Input and integrity boundary
Only valid, strictly pre-match rows enter the equations
Every probability vector must use one consistent scale, sum to one, identify one settled outcome and carry a publication time strictly earlier than kick-off. Invalid and post-kick-off rows are excluded before class frequencies or baselines are formed.
- match_id
- Unique stable identifier; duplicate rows are excluded
- published_at
- ISO 8601 time with Z or a numeric UTC offset
- kickoff_at
- Must be strictly later than publication
- p_home / p_draw / p_away
- One 0–1 or 0–100 scale whose three values sum correctly
- outcome
- H, D, A, home, draw or away
- SHA-256
- Fingerprint of the exact input bytes, not proof of historical existence
Download the synthetic example CSV. It demonstrates the contract and must not be cited as model performance.
Direct probability error
The same multiclass Brier score has two common scales
- Σ3
- Average the sum of the three squared class errors. Uniform 1X2 scores 0.6667.
- ÷3
- Divide the identical summed value by three. Uniform 1X2 scores 0.2222.
- Same ranking
- Multiplying every score by the same constant cannot change model ordering or skill score.
For match i and class c, the summed convention is BS = N⁻¹ Σᵢ Σ꜀ (pᵢ꜀ − yᵢ꜀)². The class-averaged convention is BS ÷ 3. This page always publishes both.
Discrete sample decomposition
The residual prevents a coarse-bin estimate from posing as an identity
Each class is treated as a one-vs-rest probability forecast and assigned to one of ten intervals: [0,.1), [.1,.2), …, [.9,1]. Reliability and resolution use each occupied bin's mean probability, observed frequency and sample weight. Uncertainty uses the accepted class base rate.
With finite-width bins, probabilities can vary inside a bin. The residual reports the resulting approximation difference instead of silently forcing it to zero: residual = Σw Varbin(p) − 2Σw Covbin(p,o). The tool exposes both within-bin terms, their per-bin contributions and their correction in its report exports.
Calibration made visible
A reliability diagram asks whether 60% actually behaves like 60%
Each point uses one fixed probability bin for the selected home, draw or away class. Its horizontal position is the mean forecast probability and its vertical position is the observed frequency. Perfect calibration lies on the diagonal; circle size and the printed n keep sample support visible.
Vertical bars are Wilson 95% intervals for the binary event count inside each bin. They quantify finite-bin sampling uncertainty, but assume independent Bernoulli observations; repeated teams, leagues and time clusters can make that interval too optimistic. The downloadable SVG embeds the formula version, selected class, accepted-row count and input SHA-256 in its metadata.
Interpretation
Three components answer different questions
- REL
Reliability
Weighted squared gaps between each bin's mean probability and observed frequency. Lower is better under this estimator.
- RES
Resolution
Weighted separation of bin outcome frequencies from the overall class rate. Higher resolution reduces the estimate.
- UNC
Uncertainty
The accepted class rate times one minus that rate. It belongs to the observed sample, not to the forecasting model.
Reference-dependent skill
Skill is meaningful only after the baseline is named
Brier skill score is 1 − BSmodel ÷ BSreference. Positive values beat the named reference on these accepted rows; zero matches it; negative values perform worse. The uniform baseline assigns one third to every class. The empirical prior assigns the same accepted home/draw/away frequencies to every match.
The empirical prior is constructed and scored on the same accepted sample. It is a transparent descriptive comparator—not an out-of-sample benchmark, bookmaker benchmark or claim of future performance.
Research boundary
Versioned and tested does not mean independently certified
The scoring equations are grounded in the cited forecast verification literature. This particular browser implementation, fixed-bin policy, export format and tests have not been independently externally peer reviewed. Results depend on the supplied rows, binning choice and sample size.
- A SHA-256 is not a publication archive.It binds a report to the same bytes but cannot establish when those bytes first existed.
- Small bins are unstable.Always inspect n beside probability and outcome frequency; do not interpret an empty or tiny bin as a population law.
- Components are diagnostic, not causal.Reliability or resolution estimates do not identify which feature, league or training decision caused an error.
- A baseline is not a guarantee.Positive sample skill does not imply betting value or future superiority.
Primary literature
Probability scoring and decomposition foundations
These references define the underlying forecast-verification ideas. They do not certify this website's code or any supplied dataset.
- Brier (1950), verification of probability forecasts.Original article DOI
- Murphy (1973), probability-score partition.Original article DOI
- Gneiting & Raftery (2007), strictly proper scoring rules.Journal article DOI
- Bröcker (2009), proper-score decomposition for finite-valued outcomes.Journal article DOI
- Stephenson, Coelho & Jolliffe (2008), within-bin decomposition terms.Journal article DOI
Cite this tool as: Football Proof AI. “Football Brier Score Calculator & Decomposition Lab.” Version football-brier-decomposition/1.1.0, 13 July 2026, https://footballproofai.com/tools/football-brier-score-decomposition. Editorial technical note; not externally peer reviewed.