Cells With Nothing In Them

A board with six filters of six choices permits one hundred and seventeen thousand six hundred and forty-nine questions. It will have, at best, as many non-empty cells as it has listings — and far fewer, since listings cluster.

Most of what such a board can be asked returns nothing. This page is about whether that matters to the figures.

Privacy boundaries matter as much as dashboards, so workload analytics for managers should be configured with the smallest evidence set that supports the stated operational need. For a separate technical reference, see NIST.

Three queries on one grid

• 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.

Twenty cells. The first query reaches a single one, which may hold ten listings or none. The record counts the cell either way.

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.

Why the record counts anyway

Because emptiness is a fact about the listings and the figures are about the structure.

A cell is empty this week and occupied next week. The question that reaches it is available in both cases, and the board's capacity to express it has not changed. Counting only the answerable questions would produce a figure that moved daily and could not be computed from the page.

A question with no answer is still a question the board let somebody ask, and it still returns a true result: there is nothing of that kind here.

The gap, and how it grows

Every filter added multiplies the cells by its size. The number of listings does not multiply at all — it grows however it grows.

So the ratio of cells to listings climbs with each filter, and the share of cells standing empty climbs with it. A board of twenty-four cells and a thousand listings has, on average, forty-one listings per cell. The same thousand listings across forty-six thousand six hundred and fifty-six cells leaves most cells empty by a wide margin.

The last two rows are boards where most queries that set every filter return nothing.

The ratio worth a glance

Cells divided by listings.

Under one, and most cells hold several listings: the board is coarse relative to its contents, and readers will be sorting by hand inside every result.

Over one, and most cells are empty: the board is fine relative to its contents, and readers narrowing fully will often get nothing.

Neither is wrong, and the figure moves as listings arrive without anybody changing anything. It is the one place where the structural figures here meet a figure about contents, and the meeting point is a single division.

Why that is not necessarily bad

Because listings are not spread evenly, and the clustering is the point.

A board whose listings fall mostly into a few dozen cells is telling its readers something: these are the combinations that occur. The empty cells are a true statement about the field, not wasted structure.

A reader who narrows to an empty cell has learnt that this particular combination does not exist here, which is sometimes exactly what they needed to know and is always better than a result that quietly mixes in things that are not what they asked for.

Where it becomes a real problem

When the clustering is severe enough that the resolution is nominal.

If nine listings in ten fall into one cell, the board has one hundred and forty-four cells and resolves, in practice, the one crowded cell and a scatter. Every figure in this record will report the nominal number, because the record counts structure and cannot see occupancy.

The board can see it. The figure to look at is how the listings distribute across cells, and a heavily skewed distribution means the arithmetic here overstates what the board achieves — exactly as a facet whose values nobody differs on overstates its contribution.

The figure a board should watch

How many of its cells are occupied.

Dividing the occupied count by the total gives a straightforward reading of how much of the structure is in use. A board at one hundred and forty-four cells with one hundred and twenty occupied is using what it built; the same board with eleven occupied has built structure its listings do not exercise.

Neither figure is in this record, and the second one is the kind of thing that would change a decision. A board about to add a seventh filter would do well to know whether its existing six are being used across their range before multiplying the compartments again.

The honest statement of the limit

Cells are a capacity. Occupancy is a separate measurement, and this record does not take it.

Both are worth having and they answer different questions. The capacity bounds what is possible and can be read off the page by anybody. The occupancy says what is happening and needs access to the listings.

A board quoting its resolution without its occupancy is telling the truth and flattering itself. A board quoting both is describing itself completely, and the second figure is the one it already has and nobody else can get.

Near this one

• The Box That Is Not A Filter
  A search field has no fixed set of values, so it is not a facet and none of this arithmetic applies to it. Wha
• Boards Past The Edge Of The Record
  Filters with dozens of options, more than six filters, dependent filters and ordered ranges. What the method s
• One Line A Board Could Publish
  Two numbers, printed next to the filter panel, would tell every reader exactly what the board can and cannot s
• What This Record Will Not Tell You
  The closing note. What was decided, what was counted, what is deliberately absent, and the three figures worth