Sieges allow the more militarily inclined to force their way into a defended location, incrementally working their way through multiple layers of defenses. When a siege is first declared a calculation is done based on the types of defenses present at a location to determine the number of Stages a siege will have. This can be anywhere from a base value of one up to a max value of five. The following structures directly influence this: Wood Walls, Wood Castle, Fortress, & Citadel.
Battle types for sieges are dependent on the stage of siege, who is initiating the battle, and how many stages the siege is limited to.
If the attackers declare the battle, it will be a "Take the Walls" battle if it is stage 1, stage 2, or any greater stage that is not the final stage. If the battle is during stage 3 or higher, and it's the final stage, it'll be a "Storm the Castle" battle.
If the defenders declare the battle, it will be an "Urban" battle if the stage is greater than 1. On stage 1, defenders declaring battle will create a "Field" battle, as the battle will primarily take place outside of the walls.
In "Take the Walls" battles, defenders gain avoidance of ranged attacks based on the defensive structures present in that stage of the battle. In first stage, defenders gain benefits from walls, towers, castles, palisades, and moats. In stage 2, this is reduced to just stone walls, towers, and castles. Stage 3 grants benefits from the fortress. And stage 4, the citadel.
All types of walls and palisades grant +10 chance to avoid. Apothecaries, alchemists, all moats, and each seat of power grant +5 to avoidance. Fortresses and Citadels grant +50 and +70, respectively. This is primarily to simulate the battle getting more difficult as the siege line is pushed to the most defensible parts of the settlement.
For those used to battles prior to the siege update, it's important to note that defensive structures no longer affect your ability to absorb a hit, but your ability to avoid the hit altogether. It's also worth noting that this avoidance only applies when taking ranged hits.
Finally, the ability to reach the walls is limited. Only so many soldiers will be able to engage in melee at any time. Presently this is determined by the number of attacking soldiers. Defenders get 1/9th the number of attacking soldiers as Contacts, while Attackers get 1/10th. In the future, this will be calculated by the number of created and manned siege tools.
Storm the Castle battles bypass ranged combat altogether, skipping both the ranged phase and all ranged combat in the melee phases. Ranged soldiers that have melee capabilities will use them, while those that do not will be skipped.