path: root/docs/simulation/calculations.yaml

Diplomacy:
  Monthly diplomatic points gain: defines.country.BASE_MONTHLY_DIPLOPOINTS * (1 + sum of diplomatic_points + sum of diplomatic_points_modifier)
  Influence:
    Total base daily influence gain:  defines.country.BASE_GREATPOWER_DAILY_INFLUENCE * (1 + sum of influence) * (1 + sum of influence_modifier)
    Base daily influence gain per country:
      if total priority bars > 0: Total base influence gain * priority bars / total priority bars
      else: Total base influence gain / number of countries (excluding banned)
    Country influence gain modifier:
      note: 'our' and 'we' refers to the influencer. 'target' is the country being influenced.
      formula: 1 + score mod + relations mod + population mod + investment mod + puppet mod + neighbour mod + continent mod + discredit mod
      score mod: 1 - target score / our score
      relations mod: relations / defines.diplomacy.RELATION_INFLUENCE_MODIFIER
      population mod:
        if target population > LARGE_POPULATION_LIMIT:
          formula: floor((target population - LARGE_POPULATION_LIMIT) / LARGE_POPULATION_INFLUENCE_PENALTY_CHUNK) * LARGE_POPULATION_INFLUENCE_PENALTY
          target population: total of pop sizes
          LARGE_POPULATION_LIMIT: defines.pops.LARGE_POPULATION_LIMIT
          LARGE_POPULATION_INFLUENCE_PENALTY_CHUNK: defines.pops.LARGE_POPULATION_INFLUENCE_PENALTY_CHUNK
          LARGE_POPULATION_INFLUENCE_PENALTY: defines.diplomacy.LARGE_POPULATION_INFLUENCE_PENALTY
        else: 0
      investment mod:
        if value of total investments in target > 0: (1 - value of our investment / value of total investments in target) * - defines.diplomacy.INVESTMENT_INFLUENCE_DEFENSE
        else: 0
      puppet mod:
        if is our puppet: defines.diplomacy.PUPPET_BONUS_INFLUENCE_PERCENT
        else: 0
      neighbour mod:
        if target is direct neighbour: defines.diplomacy.NEIGHBOUR_BONUS_INFLUENCE_PERCENT
        else if target has a sphereling as neighbour: defines.diplomacy.SPHERE_NEIGHBOUR_BONUS_INFLUENCE_PERCENT
        else: 0
      continent mod:
        if target is on a different continent: defines.diplomacy.OTHER_CONTINENT_BONUS_INFLUENCE_PERCENT
        else: 0
      discredit mod:
        if we are discredited: defines.diplomacy.DISCREDIT_INFLUENCE_GAIN_FACTOR
        else: 0
    Daily influence gain per country: Base daily influence gain per country * Country influence gain modifier
  Colonisable life rating: defines.country.COLONIAL_LIFERATING + sum of colonial_life_rating
Economy:
  Budget:
    Loan interest per day:
      formula: (NBD + FBD * (1 + FIM)) * max(0.01, LBI+BIM)/30
      NBD: National bank debt = debt owed to your national bank.
      FBD: Foreign bank debt = debt owed to foreign national banks and private investors.
      1+FIM: Foreign interest modifier = sum of loan_interest modifiers from non-tech
      max(0.01: Hardcoded value. Reasoning unknown.
      LBI: defines.economy.LOAN_BASE_INTEREST
      BIM: Base interest modifier = sum of loan_interest modifiers from technology.
      /30: Hardcoded value to represent days in a month.
    Gold income daily:
      formula: MGQ * GOLD_TO_CASH_RATE
      MGQ: Money good quanity = total production of goods with money = yes
      GOLD_TO_CASH_RATE: defines.country.GOLD_TO_CASH_RATE
    Overseas maintenance:
      See: https://github.com/schombert/Project-Alice/blob/main/docs/rules.md#overseas-penalty
  Production:
    Resource gathering operation:
      base workforce: defined in common/production_types.txt as workforce
      rgo size:
        formula: floor(1.5*ceil(n_workers_in_state / (base workforce * (1 + terrain rgo size modifier)))
        n_workers_in_state: Total size of POPs in state where POP type is in employees (common/production_types.txt).
        note: Calculated when starting a new game.
      Output:
        formula: base output * rgo size * (1 + overseas penalty) * throughput from workers * (1 + throughput modifier) * (1 + output from workers) * (1 + output modifier)
        base output: defined in common/production_types.txt
        overseas penalty:
          if province is 'overseas': overseas penalty (see economy > budget > overseas maintenance)
          else: 0
        workforce:
          formula: base workforce * rgo size * (1 + rgo size modifier)
          base workforce: Defined in common/production_types.txt as workforce.
          rgo size modifier: sum of rgo size modifiers + sum of farm size modifiers (if farm=yes) + sum of mine size modifiers (if mine=yes)
        job portion of workforce:
          formula: employees with job / workforce
          employees with job: Number of POPs employed with the job. Job being an entry in employees in common/production_types.txt.
        effect from job:
          formula:
            if effect_multiplier == 1: effect_multiplier * employees with job / workforce
            else: effect_multiplier * min(employees with job / workforce, amount)
          effect_multiplier: defined in common/production_types.txt (default 1)
          amount: defined in common/production_types.txt (default 1)
        throughput from workers: sum of effect from job for each job with `effect = throughput`
        output from workers: sum of effect from job for each job with `effect = output`
        throughput modifier: sum of throughput modifiers (including from owner)
        output modifier: sum of throughput modifiers (including from owner)
        modifier from owner:
          formula: effect_multiplier * n_owners_in_state / n_pops_in_state
          effect_multiplier: see throughput from workers
          n_owners_in_state: total size of owner POPs in state
          n_pops_in_state: total size of all POPs in state
          note: included in throughput or output modifier
    Human resource management:
      Vacancies: max employees - employees count
      Maximum employees hired per day:
        formula: max(employees available, relative maximum)
        employees available: unemployed employee pops in state
        relative maximum:
            if employees count = 0 & max employees >= 6667: 0.2775 * Vacancies
            else: ceil(0.15 * Vacancies) - 1
          0.15: Hardcoded value.
          0.2775: 1 - (1 - 0.15)^2
          note: Rounding is unknown for the 0.2775 case. See https://discord.com/channels/1063392556160909312/1063416834650554398/1204520366643347476
      Minimum employees hired per day:
        formula: max(absolute minimum, relative minimum)
        absolute minimum: 50 (hardcoded value)
        relative minimum: floor(defines.economy.EMPLOYMENT_HIRE_LOWEST * employees count)
Military:
  Maximum regiments per soldier POP:
    if POP size < defines.military.POP_MIN_SIZE_FOR_REGIMENT: 0
    else:
      formula: 1 + trunc(POP size / (POP_SIZE_PER_REGIMENT * location factor))
      POP_SIZE_PER_REGIMENT: defines.military.POP_SIZE_PER_REGIMENT
      location factor:
        if is protectorate: defines.military.POP_MIN_SIZE_FOR_REGIMENT_PROTECTORATE_MULTIPLIER
        else if is colony: defines.military.POP_MIN_SIZE_FOR_REGIMENT_COLONY_MULTIPLIER
        else if location is core: 1
        else: defines.military.POP_MIN_SIZE_FOR_REGIMENT_NONCORE_MULTIPLIER
  Reinforcing:
    Regiment reinforcements fraction * 1000:
      formula:
        if regiment is full strength: 0
        else: min(trunc(regiment reinforce rate * supply factor * reinforcements multiplier * 1000), 1000)
      unit type strength: as defined in /units/<unit>.txt
      1000: strength is defined in thousands of soldiers. Reinforcements per army uses the number of soldiers.
      regiment reinforce rate:
          if regiment is mobilised: 0.5
          else if pop is too small for a single regiment: 0.5
          else if pop supports too many regiments: Maximum regiments per soldier POP / number of supported regiments
          else: 1
      reinforcements multiplier:
        formula: REINFORCE_SPEED * local reinforce rate * (1 + reinforce_rate) * (1 + reinforce_speed)
        REINFORCE_SPEED: defines.military.REINFORCE_SPEED
        local reinforce rate:
          if location owner == army owner: 2
          else if army is exiled: 0
          else if location is uncolonised: 0
          else if location controller is hostile:
            if location neighbours a province controlled by an ally in this war: 0.5
            else if location is coastal & not blockaded: 0.25
            else: 0.1
          else: 1
        reinforce_rate: sum of reinforce_rate modifiers from tech
        reinforce_speed: sum of reinforce_speed modifiers on country
      supply factor:
        if army received all its supplies: 1
        else:
          formula: x^(1+i)
          x: received supply
          i: 0 based index of regiment in the army
      trunc(... * 1000): Truncated to 1/1000th.
      min(..., 1000): Capped at max strength.
    Regiment reinforcements:
      formula: trunc(unit type strength * Regiment reinforcements fraction * 1000)
      unit type strength: as defined in /units/<unit>.txt
      trunc(unit type strength * ...): Truncated to integers in the case unit type strength isn't an integer already.
    Reinforcements per army (tooltip): sum of Regiment reinforcements
    Regiment experience after reinforcing:
      formula: xp before reinforcing / (1 + trunc(Regiment reinforcements fraction * 1000 / 3) / 1000)
      trunc(... / 3): Hardcoded.
      / 1000: to counter * 1000.
  Regiment experience gain per day of combat:
    formula: d6 * defines.military.EXP_GAIN_DIV * (1 + sum of experience gain modifiers) + unexplained
    d6: random integer (inclusive) 1-6
    unexplained: see https://discord.com/channels/1062018115275325480/1062021872545447936/1278664121323356190 or https://media.discordapp.net/attachments/1062021872545447936/1278666211848228906/image.png?ex=66d1a235&is=66d050b5&hm=47bafd0f86451a25aebd7b728e96dda264bc0704a4e398ca59931390a902b968&=&format=webp&quality=lossless
Politics:
  Westernisation:
    Upper house reform support:
      formula: sum of (Ideology support factor * Ideology upper house share)
      Ideology support factor: common/ideologies.txt add_economic_reform or add_military_reform
    Economic reform cost modifier: defines.country.ECONOMIC_REFORM_UH_FACTOR * Upper house reform support + self_unciv_economic_modifier
    Military reform cost modifier: defines.country.MILITARY_REFORM_UH_FACTOR * Upper house reform support + self_unciv_military_modifier
POPs:
  Monthly pop growth:
    formula: BASE_POPGROWTH + (min(40, LR * (1 + LRM)) - MIN_LIFE_RATING_FOR_GROWTH) * LIFE_RATING_GROWTH_BONUS + population_growth + pop_growth + global_population_growth/10
    BASE_POPGROWTH: defines.pops.BASE_POPGROWTH
    min(40,: Hardcoded limit to life rating.Reasoning unknown.
    LR: Province life rating
    1+LRM: Life rating modifier = sum of life_rating modifiers
    MIN_LIFE_RATING_FOR_GROWTH: defines.pops.MIN_LIFE_RATING_FOR_GROWTH
    LIFE_RATING_GROWTH_BONUS: defines.pops.LIFE_RATING_GROWTH_BONUS
    population_growth: Sum of population_growth modifiers
    pop_growth: Sum of pop_growth modifiers
    global_population_growth/10: Sum of global_population_growth modifiers
  Attitudes:
    Consciousness from literacy: defines.pops.CON_LITERACY * Plurality * POP literacy * (1 + literacy_con_impact)
    Monthly literacy change:
      formula: defines.pops.LITERACY_CHANGE_SPEED * local clergy factor * (1 + education_efficiency) * (1 + education_efficiency_modifier) * educational spending slider
      local clergy factor: ((clergy POPs in province / total POPs in province) - defines.pops.BASE_CLERGY_FOR_LITERACY) / (defines.pops.MAX_CLERGY_FOR_LITERACY - defines.pops.BASE_CLERGY_FOR_LITERACY)
      note: clergy POPs are all pop types with can_reduce_consciousness = yes
  Needs:
    Base needs scalar: (1 + Plurality) * (1 + 2 * Consciousness / defines.pops.PDEF_BASE_CON) * (1 + sum of goods_demand) * defines.pop.BASE_GOODS_DEMAND * POP size / 200000
    Life needs scalar: Base needs scalar * (1 + <strata>_life_needs modifier)
    Invention needs scalar: 1 + number of inventions * defines.pops.INVENTION_IMPACT_ON_DEMAND
    Everyday needs scalar: Base needs scalar * Invention needs scalar * (1 + <strata>_everyday_needs modifier)
    Luxury needs scalar: Base needs scalar * Invention needs scalar * (1 + <strata>_luxury_needs modifier)
  POP income:
    Base life needs costs: Base needs scalar * sum of (life need quantity * good price)
    Pensions: 2 * pension_level * administrative efficiency * social spending slider * Base life needs costs * (1 - effective tax) * POP size / 200000
    Unemployment subsidies: 2 * unemployment_benefit * administrative efficiency * social spending slider * Base life needs costs * (1 - effective tax) * POP size / 200000
    Wages:
      Minimum (worker) wage: 2 * minimum_wage * administrative efficiency * Base life needs costs * (1 - effective tax) * POP size / 200000
      RGO wages:
        Owners:
          if minimum worker wages > normal worker wage:
            formula: (RGO income - total worker income) * owner POP size / n_owners_in_state * (1 - effective tax) 
          else:
            formula: RGO income * min(0.5, 2 * n_owners_in_state / n_workers) * owner POP size / n_owners_in_state * (1 - effective tax) 
            n_owners_in_state: total size of owner POPs in state
            n_workers: number of employed workers in RGO
            min(0.5: Hardcoded maximum of half the RGO income.
            2 *: Hardcoded value.
        Workers:
          if is_slave: 0
          else:
            if minimum wage > normal wage:
              formula: min(minimum wage, RGO income * employed workers in POP / total non-slave employed workers) * (1 - effective tax) 
            else:
              formula: RGO income * max(0.5, 1 - 2 * n_owners_in_state / n_workers) * employed workers in POP / total non-slave employed workers * (1 - effective tax) 
              n_owners_in_state: total size of owner POPs in state
              n_workers: number of employed workers in RGO
              max(0.5: Hardcoded minimum of half the RGO income.
              2 *: Hardcoded value.
Scores:
  Industrial power:
    formula: sum of investment scores + sum of state factory scores
    investment score: money_invested * defines.country.INVESTMENT_SCORE_FACTOR / 100
    state factory score:
      if n_workers > 0:
        formula: sum_factory_levels_in_state * max(0.2, min(4, floor(n_workers_in_state / 100) * 400 / total_factory_jobs_in_state))
        sum_factory_levels_in_state: sum of factory levels in the state
        max(0.2: Hardcoded minimum score per factory level.
        min(4: Hardcoded maximum score per factory level.
        floor(n_workers_in_state / 100): Hardcoded number step.
        400: Hardcoded value.
        n_workers_in_state: Total size of POPs in state (employed or not) where POP type has `can_work_factory = yes`.
        total_factory_jobs_in_state: Sum of (factory level * workforce), defined in /common/production_types.txt.
      else: 0
  Military power:
    formula: soldier & army score + capital ship score + leader score
    soldier & army score:
      formula: disarmed penalty * regular army size * supply consumption * sum unit stats / (7 * (1 + n_unit_types))
      disarmed penalty:
        if is_disarmed: defines.diplomacy.DISARMAMENT_ARMY_HIT
        else: 1
      regular army size: min(4 * number of deployed non-mobilised regiments, possible regiment count)
      supply consumption: From army tab, not unit types.
      sum unit stats: Sum of ((attack + defence + land_attack_modifier + land_defense_modifier) * discipline) for each land unit type (including locked).
      n_unit_types: Number of land unit types (including locked).
      7*: Hardcoded value.
    capital ship score:
      formula: sum ship stats / 250
      sum ship stats: Sum of ((hull + naval_defense_modifier) * (gun_power + naval_attack_modifier)) for each capital ship instance.
      /250: Hardcoded value.
    leader score: min(number of admirals + number of generals, number of deployed non-mobilised regiments)