Cross-League Projection

Cross-league projection answers the question every recruiter asks about a player from a different division: "yes, but how would he do here*?"* A 7.4 average rating in one country does not mean the same thing as a 7.4 in another, and a game built on dominating possession in one league may or may not survive the pace of another. Projection translates a player's recent performance fingerprint from his current league into a target league, and reports how his profile would be expected to change on the move.

In one line: moving leagues changes two different things — where you'd rank (the level) and what you'd see (the shape of the performance). Our rating and club-strength systems handle level; this system handles shape, by learning — from thousands of players who actually made each move — an empirical "translation" that says which parts of a player's game hold up and which wash out.

Two questions, kept separate

A complete cross-league answer needs both, and we keep them apart because they fail in different ways:

• Level — "how good, on one global scale?" Answered by the ability score and by how hard each division is to play in. These say where a player sits on a shared axis.
• Shape — "what would his game actually look like there?" Answered here. We move a player's whole profile — passing, ball progression, pressing, defending, aerial duels, shooting — into the target league's context, and report which parts of his game the new level would sharpen and which it would erode.

This page is about the shape system. It is deliberately additive on top of level: a player can translate to a flattering shape and still be below the target league's standard, which is exactly why the product always shows ability and league difficulty alongside it.

The translation, learned from players who actually moved

The core idea is an empirical translation for each (source league → target league, position). Apply it to a player's current fingerprint and you get his projected fingerprint — what his game is expected to look like once he steps into the new league.

The translation is learned by comparing players to themselves — their profile in the season before a move against their profile in the season after. Differencing a player against his own earlier self cancels out his individual ability and leaves behind the league-move effect common to everyone making that step. We take a robust average across all the players who made each move, throwing out the freak cases (a player whose season was wrecked by a long injury, say) so that one outlier can't poison the result.

The selection-bias problem — and the fix

The hard part of any transfer-based translation is selection bias: the players a club chooses to buy up a level are the best of their league, so a naive before-and-after comparison flatters the move and understates the real gap.

The fix is promotion and relegation. When a club goes up or down, its entire squad crosses the division boundary together — not just the cherry-picked few a richer club wanted. Every player who featured for that club in both seasons is a clean before-and-after observation with no selection at all. This matters enormously for reliability: between two adjacent tiers there might be only a handful of direct transfers in a given position, but promotion and relegation contribute hundreds of unselected player-pairs. That unselected signal is the backbone of every league pairing we model.

When the data is thin

Most league pairings still have limited movement, so the translation borrows strength sensibly rather than overfitting a handful of cases. Where there is plenty of direct movement, we trust it. Where there is little, we lean partly on leagues of similar difficulty; where there is almost none, on the broad, all-positions pattern of moving up or down, scaled by how big the strength gap between the two leagues is. Every projection carries an explicit confidence level and the size of the sample it rests on, so the product can be honest about which case you're looking at.

What a projection tells you

Given the projected fingerprint, the product reads it three ways depending on the question:

• "How would he change?" It scores both the current and the projected profile across the main skill axes and reports the shift — "his ball progression sharpens, his pressing washes out" — against the target league's own benchmarks for that position, so the comparison is to a real standard rather than an invented one.
• "Find me players who'd translate cleanly." It can search the other way round — starting from a profile your league rewards, and finding players elsewhere whose game, once translated, would land near it.
• "Who actually fits us?" The translation feeds the signing shortlist: a candidate is projected into your league, the skills your club actually relies on are weighted up, and a player whose key strengths are expected to survive the step up is nudged up the ranking.

How we keep it honest

This is the part we are most candid about. The translation rests on sound foundations — real movers, the unselected promotion-and-relegation signal, robust averages, and a graceful fall-back when data is thin — and it survives the spot-checks we throw at it. But the formal out-of-sample backtest — recomputing each projection as of the move date and scoring it against what the player's profile actually became — is ongoing work. Until that is complete, the confidence level and sample size are the trust signal, and they are shown everywhere a projection appears, rather than hidden behind a single confident number.

What it can't do

• Shape, not level. The translation moves a player's profile; it does not, by itself, say he clears the target league's bar. Absolute standing comes from ability and league difficulty — and the product shows all three together, never the shape alone.
• Residual squad selection. Promotion and relegation removes individual cherry-picking, but a promoted squad did, as a unit, over-perform the tier below. Mixing in direct transfers softens this; it doesn't erase it.
• One translation per move. The translation is a single shift for everyone making a given step in a given position; it can't capture a particular player's idiosyncratic interaction with the move.
• Recent form, outfield only. It works from a recent window of a player's game, and goalkeepers are not modelled this way. A player caught mid-transfer has a mixed window, so the tool lets you set his source league explicitly.
• Coverage, not model. As everywhere, players in leagues we don't cover are invisible to it.

The research behind it

The design sits at the intersection of cross-league translation, vector-space representation, and robust statistical estimation.

• Desjardins, G. — NHL Equivalency. League Equivalencies. — The canonical cross-league translation: a ratio of production for players who switched leagues. It acknowledges survivorship bias without correcting it — the gap our promotion-and- relegation anchor is built to close.
• James, B. (1985); Davenport — Major League Equivalencies. — Baseball's translation systems from players moving between levels; the precedent for an empirical, mover-based approach.
• Schuckers, M., Lopez, M. & Macdonald, B. (2022). Estimating player aging curves. — Establishes the "delta method": identify an effect from within-player change to difference out individual skill. Our translation is a within-player before-and-after difference.
• Mikolov, T., Yih, W. & Zweig, G. (2013). Linguistic regularities in continuous space word representations. — The additive-offset analogy (king − man + woman ≈ queen). The translation is the same idea: player + league-move ≈ projected player.
• Efron, B. & Morris, C. (1975). Data analysis using Stein's estimator. — The empirical-Bayes idea of borrowing strength from broader groups when a specific one is thin.
• Leys, C. et al. (2013). Detecting outliers: use absolute deviation around the median. — The robust outlier rule used before averaging the movers.