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 The Basics
In a battle, each side has up to three flanks. These flanks will generally fight separately against the same flank on the opponent's side. Each flank has a commander, and its own units. To have more than one flank you need multiple armies, though they can be merged into one. An army composed of the soldiers from a church, city, and castle in the same province will suffice, but a single mercenary band will not.
Combat is divided into three phases:
All battles will start in the Skirmish phase. This is when archers and horse archers excel, and they will be the only ones doing any major damage. After a few days, it will switch to the Melee phase, where melee oriented units like heavy infantry and pikemen excel. Note that flanks do not necessarily have to be in the same phase as each other, and they'll usually enter Melee at slightly different times. When the morale of a flank reaches 25%, they will start retreating, and combat will switch to the Pursue phase. This is where light cavalry truly excels, but heavier cavalry does well as well. After 5 days, the flank will be removed from combat.
When a flank no longer has an equivalent flank to attack, it will help another flank instead. It will now also get a flanking bonus of 10%, meaning it does 10% more morale and troop damage. The enemy flank will now be under attack from two flanks, thus taking more damage. However since the stats of all the troops in a flank are stacked together it is almost always better to put your entire army into a single flank.
 Combat Statistics
Each unit type has base statistics. These statistics are further modified by certain technologies and buildings, but generally they'll be quite similar for both sides. The base stats are as follows, in x/y format meaning attack and defense:
Attack controls how much damage a unit does, while defense controls how much damage it takes. The higher the morale of a unit, the more damage is needed for it to retreat.
As you can see, only two units are any good at skirmish, archers and horse archers. This means that an army with many of these units has the advantage of damaging the enemy severely early in combat, which can at times make the difference between victory and defeat. Further, heavy infantry and cavalry excel at melee, which is generally the largest part of combat. They're also not very vulnerable to the skirmish phase, and as such they can often win you the battle. Light cavalry on the other hand are only good at pursuit, so are as such only useful if you've already won the battle and want to inflict further casualties.
For the most part you and your opponent will have similar unit compositions, so this generally won't come into play much. However, when hiring mercenaries you should pay attention to what units you're actually hiring, and try to avoid mercenaries that are high on light infantry and archers, instead going for heavy cavalry and infantry.
Further, commanders have a moderate effect on combat. Every point a commander has in the martial skill increases the damage of his flank by 2%. As such, you should before important battles ensure that your flanks are using your best commanders so as to maximize your enemies' losses and reduce your own.
 Improving Your Army
There are five ways to improve your army:
- Construct army buildings, covered in further detail here
- Research technology, covered in further detail here
- Strike the right balance between levy law and vassal opinion, covered in further detail here
- Improve your commanders
- Make your vassals happy
As the rest is covered in other installments, I'll focus on the last two points. The first, improving your commanders is relatively simple. First, you need at least Limited Crown Authority, as that enables you to assign commanders. Once you have that implemented, you can invite high-skill commanders to your realm, either via inviting them normally and giving them some land or a councilor position, or by marrying them into your realm. Then you just have to make sure that the best possible commanders are appointed before any major battle. This could improve the damage your army does by several percent, making it easier for you to win battles, and reducing your losses. It will also decrease how much attrition you take, and you'll also get someone great for the Marshal position. This tactic is seldom necessary for a large realm, as you'll then generally have good commanders available already, just make sure to assign them.
Second, you can make your vassals happy. As mentioned in the installment on levies, the higher your vassals' opinion of you, the more levies they'll provide. As such it can be a good idea to send out gifts and honorary titles before raising levies so as to maximize how many troops you can raise.
There are certain tactics you can employ to improve how well you do in war. Many of these tactics are common sense, but I'll mention them anyway.
- Attack a weakened enemy. If your enemy is deeply unpopular with his vassals, has just lost an offensive war, is dealing with a rebellion, or is fighting a war over a different CB, you can beat him more easily. Be aware, however, that a war against a rebelling lord will end if his rebellion ends.
- Raise only the vassal levies you need to avoid unnecessarily angering your vassals. If you only need the troops of a single vassal to fight a war, only raise those troops. This vassal will now be the only one getting annoyed at you, while the rest will continue to be happy. The other vassals' levies can then be raised later if ever needed. If you're rich enough to support it, you can also consider using only your own levies and retinue, as then no one will be getting annoyed with you.
- Raise vassal levies in the best location. You can raise your vassal's "liege levies" in any county belonging to his sub-realm. This is especially powerful if you plan ahead by giving each major vassal a well-placed county (coastal or near your enemies). You can even disband a levy in one place and immediately re-raise it in another.
- Consider hiring mercenaries. They can pay for themselves if they allow you to win a defensive war, or allow you to storm castles rather than slowly siege them.
- Bankrupt your enemy. His armies will lose a quarter of their morale, and his mercenaries may turn on him or even join you. You can drain your enemy's cash reserves and deny him income by capturing his demesne holdings. (His yearly income and expenses are shown if you hover over his cash balance, and his budget details are visible in his demesne screen.)
- Target part of an enemy's army while it is split up. While you might not be able to defeat the entire enemy army at once, you're likely to be able to defeat half their army, and the rest is then easy to mop up.
- Bait enemies into taking attrition. Using an army smaller than theirs you can continuously pull back, leaving them in a province where their units will slowly die. Only works against large armies or when playing as pagans. Does not work against the attrition-free doomstacks of the Hordes.
- Bait enemies into attacking smaller armies, then send in reinforcements. Immediately once combat has started, send in your larger army. If the enemy can't see your reinforcements due to fog of war, even better: you can have your reinforcements already be on the way by the time the battle begins. This means you won't have to spend half an eternity chasing the army down, instead being able to quickly destroy it in a single or a series of decisive battles.
- Bait enemies into attacking fortified positions. Ideally, your army is on a mountain, and across a major river from the attacker.
- Avoid attacking across rivers and into hills. You'll get a moderate combat penalty, which could make a major difference. These penalties don't matter much if you outnumber the enemy by a lot, though.
- Avoid splitting your army up into pieces smaller than the total size of the enemy army. If you do, you risk losing a large part of your army, and being reduced to a position where you can no longer fight back. If you have a really good reason to do so, go ahead, but make sure you keep the rest of your army close. (You can see your enemy's army size in the ledger, or the realm tree accessible from his portrait.)
- Use Organizers to move armies faster. Useful for gathering your levies, chasing down scattered enemies, and beating enemies to defensive positions.
- Utilize the mobility ships give you. You can transport units much faster by ship than on land, which can enable you to quickly strike at isolated enemy armies, then retreat back to sea.
- When being chased, consider sacrificing a small number of men to let the rest escape. Let a few men remain while the rest go to another province where they can hopefully recover or merge with a larger army. Make sure you leave more than 1/25 of the enemy army, as anything less than this will be destroyed instantly, and as such will not slow the enemy's advance down.
- Disband any levies that are doomed. You'll lose half your men if not in friendly territory, but you won't lose warscore. And you can re-raise the levies immediately in another location.
- Order early retreats when losing a battle. Simply order your army to move to another province, and it will begin retreating regardless of morale.
- Consider what will give you the most warscore. You may be able to get to 100% and enforce demands without certain battles or sieges, or even without really appearing to have the upper hand.
- Winning battles gives warscore based on the number of enemy soldiers killed. Defeating the entire enemy army will net 75% warscore.
- Occupying enemy territory can give up to 120% warscore, with significant bonuses for the enemy's demesne (which tends to be easier to capture due to depleted levies), capital, and the territory contested by the CB.
- Continuously occupying territory contested by the CB will slowly add warscore.
- Occupying all enemy holdings gives automatic 100% warscore.
- Capturing the enemy in battle or siege give automatic 100% warscore. His portrait will tell you which army he is leading, if any.
By outmaneuvering or overpowering the enemy you'll be able to win most battles, and eventually the war itself. Overall my tips are these:
- Construct buildings to increase the size of your army. More detail in the guide on construction
- Research relevant tech, it can give you the edge you need. More detail the guide on technology
- Appoint good commanders. Gain good commanders through marriage and invites
- When hiring mercenaries, go for heavy infantry and cavalry
- Keep your vassals happy
- Strike the right balance between levy law and opinion. More detail in the guide on levies
- Don't raise more troops than you need
- Ambush the enemy if possible
- Slow down the enemy's advance by sacrificing units if needed
- Go for the wargoals first
- Go for 100% warscore ASAP
- Divide and conquer
- Utilize the mobility ships give you
- Avoid attacking across rivers and into hills