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What A Board Lets You Ask

Fifty notes on what a board of listings lets you ask

Telling apart

Seven Boards, One Resolution

Seven schemas all tell one hundred and forty-four listings apart, from three filters to six, with questions from 245 to 1296.

Telling apartReference2 to 46 656

cells

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One hundred and forty-four is reached seven different ways inside this record's bounds. No cell count is reached more often.

Facets Sizes Questions Result sizes
three 4·6·6 245 6 of 8
four 3·3·4·4 400 9 of 16
four 2·3·4·6 420 13 of 16
four 2·2·6·6 441 9 of 16
five 2·2·3·3·4 720 15 of 32
five 2·2·2·3·6 756 13 of 32
six 2·2·2·2·3·3 1296 15 of 64

Every row tells the same number of listings apart. Everything else about them differs.

Teams can look through the reporting options, state the question the data is meant to answer and set a date for removing any setting that adds no value. For a separate technical reference, see Project Jupyter.

The seven, in order of what they allow

the facetscellsqueriessizes144245614440091444201314444191447201514475613144129615
  • one bar is one facet; the divisions are its values
  • cells: how many listings the schema can tell apart
  • queries: how many different questions it lets anybody ask
  • sizes: how many different result sizes are reachable

Seven schemas drawn; all of them tell the same 144 listings apart, across four different facet counts.

Identical resolution throughout. The bars change shape, the first figure never does, and the second runs over a factor of five.

Computed from the schema alone. How many facets and how many values in each is a stated convention; the three figures are products of whole numbers.

The two ends

The top row is three filters: one of four choices and two of six. A reader sees three dropdowns. The board resolves one hundred and forty-four kinds of listing and allows two hundred and forty-five different questions.

The bottom row is six filters: four of two choices and two of three. A reader sees six controls, four of them simple yes-or-no toggles. The board resolves exactly the same one hundred and forty-four kinds of listing and allows one thousand two hundred and ninety-six different questions.

The second board looks far more capable. On the measure most people reach for — how much can this thing tell apart — it is identical. On the other measure it is more than five times richer.

The same resolution can be cut into three filters or six, and the reader has no way of knowing which they are looking at without doing the arithmetic.

Why the question count varies so much at fixed resolution

Because resolution multiplies the sizes and expressiveness multiplies the sizes each raised by one, and adding one hurts small numbers far more than large ones.

A facet of six contributes six to the cells and seven to the questions: a ratio of seven sixths. A facet of two contributes two to the cells and three to the questions: a ratio of three halves. So splitting a resolution into many small facets keeps the product the same while piling up those ratios.

Four facets of two and two of three multiply to one hundred and forty-four, and their question count is three to the fourth times four squared, which is one thousand two hundred and ninety-six. One facet of four and two of six multiply to the same one hundred and forty-four, and their question count is five times seven times seven, which is two hundred and forty-five.

Same resolution. Many small facets against few large ones.

Which of the seven is best

The record cannot say, and will not pretend to.

More questions is not automatically better. Each additional filter is another control a reader has to understand, another value every listing must carry, and another thing to get wrong when posting. Six toggles that nobody sets are worse than three dropdowns that everybody uses.

Fewer questions is not automatically better either. The three-filter board offers two hundred and forty-five ways to ask, and if the distinctions people actually want fall across combinations it does not express, those readers are stuck with a result larger than they wanted and no way to narrow it.

What the record provides is the figures. Which structure suits a particular field depends on what the listings vary in and what readers come looking for, neither of which is in a schema.

What a reader actually experiences

On the three-filter board, a reader makes three decisions at most. Each one is substantial: a six-way choice is a real commitment, and getting it wrong means starting again.

On the six-filter board, a reader makes up to six decisions, four of them trivial. A toggle is easy to set and easy to unset, so the cost of being wrong is small and the reader can explore.

Those are different experiences and the arithmetic cannot rank them. What it can say is that both end up at the same one hundred and forty-four compartments, so whatever the reader gains from exploring is gained inside a fixed space rather than by reaching further into it.

The one firm conclusion

Reading the number of filters tells you nothing about resolution.

Three filters and six filters appear in this table side by side with identical cell counts. Doubling the number of controls on the page did not improve what the board can tell apart by a single listing.

It is tempting to treat a long filter sidebar as evidence of a well-structured board, and this table is the counter-example. The longest schema here and the shortest resolve exactly the same number of listings, and the long one differs only in how many ways it lets a reader approach them.

That second property is real and worth something. It is simply not the property anybody thinks they are reading when they count the dropdowns.

Near this one