§ About · the colophon
This page is the project's reference: the method in plain English, every technical term defined, the data layer described, the pipeline summarised so it can be re-run, and the scope and limitations stated plainly. The one-line summary is the same one that sits under every chart on the site — the ensemble matches the de-vigged market on out-of-sample accuracy (0.1891 vs 0.1905); it does not significantly beat it, and at three out-of-sample tournaments the margin sits inside the noise.
§ 01
No equations required to follow the idea. The forecast asks one question — who wins WC2026, and why — and answers it by combining what a century of results says with what each squad is worth today, then playing the real bracket out a million times over.
Every forecast on this site rests on a single idea: a national team's chances come from two things that do not always agree. The first is history — the long record of who has beaten whom, distilled into a self-updating strength rating that stretches back to the nineteenth century. The second is the squad on the plane today — the clubs its players turn out for, the minutes they are getting, the market that prices their talent. A team can be richer than its results, or be winning more than its price tag says it should. The model's job is to hold both pictures at once.
Those two pictures are turned into match odds by a ladder of models, each a little more ambitious than the last. At the bottom is Elo — cheap, transparent, reproducible from the results file alone, and the floor everything else must clear. Above it, a goals model (Dixon–Coles) that predicts scorelines, a Bayesian model that deliberately shrinks its opinion of teams it has barely seen, and a gradient-boosting learner that reads 36 engineered features per team. No single one of these is trusted on its own. They are pooled — a weighted geometric average of their probabilities — into one ensemble, which out of sample was both more accurate than any individual learner and steadier than a cleverer combination rule we tried and rejected.
The ensemble only gives the odds for a single match. To get a champion, the real 48-team bracket is simulated 1,100,000 times — every group, every tie-breaker (down to the head-to-head rule we had to correct by hand), the eight best third-placed teams, extra time and shoot-outs calibrated to hundreds of real ones — and the share of simulations a team wins becomes its title probability. Because that share is an average over simulations, it carries a small, reported margin of its own.
The headline: the model matches the market. It does not beat it.
That last point matters most. Measured the hard way — trained only on matches before each test tournament, never on the answers — the ensemble's accuracy (0.1891) edges the de-vigged bookmaker consensus (0.1905) and clears the Elo floor (0.1938). But the margin over the market is a fraction of its own uncertainty, and the test set is only three out-of-sample tournaments. So the claim we stand behind is parity, not conquest: a model that has earned a seat next to the market, carries genuinely independent information (a 66%-weight blend improves on either alone), and is transparent enough that you can check every step below.
Fig. A1 Each rung, its role, and its out-of-sample RPS (lower is better)
Seven anchors between an Elo floor and the de-vigged market ceiling. The locked forecast is the ensemble of three of them — Dixon-Coles, the global gradient booster and the Bayesian hierarchical model — run through the Monte-Carlo simulator.
Self-updating strength from results; movement-of-victory and importance weighted.
Bivariate-Poisson goals with low-score correction and host gating.
Partial pooling so newcomers borrow strength; NUTS/MAP, horseshoe priors.
Gradient boosting on 36 features with monotone constraints; the de-biasing win.
Simple-average log-opinion pool; beat stacking out-of-sample.
1.1M simulations of the real 48-team bracket with full FIFA tiebreakers.
De-vigged bookmaker probabilities; the market benchmark we match, not beat.
The simulator turns match odds into a tournament; it is not itself scored on match RPS, so its cell reads “—”. The market is a benchmark, not a model we fit.
Read top to bottom as increasing ambition. The ensemble is the only rung that clears both the Elo floor and (just) the market rail — but inside the noise, which is why the operative verb is “matches”.
The kernels, for the record
The exact equations behind the ladder, rendered from the same strings the model pages read. Full derivations live on each model page; these are here so the method is on the table, not behind a link.
Elo update
Dixon–Coles goals
Log-opinion pool (the ensemble)
Champion probability (the simulator)
Hypothesis H1 — that the ensemble beats the Elo floor — gives ΔRPS −0.0046 with a conservative 95% interval of [−0.0122, +0.0061], which includes zero (NOT supported (CI includes 0)). The blend-weight test H2 is the one that clears the bar: the optimal model weight w* = 0.656 sits in a 95% interval [0.20, 1.11] that excludes zero, so the model adds information to the market even though it does not, on its own, significantly beat it. With n = 3, the effect and its uncertainty are reported in the same breath.
§ 02
Every technical term the site leans on, defined in one or two sentences — and where a definition touches a result, it carries that result's real uncertainty.
§ 03
Every figure on every page binds to one curated data layer, exported from the locked pipeline. This section describes what that layer contains.
Curated data tables
forecasts, rankings, features, validation
Rows across the tables
every figure on the site traces to one of them
Documented fields
a field dictionary spans all 13 tables
Database tables
4,269 rows in one queryable database
The site reads from 8 curated tables — the locked forecast itself, the group and knockout probabilities, the two rankings (Power and Reality), the match-level head-to-heads, the engineered team features and the full validation results — 2,401 rows in all. A field dictionary documents every table and every field with its type and a plain-English note, so nothing on the site depends on an undocumented column.
The same layer is packed into a single queryable database of 12 core entities — teams, players, coaches, matches, features, model results, the forecast and the rankings (4,269 rows) — which powers the in-browser SQL console on the Data page. Each table carries a SHA-256 checksum, and the locked forecast's own hash — reproduced in §4 below — stamps the exact vintage of every number on the site.
The data layer consists of derived outputs of the project (forecasts, engineered features, validation results). It is not a redistribution of the licensed upstream feeds it was built from — see the credits below for the original sources and their own terms. The locked-forecast hash identifies the vintage unambiguously.
§ 04
The forecast is a deterministic function of committed data and code. Same inputs, same seed, same numbers — and the locked forecast carries a checksum so you can prove you reproduced this exact one.
The pipeline
Raw data — 20 sources
49,445 international results (1872→2026), Elo histories, a global club-stats feed of 107 leagues across 68 countries, squads, the odds feed, environment and structure tables.
A 61-step pipeline
A numbered, ordered chain that cleans the raw feeds, engineers 35 processed tables including the 36-feature team panel, fits the 7 models, runs the backtest, simulates the bracket and exports the site's data layer.
A seeded, repeatable simulation
The Monte-Carlo simulator runs from a fixed seed and uses common random numbers across teams, so the 1,100,000 simulations are bit-for-bit repeatable and re-draws are compared on the same randomness.
Strict fit-cut at 2026-06-07
Models train only on results dated on or before 2026-06-07 — strictly pre-kickoff — and never on the 152 odds-tournament matches or any tournament stage labels. No refit after kickoff.
A single source of truth
Everything the site shows is reconciled to one locked forecast file. The site's data layer is regenerated from it by the pipeline's export step — no number is ever edited by hand.
Two protocols guard against leakage. The expanding window trains on everything before each held-out tournament and predicts forward — the number we quote as expected skill. Leave-one-tournament-out holds a whole tournament out and trains on the rest; it is more optimistic, so it is reported alongside but not headlined. In neither case does any model ever see a test-tournament match, a closing odds line, or a stage label during training. The 152-match test set stays untouched throughout.
§ 05
The reasons to read every probability on this site as a careful estimate rather than a promise — collected in one place on purpose.
01
The out-of-sample evidence is 152 matches across three odds tournaments (plus five for the stage models). At that resolution confidence intervals are wide by construction — the de-biasing gain, the decoupling slope and the draw-luck advantages all have intervals that include zero. We treat this as the ceiling on every claim, not a footnote.
02
On the hard, forward-looking test the ensemble (0.1891) edges the de-vigged market (0.1905) by −0.0014 — a margin far smaller than its own uncertainty (H1 interval includes zero). The defensible claim is parity. Anyone promising a market-beating edge from three tournaments is over-reading the data.
03
Extending squad coverage worldwide was the project's central data contribution: a global feed of 68 countries lifted average squad coverage from roughly a half to 85%. It is still uneven: the residual gaps are concentrated in the lower-coverage confederations — AFC above all — so odds for some Asian and Oceanian sides rest on a thinner club-data base than those for European ones. The conformal sets widen there to say so.
04
The inputs are public results, a free-tier global club-stats API, public Elo, market value and odds feeds. That makes the project reproducible and open, but it inherits those feeds' limits — coverage holes, occasional staleness, and value/odds series that are themselves estimates. The published bundle is the derived data, not the licensed raw feeds.
05
The hierarchical model shrinks debutants toward the field and lets their squad value speak where their international record cannot. It is a principled mechanism — but with so few true newcomers in the held-out tournaments, it is the one part of the model that cannot be properly validated out of sample. For genuine first-timers, read the odds as the model's best-structured guess, with the widest uncertainty on the site.
06
This is a forecast locked on 2026-06-09, before a ball is kicked. It does not update for injuries, form swings or in-tournament results after the lock; the whole point of the checksum is that it is a fixed, falsifiable prediction. Late squad changes after the fit-cut are not reflected.
§ 06
The forecast is only as good as the open data and open tools beneath it. Here is what it stands on.
Each feed is used under its own terms; this site redistributes only the derived tables in §3, not the licensed raw data.
Open-source throughout; the analytical choices, and any errors, are the project's own.
If you read nothing else: every number carries its uncertainty, and the model matches the market without beating it. Everything above is here so you can check that for yourself.