One more facet

The Edits Ranked By What They Buy

Five edits, priced against one board. The largest multiplies the resolution by six; the smallest multiplies it by one and changes the questions anyway.

One more facetReference×k against ×(k+1)/k

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Take a board of two filters, four choices and six: twenty-four cells, thirty-five questions.

Every edit available to it, ranked by what it does to the resolution:

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Edit	Cells	Questions	Resolution
add a facet of six	144	245	×6
add a facet of three	72	140	×3
add a facet of two	48	105	×2
take the four to five	30	42	×5/4
take the six to…	past the bound	—	—
split the six into 2·3	24	60	×1
add a one-value facet	24	70	×1

The top three multiply. The fourth adds a quarter. The last two multiply by one and change the question count anyway.

The two edits that buy no resolution

They are at the bottom of the table and they are not the same as each other.

Splitting the six into two and three leaves the resolution at twenty-four and raises the questions from thirty-five to sixty. The extra questions are real: they let a reader use half of a distinction that previously had to be used whole.

Adding a one-value facet leaves the resolution at twenty-four and raises the questions from thirty-five to seventy. Every one of those extra questions returns exactly what its twin returned, because setting a filter with one option excludes nothing.

So one of them doubles the question count and adds nothing, and the other adds less to the count and adds something. The question figure ranks them the wrong way round, which is the strongest argument in the record for never quoting it alone.

Two edits, both leaving the resolution untouched. One doubles the questions and is hollow; the other raises them by less and is real.

The ranking by work rather than arithmetic

Almost exactly reversed.

Edit	Listings to reclassify
split a facet	none — values follow mechanically
add a value	those in the category being split
add a facet	every listing on the board

So the edit that buys most costs most, the edit that buys least costs least, and the edit that buys nothing in resolution — splitting — costs nothing either and improves two other figures.

The recommendation, such as it is

Split first, because it is free. If a facet is really two distinctions crossed, splitting costs no reclassification, raises the question count, and usually improves the grain.

Then widen existing facets where they are genuinely too coarse. Cheap, modest, and solves the problem readers actually complain about.

Add a facet when a dimension is missing, and expect it to cost. It is the only edit that reaches listings merged by an absent distinction, and it is the one nobody asks for, because readers cannot name a dimension they have never been offered.

What not to do

Do not add a filter with one option, for any reason. It is the only edit in the record that moves a figure while doing nothing at all, and a board carrying two of them has doubled its question count twice over on apparatus that cannot narrow a result.

If a filter is there to label, to explain, or to hold a place for later, it can be all of those things outside the filter panel, where it will not be counted as a facet by anybody reading the structure.

What the table looks like from the other side

Ranked by work rather than by what they buy, the same seven edits come out nearly reversed.

Splitting a facet is free: no listing is reclassified, because each one's new values follow from the old. Adding a value touches only the listings in the category being split. Adding a facet touches every listing there has ever been.

So the edit at the top of the arithmetic table is at the bottom of the practicality table, and the one that buys nothing at all — adding a one-value facet — is the easiest of the lot.

That ordering is why boards accumulate the edits they do.

The figure to compute before any of this

The current pair.

Every edit in this table is a multiplier on figures the board already has. Without those figures, the multipliers are abstract and the argument is about adjectives again — bigger, better, more thorough — which is where it was before anybody counted anything.

Two numbers, one minute, and the whole table above becomes a statement about a specific board rather than a general one.