Finding undervalued footballers in Europe’s Big Five

The question

A forward who scores fifteen goals might be valued at €50M. A centre-back with four interceptions a game and 90% passing accuracy might be valued at €25M — even though both are performing at an elite level for their position.

That gap is the whole project. The transfer market does not price all contributions equally. Some of that is rational — goals win games, and scarcity is real. Some of it is narrative: visibility, league prestige, age optics, agent noise. If you can separate the rational part from the narrative part, the residual is a shopping list.

So: can we predict what the market will pay for a player from what that player actually does — and are the players the model disagrees with systematically undervalued?

Why three data sources

No single dataset contains both what a player does and what the market thinks they’re worth. We assembled three, each contributing something the others could not:

Source	Contributes	Why it was necessary
FBref	Per-90 performance across shooting, passing, possession, defensive actions, goalkeeping	The behavioural ground truth — what actually happened on the pitch
Transfermarkt	Market valuations by season	The target variable. Without it there is nothing to predict
League financials	Total revenue per league-season	Controls for the fact that richer leagues inflate every price inside them

The join was on player-season, with league financials joined on league and season. The result: 4,056 player-seasons, 203 columns, split temporally — 2021–22 and 2022–23 for training, 2023–24 held out as the test season.

The split is temporal on purpose. A random split would let the model see a player’s 2023–24 valuation while training on their 2022–23 one, and player valuations are heavily autocorrelated. That would produce a beautiful score and a useless model. Splitting by season forces it to do the real task: predict a valuation it has never seen for a season it knows nothing about.

Guarding against leakage

More time went into deciding what to exclude than what to include. Explicitly dropped:

• market_value_eur — the raw target
• highest_market_value_in_eur — circular; it encodes future valuations
• valuation_date, contract_expiration — leak information from after the prediction point

The target itself is log market value, not raw euros. Transfer values are heavily right-skewed — a handful of superstars sit orders of magnitude above the median — and regression on raw euros lets those few observations dominate the loss. Logging makes the residual structure roughly homoscedastic and turns the model’s errors into something closer to percentage error, which is how club valuations are actually reasoned about.

Multicollinearity

203 football statistics are enormously redundant. passes_completed, passes and passes_pct are three views of one thing; touches by pitch zone sum to total touches. Feeding that directly into a linear model produces unstable, uninterpretable coefficients.

We ran variance inflation factor analysis on the training data only — running it on the full dataset would leak test-season structure into a preprocessing decision — and pruned iteratively.

One judgement call worth recording: plus_minus_per90 was the single strongest predictor in the model (t ≈ 27), and it was also collinear with several team-level features. We kept it and dropped its correlates instead of the reverse. Statistical hygiene shouldn’t cost you your most informative variable — when VIF forces a choice, drop the one that explains less.

The four hypotheses

Rather than jumping straight to prediction, we tested the market biases explicitly. A model that predicts well but can’t tell you why the market misprices anyone is not an investment thesis.

1. League premium — do Premier League players command higher values than statistically comparable players elsewhere? Tested with ANOVA on log market value, controlling for performance.
2. Positional valuation gap — are forwards valued above defenders after controlling for age and minutes played?
3. Age–performance interaction — does the market discount older players for identical statistical output?
4. Contract length effect — do players with longer remaining contracts command higher valuations? (They should — leverage sits with the selling club.)

Testing these separately matters because each one is a different kind of inefficiency. A league premium is arbitrage across competitions. An age discount is arbitrage across time. They imply different buying strategies.

The mistake I want to keep in the write-up

The first version of the undervalued-player ranking returned a defender with a predicted value of €1.55 × 10²⁹. Which is, generously, more money than exists.

The cause was a classic one: the model predicts in log space, and I compared predictions to actual values without correctly back-transforming — so a modest error in logs became an astronomical error in euros, and the “most undervalued player” ranking was really just sorting by whose back-transform blew up worst.

I’m keeping this in the case study deliberately. The lesson isn’t “check your maths” — it’s that a result which is absurd on its face is a gift, because it’s the only kind of bug that announces itself. The dangerous version of this error is the one that produces a plausible-looking number. The fix — back-transforming both sides consistently and ranking on the residual in log space rather than on a euro difference — is small. Catching it required looking at the output and asking whether it made sense in the real world, which is a habit no cross-validation score will give you.

What it’s for

The output is a ranked list of players whose modelled value exceeds their market price, alongside statistical evidence for which market biases are real. For a club with a finite budget, that’s a shortlist — and, more usefully, a reason attached to each name: this player is cheap because he plays in the wrong league, that one because he’s on the wrong side of thirty for a market that over-weights age.

Limitations

• Market value is not transfer fee. Transfermarkt valuations are crowd-informed estimates, not observed transactions. The model predicts perceived value, and the honest framing is that it finds players the market’s own consensus underrates.
• Injuries aren’t in the feature set, and they’re a large part of why some players look cheap.
• Three seasons is a short panel for claims about structural market bias.