The form half against a field — #639, part two

The attributes half compares an anchor against everybody (#463, #640). The form half still draws a pair: two lit dots, two bars of minutes, a roll-up against the man next in the order. This asks what each of those three was FOR, and whether the same question has an answer against a field.

Every figure is the real save, December, season-to-date — six centre backs read straight out of squadvision.db. Priors, shrinkage and share are computed here the way RoleScoring computes them, so moving a control moves real arithmetic.

1. What the three charts ask

Today, for a pair

chart	the question
Measured over	can you trust the per 90s below?
Where the gap comes from	which parts of the role make the gap?
By column	which columns does he win, by how much?

Against a field

chart	survives?
Measured over	question yes, shape no
Where the gap comes from	already solved
By column	yes — on the right track

The roll-up is nearly free #640 built FieldColumns and it already takes a columnsOf function. The attributes half calls it; the form half doesn't, only because its rows were still a pair. It is the same call with ColumnsFor passed in — that is section 4.

2. The problem: a raw track cannot mean one thing

A dumbbell plots raw values, so position carries "better". With two dots the colour and the "2.1 Min-Jae" label rescue it. With a field there is no label per dot and position is all you have — and direction flips per row.

Track: Raw value Share (direction-adjusted) Share, stretched to the row Reference: the median the best

Kim Min-Jae, against the five other centre backs.

Kim Min-Jae (the anchor) the rest of the field the median ↑ higher is better ↓ fewer is better

On the raw track, Possession Lost runs backwards Every other row puts the better man further right. Possession Lost per 90 is fewer is better, so on that row the leftmost dot is the best one — and nothing on screen says so. Today two dots and a label hide it. Six dots cannot.

3. What share does NOT fix found by building it

Share fixes direction. It does not give the rows a shared ceiling, and the difference is visible on the track. A higher-is-better row is value/max, so somebody always sits at 100. A fewer-is-better row is 1 − value/max, which reaches 100 only for a man who never loses the ball at all — so it stops wherever the squad happens to bunch.

Where each row's best dot lands

Four rows top out at exactly 100. The fewer-is-better row tops out at — its best dot never leaves the left half.

Correcting the claim this page started with I argued share would give the form rows "the same property the attributes rows get free from the 0–20 scale". It does not. It restores direction, not cross-row comparability. The form half never had that and does not claim it — ColumnRowsFor already says a dot "means something WITHIN its row and nothing down the column" — so this is consistent with what the half already is. But it is not the attributes half's property, and the stretched track is the option that buys it, at the price of absolute meaning.

4. How often the direction problem actually bites

Counted over the seeded roles rather than guessed:

Roles with a form half	88
…whose form half mixes directions	58
Seeded columns that are fewer is better	10 of 80

Almost always exactly one column, and almost always the same one: Poss Lost/90 in possession, Fouls Made out of possession.

Two thirds of roles

This is not an edge case to handle later. On the screenshot that started this, Possession Lost sits directly beneath Headers Won — opposite directions, same card, five rows apart from nothing.

5. Where the gap comes from, against the field

The same call the attributes half makes. Each category is the anchor's weighted points minus the reference's, where the reference is the median (or best) share per column across the field — not one man.

Today — against Lisandro Martínez

One man, picked because he is next in the order.

Proposed — against the median

The field, following the same chip as the rows above.

They disagree, and that is the point

6. "Measured over" — the one that should change shape

Six bars of minutes is a ranking of who played most, which was never the question. And the data view already puts minutes on every column head, so the per-player fact is answered elsewhere.

Scaled up — six bars

Correct, and not an answer to anything.

Proposed — one line

The caveat the strip existed to carry, said once.

7. What the share track does to a thin sample

This fell out of building it, and it is the strongest argument for the share track — it was not the reason for proposing one.

A dot on the share track is the scored figure, which is shrunk toward the squad's ordinary by how little football stands behind it (#376): (value×mins + prior×600)/(mins+600). So a thin-sample player is visibly pulled to the middle rather than sitting at an extreme he has not earned.

Possession Lost per 90 — raw against scored

prior (minutes-weighted ordinary) =

The strip's job, done by the rows

The cost, stated The printed figure stays raw and the dot is the scored one, so on a thin sample they disagree — Yoro reads 6.8 and sits mid-track. That is honest (it is what the score used) but it is a real change in what a row shows, and it is the thing to decide rather than discover later.

8. What this would settle

question	answer this page argues for
Do the form rows get a field?	Yes — one dot per player, anchor lit, field faint.
Plotted on what?	Share, not raw value — the only track where right means better on a mixed-direction card, which is 58 of 88 roles. Plain or stretched is the open question: plain keeps absolute meaning and leaves a fewer-is-better row in the left half; stretched fills the track and gives that up.
Does the roll-up follow?	Yes — the call already exists.
Do the sample bars scale up?	No — one line about the thinnest sample; the rows now carry the rest.
The raw figures?	Stay printed on the row. Only the dot's position changes meaning.