Scoring — Game Value, player board

Every figure on the board is a ratio of counted pairs. This page is the chain from a delivered rating to a published number, in the order it runs, so that a published figure can be checked rather than argued about.

1  the scored unit        a fixture-segment
2  the signal             the mean prior rating of the eleven on the pitch
3  the outcome            the goals scored during that segment
4  the strata             what a pair may form within
5  the statistic          Somers' D, over pooled pair counts
6  the baseline           naive plus-minus, on the identical segments
7  the floor              the league table alone, on the identical segments
8  the score              skill = D − D(plus-minus), with a paired interval
9  the second column      does the coach pick who you rate
10 the deadline rule      what a rating is allowed to have known

1. The scored unit: a segment, not a match

Each match is cut into three segments — kick-off to half-time, half-time to the 70th minute, and the 70th to full time.

A whole match would compare two elevens that both changed during it. A segment compares the same team with and without a player, against the same opponent, on the same afternoon: a substitution at 70' makes the last segment a different XI facing an unchanged one.

The clock overlaps itself between halves — the first half can run to minute 48 while the second starts at 45 — so every moment is keyed (period, minute, second) and mapped onto a monotone seconds axis before anything is cut.

Who counts as on the pitch

Occupancy is replayed from the event stream: the starting eleven, then substitutions and sendings off. A player is on the pitch for a segment if he was on for more than half of it.

A segment resolves only when each side's replayed XI is eleven, less anyone sent off. One that does not resolve is scored for nobody — it forms no pairs, and nothing is imputed to fill it.

2. The signal

For each side of each segment: the mean prior rating of the players on the pitch, weighted by minutes played, over that player's appearances before this match. The segment's signal is home mean minus away mean.

Two times meet in one number, and that is the point. The ratings come strictly from earlier football; the eleven comes from this match. A rating for the match being scored never informs its own signal.

A side needs prior ratings for at least nine of the eleven on the pitch, or the segment is not scored for that participant. A mean over a partial XI is a mean over a selected XI, and a rating covering only attackers would otherwise be compared against a baseline covering everyone.

3. The outcome

The goal difference during that segment — goals scored while those players were on the pitch, not the match's final score.

4. What a pair may form within: the eleven strata

A pair is two segments compared with each other. Pairs form only inside a stratum, and a stratum is (segment index, the score state the segment began at):

	≤ −2	−1	0	+1	≥ +2
segment 1	—	—	✓	—	—
segment 2	✓	✓	✓	✓	✓
segment 3	✓	✓	✓	✓	✓

Eleven cells, because segment 1 always begins level.

Both halves of that key close a real loophole. Substitutions are made because of the score, so a signal built from who is on the pitch tracks the scoreline — and the score state predicts the segment's own goals. Pairing across score states would let a signal earn credit for knowing who was already ahead; pairing across segment indices would compare a 45-minute window with a 20-minute one.

It is worth what it looks like it is worth. Scoring the same rehearsal with no strata at all moved the row +0.002 in 2024/25 and +0.003 in 2025/26 — a couple of thousandths handed to a participant for nothing, on a board where two real products are separated by fifteen.

5. Somers' D, over pooled counts

Within each stratum, every pair of segments is counted as concordant (signal and goals order them the same way), discordant (opposite), tied on the signal, or tied on the outcome.

The counts are then summed across strata before a single statistic is made of them — never averaged as per-stratum statistics, which would let a stratum of four pairs weigh as heavily as one of four thousand.

Somers' D = (C − D) ÷ (n₀ − n_Y)
τ-b       = (C − D) ÷ √((n₀ − n_S)(n₀ − n_Y))

n₀ all pairs, C concordant, D discordant, n_S tied on the signal, n_Y tied on the outcome. Segments with the same goal difference leave Somers' D's denominator rather than counting against you, so a perfect ordering can reach 1. τ-b keeps them, which penalises a rating that hands many players the same number — published beside D so that being vague cannot look like being right.

6. The baseline: naive plus-minus

Every participant is measured against the same construction: each player valued by the mean on-pitch goal difference he has accumulated in earlier segments this season, aggregated into a signal in exactly the same way.

This is the demanding zero. It already absorbs team strength — a player at a strong side accumulates goal difference while standing there — so a rating that knows only which team is better adds nothing to it.

A player with no prior segment takes his club-and-role peers' figure, not the league mean: club-and-role → club → league. Valuing a newcomer at a strong club identically to one at a weak club would leave exactly the team strength this baseline exists to absorb sitting there to be collected.

The published baseline differs slightly between rows. It is recomputed over each participant's own scored segments — the same signal, different football — which is what makes the difference between a row and its baseline a statement about ratings rather than about coverage.

A third signal, published and ranked by nothing: each side's mean points per match before the match, home minus away. No lineups, no ratings, no knowledge of who played.

Any lineup-aware signal ought to beat it easily. It does not. In both complete rehearsal seasons the floor landed about 0.004 below plus-minus — Somers' D of +0.2142 against +0.2185 in 2024/25, +0.1834 against +0.1879 in 2025/26.

Knowing who is on the pitch is worth about half a hundredth over knowing only which two teams are playing. That is the most consequential measurement behind this board, and it cuts both ways: the bar a participant is asked to clear is honest but nearly saturated, and a flat row may be a property of football — one segment of one match is very little evidence about an individual — rather than proof of a worthless product.

So beating plus-minus is the claim; clearing the floor is the precondition. The floor is on the board so a reader can see that directly rather than taking our word for it.

8. The score, and its interval

skill = Somers' D (participant) − Somers' D (plus-minus), on the identical segments

Zero means adding nothing to what each player's own on-pitch goal difference already says.

The interval is paired and resamples fixtures, never segments. The three segments of a match share an outcome, a squad and an afternoon; treating them as independent observations would understate the interval badly. A drawn fixture brings all of its scored segments with it, and both series are scored on the same resampled football before the difference is taken — so their errors are correlated and the difference is far better resolved than either number alone.

Fixtures are resampled within competition, so a participant scored on a subset of leagues gets its own within-competition bootstrap.

Read the interval, not the point. A row counts as separated from plus-minus only when the interval excludes zero, and over three rehearsed seasons that was rare: one of the two real products was flat in all three, the other sat above the baseline in all three but cleared zero in one of them (+0.0130 [+0.0015, +0.0263], 2024/25). Paired against each other the same two separated cleanly, by +0.015 in both complete seasons.

So level with plus-minus is the expected first-season result, the board says so in words, and the difference between two rows is better evidence than either row against the baseline.

9. The second column: does the coach pick who you rate?

A separate ranking, never blended with the first.

For each club match, look back five club matches and forward five. For every player in the squad over the window before, compare what he was rated then with the minutes he played after. Windows roll one match at a time, so the column recomputes every week.

The bar is his own prior minutes share. Without it, a rating would be credited for telling a regular from a reserve, which is not a claim. What is published is the difference.
Pairs form inside one club, one broad role, one window and one minutes band — so the comparison is always between players competing for the same place, already playing about as much as each other. The question is not who is the better player but which way is the coach about to move.
The interval resamples clubs, because one coach makes every selection at his club and one player appears in seven or eight windows. Resampling rows would treat one coach's habits as dozens of independent observations.

It resolves several times coarser than the score and separates two products far more rarely. It is agreement with the people who pick the team, not a measure of truth, and it is named that way.

It needs five club matches before a pivot and five after, so the first reading of a season appears only once every club has played about ten.

10. What a rating is allowed to have known

A match informs a later one once its own ratings were due, not merely once it was played. A midweek fixture kicks off before the weekend round's ratings are due, so ordering by kick-off alone would credit a participant for football it was still allowed to rate afterwards.

The baseline and the floor are gated by the same rule. Read over different football, the comparison between them would not be one.

The rule withholds about 3.1% of the prior football and some 30 segments a season, and moves the score by +0.004 in 2024/25 and +0.001 in 2025/26 — in both cases toward the participant, because the extra football kick-off order folds in early reaches the baseline too, and the baseline uses it better.

Every rehearsal figure on this page was measured by kick-off order, because the rehearsal had no deadlines to work from. The live board applies the deadline rule. So a live row sitting a thousandth above its rehearsed value is agreement with the rehearsal, not drift away from it.

11. Determinism

Every published week carries the bootstrap seed and the number of replicates drawn. The seed is derived from the week label, so re-running week 39 draws week 39's resamples. Snapshots are appended and never recomputed: a published row says what it was computed under, including whether an exception was in force.

12. Recomputing a published figure

Each participant's page publishes the five pair counts for the participant, plus-minus and the floor, all on the identical segments:

Somers' D = (C − D) ÷ (n₀ − n_Y)
skill     = D(participant) − D(plus-minus)

That is enough to reproduce every statistic on the row without this code. If your arithmetic disagrees with ours, the counts say whether the disagreement is in the counting or in the arithmetic — which is the whole reason they are published.