed out mass assault doctrine) show more ORG per width for the 5 width divisions than 20 width divisions, but less strength per width.
Is that the real disadvantage?
My interpretation is that such a small division is going to take oversized losses from hits to HP relative to ORG. Small divisions have a heavy penalty in terms of overall defense.
BASE_CHANCE_TO_AVOID_HIT = 90, -- Base chance to avoid hit if defences left.
CHANCE_TO_AVOID_HIT_AT_NO_DEF = 60, -- chance to avoid hit if no defences left.
The average chance to hit a division is 10% with defense, and 40% without. This means your smaller divisions are going to get destroyed far more easily in an even contest between equal production cost. There is a twist since you *should* have 4x the number of support brigades which at a glance, could give between 21-50 soft attack per support artillery (more with doctrines) and support rocket artillery which gives between 25-57 soft attack.
Some rough numbers from 1941 tech in my game with bltiz doctrines, which isn't the ideal path for this strategy.
2 INF brigade, 1 AT, support ART/AT/RART
94 soft attack, 46 hard attack, 84 defense, 17 breakthough, 51 HP and 25 org. 480-642 production cost
8 INF brigade, 4 AT, support ART/AT/RART
165 soft attack, 134 hard attack, 289 defense, 44 breakthrough, 203 HP and 48.2 organisation. 1092 -1632 production cost
I have no idea who would ever use 4x AT in the same divisions even if facing HARM but lets run with this example.
Defensively both divisions are pretty decent. Your call of less strength per width is not exactly true if you use an exact 4x copy since support provides minimal HP gains at best. If you can afford it, on the surface using a small width division seems good. The real problem lies in the defense/breakthrough stat. 84 defense is almost always going to be below the average soft attack coming in at a single division even with modifiers. I've seen my panzer divisions get up to 700+ in a good fight with nice modifiers. As such, the smaller divisions are going to be taking an average of 4x the damage relative to the large division once defense runs out. Offensively these small divisions would be even more wrecked by the high defense of the defender, and low breakthrough value making their relatively higher soft attack irrelevant while taking larger losses.
Before wading into the math of min-maxing a way to make soft attack support brigades relevant, I think in most prolonged battles width might be not the largest issue (against the AI, I'm sure people in MP might encounter far more troops). Instead, consider what the divisions are meant to do. I personally think that against a well prepared enemy the only way to breakthrough is using tanks. This is of course due to the oversized penalty of insufficient breakthrough when pitting two otherwise equal divisions against each other. The defender almost always wins.
The real question to ask is at what point does the extra soft/hard attack overcome the increased losses taken to end the battle faster (hence minimizing losses). In the above example, we see a rough increase in firepower per 20 width by approximately 94*4 / 165 for 2.3x soft attack firepower. In exchange, you have about 1/4 the HP and organisation per division (I believe organisation damage is to total rather than averaged organisation if it works like HOI3 but is averaged for display reasons). Given the same attacker hitting both, I think we'd see the small divisions dropping out much faster over time and taking higher losses as they do so. This could of course be different with better doctrines (+50% support company soft attack) but there are many disadvantages to using small divisions outside of the increased firepower per width metric. Lasting power, defense/breakthrough, and cost all play a part in determining a suitable path for your country to take.