The definition
Menu penetration is the share of restaurants whose published menus carry a given item, ingredient or format. If sixty restaurants out of a hundred list a dish, penetration is 60%.
It answers a question no price can answer: not what something costs, but how normal it is. A high penetration means an item is expected. A low one means it still marks a choice.
Why the denominator decides everything
The same numerator produces wildly different figures depending on what it is divided by, and all of them can be arithmetically correct at once.
Take an ingredient carried by ninety restaurants. Divided by every restaurant in a dataset, that might be 50%. Divided by the restaurants that serve food at all, it might be 53%. Divided by every individual menu document, it might be 11%, because one restaurant publishes several menus and the ingredient appears on only one of them. Three true numbers, three different impressions, and only one of them answers the question the reader had in mind.
This is why every MenuIndex figure names what it is a share of in the same sentence. A bare percentage is not a finding, it is an invitation to misread.
The trap of counting menus instead of restaurants
A restaurant does not publish one menu. It publishes a food menu, a drinks list, sometimes a brunch menu, a breakfast menu and a separate bar list. In our own dataset a restaurant publishes close to four food menus on average.
So a share of menus mixes two different things: how much of the market carries an item, and how often each restaurant repeats it across its own documents. A restaurant that lists a dish on its dinner menu but not on its lunch menu counts once in the numerator and several times in the denominator. The result reads like penetration and is not.
Penetration against a named sub-population
The most useful version is often narrower. Instead of asking what share of the whole market uses an ingredient, ask what share of the restaurants that already use it put it in a particular section of the menu.
That figure has two advantages. The denominator is small enough to state, so the reader can check it. And it answers the question a kitchen actually has: not whether the product exists in the city, but whether the restaurants already using it have taken it as far as they could.
When penetration should not be published at all
Below a certain count, a percentage stops describing a market and starts describing a short list of identifiable businesses. If four restaurants carry something, 4% is not a market statistic; it is a way of pointing at four people.
MenuIndex withholds any breakdown narrow enough to point at individual businesses. The row stays visible in the table, marked as withheld, so a reader can see where the data stopped rather than assuming it continued.
How to read a penetration figure someone else published
- Find the denominator. If it is not in the same sentence, the figure cannot be checked.
- Ask whether it counts businesses or documents. The two differ by a factor of several.
- Ask what the frame is. Penetration inside a premium segment and penetration across a whole city are different measurements with the same name.
- Ask what happens below the floor. A dataset with no suppression rule is publishing figures about individual businesses whether it says so or not.
MenuIndex prints a share only where it holds still as our coverage grows. A share that moves while we are still adding restaurants is describing our own list rather than the market, so it is withheld and marked as withheld. Where a share does not hold, we report the same product through figures read inside one menu, which the growth of the dataset does not move.