Actually, tactics usually base on what kind of army composition you have, but the role of each type of units is usually the same.
Infantry:
They are usually the majority or second majority of your army if you are not going for a horse archer based army.
In normal circumstance, their only purpose is to hold the line and to be the meat shield, but not to be the main attacking power. They only push when enemy infantry formation is broken, unbalanced, or when you are trying to prevent AI from regrouping, especially in a big pitch battle where enemy has reinforcement.
I usually deploy them in a deep column formation in front of my archer line as it is much easier to maneuver than a spread out infantry line, and also you generally want your AI opponent to half encircle your infantry line so your archers can shoot from their back. The best formation fpr infantry when deploying in this way is Square formation.
Line formation is only used for attack, deployment or regroupomg after a chase since Shield formation and Square formation really slow down the infantry movement a lot. Personally, I found Shield formation to be the least used one, I only use it when enemy archer line are still strong after enemy infantry line is broken, and it also depends on if enemy archer line is distracted by your other types of unit. A quick line formation charge will work better if enemy archers are distracted.
Shock infantry. If you are really playing the infantry game, then shock infantry should be put under a different group. Despite I never use them in a separate group, I know they are extremely effective when charging normal infantry unit from testing. They should avoid be in the line of sight of archer units, especially when in small groups. Beside that, a line formation or loose formation charge on the front or the flank (like cavalry) seems to be a reasonable use of this type of unit, but I am not really familiar with the use of shock troop so I can't say for sure.
Archer:
They can be the majority of your army, but you need to be awared of the fact they need meat shield to protect them, because their close combat skill is nowhere as good as a dedicated infantry unit. Unless, you are going for a full Battanian Fien army, then it would be very different, because Battanian Fien can be used as shock infantry too.
I believe most players will agree that in this game, Archer/Crossbowman's role on the battlefield is to be the killing power behind the infantry square or line. They should stay at a distance from your infantry line, so your enemy won't rush straight toward your archer line which can be disasterous. They are best deployed in 2-3 ranks, better on a high ground and in Loose formation. This would maximize their firepower while minimize the damage they take.
Base on my experience, Crossbow is usually a better choice than bow unit, especially when fighting cavalry or horst archers. You only need one bolt to kill a horse archer or a horseman, but Crossbow usually don't have that much ammo which means they are not always that great for a prolong pitch battle, unless you intend to turn your crossbow into a melee unit after they exhaust all their ammos or a bow-crossbow mixed archers unit is usually better.
In case you are fighting Aserai or Khuzait where horse archer is a thing, I would usually deploy my archers on the left wing at the begining before pulling it back since most Horse Archer attack from that flank. Archer can be incredibly effective in repelling horse archer if horse archer comes without any support unit. Or, if it is in the mid of battle and enemy horse archers emerge and start to circle around your formation, then I would simply charge the archer line or have a second line of archer in the behind to deal with it. Horse archer usually circle the closest formation, so having a second line of archer at a distance can be effective.
Now, if you are playing Sturgia, then you should probably abandon the idea of having a native archer line completely, because Sturgian bowman sucks so hard. It would probably be more effective if you just treat it as trash infantry unit with fancy bow skills.
Cavalry:
Cavalry can be a decisive force on the battlefield, but it also can take heavy casualty if it is caught in the mid of infantry line, so how and when to use them is always a good question to ask.
Base on my experience and understanding, cavalry can play multiple roles on the battlefield, it can be used to break enemy formation, or as screening force, the role it plays depends on the circumstance and also your playing style. If your army composition has a great number of shock troops and heavy cavalries, a frontal or side charge to break enemy formation after skirmishing, following by the charge of shock infrantry at the centre is very classic.
Though it is probably more common to use it as a screening force, to protect the flank of your infantry line and also to flank the enemy infantry line or the archer line from behind or from the side. I sometimes would just let AI to take it over, since it does a better job than me when it comes to micro, the downside is just that AI would only use cavalry to protect infantry line but not archer line, and they don't charge archer line unless you move the cavalry behind enemy main line.
Personally, I like to put Cavalry in skein formation, or sometimes even shield formation, so the formation looks tighter, but I don't know if that will give our cavalry any buff at all, probably nothing at all.
Horse Archer:
Horse Archers are the best unit in the game without doubt. They are best used as a very mobile archer unit that can quickly deploy at the flank or behind enemy line, they can also be used as a cavalry unit when you are fighting against enemy cavalry unit. Their role on the battlefield can be harrassment (forcing enemy to attack you), screening (defending your flanks against enemy cavalry charge), fire support (supporting your archer line) and flanking (shooting arrows from the flank of enemy infantry or archer line).
However, I won't charge straight ahead my horse archers without the support of other units in a big pitch battle like AI did. They can be vulnerable when facing a numerical superior archer line, especially when caught by cavalry unit at the same time. Horse archers can also be vulnerable if they got trapped in the middle of an infantry or archer formation, so you always want to manually control them to keep minimize the chance of being caught by infantries or archers.
I usually split my horse archer unit into 2 formation, that's partially because I usually will have more than 100 horse archers in my army, but I think 80 horse archers in an army is enough for any army if use carefully. I don't like to deploy it at the centre in the middle of two archer formations for that would block the maneuverability of horse archers, but I sometimes put my horse archer behind my archer line to give my centre a stronger kill power, and also this way I wouldn't have to micro it (because it's really hard to micro everything when there's no high ground on a map). I will usually lead my secondary horse archer formation to harrass or to flank enemy infantry line.
Due to the difficulties of replenishment in the vanilla game, I am usually very protective of my horse archer unit, and that's why I am against the idea of a horse archer charge, unless I am fighting for Khuzait which I rarely do.
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The battle mechanic of Bannerlord is really just about if you can find a way to utilize each type of unit and let them play the roles they should play, and i think that's why it's fun game.
