What is a defender's win contribution?

The problem

Contribution to winning is what a contract is priced on, and in football we price it almost entirely on goals and key passes. That is not a measurement problem alone — it is why every child wants to be a striker, and why the holding midfielder and the target man who sacrifices himself are the two roles the game is now short of. A centre-back who wins every duel for ninety minutes appears in the model as a zero. I wanted to know whether that zero is real or just unmeasured.

What baseball already does

Baseball's WAR is not one number but a stack: value every event against a 24-state run-expectancy matrix, express it as runs above average, add a positional adjustment (a catcher is credited +12.5 runs per 162 games, a designated hitter −17.5), then convert runs into wins and subtract a replacement-level baseline. Two parts of that stack transfer to football and one does not. The event-value layer transfers — xT and VAEP are already the same idea. The positional adjustment transfers, and nobody has built it. Replacement level does not.

Why replacement level does not transfer

In baseball a substitution is like-for-like into a fixed batting order, so "what a freely available player would have done in that slot" is a well-defined question. In football the substitution changes the shape, sometimes the game model, sometimes the plan; the same player at 0-0 and at 1-0 down is being asked for different things. There is no slot to hold constant, so the counterfactual has no referent. I dropped replacement level entirely and kept the two layers that survive contact with football.

Two categories, not one

Everything a player does toward winning falls into one of two boxes. Category A is creation — the shot and key-pass value that the existing metrics already capture well. Category B is role fulfilment — how completely a player discharged the job his position actually asks of him: denying threat, carrying the ball through the first two thirds, counterpressing, winning duels, progressing under pressure. Then the empirical question: are these two things actually different, or is B just a noisy version of A? Put all six components into a goal-difference model and a threat-conceded model at once and they scatter across different quadrants — creation explains goal difference and almost nothing else; counterpress and duels explain threat conceded and nothing else. Measured on one axis, half the contribution is invisible.

Phase changes who scores

Before any of this can be scored, the phase has to be conditioned on. Across 1,946 matches, centre-backs are last of eight positions in open-play scoring rate and second of eight in set pieces — the rank order of who scores is not a property of a position, it is a property of a position within a phase. The independent women's sample reproduces the same structure. So the model scores ten phases separately rather than aggregating a match into one number, and a defender's set-piece goal is credited as what it is rather than as noise in a defensive profile.

Football's positional adjustment

Baseball earned its positional adjustment by tracking players who changed position — the same bat, a different chair, and the difference is the chair. There are 372 players in this data who changed position, and a player fixed-effects regression across 9,758 player-matches gives football the same shape: centre-back +65.8 goal-equivalents per 1,000 starts, forward −65.2, monotonically decreasing from the defensive line through midfield to the attacking line. The gap between the two ends is 131.0. This says a defender is not failing to score; he is not standing where goals are scored. As far as I can find, nobody has published this number for football before.

Nominal position is not the position played

A full-back in a 4-4-2 who pushes on is a winger for half the match and a full-back for the other half, and grading him as one or the other throws away whichever half you discard. So the model reads each player's measured activity grid separately in the attacking and the defending phase, assigns an effective role to each, and grades the attacking metrics against the attacking role and the defensive metrics against the defensive one. Marcelo's two centres of activity sit 25.8m apart across 30 La Liga matches: 90% full-back when Madrid have the ball, 57% full-back and 30% wide midfielder when they do not. His creation runs at 2.2× the full-back average and his build-up contribution at 2.7×.

The two corrections that mattered

Two defensive components came out of the first build with the wrong sign, and fixing them is the part of this work I would defend hardest. The first: a centre-back's threat-denial score correlated with more danger conceded, because being involved at all means the opponent already reached the box — reverse causality. Subtracting each player's own exposure, computed by weighting his defensive heat map against opponent threat by zone (the logic Statcast uses for outs above average), flipped the sign. The second: counterpressing looked like it made results worse, because the metric was count-proportional and therefore a proxy for how often the team lost the ball, and because "recovery" was counting clearances and failed duels — the cleanup after a counterpress fails. Rebuilt on the counterpress flag with a five-second possession check and a conditional baseline, it stops predicting goal difference at all and starts predicting threat conceded.

What this is not, yet

Everything above is in-sample. There is no out-of-sample validation, no goalkeeper track, no conversion from goals to points, and no set-piece-specific threat grid. The aerial-duel component is not fixable on this data at all — StatsBomb records only aerials lost, so a won header is invisible by construction. The multi-role bonus, which is the idea I care most about, is not yet stable across specifications. I am publishing it at this stage because the two sign corrections are the useful part: they are a demonstration that a defensive metric which is not exposure-normalised will tell you the opposite of the truth, confidently and with a small p-value.