§ I · Methodology
20 min readlast revised 2026-04-27snapshot 2026-06-15T03:47ZMethodology
The full specification: what the framework does, why it does it that way, and how each piece is calibrated, frozen, and evaluated.
Contents
This essay is the long-form home of the methodology. It is the web-native counterpart to the Phase 1 framework PDF: the same argument, written for the page rather than the printer.
The premise (borrowed from Hoffmann, Ging & Ramasamy 2002) is that structural variables explain roughly fifty-five percent of World Cup performance variance. The remaining is the residual this project takes as its subject. We do not predict through it. We price under it, with calibrated uncertainty.1
Every calibrated component below was fit on the same 347 major-tournament match corpus (2010 through 2021, with the 2022 World Cup held out as the final exam). The corpus is well below the roughly 12,000 international matches a fuller dataset would contain, and the resulting confidence intervals are wider than we wished. We document the constraint rather than disguise it; the Phase 8 firing of the kill criterion is one direct consequence.
The model identity
Every model in the roster shares the same simulation engine. Only the strength-estimation function differs. The canonical identity, written once for the whole project, is:
That is a placeholder while the full derivation is in draft. The renderer that produced it is the same KaTeX pipeline that will carry the bivariate Poisson likelihood, the Dixon-Coles correction term, and the de-vigging identity in the sections below.
Sections in draft
Simulation engine
Bivariate Poisson with Dixon-Coles low-score correction; extra-time scaling; shootout model; ten thousand Monte Carlo runs for the website, one hundred thousand for the paper.
Market layer
Power-method de-vigging, edge thresholds at three percent for mainline markets and five percent for derivatives, fractional Kelly sizing under per-event and drawdown caps.
Volatility gate
Five suppression rules (named-event, price-discovery, exchange spread, liquidity, and sizing) gate the M★ recommendations.
Evaluation
Brier, RPS, log-loss, Diebold-Mariano, Nyberg market efficiency tests; CLV telemetry for M★, pseudo-CLV for the shadow models.
Notes
- Hoffmann, Ging & Ramasamy (2002), “The Socio-Economic Determinants of International Soccer Performance,” Journal of Applied Economics 5(2), 253 to 272. ↩