Regression lab · ridge + cross-validation

What Moves What

Every other page here hands you a finished model. This one hands you the fitting. Pick an outcome, pick the metrics you think drive it, choose the cohort to fit inside — and a ridge regression runs in your browser: standardised coefficients you can compare to each other, the out-of-fold r² sitting beside the in-sample one so the overfit is visible, and every player's residual. It measures association, not cause. A metric can move with an outcome because it makes it happen, because both follow from something else, or because the squad taking those shots was always going to score.

— players — ridge, 5-fold CV fitted in-browser

Fit a model

Choose what you are trying to explain, then what you think explains it. Everything is fitted inside one position cohort, because a centre-back and a striker do not share a scale on any of these metrics — pooling them would find "strikers shoot more" and call it a discovery.

Cohort —

Target — what to explain —

League adjustment Uses the site's league-strength priors

Predictors — what might explain it (0 chosen)

Composite scores are not offered as predictors: they are built from the metrics beside them, so a model containing both would be explaining a number with its own ingredients.

Who the model misses

The residual is what a player did minus what the model expected from the metrics you chose. Read it as "unexplained by these inputs", not as "better than expected" — the model is only as good as the predictors you handed it, and every prediction here is out-of-fold, made by a model that never saw that player.

How it's computed

The model. Ridge regression: least squares with an L2 penalty on the coefficients. Plain least squares is a poor fit for football per-90s because they are heavily collinear — npxG/90 and shots/90 move together, xA/90 and key passes/90 move together. Given collinear inputs, ordinary regression answers with one huge positive coefficient and one huge negative one; the fit looks fine and the coefficients are noise. The penalty shrinks that apart-pulling and leaves numbers you can read.

The penalty strength (α) is not chosen by hand. Twenty-two candidates, log-spaced from 0.01 to 10,000, are each scored by 5-fold cross-validation and the one with the lowest out-of-fold error wins. Folds come from a seeded shuffle, so the same cohort and picks always give the same answer.

Standardisation happens inside each fold, never once across the whole sample. Centring on the full sample's mean would leak the held-out players' values into training and move the score for a reason unrelated to the model. The unit test for this page recomputes the predictions both ways and fails if the shipped answer matches the leaky one.

What the numbers mean. Coefficients are on the standardised scale: "a one-standard-deviation move in this metric shifts the target by this much, in the target's own units", which is what makes them comparable to each other. r² is reported out-of-fold as the headline, with the in-sample figure beside it — the gap between them is the overfit, and quoting only the in-sample number is the usual way a page like this flatters itself.

What it refuses. Fewer than 30 complete rows: no fit at all. A predictor with no spread in the cohort: named and refused rather than solved as a singular system. A target used as its own predictor, or a composite score used to predict its own components: not offered. Players missing any chosen metric are dropped from the fit and counted.

Sources. The same corpus The Forge scores from: Understat merged with FotMob season boards, outfielders over 900 minutes, one season, percentile cohorts as elsewhere on the site. Metrics with no coverage in the loaded pool are not offered — the picker is built from what the players actually carry, not from the catalogue.

What Moves What

01 Fit a model

02 Who the model misses

Fit a model

Who the model misses