market-sizer

A market is sized twice because one sizing is not evidence. The top down number is a universe narrowed by shares. The bottom up number is built from segments, each one a product of its own drivers. They disagree, and the size of the disagreement is the only quantity in the whole exercise that was not assumed by somebody.

What usually happens next is the failure. The two numbers are averaged, or the more convenient one is carried forward, or the gap is called conservative and left where it is. None of those answers the question the gap is asking, which is: which assumption is wrong, and by how much. A reader handed the average has lost both sizings and gained nothing.

Top down against bottom up, reconciled by inversion rather than by judgement. Top down is a universe multiplied by a chain of narrowing factors. Bottom up is a sum of segments, each a product of its drivers. The instrument does not choose between them and does not combine them. It takes each assumption in turn, holds every other assumption still, and computes the value that one assumption would have to take for the two totals to agree.

top down   = universe × f(1) × f(2) × ... × f(k)
bottom up  = sum over segments of  d(1) × d(2) × ... × d(m)
gap        = bottom up - top down

top down factor    implied = value × (bottom up / top down)
bottom up driver   implied = value × (top down - other segments) / this segment

infeasible when an implied share passes 1, or any implied value is negative

Four top down factors and three bottom up segments of three drivers each, all editable. Above, the two totals, the gap and the gap as a percentage of the top down total. Beside them, a table with one row per assumption: its current value, the value it would have to take, and the multiple between the two. Every figure in the page is illustrative and labelled as such.

It refuses to produce a market size. There is no third number anywhere in the output: no average, no midpoint, no range, no recommendation about which sizing to believe. Two totals and the difference between them are all it prints, because the difference is the finding and a single number would bury it.

It refuses to imply something impossible. An implied share above one is not printed as a value; the row is marked infeasible and the reason is written out, that the implied share would exceed 100 percent. Any negative implied value is marked the same way. Those rows are findings rather than failures: they say that this assumption cannot close the gap at any setting.

It refuses to scale a zero. A factor sitting at zero cannot be multiplied into anything else, and the table says so in place of the implied column rather than printing a division by zero or an empty cell. The same holds for a segment worth zero: scaling any of its drivers cannot move a total it does not contribute to.

It refuses the impossible segment. If the other segments already sum past the top down total on their own, no value of any driver in the segment being solved closes the gap. Every driver in it is marked infeasible and a note above them states the two figures that make it so, the other segments and the top down total.

It refuses negative and unreadable inputs. Anything that does not parse as a number, or parses below zero, is read as zero, so the arithmetic never runs on a negative count of companies or a negative price.

It refuses to claim a market it has not measured. Every money figure is labelled EUR, illustrative, in both totals and in the readouts. The numbers in the page exist to make the arithmetic legible. They are not a sizing of anything, and the instrument never lets them look like one.