The Dominance-Frontier Lens

A recurring analytical frame for any competitive system with counter dynamics — games, but also markets and portfolios. Map cost against effect, draw the edges where X dominates or counters Y, trace the frontier curve of non-dominated choices, and flag the asymmetric edges where a counter costs more than the threat it answers. Then ask the design-quality question: does every starting endowment have at least one viable path along the frontier? It’s the same construction as a Markowitz efficient frontier in finance — which is why this lens reaches past games.

Links: Capability Without Leverage (the trap this lens finds), MIRR — 4X as Capital Allocation, The Anchor Method (dominance pruning is a reducer — see below) · specimens linked in the ledger.

A thesis page (portable, source-independent), promoted from a working note. The worked graphs live in the specimens it cites; this page states the lens.

The lens

For a system where choices interact (one beats, counters, or denies another), don’t enumerate mechanics flatly. Instead:

Pick the cost axis — mana, production, BattleValue, cash, research, dollars.
Pick the effect axis — kill rate, denial rate, position value, expected return.
Draw the dominance edges — X dominates Y if it’s cheaper and more effective; X counters Y if it specifically negates Y’s effect.
Trace the frontier — the non-dominated set: the efficient choices for each cost level. Most options are dominated and can be pruned.
Flag the asymmetric edges — where the counter costs more than the threat. These are the most interesting findings: they create attrition wars (you can’t cheaply remove the threat, only grind it) and force tempo investment.

The design-quality verdict — random-start viability. Once the frontier is drawn, ask: does every starting endowment have at least one viable path along it? If a starting position has no non-dominated path, the game is unfair from that seed. This turns a descriptive map into a verdict on the design.

Three companion axes

Pre-emptive vs reactive. When miss-cost is high, a pre-cast guarantee beats a reactive option (Bloodlust > Heal in WC2; doom-stacks in MoM; pre-commitment in Newcomb’s Paradox). The frontier shifts toward pre-emption as variance rises.
Sparse vs dense graph. WC2 has a near-empty counter-graph where one edge decides the meta; CoM has a dense graph where navigation itself is the skill. Same lens, opposite design choice — and the density tells you where skill lives.
Variance compression as the system matures (Gould’s “Extinction of .400 Hitting”). The mean stays put; the standard deviation shrinks as the talent pool professionalizes. New 4X games look like .400-hitter eras (any strategy works); mature ones look like .260-hitter eras (tight optimal play). The evolved “sport closure rate” — football’s ~3 yards/play, baseball’s .333 threshold, tennis’s ~80% hold — is the equilibrium where games still close. A quantitative health-check for any strategy game’s tuning.

Why it reaches past games

The efficient frontier is not a game idea borrowed into finance — it’s the same construction. Markowitz’s portfolio frontier plots risk (cost axis) against expected return (effect axis), keeps the non-dominated set, and prunes everything below the curve. Market-share dynamics, security/counter-exploit races, and R&D portfolios all have dominance edges and asymmetric counters. The lens is domain-general; games are just where the graph is cleanest to draw.

Connection to method. Dominance pruning is a reducer — it collapses a combinatorial action space to the small non-dominated set (≈2–3 live options per turn). That’s the same move as the Anchor Method’s “enumerate the table forward” / lowering-atlas: when reactive discovery won’t close a set, draw the dominance graph and read the frontier off it.

Evidence ledger (specimens)

Monopoly — Frontier Trade Theory — the efficient frontier of cash-vs-EPT; dominance pruning of trades; the canonical worked instance.
MoM/CoM — Spell Counter-Graph — counters as a directed dominance graph with scope categories (single / area / passive-pool / resource-denial / lock / behavioral); the dense-graph case.
BattleValue — BV/Cost as the per-unit frontier ranking; the metric that draws the cost axis for combat units.
MoO1 — MIRR Analysis — MIRR as the investment-decision frontier (the factory-vs-colony non-dominated path over turns).

These four already describe themselves as “the same methodology”; this page is the hub they were missing.

Open questions