1,520 held-out EPL matches · 143 test weeks · Aggregate only
Does a sequential Dixon–Coles correction improve EPL score probabilities?
Direct answer: not detectably in this design—and this was not a full joint Dixon–Coles maximum-likelihood fit. Dixon–Coles changed mean exact-score log loss by +0.000328 nats per match; its paired 95% interval was [-0.000413, +0.001071]. Lower is better, so the point estimate slightly favoured independent Poisson, while the interval crossed zero.
Published by Football Proof AI · Published · poisson-vs-dixon-coles-football-benchmark/1.0.0 · Editorial technical note; not externally peer reviewed
Canonical publication record
Abstract
An aggregate-only, 1,520-match EPL walk-forward comparison of independent Poisson and a training-only Dixon-Coles low-score correction on identical fitted goal rates, with exact-score log loss, 1X2 proper scores, low-score calibration, paired weekly-block intervals and source hashes.
- Author and publisher
- Football Proof AI
- Technical report
poisson-vs-dixon-coles-football-benchmark/1.0.0- Published
- Last modified
- Release status
- Current release
- Review status
- Editorial technical note; not externally peer reviewed
- Version history
poisson-vs-dixon-coles-football-benchmark/1.0.0: Initial public release.
- Immutable artifacts
- 1.0.0.json
sha256:4db9a94224d06be75dbe8002dc965c7c081e64b38671f7355764237d15032a2c - poisson-vs-dixon-coles-football-benchmark-1.0.0.csv
sha256:e71a1b85a563dffc5888f228673c44c49cfb7bbae056824f33758a8102182700 - 1.0.0-manifest.json
sha256:79314f2517b6e940aa3edb770afe91485af90ec97be4f8df498bc8d8ddf02601
- 1.0.0.json
- External release resources
Cite this benchmark
One release, one identifier, two citation formats
Football Proof AI. (2026). Poisson versus Sequential Dixon-Coles EPL Score Probability Benchmark. Version poisson-vs-dixon-coles-football-benchmark/1.0.0. https://footballproofai.com/research/poisson-vs-dixon-coles-football-benchmark
- Identifier
fpai:dataset:poisson-vs-dixon-coles-football-benchmark:1.0.0- Aggregate licence
- CC BY 4.0
- Third-party source rights
- unknown/not asserted · checked 2026-07-15
First-party result
All three paired intervals crossed zero
Both methods used exactly the same fitted home and away goal rates. The only change was a rho estimated from eligible training matches before each test week. That isolates the low-score correction instead of letting a second model specification take credit for different lambdas.
| Metric | Poisson | Sequential DC | DC − Poisson | Paired 95% CI |
|---|---|---|---|---|
| Exact-score log loss | 3.01293166 | 3.01325927 | +0.00032761 | [-0.00041314, +0.00107077] |
| 1X2 Brier, class average | 0.19821609 | 0.19821578 | -0.00000031 | [-0.00011030, +0.00010353] |
| 1X2 log loss | 0.99647056 | 0.99663952 | +0.00016896 | [-0.00052658, +0.00083317] |
Season stability
The sign moved by season; there was no stable universal winner
Positive differences favour independent Poisson and negative differences favour the sequential correction. Publishing every evaluation season defined in release v1 prevents one favourable slice from becoming the whole conclusion; this release does not claim external preregistration.
| Season | Matches | Mean rho | Poisson score log loss | DC score log loss | DC − Poisson | 1X2 Brier Δ |
|---|---|---|---|---|---|---|
| 2022/23 | 380 | -0.0176 | 3.056946 | 3.058179 | +0.001233 | +0.00011109 |
| 2023/24 | 380 | +0.0256 | 3.104429 | 3.104787 | +0.000358 | -0.00005504 |
| 2024/25 | 380 | -0.0025 | 2.991591 | 2.991935 | +0.000344 | +0.00003014 |
| 2025/26 | 380 | -0.0118 | 2.898761 | 2.898136 | -0.000625 | -0.00008743 |
Where rho acts
Inspect the four adjusted scorelines instead of treating rho as magic
Dixon–Coles modifies only 0–0, 0–1, 1–0 and 1–1 in this implementation. The table compares each method's mean held-out probability with the same observed frequency across all 1,520 matches.
| Score | Observed | Poisson predicted | Poisson gap (pp) | DC predicted | DC gap (pp) |
|---|---|---|---|---|---|
| 0-0 | 5.07% (77) | 6.11% | -1.04 pp | 6.12% | -1.06 pp |
| 0-1 | 6.64% (101) | 7.65% | -1.00 pp | 7.63% | -0.99 pp |
| 1-0 | 7.83% (119) | 8.93% | -1.10 pp | 8.91% | -1.08 pp |
| 1-1 | 11.05% (168) | 10.50% | +0.55 pp | 10.52% | +0.54 pp |
Temporal contract
Every test week was invisible to both fits
The 2021/22 season supplied 380 warm-up matches. For each later ISO week, the generator refit from scratch using only rows before Monday 00:00, estimated rho from that same past-only set, and then scored the untouched week.
- 01
Past-only lambdas
Release v1 applies one fixed ridge-1 attack/defence specification uniformly to every fold; no external preregistration is claimed.
- 02
Past-only rho
The one-dimensional correction was solved inside its positivity interval; boundary optima fail closed.
- 03
Paired test rows
Both methods scored every one of the same 1,520 held-out fixtures, including seven declared cold starts.
- 04
Week-block interval
Five thousand deterministic paired bootstrap resamples retained within-week dependence and method pairing.
Read the general walk-forward protocol and use the temporal leakage auditor before publishing a football model comparison.
Interpretation boundary
This tests one shortcut, not every Dixon–Coles model
A copied fixed rho is not automatically an upgrade. This study found no detectable gain for a sequential training-only correction on one EPL ridge-Poisson design. It did not run a full joint Dixon–Coles maximum-likelihood fit, multiple leagues, shot-level xG or the site's production LightGBM candidate.
Reproduce the release
Two aggregate distributions, one manifest, five source hashes
The aggregate release is CC BY 4.0. Football-Data.co.uk source files remain at their publisher; because this project does not assert a raw-data redistribution licence, the release records URLs, fields and SHA-256 fingerprints but publishes no fixture-level source or prediction rows. The generator can rebuild only while publisher bytes still match, or from hash-matched CSVs you already hold.
Primary sources