How the figures were made
Two things were invented for this record and declared before any of the counting. Everything else was computed. This page separates them, because the separation is the only thing that makes the rest checkable.
The first convention: the shape of a list
A list of requirements is described here by three numbers.
| e | how many items must all be met |
| n | how many items are optional |
| m | how many of the optional ones are needed |
The bounds are e from none to eight, n from none to eight, and m from none to n. That gives four hundred and five shapes, and all four hundred and five were computed.
Those bounds are a choice. Eight was taken as the practical ceiling for either half of a list, on no stronger ground than that it is large enough to show every behaviour the record needs and small enough to enumerate completely. A ninth would have added rows and no new fact.
The second convention, which matters more
Each item is counted as a separate coin.
That sentence is doing an enormous amount of work and deserves to be read twice. It means that for a list of e plus n items there are two raised to that power possible profiles — every combination of met and unmet — and that the record treats all of them as one unit each when it counts.
This is a unit of measurement, not an estimate of any population. The record does not claim that people are distributed this way. It does not claim that requirements are independent, that each is equally likely to be met, or that any real group of applicants looks like the set of all subsets. It counts subsets, which is a precise thing to do, and it says what it is counting.
Every claim on this site is a claim about subsets. None of them is a claim about people. Where the two get confused, the arithmetic is not at fault.
Everything else is counted
Given the two conventions, the rest is mechanical. A list admits a profile when all of its compulsory items are met and at least m of its optional ones are. The compulsory part gives one case out of two to the power e; the optional part gives the sum of binomial coefficients from m up to n. Divide by the whole space and the answer is exact, as a fraction, with no rounding anywhere.
Every figure on this site is that calculation at some shape. A reader who disagrees with one can redo it with a pencil and a table of binomial coefficients, and will be right or wrong without any need to argue about assumptions.
What is deliberately absent
Nothing here says what anybody wants. The preferences of those who write such lists, the expectations of any industry, and the reasons one application fares better than another are all outside this record. It describes the arithmetic of filters and knows nothing whatever about anybody's.
The calculations remain the core of this record. Practical platform guides are maintained separately, use stated workflow scenarios and link to current official product information for verification.
No sums of money, no market conditions, no counts of anything happening in the world.
No advice on writing an application or sitting an interview.
Those omissions are deliberate and they share one reason. Claims of that kind go out of date quietly: the page still reads as though it were current, nothing on it announces that it has expired, and somebody acts on it. A person who loses an opportunity because of a stale page has lost something real. The arithmetic of subsets does not expire, so that is what this site contains and the rest is left to sources that can keep themselves current.
The figure that argues against the record
The median shape in this record admits one profile in thirty-nine, and one hundred and fifty-two of the four hundred and five shapes admit less than one in a hundred.
Read carelessly, those look like statements about how hard it is to get a job. They are not. They are statements about how narrow a filter is when every item is treated as an independent coin — which, as the second convention says, is a unit of measurement rather than a description of anybody.
The honest reading is narrower and more useful: a list of requirements is far more selective than its author usually intends, and the arithmetic says by exactly how much, given a stated way of counting.