Features Features · the de-biasing win
A gradient-boosted Poisson goal model that learns non-linear effects of 36 feature differences, with monotone constraints encoding football priors. This is where the de-biasing lands: a genuinely global squad signal moved it from worst to best-non-market.
OOS RPS · expanding
the headline skill (realism protocol)
OOS RPS · LOTO
optimistic ceiling (leaks future folds)
Leaderboard rank
of 7 · CI 0.1569–0.2230
§ 01
In plain English, before any mathematics.
A gradient-boosted Poisson goal model that learns flexible, non-linear effects of the 36 engineered feature differences (x_i - x_j), with monotone constraints encoding football priors (more squad value should not lower expected goals). This is the model where the de-biasing win lands: switching the squad signal from Understat top-5 to the global API-Football panel moved it from worst to best-non-market.
§ 02
A boosted-tree stand-in for the linear goal rate: the same Poisson target, flexible feature effects, and football priors enforced as monotone constraints.
01The model
One booster, applied twice per fixture: reading the features from i’s perspective gives i’s goal rate, reading them from j’s gives the reply. Features enter as team differences; venue context — the heat-by-climate-gap interaction and the host flag — enters at the reference-team level, because heat hurts the unacclimatised side in absolute terms.
02The objective
Trees are grown on the Poisson likelihood itself — the natural loss for goal counts — never on win/draw/loss labels, which would discard the count information the simulator needs. Each boosting round fits the gradient of the deviance with its curvature as weights.
03Monotone constraints
The cheapest, highest-leverage regulariser at this sample size: directions football already knows are enforced, not learned. Raising the Elo, national-team form, squad-value, club-form or fitness advantage can only raise expected goals; a hotter venue for the less-acclimatised side can only lower them. The two decoupling gaps — form-versus-value and Elo-versus-value — are deliberately left unconstrained: their shape is the research question, and constraining them would assume the answer.
04The grid, with a fixed dependence
The booster learns strength only. The low-score dependence is one global nuisance, fixed at ρ₀ = −0.10 and applied to the assembled grid exactly as in Dixon–Coles — a clean separation of strength from dependence that a small sample cannot be trusted to learn jointly. Missing inputs route natively: a squad with no club-form data falls back to Elo and value at each split.
Symbol key
§ 03
The inputs this model reads — and only these.
§ 04
A schematic of the model wired end to end.
Fig. M·LightGBM Conceptual schematic
§ 05
Where this model lands between the Elo floor and the market ceiling, on both backtest protocols.
Fig. V11 Lower is better · floor = Elo-only · ceiling = de-vigged market
On the headline expanding window this model scores 0.1921 — −0.0017 below the Elo floor (0.1938) and +0.0015 versus the market ceiling (0.1905).
Bar fills to the model’s RPS on the floor–ceiling axis; the whisker on the expanding bar is the conservative 95% CI (0.1569–0.2230). Lower (left) is better.
It clears the Elo floor; the gap to the market is small and — at n = 3 — inside the bootstrap interval.
§ 06
The squad signal was Eurocentric. Making it global is what moved this model.
The squad-quality features were first built from top-5-European club data, which is sparse for non-European squads. That is a coverage confound: a naive model reads “low coverage” as “weak team,” which is circular and suppresses the squad signal exactly where it should add the most. Switching to a genuinely global club panel lifted average squad-form coverage from 47.8% to 85.0%, and moved this LightGBM model from worst to best-non-market on out-of-sample RPS.
Fig. V10 Weakest-first · Understat top-5 → global API-Football
The uplift is largest exactly where the bias bit hardest: OFC 15%→92%, AFC 17%→71%, while UEFA — already well covered — barely moves (73%→92%).
The fix is biggest off-UEFA and on low-coverage squads — directionally exactly as predicted. The GBM gains land there too, though they are not significant at n = 3.
The gain could have come from either seeing more players or re-weighting leagues. A placebo test that re-weighted leagues without adding coverage did not reproduce the lift — so coverage, not league-weighting, drove the result. Native missing-data routing means the trees still fall back to Elo and value when a squad’s club form is genuinely unobserved (it is missing for roughly 56% of player-rows overall).
§ 07
What this model is good for — and where it is weak.
Strengths
Limits