MOO1: MIRR-Based Investment Decision

Applying Modified Internal Rate of Return to the factory-vs-colonizer decision. Instead of brute-force search, use a financial metric to determine which investment has a better return at each decision point.

Links: MIRR — 4X Framework (the portable thesis this is a specimen of), MOO1 Optimal Strategy, Risk and Entrepreneurship, Value and Profit, Bilateral Trade Valuation, The Dominance-Frontier Lens (MIRR as the investment-decision frontier) Project: moo1-opening-optimizer

The Decision

At any given turn, your homeworld’s production can go toward:

Build a factory — immediate, small, compounding return
Build toward a colony ship — delayed, large, compounding return
Research — deferred return, unlocks future capabilities

The GA optimizer found good strategies by brute-force searching parameter combinations. But it doesn’t explain why one strategy beats another. MIRR gives us that — a principled comparison of investment quality at each decision point.

Why MIRR, Not IRR or NPV

NPV (Net Present Value): Requires a discount rate chosen in advance. In MOO1, what’s the discount rate? It’s not obvious — it depends on the game state. NPV is useful for comparing two specific cashflows but doesn’t tell you the rate of return.

IRR (Internal Rate of Return): The rate that makes NPV = 0. Problem: IRR assumes reinvestment at the IRR itself, which is unrealistic. A colony that returns 50% doesn’t mean you can reinvest those returns at 50%.

MIRR (Modified IRR): Fixes IRR’s reinvestment assumption. Uses a realistic reinvestment rate (the return available from the next best alternative). In MOO1, the reinvestment rate is roughly the marginal factory return — because any production not spent on the colony ship goes to factories.

MIRR = (FV of positive cashflows at reinvestment rate / PV of costs at finance rate)^(1/n) - 1

Factory MIRR

Cost: factory_cost × base_robot_controls / 2 BC (one-time)

Return stream: FACTORY_OUTPUT × mineral_mod BC per turn, forever (until the factory is no longer manned)

Constraint: Factory only produces if manned (need pop ≥ factories / robot_controls)

Example (Normal mineral, starting tech):

Cost: 10 × 2 / 2 = 10 BC
Return: 1 × 1.0 = 1.0 BC/turn
Simple payback: 10 turns
But the return compounds (1 BC/turn → more factories → more BC/turn)

The marginal factory return decreases when:

All factory slots are manned (no more room)
Population hasn’t grown enough to man the next factory
The planet approaches its factory cap

Colony Ship MIRR

Costs (multi-part):

Construction: 590 BC (spread over multiple turns of ship spending)
Maintenance drag: ~10 BC/turn while the ship exists (fleet maintenance)
Opportunity cost: BC spent on the ship could have been factories
Transit time: colony produces nothing during transit (dead turns)
Seed population: colonists sent reduce homeworld output

Return stream:

Starts after transit (delayed)
Grows logistically (slow start, accelerates, approaches cap)
Eventually produces MORE than the homeworld if the planet is good
But “eventually” can be 20-50 turns

The marginal colony return depends on:

Planet quality (Rich/Ultra-Rich colonies have much higher MIRR)
Planet size (bigger = more compounding room)
Distance (more transit = more dead turns = lower MIRR)
Seed population (more seed = faster start but higher homeworld cost)

The MIRR Decision Rule

At each turn, compute:

Factory MIRR — marginal return of the next factory at current state
Colony MIRR — marginal return of starting (or continuing) a colony ship at current state

If factory MIRR > colony MIRR → build factory. If colony MIRR > factory MIRR → build toward colony ship.

This should converge to the same optimal strategies the GA found, but with explanation — you can see exactly when and why the decision flips from “build factories” to “build colony ship.”

What the Simulation Data Should Show

From the existing GA results, we expect:

Early game: Factory MIRR is very high (cheap, immediate return). Colony MIRR is low (huge cost, delayed return).
Crossover point: As factory slots fill up (diminishing marginal return), colony MIRR surpasses factory MIRR.
Race effects: Klackon’s 2× production makes factory MIRR higher for longer (delay colonization). Sakkra’s growth bonus makes colony MIRR higher earlier (colonize sooner). This should match what the GA found.

Initial Results (2026-04-01)

Implementation in moo1-opening-optimizer/moo1/mirr.py. Simulation-based factory MIRR (runs with/without extra factory, measures production difference) vs colony MIRR (full cost accounting: construction, maintenance, transit, pop loss).

Normal 80-pop colony @ 3 parsecs, 50-turn horizon:

Race	Crossover Turn	Factories at Crossover	Pop	Interpretation
Klackon	Turn 8	68	75	2× production makes colonies productive fast — colonize early
Sakkra	Turn 13	76	99	Fast pop growth fills colony quickly — colonize after minimal factories
Human	Turn 25	151	100	No bonus — fill factories first, colonize after pop caps
Psilon	Turn 25	151	100	Research bonus doesn’t help early production — same as Human

Key finding: The Klackon result was unexpected — the prediction was that 2× production would make factory MIRR higher for longer (delaying colonization). Instead, 2× production makes the COLONY more productive too, and the colony benefits more from the multiplier because it compounds from a fresh start. The production bonus helps colonies more than factories because colonies have more growth headroom.

Rich colony target: Colony MIRR exceeds factory MIRR from turn 1 for Klackon — the model says “colonize immediately, never build factories.” This matches experienced player knowledge: if a Rich planet is nearby, always grab it first.

Known Model Gaps

The current model simplifies several factors that would push the crossover EARLIER:

Pollution — waste cleanup eats production per factory. More factories = more waste = diminishing returns before the cap.
Starting colony ship — the game starts with one in flight. The real decision is the 2nd colony, not the 1st. Two colonies producing lowers the opportunity cost of the third ship.
Pop transfer costs — sending colonists takes transit turns and removes homeworld production during transit.
Factory outpacing pop — factories build faster than pop grows, creating unmanned factory periods where factory MIRR should tank.
Factory MIRR oscillation — discrete turn simulation creates noise in the marginal production difference.

All of these make factory MIRR worse and colony MIRR better — so the real crossover likely happens earlier than shown. The model is conservative in favoring factories.

Implementation Plan (Next Steps)

~~Compute marginal factory MIRR~~ — Done (simulation-based)
~~Compute marginal colony MIRR~~ — Done (full cost accounting)
~~Find crossover point~~ — Done (per-race analysis)
Add pollution to factory MIRR — waste cleanup reduces net return
Model 2-colony start — real decision is 2nd colony timing
Add pop transfer mechanics — transit delay, homeworld production loss
Compare to GA results — does MIRR crossover match optimal factory_target?
Sensitivity analysis — distance, planet size, mineral richness

Connection to Vault Economics

This is Risk and Entrepreneurship applied to a game:

The factory is the safe investment (predictable, immediate, linear)
The colony is the entrepreneurial bet (uncertain, delayed, exponential if it works)
The crossover point is the moment when the marginal safe return drops below the marginal entrepreneurial return
Exactly the same structure as “when should a business reinvest vs expand?”

The MOO1 simulator gives us clean data to test this because the game has no noise — no market fluctuations, no competitors (in single-player opening), no random events. It’s a pure investment optimization problem. If MIRR works here, it validates the framework for messier real-world applications.