Limits

One Hundred And Fifty-Two Shapes Under One Per Cent

More than a third of the shapes in this record admit less than one profile in a hundred. The distribution of intakes across the whole table, and how to read it.

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Sorted into bands, the four hundred and five shapes fall out like this:

Band	Shapes
admits everybody	9
half or more	29
between a tenth and a half	83
between a hundredth and a tenth	132
between a thousandth and a hundredth	113
less than a thousandth	39

One hundred and fifty-two shapes — a little over a third of the table — admit less than one in a hundred.

A responsible rollout gives employees enough information to read this practical product guide themselves and understand how records are used. For an independent technical reference, see Apache Superset.

The shape of the distribution

It is heavily weighted towards the narrow end. Only thirty-eight shapes out of four hundred and five admit half or more, and nine of those are the degenerate cases that admit everybody.

The bulk sits between a thousandth and a tenth, which is to say between extremely narrow and merely very narrow.

Why the table leans that way

Because of how the shapes are generated rather than because of anything about lists in the world.

Every compulsory item halves, and the enumeration runs the compulsory count up to eight. Every threshold above the middle of its staircase cuts hard, and the enumeration includes all of them. So the table contains a great many shapes that nobody would write, and those shapes are concentrated at the narrow end.

A table of only the plausible shapes would lean much less. The record does not contain one, because deciding which shapes are plausible would require a judgement it has no basis for.

The distribution describes the enumeration, not the world. Reading it as a statement about real documents imports a sampling claim the record never made.

What survives the caveat

Two things, and they are not small.

Narrow shapes are easy to reach. A third of the table is under one per cent, and getting there requires nothing exotic — six compulsory items, or four with a high threshold over the rest. Anybody assembling a list without computing can land in that third without noticing.

Wide shapes are rare and specific. Only twenty-nine shapes admit half or more, and almost all of them have either very few compulsory items or a very low threshold. Width has to be chosen; narrowness happens.

That asymmetry is the finding. It holds regardless of how the table was generated, because it is a statement about where in the space of shapes the wide ones sit.

The one band worth examining

Between a tenth and a half: eighty-three shapes.

That is the band most real lists are probably aiming at, if their authors were asked — selective enough to mean something, wide enough to produce candidates. Eighty-three shapes out of four hundred and five, about a fifth of the table.

Hitting a target band of that size by accident is unlikely, which is the practical case for computing a list's intake rather than assembling one and hoping.

The bands, counted out

The one hundred and fifty-two is the sum of two bands, and separating them shows how far the tail runs.

One hundred and thirteen shapes admit between one in a thousand and one in a hundred. A further thirty-nine admit less than one in a thousand, running down to one in sixty-five thousand five hundred and thirty-six at the bottom of the table.

Band	Shapes	Share of the record
1% to 10%	132	about a third
0.1% to 1%	113	about a quarter
under 0.1%	39	about a tenth

So the single largest band in the record is one to ten per cent, and the two bands below it together are larger still. The table is not symmetric around anything; it has a short head and a long tail.

What a third of the table under one per cent does not mean

It does not mean that a third of real lists are that narrow.

The record enumerates shapes, and the enumeration is not a sample of documents. It includes every combination the two caps allow, including a great many that nobody would write — sixteen-item conjunctions, eight compulsory items with eight inert optional ones, thresholds of all eight on a list labelled optional.

What the figure does establish is that narrow shapes are easy to reach. A list does not have to look extreme to be in the bottom third of this table; three compulsory items and a threshold near the top of a short optional list will do it, and both halves of that description sound ordinary.

And the figure not to quote

"A third of requirement lists admit less than one per cent of candidates" is a sentence this table does not support, in two separate ways: these are shapes rather than real lists, and profiles rather than candidates.

The supportable version is longer and duller, and it is on this page.