Value Betting Model22 European leagues, Dixon-Coles

01 — The idea

Four steps, and only one that matters

1. 01

   Fit a statistical model to historical match results → get a probability for each outcome (home / draw / away).

2. 02

   Convert bookmaker odds into implied probabilities, removing the overround.

3. 03

   Where the model's probability exceeds the market's by some margin, that's a theoretical "value" bet.

4. 04

   Backtest that rule against real historical closing odds to see whether it would have actually made money.the point

02 — The model

Dixon-Coles

Each team gets an attack strength (α) and a defense weakness (β), fit separately for each of the 22 leagues. Expected goals come from a home-advantage-adjusted exponential of the two, plus a global intercept so shrinking a team toward zero means "league-average", not "scores exactly 1.0 goals":

A τ correction adjusts the independent-Poisson assumption for low-scoring outcomes (0–0, 1–0, 0–1, 1–1) — the scores plain Poisson gets wrong most often. The model is fit by maximum likelihood (scipy.optimize.minimize, L-BFGS-B) with explicit parameter bounds and an L2 (ridge) penalty on attack/defense strengths, which matters far more on a single thin season than on the full nine-year window.

Home advantage alone doesn't transfer across leagues — fitted γ ranges from 0.147 (Serie A) to 0.269 (La Liga), nearly a factor of two. Every parameter is fit per league; nothing is shared or ported.

score_matrix(home, away) returns the full joint scoreline distribution, from which match_probs() derives 1X2 and markets.py derives over/under, BTTS, and Asian handicaps.

03 — The backtest

Strict walk-forward, no lookahead

For each matchday, the model is refit using only matches before that date — no lookahead, no season-level leakage. Probabilities are compared against the sharpest available closing line (Pinnacle → Bet365 → market average, overround removed). Two staking rules are simulated: every selection where the model's edge clears a fixed threshold (used for totals), and the ten highest-edge selections per matchday per league (used for 1X2, so one busy Saturday can't dominate the sample).

Two metrics get reported. Log-loss compares model calibration against the market and is threshold-independent — it's the more reliable signal. ROI depends on the staking rule and is noisier, so every ROI figure below carries a bootstrapped 95% confidence interval (3,000 resamples, resampling bets with replacement).

04 — Results

61,412 matches, 22 leagues, nine seasons

31,625 and 7,090 bets held out on the 2024/25 and 2025/26 seasons — never touched during tuning.

Both intervals sit entirely below zero across tens of thousands of bets — this isn't a noisy small-sample result, it's a settled one.

Adding 16 lower-division leagues was meant to test whether smaller markets are priced more loosely. They're not — the model's disadvantage to the market grows, not shrinks, down the pyramid, while the commission charged grows with it:

Soft markets are soft because they're hard to model — thin squads, high turnover, more randomness — not because the price is lazy. One of the 22 leagues (Scottish League Two, 359 matches) finished positive at +1.3%. With 22 tested, that's exactly the false-positive rate you'd expect by chance, not a lead.

05 — Why it loses

The selection gap

This is the core finding, and it isn't that the model is bad. It's what happens when you use the model's own errors to decide which bets to place.

Across every match the model prices, it's well calibrated — within about a percentage point almost everywhere:

Conditioned on the 6,128 selections the betting rule actually bets — where the model's edge over the market exceeds 5 points — that calibration collapses:

Same model, same matches, same day. The only difference is conditioning on model_prob − market_prob > 5pp. The market stays honest under that filter; the model doesn't, because the filter selects for the model's own errors. Log-loss tells the same story: the model looks better in absolute terms on those rows (0.5568 vs. 0.5778 overall) and is further behind the market there (0.5259 vs. 0.5642 overall).

"A model can be well calibrated on average and lose money on every bet it recommends. Overall calibration is not evidence for a betting strategy." The one sentence worth remembering from this project

06 — Reading this honestly

This is a valid result, not a bug

This is the expected outcome for a goals-only model up against markets priced by professional trading desks — now confirmed across 22 leagues and 61,412 matches rather than one partial season.

07 — Open leads

What's actually left to try

1. Best-price shopping — the only live lead, and it isn't a model. Switching from one sharp book's closing price to the best available across a panel is worth +2.84 points at 1X2, +2.27 at totals, +1.66 on Asian handicaps, measured across all 22 leagues. Needs its own held-out test before it's trusted.
2. Favourite–longshot bias is real here too — backing every favourite returns −2.7% against −7.4% for longshots. It doesn't make money; it's a way to lose more slowly, and it's already priced in.
3. BTTS is still unpriced — markets.py already computes it, but neither ESPN nor football-data's standard columns carry the odds. Needs a different feed before it can be tested at all.
4. Features — xG, rest days, lineup strength — only after there's an answer to the selection gap. A model whose own bet selection is its weak point doesn't obviously improve by getting more inputs.

08 — Files & setup

Reproduce it

Where it started: dixon_coles.py and backtest.py — the original single-league, single-season model. Kept in the repo for reference; dc_model.py and validate.py replaced them once the small-sample failure mode became clear.

Data comes from football-data.co.uk — nine seasons, 22 leagues, the sharpest available closing line per season (Pinnacle where available).