Gimmikghoul, a Gimmighoul in a lab coat with coin spectacles

GIMMIKWATCH · THESIS

A metagame is a market of plans

Players copy what won last week, and they prepare for what they expect to face. So a plan's edge depends on two things: how strong it is, and who else shows up. Represent each team by the plans it runs, learn how plans do against each other from real matches, and you can say why a team won at that event, why a near-identical team didn't, and where the field left room.

Three claims, each tested on 3,004 open team sheets and 12,217 decided matches from Frankfurt, Louisville and Nice (Reg M-C, 2026):

Plans are learnable. Sparse dictionary learning recovers 16 plans players already name: Psyspam, Perish Trap, Protect the Queen, SunRain.
Some matchups loop. Raw records show rock-paper-scissors cycles among plans, so no single plan beats every other.
"Why now" is a field shift. A plan's value moves when the mix of opponents moves, and the change splits exactly into per-opponent terms.

1 · Teams as documents

Representation

A team $t$ is a bag of tokens: its battle forms (Mega forms included), engine-derived mechanics (weather, terrain, speed control, redirection, sleep, Perish Song, key abilities) and set details (item, each move). With $N$ teams and document frequency $\mathrm{df}_k$,

$$x_{t,k} \;=\; \mathbb{1}[k \in t]\,\log\frac{N}{\mathrm{df}_k}, \qquad \hat x_t = \frac{x_t}{\lVert x_t\rVert_2}.$$

Rare tokens weigh more, so a Raichunite X says more about a team than Protect does.

2 · Dictionary learning

Plans

Stack the team vectors into $\hat X \in \mathbb{R}_{\ge 0}^{N\times V}$ and factor it with non-negative matrix factorisation, the same move interpretability work uses to find sparse features inside a network:

$$\min_{H \ge 0,\;C \ge 0}\; \lVert \hat X - H C \rVert_F^2, \qquad H \in \mathbb{R}^{N\times K},\; C \in \mathbb{R}^{K\times V},\; K = 16.$$

Row $c_f$ of $C$ is a plan: a weighted set of tokens. Row $h_t$ of $H$ says how much of each plan team $t$ runs. Each team's dominant plan is $\arg\max_f h_{t,f}$.

3 · The probe

Who beats whom

Read match results off the plan activations with a pairwise logistic model:

$$\Pr(A \succ B) \;=\; \sigma\!\big(\, s^\top (h_A - h_B) \;+\; h_A^\top W\, h_B \,\big), \qquad W = -W^\top.$$

$s$ gives each plan one strength, like an Elo rating. The antisymmetric $W$ holds plan-vs-plan terms: $W_{fg} > 0$ means plan $f$ does better against $g$ than strength alone predicts. Antisymmetry keeps the model consistent: $\Pr(A \succ B) = 1 - \Pr(B \succ A)$. Fit by L2-regularised log loss, regularisation picked by five-fold cross-validation.

Held out, the probe calls 53.75% of match winners. A coin calls 50%. That is pooled five-fold cross-validation, not a test on a later, unseen event, and it says nothing about how much of a result the pilot caused. It does say the sheets alone carry only a little signal, which is why every claim here is about shifts and splits, not certainties.

4 · Strength and loops

Transitive vs cyclic terms

The logit splits into two parts:

$$z_{AB} \;=\; \underbrace{s^\top (h_A - h_B)}_{\text{transitive}} \;+\; \underbrace{h_A^\top W h_B}_{\text{cyclic}}, \qquad \text{cyclic share} \;=\; \frac{\operatorname{Var}(z^{\text{cyc}})}{\operatorname{Var}(z^{\text{tr}}) + \operatorname{Var}(z^{\text{cyc}})} \;\approx\; 0.25.$$

Balduzzi and colleagues separate symmetric zero-sum games into a transitive part and a cyclic part. The ratio above is only a description of this fitted model. It ignores the covariance between the two terms, and an antisymmetric term on overlapping plan activations isn't a purely cyclic component, so it doesn't say what share of wins comes from strength or from loops. The evidence for cycles is in the raw records. Staraptor Offense beats Tyranitar Sand (67-46), which beats Froslass Snow (39-33), which beats Staraptor Offense (59-32).

5 · Value against a field

Why now

Let $f^{(e)}$ be the share of each plan at event $e$, and $P_{ab}$ plan $a$'s win rate against $b$, shrunk toward one half with $\alpha = 20$ virtual games so thin records can't dominate:

$$P_{ab} = \frac{w_{ab} + \alpha/2}{w_{ab} + l_{ab} + \alpha}, \qquad V_a\big(f^{(e)}\big) = \sum_b f^{(e)}_b\, P_{ab}.$$

Shares sum to one, so their changes sum to zero, and the change in a plan's value between events splits exactly into opponent-by-opponent terms:

$$\Delta V_a \;=\; \sum_b \Delta f_b\,\big(P_{ab} - \tfrac12\big).$$

A term is large when an opponent both grew and matches up lopsidedly. Between Louisville and Nice the SunRain plan grew, and inside it Choice Scarf Garchomp (13 → 27%) and Snarl Archaludon (18 → 47%) rose. Against those, the Raichu Y rain team went from 4-0 to 0-4.

6 · Crowding

Why copying eats the edge

Even without counter-picks, popularity drags a plan toward 50%. If plan $a$ holds share $f_a$, its mirrors are coin flips:

$$V_a - \tfrac12 \;=\; (1 - f_a)\,\big(E_a - \tfrac12\big), \qquad E_a = \text{win rate against everyone else}.$$

Add counter-adaptation (the field brings answers to what won last week) and the edge falls faster. Weatherless Setup grew from 3.5% to 8.6% of teams while falling from 55.7% to 50.7%.

7 · Equilibrium and dynamics

Where the field left room

Treat plans as pure strategies in the symmetric zero-sum game $G = \tfrac12 (P - P^\top)$. Regret matching in self-play, with the time-averaged strategy, approaches an equilibrium mix $x^{\ast}$. The gap $x^{\ast}_a - f_a$ marks plans the field under-played. Mega Gengar's Perish Trap was the clearest at Nice: 59.5% on Day 1, from 6% of teams.

The field's week-to-week movement looks like replicator dynamics,

$$\dot f_a \;=\; f_a\,\big(V_a(f) - \bar V(f)\big), \qquad \bar V(f) = \textstyle\sum_a f_a V_a(f).$$

On the transitive part this behaves like gradient ascent: shares flow toward stronger plans. Where real cycles exist, it can orbit instead of settling. Three events are too few to tell which of the two the Reg M-C field is doing.

8 · Checks and limits

What holds and what doesn't

Every report number is recomputed from the published dataset by meta/cases.mjs. Mechanics (Electric Seed, terrain blocking sleep, Lightning Rod) are re-run in the pinned Showdown Champions engine by meta/mechanics.cjs.
Patching Raichu X to Raichu Y on the winning team doesn't move the probe. It averages Raichu Y over its 236 other teams. The Raichu story rests on matched teams and engine checks, not the probe.
Leads, which four were brought, the Mega used each game, and stat spreads aren't in open sheets.
Samples are small where it matters: 18 players ran the exact six, and removing one 0-8 entry moves Raichu Y from 39.1% to 47.4%.
The next test: fit on Frankfurt and Louisville only, then score Nice without refitting, against a coin and a species-only model.
Numbers were cross-checked in an independent Codex review, which also found the corrections above.