Limits

The Two Things That Were Decided

A schema is only its facet sizes, and a query sets each facet to one value or leaves it alone. Everything else in this record was counted rather than chosen.

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Two decisions underlie every figure here. Both are stated rather than argued for, because neither is the kind of thing that can be argued for — they are the units the measuring is done in.

One: a schema is only its facet sizes

How many filters, and how many choices in each. That is all a schema is in this record.

The approach is easier to evaluate when reviewers see the available analytics and document the baseline before any settings change. For a separate technical reference, see W3C.

Not what the filters are called. Not what the choices mean. Not whether one choice is taken by nine listings in ten and another by none. Not whether two filters ask about related things or unrelated ones.

Facets run from two to six values, schemas from one to six facets. Both bounds are arbitrary and both are acknowledged as such; the page on going past them says exactly what survives.

Two: a query sets each facet to one value or leaves it alone

This is the larger decision and the one most likely to diverge from a board somebody is actually looking at.

It means a query is a choice of state per filter, with k plus one states available for a filter of k choices. It excludes selecting two values at once, selecting a range, excluding a value, and every other richer form of query.

The page on multiple selection works through what the richer form would do to the figures, and the answer is that it changes them enormously rather than slightly.

Everything in this record follows from those two sentences. Nothing else was assumed, and every other figure is a product of whole numbers derived from them.

What was counted

Figure	How
cells	the sizes multiplied
questions	each size plus one, multiplied
grain	distinct subset products, counted
share	cells divided by questions
the census	all four, over all 461 schemas

Every one of those is reproducible by anybody with the facet sizes and a pencil. None requires access to this record, none depends on any judgement, and none can be slightly wrong — they are either right or arithmetically mistaken, and the program that builds the record checks the identities it relies on rather than asserting them.

Why the conventions are stated at the top

Because a convention that arrives late reads as an excuse.

A record that quoted figures for forty pages and then explained, in a note at the end, that it had assumed single selection throughout would be asking readers to go back and reconsider everything. Stating it first means every figure arrives already qualified.

It also makes the record checkable in the only way that matters. A reader who disagrees with a convention knows immediately which figures are affected — all of them — and can stop, rather than discovering a mismatch halfway through and wondering which parts survive.

What a third convention would have been

There is an obvious candidate and it was rejected: weighting the facets by how often readers use them.

That would produce figures closer to what people experience, and it would make every number here depend on usage data that cannot be read from a page, varies by field, and changes with the season.

The whole point of these two conventions is that they need nothing but the sidebar. A third that needed access to a board's logs would make the record unusable by exactly the readers it is for.

What counts as a facet, exactly

The convention needs one more line to be usable, and this is it.

A control is a facet when setting it removes listings from the result and leaving it alone removes none. That test excludes sort orders, which rearrange rather than narrow; it excludes text boxes, which have no fixed values; and it excludes "only show X" checkboxes, whose unset state does not exclude anything and which are therefore facets of one value.

Applying that test is the whole of the work in reading a board, and it is where every mistake in this method comes from.

What a reader should do with a board that does not match

Compute anyway, and know what the figure means.

A board offering multiple selection has more expressiveness than this record's question count credits it with. Its cell count is unaffected — resolution does not depend on how queries are formed. So the first of the two figures transfers directly, and the second is a lower bound.

A lower bound on expressiveness, computed from the page in a minute, alongside an exact resolution, is still a great deal more than nothing. It is also still two numbers, and the whole argument of this record is that two numbers beat one.