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Combat

Combat is the solemn duty of any good knight or mercenary, and until we have a working fashion module, it'll be what players spend most of their time doing. So let's get it right!

Attacking

When the player clicks the Attack button, initiating an attack animation, we run a shapecast in front of the player character. If there is an intersection between the attacker's hitreg and some other actor's hitbox, we calculate input precision. Then comes the skill check algorithm.

Skill check algorithm

Broadly speaking, the flow goes like this:

  1. Calculate accuracy based on:

    1. The attacker's melee skill check
    2. Multiply by weapon term (small knife: 2.0, long hammer: 0.5)
    3. Multiply final value by input precision

  2. calculate dodge_defense:

    1. Calculate armor_dodge_term from their armor.
      1. This isn't actually the weight of the armor; it's based on articulations on joints.
      2. Full-plate gives 0.6, full-body chainmail is 0.8, and unobstructed joints is 1.0.
    2. Calculate encumbrance_term from total weight versus leg-strength
    3. Multiply a dodge skill_check by armor_dodge_term and encumbrance_term

  3. calculate block_defense:

    block = defender.skill_check(block)
shield = defender.shield_bonus()
    1. shield_bonus() = 0 for weapon; 1–2 for a small shield; 2–4 for normal; 5 for pavise

$$\mathrm{defense}(\mathrm{shield},\mathrm{block}) = 5 \cdot \left(1 - e^{-\tfrac{\mathrm{shield}+\mathrm{block}}{2}}\right)$$

  1. Calculate defense from input reflex:

    if defender is parrying:
		defense = block_defense * 1.5 * input_reflex
elif defender is dodging:
		defense = dodge_defense * input_reflex
else:
		defense = block_defense

  2. Attack value is accuracy - defense

  3. If attack is less than 0, miss and apply surplus defense as unbalance penalty to attacker

  4. If attack is between 0 and 1, multiply attack force by attack

    1. 0.1 barely grazes the opponent, 1 is square-on, 0.5 is a glancing blow

  5. If attack is above 1 and the attacker's weapon is precise, attacker now attempts to bypass armor with surplus attack.

    1. An armor's "coverage" is subtracted from the surplus attack to obtain the "critical attack"
    2. If critical attack is greater than 0, attack bypasses armor completely and its final damage is multiplied by this number
    3. Though not necessarily relevant for the MVP, critical attacks are relevant even when targets are unarmored because this allows the damage multiplier to exceed 1.0, allowing for instantaneous stealth one-hit-kills.
    4. If a critical hit cannot be made, then attack just stays at 1.0 for a direct hit

Incapacitation

A character's incapacitation represents the sum of all disabling effects on them and corresponds to the state of their animation. When above half, they are "staggered" and each additional 1% of incapacitation causes a 2% penalty to movement and attribute checks, and when above 100% they are completely incapacitated (which also causes knockdown). Most negative effects that a character has can affect their incapacitation, past a certain threshold. Your incapacitation is displayed as a wheel in the center of the screen. If it is at 0%, the wheel is invisible, and as it increases it starts from 12 o'clock and extends as an arc clockwise. Each factor that contributes to incapacitation has a different color to differentiate them.

Each of the following factors range from 0% to at least 100%.

Imbalance (white)

Halbe: This was written in terms of energy, but might make more sense in terms of momentum.

The most direct way of being incapacitated, attacks which impart force on your character or losing your footing in difficult terrain can cause imbalance. Imbalance constantly recuperates. Your mass and the directness of an attack determine how much imbalance you actually take, and your agility determines how quickly it is regenerated.

# use these for calibration
# direct hits by trained warrior in joules: halberd ~120, longsword ~70, shortsword ~30 dagger ~20
# longbow arrow 80
# kg: armored knight ~90, goblin ~40
const STAGGER_RESISTANCE_JOULES_PER_KG = 10
const UPPER_MUSCLE_KG_PER_STRENGTH = 5
const MUSCLE_KG_TO_JOULES = 2
const UPPER_MUSCLE_KG_TO_PUNCH_KG = 0.1

# attack_directness is 1.0 if square-on, 0.01 barely grazes, in-between is a glancing blow of some magnitude
fn balance_damage(attacker, defender, attack_directness):
	# todo: equation for calculating striking mass for a given weapon, for now its fixed
	# balance_factor is 0 for a weapon balanced at the hilt, 1 for a weapon balanced at the tip
	attacker_upper_muscle_kg = attacker.strength * UPPER_MUSCLE_KG_PER_STRENGTH
	punch_kg = UPPER_MUSCLE_KG_TO_PUNCH_KG * attacker_upper_muscle_kg
	striking_mass_kg = punch_kg + attacker.weapon.mass_kg * (1 + attacker.weapon.balance_factor * attacker.weapon.length_meters)
	joules_of_attack = attacker_upper_muscle_kg * MUSCLE_KG_TO_JOULES * striking_kg
	imparted_joules = attack_directness * joules_of_attack
	resistance = STAGGER_RESISTANCE_JOULES_PER_KG * defender.mass_kg
	defender.imbalance += imparted_joules / resistance

Exhaustion (grey)

Exhaustion represents how out of breath your character is. Most actions will not actually exhaust faster than it recuperates, but climbing, sprinting, and fighting with heavy weapons, shield, and armor can.

const BREATH_RECOVERY_PER_ENDURANCE_PER_SECOND = 0.002
# someone with 2 endurance (poorly fed Napoleonic soldier) can march 1.2m/s all day. Therefore a simple linear ratio between velocity and breath must be about:
const BREATH_PER_METERS_PER_SECOND = 0.0034
 
fn update_stamina(player):
	player.breath_damage += dt * character.velocity * BREATH_PER_METERS_PER_SECOND
	player.breath_damage -= dt * character.endurance * BREATH_RECOVERY_PER_ENDURANCE_PER_SECOND

Pain (pink)

Injuries are a source of constant pain. Pain is divided by will.

$$ \mathrm{pain}(\mathrm{damage}, \mathrm{will}) = \frac{\mathrm{damage}}{\mathrm{damage} + \alpha\cdot\mathrm{will}}\cdot e^{-\beta\cdot\mathrm{will}};\ \alpha=0.5,\ \beta=0.2 $$

fn update_pain_factor(character):
	damage = character.body_parts.iter().map(|p| p.damage).sum()
	character.pain = pain(damage, character.will)

Blood loss (red)

Unbandaged wounds will cause you to bleed out, which will eventually incapacitate you.

Fear (blue)

Morale only starts affecting incapacitation when it goes below 0, at which point each negative point of morale becomes fear, translating to 1% incapacitation.

Fatigue (black)

This does not significantly accumulate in the course of combat, but is more a function of marching all day or going too long without sleeping. This probably has a threshold after which it starts applying nonlinearly ~halfway through the day.

Penetrating

Each piece of armor has a "resistance" and "padding", both are in terms of joules. When attack connects, the imparted_joules is subtracted by the resistance to determine how much energy penetrates the armor, if any. Weapons also have a "penetration" coefficient. The actual resistance used for the attack is: $$ finalResistance = resistance-flexibility\cdot{resistance}\cdot{penetration} $$ Penetration coefficient examples:

  • Clubs: 0.1
  • Maces: 0.5
  • Swords/axes/musket ball: 1.0
  • Broadhead arrows or spear: 2.0
  • Mail breaker, rapier, or bodkin arrows: 4.0

Any energy that penetrates is then applied as cut damage.

Energy which is absorbed by the resistance, is the blunt energy. 50% of blunt energy is applied as unbalance, as described above, and the other 50% is subtracted by the padding to determine blunt damage.

Damage

Cut

Cut damage is divided by the penetration coefficient before being applied. This represents the greater surface area of flesh that is being torn up. Essentially, this makes axes and swords particularly ineffective against armor, but does extra damage against flesh.

Calibration:

  • 80kg male's forearm is about 1.2kg
  • A 20j direct hit dagger stab against an unarmored forearm should do just enough damage to incapacitate
  • The point of having more powerful attacks is not to do more damage to flesh, but to get past armor
  • A knight in full-plate still should be vulnerable to a mail breaker or bodkin arrow in the gaps between plates which are guarded only by chainmail
  • A 20j stab from a mail breaker should just barely be able to penetrate chainmail and damage flesh

Blunt

Halbe: We may want to distinguish between bruising and bone fracturing, perhaps by picking an arbitrary amount of blunt damage energy after which it starts to fracture the bone.

Halbe: I'm not certain what a good physical base measurement is that we could use for mapping kj of energy to damage. Damage might be best represented as how many kgs of mass have been rendered inoperable, but its not clear to me how to convert between the two. Ultimately though, the damage value relevant to stats maps "0" to "gains no function from the body part" and "1" means "body part is fully functioning", so the "displaced kgs of mass" would itself be an intermediate value not displayed to the player.

Durability

Each material has two numbers relevant to durability, one is durability itself, the other is "resilience". Resilience refers to how much durability damage the armor takes from hits which do not penetrate. $$ DurabilityDamage = 1 - resilience * (ImpartedJoules - threshold) $$ Extremely hard and brittle materials, such diamond, have 1.0 resilience (but low durability). Solid, ductile materials which deform plastically have very low resilience (like metal plate). And most flexible materials have fairly high resilience, since they are able to absorb a lot of the force as they bend.

Examples

(resistance, padding, durability, flexibility, brittleness)

Halbe: These numbers are not super well thought out

  • 3mm steel breastplate (120r, 60p, 1000, 0, 0)
  • Steel chainmail (70r, 40p, 1000, 0.8, 0)
  • Padded gambeson (60r, 40p, 250, 0.3, 0.6, 0)
  • 3mm steel brigandine (100r, 40p, 600, 0.4, 0)
  • 7mm wooden shield (100r, 20p, 100, 0.1, 0.9)