Reaching one

The Questions That Reach One Answer

Only queries that set every filter reach a single cell, and there are as many of those as there are cells. The share is one over the other.

Reaching oneReference64/729 to 6/7

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A query reaches a single cell only when it sets every filter. Leave one alone and the result spans all the values of that filter at once.

So the questions that pin down a single kind of listing are exactly the questions with no filter left untouched — and there is one of those per cell.

An analytics team may look through the available settings, assign one pilot owner and review useful findings and false signals together. For a separate technical reference, see Preset.

The number of pinning questions is the cell count. The number of questions altogether is the question count. The share is one divided by the other.

Setting all, setting some, setting none

one cell: one combination of values
the heavy outline with corner ticks: what the query returns

Three grids drawn; one of them sets every facet and so reaches a single cell; one sets none, and so returns everything.

Twelve cells. The first query sets both facets and reaches one; the second sets one and returns three; the third sets neither and returns everything.

Computed from the two facet sizes. A query sets a facet to one value or leaves it unset: that is the convention, not a claim about how anybody searches.

The share, worked

A board with facets of four and three choices has twelve cells and twenty questions. Twelve of the twenty set both filters; the other eight leave at least one alone.

Twelve over twenty: three fifths. On this small board, most available questions do reach a single cell.

Schema	Cells	Questions	Share
4·3	12	20	3/5
4·6·6	144	245	144/245
2·2·2·2·3·3	144	1296	1/9
2·2·2·2·2·2	64	729	64/729

The last two rows are the warning. Both resolve more than a hundred kinds of listing, and on the fourth board fewer than one question in ten narrows to a single one.

The bigger and busier a filter panel looks, the smaller the share of its questions that actually pin anything down.

Why the share falls as facets are added

Each facet contributes its size to the cells and its size plus one to the questions. So each facet multiplies the share by its size divided by its size plus one — a fraction always less than one.

A facet of six multiplies the share by six sevenths. A facet of two multiplies it by two thirds.

Six facets of two: two thirds raised to the sixth, which is sixty-four over seven hundred and twenty-nine. Under a tenth.

That is the floor of this record, and it belongs to the schema with six small facets rather than the one with six large ones. Small facets cost the share more than large ones do, because adding one to two is a bigger proportional change than adding one to six.

What falls on the other side

Everything that leaves at least one filter alone, which on a large schema is almost everything.

Those queries are not failures. A reader who sets two filters out of six and gets a manageable list has done exactly what they meant to. The share measured here is not a success rate; it is a structural property of what the board permits.

The page on what the share is not goes through this carefully, because the figure is easy to read as a judgement on readers rather than a description of a board.

The derivation in one line

Cells over questions equals the product of the sizes over the product of the sizes each plus one, which rearranges to the product of the fractions size over size-plus-one.

That rearrangement is checked by the program that builds this record rather than asserted — it recomputes the share both ways for every one of the four hundred and sixty-one schemas and stops if they ever disagree.

It matters because the second form is the useful one. It says the share is built facet by facet, each contributing a factor that depends only on its own size, and it makes the effect of adding a facet immediate: multiply by a fraction a little under one.

Why it is not the same as narrowing successfully

A query that sets every filter reaches one cell. That cell may hold forty listings.

So pinning a cell is not pinning a listing. It is reaching the finest compartment the board has, and how many listings sit inside depends on how the board's contents are distributed.

The share measured here is therefore a ceiling on precision rather than a measure of it. A reader who sets everything has done all the narrowing available to them; what they get is whatever the board holds in that compartment.

The figure across the record

The share runs from sixty-four over seven hundred and twenty-nine at the low end to six sevenths at the high end. The median is sixty-four over two hundred and twenty-five.

Three schemas sit exactly at that median, and the first of them is the tidiest illustration in the record: facets of two, two, four and four, giving sixty-four cells and two hundred and twenty-five questions. The share is literally the pair of figures, one written over the other.