I am late, so I'll keep this short: Here is a brief guide where I try to explain all units and what they are useful for.
[SPOILERS]
Abbreviations:
DEF - Defence - Used to deflect attacks when defending.
BRK - Breakthrough - Used to deflect attacks when attacking.
SA - Soft Attack - Used to attack soft targets.
HA - Hard Attack - Used to attack hard targets.
HARD - Hardness - Used to define how many % of the SA and HA of an enemy will actually be used against this division.
ARM - Armor - Average thickness of the armor for the division. If enemy can't pierce you deal extra damage and take less.
PIER - Pierce - Used to penetrate Armor, if you can't pierce your enemy, he will suffer less damage and he will deal more
SPD - Speed - Determines how fast the unit can move. High Speed gives a bonus to reinforce chance in combat.
MP - Manpower - How many men you need.
SUP - Supression - Used to keep partisan resistance in check.
REC - Recon - Used to determine which side has the initative, which gives a better chance to pick a good tactic.
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Infantry (INF) - Your basic combat unit. High DEF, but low stats otherwise - Use as main body for your army.
Mountaineer (MTN) - Slightly better BRK than INF, but also much more costly - Use these for mountain warfare.
Paratroopers (PAR) - Weak stats and limited in terms of design options - Use them to snatch provinces to delay an enemy or cut him off.
Artillery (ART) - Very high SA, decent BRK, excellent firepower per frontage - Use them to increase your division's SA and offensive capacity.
Anti-Tank (AT) - High HA and PRC - Use them to counter enemy tank divisions.
Anti-Air (AA) - High Air Attack, decent HA, minor PRC - Use them to shoot down enemy air units that attack in combat and get a bit of extra HA against enemy tanks, particularly LARM.
Rocket Artillery (R-ART) - High SA, decent BRK, excellent firepower per frontage. Almost the same as ART, but slightly better at offense - Use them to increase your division's SA and offensive capacity.
Cavalry (CAV) - Good SPD, high SUP, subpar stats - Weak and more costly version of INF that's faster and better at garrision duty - Use them to supress partisans.
Motorized (MOT) - High SPD- Faster version of INF - Use them to provide ORG for your tanks or for fast encirclement moves.
Mechanized (MECH) - High Hardness, good stats, high HA. Much stronger stats than MOT, but also way more costly and much slower - Use them to provide ORG for your MARM and HARM or to create semi-armored attack divisions.
Light Armor (LARM) - High SPD, high hardness, good BRK, low DEF, ARM, HA and PIER. Very low ORG. Weak against enemy armor - Use them for fast exploit divisions, to add BRK and a bit of ARM to your combat units or as breakthrough units against inferiour enemies.
Medium Armor (MARM) - Good SPD, High hardness, good ARM and PIER, balanced DEF/BRK and SA/HA, but low SA per IC cost. Very low ORG - Use them as Breakthrough units and to counter other LARM and MARM.
Heavy Armor (HARM) - Very high hardness, ARM, PIER and HA. Low SA per IC cost. Rather low SPD. Very low ORG - Use these to counter enemy tanks if you have too much IC for some reason.
Super Heavy Armor (SHARM) - Extreme Hardness, ARM, PIER and HA. Low SPD. Very low ORG. Insane IC cost - Use these if you are a maniac for whom HARM wouldn't drain enough ressources.
Self Propelled Artillery (SP-ART) - Extreme SA, terrible HA, bad BRK, okay DEF, lower hardness, ARM and PIER. Trade stats for SA. Excellent firepower per frontage - Use these to give your tank divisions a big boost against soft targets.
Tank Destroyer (TD) - Good HA and PIER, terrible SA, bad BRK, okay DEF. Trade stats for HA and PIER. Rather low HA difference to regular armor - Use these to counter enemy tanks of a higher class (LARM -> MARM, MARM -> HARM) or better tech level.
Self Propelled Anti-Air (SP-AA) - Mediocre AA. Bad DEF, BRK, ARM, HARD, SA, HA. Trades stats for AA - Don't use them - they are terrible.
Self Propelled Rocket Artillery (SP-R-ART) - High SPD and SA, decent BRK, excellent firepower per frontage. Lower ARM and HARD than SPART, but slightly cheaper - Use them as a lot-tech replacement for SP-ART.
Engineer (ENG) - Better dig-in, better SPD and defence for some terrain, better attack for invasions. Later models increase dig-in significantly and give minor benefits for fort, river and urban combat - Use these to make your units significantly stronger at defence, particularly when defending a river.
Recon (REC) - Better SPD in difficult terrain. Provides REC. Later models provide more REC - Use them to make your units a bit faster and pick better tactics slightly more often. Seems more important when your leaders are inferior (or just on par) to the enemy.
Military Policy (MP) - Improves SUP. Later models improve SUP bonus - Use these to supress partisans more efficiently.
Maintenance (MAIN) - Improved Reliability. Reduces equipment losses (including attrition and training). Later models increase reliability - Use these with your most costly divisions to reduce equipment losses.
Field Hospital (HOS) - Grants trickleback (returns some MP losses to your pool) and lower XP loss from combat losses. Later models improve trickleback and XP loss reduction - Use these to preserve precious manpower and boost XP gain from combat.
Logistics (LOG) - Reduces Supply Usage - Later models reduce usage further - Use these to reduce your supply weight and field more units inside a supply region.
Signal (SIG) - Increases Iniative, which givs a better chance to reinforce in comabt and improves planning speed. Later models gran more iniative - Use these to speed up your Battle Plans and to reinforce faster in combat.
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Division Design Notes:
(1) Always aim for a width of 5, 10 or 20. The regular frontage in combat is 80 + 40 per extra attack vector (from a different province). Exceeding frontge gives you signfiicant combat penalties. Design with width 11 or 22 if you plan to attach the unit to a leader with Offensive trait (-10% unit frontage).
(2) Support brigades don't increase frontage, so it's a good idea to add ART (and maybe AT, AA) to all your designs. They don't affect speed or hardness of a divsion, but do lower ARM and PIER.
(3) This means that a base design with 10/11 width has higher firepower per frontage than 20/22 (because you can squeeze in more support ART), but it also costs more equipment and Land XP to design (since most nations start with 8+ INF in their main template).
(4) Do not use pure Armor divisions. Armor has extremely low ORG and should be teamed up with MOT or MECH. Even when using the Blitzkrieg Doctrine Tree a pure Armor division will be barely more than a breakthrough unit that can't sustain combat for more than a few days.
(5) SP-ART has, by far, the highest SA per frontage (followed by ART). It also needs far less equipment per brigade, so you actually pay ~30 less for it than for a regular ARM brigade, even if production cost per unit are the same.
(6) Related to that: Support ART, AT, AA and R-ART need less equipment than Frontline variants (but also provide less stats). LARM, MARM and HARM also have different equipment numbers (60, 50, 40), so while '41 costs are 10/13/27 IC less per equipment, the total IC cost per brigade is 60 * 10 = 600 vs. 50 * 13 = 650 vs 27 * 40 = 1080.
(7) Remember you can use the DUPLICATE function to create new templates. Since every change to a template costs 5 XP per unit removed, exchanged or added (10 for support brigades), the duplicate function can save you a lot of Land XP. For example, if you want to have both LARM and MARM divisions with a few extra MOT, first finish your LARM template, then duplicate it and replace all LARM with MARM. That way you don't have to add the MOT units to both templates.
(8) Any unit can capture territory, regardless of size. So if you want you can build single brigade MOT divisions to swarm out and capture territory. Just pray you aren't stopped by a "real" division.
(9) ORG, ARM and PIER are calculated as an average (with some additional weights in it) of all your existing brigades. This means that adding a low ORG unit will lower your division's ORG, while adding a high ORG unit will slightly improve it (same for ARM / PIER).
(10) ENG combines extremely well with a Defensive trait leader (+30% digin), even more so when the country also has Grand Battleplan (+10 dig-in) or Mass Assault Doctrine (+5 dig-in). France in particular can pull off some amazing dig-in values if they manage to grab the '39 model before the outbreak of the war - I have seen values up to 59% (just don't ask me HOW it is calculated).
(11) When more comes to mind (or if there are some good questions in this thread), I'll add it here.
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Example Division Designs:
(Keep in mind these are just SUGGESTIONS to demonstrate how the system works, not necesarily the BEST DESIGNS). Support brigads are listed in [brackets].
Basic Main Combat Infantry:
10xINF [+ ART/ENG] (20 width)
Cheap and affordable, but not much else. Good on defence. Useful for poor minors.
Intermediate Main Combat Infantry:
7xINF + 2xART [+ ART/AT/EN] (20 width)
Same as above, but much better when attacking. Good for minors.
Deluxe Main Combat Infantry Division:
7xINF + 2xART [+ ART/AT/AA/ENG/LOG] (20 width)
Good all-around division that can fend off tanks on it's own and even inflict minor losses to air units. LOG means you can squeeze in more divisions per Supply Region (great for GER / SOV / USA), ENG gives a good advantage when defending. Good for majors.
XL Deluxe Main Combat Infantry Division:
8xINF + 2xART [+ ART/AT/AA/ENG/LOG] (22 width)
Same as above, just with an extra INF to get to 22 frontage. Good for majors with an Offensive leader.
Mass Assault Division:
10xINF + 2xART [+ART/AT/R-ART/ENG/LOG]
Adjusted template that adds a few extra INF divisions to make use of the -0.4 frontage reduction from the Mass Assault Doctrine tree.
Artillery Division:
4xINF + 4xART [+ ART/R-ART/LOG] (20 width)
Has lower ORG than regular Infantry, but more firepower per frontage. Good for breakthroughs.
Anti-Tank Division:
4xINF + 2xAT [+ AT/ENG] (10 width)
Great balance between SA, HA and cost. Keep them in reserve and use them in large stacks (8+) to halt enemy armored spearheads.
Anti-Air Division:
2xINF + 6xAA [+ AA/ENG] (10 width)
Low ORG, but high AA. Keep them as a reserve in the rear and strat redeploy them into important battles where the enemy airforce is harassing you.
Armored Spearhead:
2xSP-ART + 3xARM + 4xMOT [+ ART/AT/MAIN/LOG] (20 width)
Has great SA, good HA and decent ORG. A good spearhead and breakthrough division that can hold against counter-attacks.
Assault Gun Division:
4xSP-ART + 2xARM + 2xMOT [+ART] (20 width)
Incredible SA that rips through enemy Infantry, with (barely) acceptable ORG value.
Mixed Armor Division:
2xSP-ART + 3xARM + 1xTD + 3xMECH (20 width)
Mixed armor division that can deal with any situation.
Motorized Division:
7xMOT + 2xSP-ART [+ART/REC/ENG]
A fast division with decent speed modifiers. Even rivers won't stop these guys.
Security Division:
5xCAV [+MP]
Partisan supression unit
Garrison Division:
4xINF + 2xAA [+ENG/AA]
A defensive unit designed for island garrison duty where enemy air power is more threatening than tanks.
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