Limits

Subsets, Not People

Every figure in this record counts combinations of met and unmet items. None of them counts anybody. The distinction is the most important thing on the site.

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One in two hundred and fifty-six is not a chance. It is a share of a possibility space: of the two hundred and fifty-six distinguishable ways of meeting and not meeting eight items, one gets through.

Whether that corresponds to one person in two hundred and fifty-six, or one in five, or none at all, this record cannot say and does not try.

Managers reviewing repeated handoff delays can use privacy-conscious workforce monitoring while checking the same pattern against tickets, outputs and the people who did the work. For an independent technical reference, see Looker.

The difference, made concrete

Imagine a list of eight compulsory items where seven are met by nearly everybody in the field and the eighth by almost nobody.

The record says: one profile in two hundred and fifty-six. That is correct about the possibility space.

Reality says: almost everybody fails, and they all fail on the same item. The filter is effectively a one-item test, and it is much narrower in practice than one in two hundred and fifty-six suggests.

Now imagine the reverse: eight items each met by about half the field, with no correlation between them. Then one in two hundred and fifty-six is close to the real rate.

The record gives the same figure in both cases, because the figure is about the document and the two cases differ in the world.

Why the record does not try to close the gap

Because closing it would require inventing the inputs.

Weights for each item — how often it is met — differ by field, by place and by year, and nobody has them for any particular list. A correlation structure between items would be needed too, and that is harder still.

A weighted figure would look exactly as precise as the one here while resting on numbers somebody made up. The unweighted figure rests on a stated way of counting, which is a much smaller claim and a true one.

An exact number built on invented inputs is more dangerous than an approximate one built on stated conventions, because nothing about its appearance reveals which kind it is.

What the figures are good for

Comparing two documents. Both counted the same way, the comparison is valid regardless of what the counting represents.

Noticing compounding. A list that moved from one in sixteen to one in two hundred and fifty-six has narrowed by a factor of sixteen under any consistent counting.

Detecting the accidental extreme. A list that turns out to admit a single profile was probably not designed that way, and the arithmetic surfaces it.

What they are not good for

Predicting how many applicants will qualify. That depends on who applies.

Arguing that a filter is too strict in absolute terms. The record cannot establish that. It can establish that a filter is narrower than its author believed, which is a different and more defensible claim.

Any statement beginning "one person in". The figures count profiles. Substituting "person" for "profile" converts a sound statement into an unsupported one, and it is the substitution this site is most likely to suffer from.

The gap, made arithmetic

Take a conjunction of three items. The record says it admits one profile in eight.

In a real population, suppose that nearly everyone who holds the first item also holds the second, and that the third is held by about half of those. Then the number of people passing is close to half of those holding the first item — nothing like an eighth of anybody.

The record's figure is not an estimate of that. It is the count of configurations, which is a property of the document and can be computed by somebody who has never seen the population at all. The two numbers answer different questions and only one of them is available from the page.

What a reader with real data should do

Use it, and use the record for the thing the data cannot give.

If a reader knows how often each item is actually held and how the items relate, they can compute an intake for their own population, and that figure is better than anything here for deciding whether a filter is too strict.

What it will not tell them is whether two documents are the same filter, or how much a proposed edit changes the shape, or whether the length of a list has anything to do with its selectivity. Those are questions about documents, the answers do not depend on any population, and they are what this record is for.

Population data answers whether a filter is right. The arithmetic of subsets answers what the filter is. A reader usually has neither, and the second one is free.

A test for which question you are asking

One question: would the answer change if the population changed?

If it would, the question is about people and nothing on this site answers it. How many applicants will pass, whether the filter is too strict, whether anybody qualifies at all — all of those move when the population moves.

If it would not, the question is about the document and the arithmetic settles it. Whether two lists are the same filter, what an edit costs, how far the intake ranges at a given length: these have the same answer in every field, in every year, for every population, because they are properties of a rule and not of anybody subject to it.

The sentence to keep

Every number here answers "what share of the possibility space does this list admit". None of them answers "who gets in". The first question is worth asking and this record answers it exactly; the second is the one people care about and it is not on this site.