NFELO is a static, searchable rating and prediction site for senior men's international football. It covers results from 1872 to the present, current and historical rankings, tournament snapshots, every source match, team peaks, number-one chronology and totals, top match instances, largest upsets, Best tournaments, team comparison and a date-aware probability calculator.
NFELO publishes one rating everywhere: current rankings, rankings on historical dates, team peaks, team pages and match records all use the same evidence-adjusted network rating. A hidden attack/defence state refines match probabilities only; it never changes ratings, ranking order, peaks or points gained from results.
Current methodology version: 2026-07-26-global-as-of-consistency.
Tournament snapshots use the same published rating immediately before and after each completed edition. Tournament rating change and Best tournaments include only published movement from that edition’s matchdays, excluding annual recalibration and unrelated results. Tables use the team name active during the edition; selectors use joined lineage labels so successor names remain easy to find.
The rating state is a full-covariance dynamic Gaussian opponent network. The base-10 Elo expectation remains the observation link, while the model also represents uncertainty shared through common opponents, era-specific home and draw conditions, an active-pool debut prior and goal-margin information. Competitive and unresolved results use information ratio 1.00; evidence-backed friendlies use 0.78621.
Every match with a complete shared date is forecast from one frozen start-of-day state. Same-date debutants receive the same pre-date pool prior, and all results on that date are learned in a single order-invariant Gaussian update. Historical rows without a complete day remain in their source sequence.
Recent opponent weights have an eight-year half-life. Their effective distinct
count gives reliability rho_i = N_i / (N_i + 4). If B is the mean latent
strength of the ten strongest eligible active teams, the published rating is:
M_i = 2000 + rho_i × (mu_i - B)
NR_i = M_i - 1.6448536269514715 × sqrt(Sigma_ii)
After every complete matchday, a compact global snapshot stores the network mean and marginal variance for every eligible team. This matters because the full covariance update can move a connected team even when that team did not play. Current Rankings and the latest History view are reconstructed from the same global state and checked for identical membership, order and displayed values.
For a ranking or prediction date after a team's latest appearance, the model projects its marginal variance forward without changing its latent mean:
Sigma_ii(as of t) = Sigma_ii(last match) + 19.750212594949737² × Delta t
This gradually lowers the cautious public rating while a recently active team is inactive and widens future-match uncertainty. Ranking eligibility means an appearance in the selected calendar year or one of the preceding four calendar years. The projection is read-only: completed matchday ratings, historical peaks and the fitted replay are not rewritten.
The marginal variance Sigma_ii is retained deliberately. Cancelling uncertainty
shared with a contemporaneous elite reference can make a small, inward-looking
historical network appear far more certain—and therefore far stronger across
eras—than the evidence warrants. The latent posterior mean remains available
inside the forecast calculation but is not published as a competing ranking.
Because match forecasts use that latent strength distribution, venue and the
attack/defence layer, the higher-rated team is not guaranteed to have the higher
win probability. The rating is the cautious ranking output; the forecast is the
full predictive output for one match.
For an eligible match instance:
Q_ij = M_i + M_j
- 1.6448536269514715
× sqrt(Sigma_ii + Sigma_jj + 2 Sigma_ij)
Both participants need 30 prior matches. Every match instance is retained; repeat pairings are not collapsed.
The network forecast integrates uncertainty in the strength difference and uses separate friendly and competitive probability temperatures. A parallel team-specific attack/defence model produces a score-based W/D/L vector. Annual draw calibration, probability powers and the pool weight are fitted using only the preceding eight complete calendar years. Before use, the four fitted coefficients are placed on a fixed six-decimal publication grid. This removes platform-level optimiser jitter without changing any displayed probability.
The score correction is boundary-gated: NFELO moves toward the pooled forecast only as far as it can without changing the network model's most likely W/D/L outcome. The exact-score table is then raked so its win, draw and loss regions sum to the displayed final probabilities; omitted scorelines above 5–5 remain in the reported tail mass.
Completed matches retain the exact pre-match probability vector. The arbitrary historical calculator reconstructs the exact selected-date marginal states, but the static archive does not retain every historical off-diagonal covariance; those W/D/L values are therefore labelled as approximations. Its rating-effect table is an isolated one-match scenario that holds the elite reference, opponent breadth and other same-date results fixed.
The 0.78621 friendly multiplier applies to the opponent-network update before the joint matchday calculation. It scales both gradient and curvature, so a friendly's displayed point movement is not mechanically 78.6% of an otherwise similar competitive match.
Every match on a complete date is forecast from the same frozen start-of-day state. Same-date debutants receive the same prior, and all results from that date enter one joint, order-invariant update. The attack and defence state is also held fixed until every forecast for the date has been stored.
The probability layer keeps the largest score-based correction that does not change the network model's most likely outcome. Exact-score probabilities are then reconciled with the displayed win, draw and loss vector. First-published future forecasts are stored by methodology version so later evaluation can use probabilities recorded before the result was known.
NFELO publishes one evidence-adjusted rating for rankings, records and historical comparisons. The latent network mean remains part of the forecast calculation rather than appearing as a competing public table.
Tournament importance and match class are separate. The maintained registry contains 188 friendly codes covering 21,529 matches, 239 competitive codes covering 30,165 matches and 233 uncertain codes covering 618 matches. Uncertain and unknown competitions use the competitive information weight.
Every family previously placed in the fallback Other tournaments category has been reviewed. Seventy-two source codes represent invitationals, preparation events or friendly series; sixteen represent formal regional, federation or multi-sport competitions. Friendly families are excluded from both Tournaments and Best tournaments.
Under this classification, the full 52,312-match replay jointly fitted:
- friendly information ratio
0.78621; - friendly network temperature
0.896294991479; and - competitive network temperature
1.061356232973.
The scoring period contains 46,801 forecasts from 1960 through 11 July 2026,
including 18,546 friendlies. The network-only log-loss minimum is
0.881475145850. At the previous ratio of 0.76064, with both temperatures
refitted under the same classification, it is 0.881478166958.
These are reproducible full-sample constants for the fixed ledger and objective, not claims of equivalent population precision. Classification evidence, future results and prospective scoring can move the preferred value.
The primary comparative result is the original five-block nested historical holdout over 46,801 matches from 1960 onward:
| Model | Three-way log loss | Most-likely W/D/L correct |
|---|---|---|
| NFELO network | 0.884219 | 59.095% |
| Best tested scalar Elo | 0.892970 | 58.527% |
| G-Elo comparison | 0.895187 | 58.779% |
| Published World Football Elo forecast | 0.902619 | 58.804% |
Choices used earlier periods and were scored on later periods. The aggregate result is retained, but the original fitter programs and frozen derived dataset were not committed, so it cannot currently be reconstructed bit-for-bit.
The site also calculates a retrospective diagnostic on every build by replaying the final constants through the fixed 1960–11 July 2026 window. It is useful for checking date batching, the boundary gate and other mechanics, but it is not a second out-of-sample estimate and must not be compared as if it were the same experiment as the nested holdout.
First-published fixture probabilities are stored in
source/prospective_forecasts.jsonl by methodology version, source hash,
model-state hash and results-through date. That ledger supplies genuinely
prospective evidence as matches are completed.
See Model validation and the
19 July 2026 methodology audit. The
executable reproduction materials are retained under
research/methodology-audit-2026-07-19/.
The Pages workflow checks results and fixtures at 06:20, 15:20 and 23:20 UTC. It validates and stages external data, replays the complete history, runs the test suite and deploys only a verified static artifact. If input or model checks fail, the last good site remains online.
Routine updates do not refit core rating or score-state structure. At each January boundary, only the declared forecast calibration is refitted from the preceding eight complete years, then canonicalised to six decimal places. Every rebuild applies the tournament classifier to new source codes; unresolved events remain competitive until positive friendly evidence is recorded. The standalone audit command can be run whenever a classification review report is needed.
python -m venv .venv
. .venv/bin/activate
python -m pip install -r requirements.txt
python scripts/build_site.py --source source --config config --output public
python -m unittest discover --start-directory tests --verbose
node --check public/assets/app.js
python -m http.server 8000 --directory publicsource/— validated results, fixtures and the prospective forecast ledger.config/— frozen deployment parameters and tournament metadata.scripts/ledger.py— identity mapping, deduplication and source ordering.scripts/tournament_classification.py— evidence registry, future-code rules and audit.scripts/model.py— date-batched opponent-network replay and public rating.scripts/forecast_layer.py— hidden score state, annual calibration and gate.scripts/build_site.py— static data, history, records and fixture generation.scripts/fetch_sources.py— guarded multi-source updater.public/— GitHub Pages application shell; generated data is ignored by Git.tests/— model, data, UI and historical regression checks.docs/andresearch/— validation, audit and reproduction materials.
Historical rows and labels are based on World Football Elo Ratings.
The ledger follows recorded senior international histories rather than FIFA
membership alone, so it includes some territories, regional selections and
defunct teams. Inclusion is a data-scope decision, not a statement about
political status or eligibility for a particular competition.
Recent results also use the CC0 international_results dataset and OpenFootball's
public-domain World Cup data. Future fixtures use the World Football Elo schedule
plus TheSportsDB. Duplicate events are merged; conflicting scores stop publication.
NFELO does not use squads, injuries, red cards, tactics, travel, rest, weather or betting markets. Political successor mappings and cross-era comparison remain modelling assumptions. Ratings and probabilities are estimates, not certainties or betting advice.
Project code is MIT-licensed. Source data remains attributable to its publisher and is not relicensed by this repository.