Grain

Choosing Sizes, Not Just Counts

Two boards with the same filters and the same resolution can differ fivefold in grain. The difference is free and nobody chooses it.

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A board deciding how to structure its filters usually asks how many to have. The sizes get chosen afterwards, by whatever the field seems to suggest.

The arithmetic says the second decision carries more than anybody expects, because resolution and questions depend on the sizes only through their products — and grain depends on their factors.

The next practical step is to compare the current capabilities, choose one real analysis cycle and compare the report with what was delivered. For a separate technical reference, see Databricks.

Twelve cells, two ways

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

Four grids drawn; two set none, and so return everything.

Four by three and two by six both give twelve cells. Setting one facet returns three on the first board and six on the second: same resolution, different rungs.

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.

Two boards, twelve cells each

Facets of four and three: twelve cells, twenty questions, four reachable sizes — one, three, four and twelve.

Facets of two and six: twelve cells, twenty-one questions, four reachable sizes — one, two, six and twelve.

Both have four rungs, and the rungs are in different places. A reader on the first board who sets the four-value facet gets three cells; on the second, setting the two gets six.

Neither is better in the abstract. What matters is which intermediate sizes a reader is likely to want, and that is a question about the field.

Why the sizes get chosen last

Because the facets come from arguing about what the board is for, and the sizes fall out of that argument as a detail.

A meeting decides the board needs a filter for region. Somebody then produces a list of regions, and the number of them is however many the list has. Nobody treats that number as a design decision, because it looks like a fact about the world.

Often it is. Often it is a choice between four coarse regions and six fine ones, made in a minute by one person, and it is the choice that determines the grain.

Where the difference gets large

Six facets, same resolution, and the grain runs from seven to thirty-nine depending on the sizes.

Schema	Cells	Sizes
2·2·2·2·2·2	64	7
2·2·2·2·3·3	144	15
2·3·4·5·5·6	3600	39

Three six-facet boards. The grain more than quintuples across them, and in this case so does the resolution — the comparison at fixed resolution is the class of seven, where grain still runs from six to fifteen.

The point holds either way: the number of filters tells you almost nothing about grain, and the sizes tell you everything.

The rule, as far as there is one

Prefer sizes that do not share factors, and avoid repeating a size if something else will serve.

That is the whole of it, and it is cheap advice: it does not change how many controls are on the page, it does not reduce resolution, and it does not make any listing harder to classify.

A board that needs about twelve cells can take four and three, or two and six, or three and four. They are different ladders, and nothing except the arithmetic distinguishes them.

Why nobody does this

Because the facets come from the field, not from the arithmetic.

If a field has four natural categories, the facet has four values. Nobody splits it into five to improve the factor structure, and nobody should: a facet that does not match the field is worse than any grain problem.

So the advice only bites where there is genuine latitude — which happens more often than it sounds. Bands of a continuous quantity can be cut into four or five. A list of options can be grouped coarsely or finely. Whenever the number is a judgement call rather than a given, the factor structure is a free tie-breaker.

The case where the field decides everything

Some facets have no latitude at all.

A yes-or-no property is two values. A property with exactly four legal states has four. Nothing about factor structure justifies inventing a fifth state or merging two real ones, and a board that did so would be lying about its own field to improve a figure.

So the advice applies to the remaining facets — the ones where a continuous quantity is being banded, or a long list grouped, or a range cut. Those are usually a third of a sidebar or more, and a third of a sidebar is enough to move the grain substantially.

The order to decide in

Resolution first, because it is the ceiling nothing else can raise. Decide roughly how many kinds of listing the board must tell apart, and pick facet counts and sizes that reach it.

Then the sizes, among the options that reach it. Several combinations usually do. Among them, prefer varied sizes over repeated ones, and prefer a five over a four or a six where the field is indifferent.

That second step costs one minute and buys, in the worst case, a factor of five in how finely a reader can adjust. It is the best return available anywhere in this record for the effort involved, and it is currently nobody's step.