Methodology

Every full international since the 19th century. After cleaning (dropping unplayed and unparseable rows), 49,291 matches feed the model. Each match carries a competition tier — a World Cup final counts for more than a friendly — and the exact tier weights were tuned on the backtest (below).

Source pinned by SHA-256 37e5ce3b82849279… — see the reproducibility note.

For a match between teams i and j, the log goal rates are log λ = c + attack₍ᵢ₎ − defense₍ⱼ₎ + h·home₍ᵢ₎ − altitude·burden₍ᵢ₎. The Dixon–Coles τ correction fixes the well-known under-counting of 0-0, 1-0, 0-1 and 1-1 scorelines. An Elo priorpulls each team’s attack/defense toward its rating-implied strength, and the fit is time-weighted (recent matches count more).

Host advantage. A single coefficient (h = +0.29) lifts the home/host side’s goal rate. For 2026 it applies to the three hosts (USA, Mexico, Canada) on their genuine home fixtures; it is discounted at neutral World Cup venues, and the altitude term handles Mexico City’s elevation separately.

Fit on data from 2008-01-01, 4-year half-life (1460 days), Elo-prior strength 20. Training cutoff 2026-06-03.

Assessed finding: adequate as-is, no map applied. Isotonic regression overfits the small World Cup window (+2.3% Brier on 2022); Platt scaling is net-neutral on Brier and degrades log loss. The raw model is acceptably calibrated — visible in the reliability diagram below — so the published run records calibration_method = none. This is a checked-and-adequate result, recorded with its evidence, not an omission.

Both years beat a uniform (⅓, ⅓, ⅓) model comfortably (Brier 0.667 / log loss 1.099). The comparison column is an Elo-logistic baseline on the same information.

With only ~64 matches per World Cup the bins are sparse — large bubbles carry the signal, small ones are noise-dominated, so read the diagram by bubble size. The points hug the diagonal without a systematic over- or under-confidence bias, which is why no calibration map was applied.

Rendered from reliability_2018.csv / reliability_2022.csv.

1. 1a–1cHead-to-head first — among the tied teams only: points, then goal difference, then goals scored.
2. re-applyIf head-to-head separates some but not all, re-apply 1a–1c to the teams still tied (the step does not restart from scratch).
3. 2d–2eOverall goal difference, then overall goals scored across all group matches.
4. 3gMost recent FIFA / Coca-Cola Men's World Ranking — FIFA's official terminal step.

For the best-8 third-placed ranking across groups the chain is identical except head-to-head is skipped (those teams have not played each other): points → overall GD → overall GS → FIFA Ranking.

Read live from the published forecast run (the current_run view) — the same source the forecast page uses, so it refreshes at every re-run.

• No team news. Injuries, suspensions, lineups and form within a camp are invisible to it — it sees match results, not who is on the pitch.
• No market signal. By design it ignores betting odds, so its champion shares are more compressed than the market’s (favourites land near 7–10%, not 12–15%).
• Sparse World Cup evidence. Only two tournaments (128 matches) back the calibration; reliability bins are noisy and a single tournament cannot fully validate tail behaviour.
• Grid-boundary tuning. Half-life and the Elo prior both landed at the top of their search grids — the true optimum may sit beyond, suggesting even more weight on long-run strength.
• Static within a day. The forecast updates when results are entered, not continuously; between updates it does not react to news.

• Pre-tournament. A final model re-run on the June 10 data freeze sets the published opening forecast — superseding any earlier provisional run.
• During the tournament. As each result is entered, the simulator re-conditions on completed matches and re-runs, so standings and championship odds shift to reflect what has actually happened.
• Provenance preserved. Each re-run writes a fresh reproducibility block (above), so any past state of the forecast remains traceable.