How mixed: the Simpson diversity index, explained simply
Forty restaurants that are all Italian and forty split across six cuisines are the same forty on a plain count. 'How mixed' (the Simpson index) tells them apart. Here it is, worked through with Italian, Indian, Chinese, Thai, Mexican and Lebanese restaurants in London.
Forty restaurants can mean two very different streets
Picture two London streets, each with forty restaurants. On the first, thirty-seven are Italian. On the second, they are split more or less evenly between Italian, Indian, Chinese, Thai, Mexican and Lebanese. A count says these streets are the same. Anyone who has walked down both knows they are not.
How mixed is the number that tells them apart. It answers a wonderfully concrete question: if you picked two restaurants here at random, how likely is it that they are different kinds? On the Italian street, hardly ever. On the mixed street, nearly always. The field calls this the Simpson diversity index - the app's badge shortens it to Simpson index - and it runs from 0 (one kind only) to 1 (as mixed as your set of kinds can be).
How mixedthe field's term: Simpson index
How mixed six cuisines are - Italian, Indian, Chinese, Thai, Mexican and Lebanese - within a 10-minute walk. Where the map is yellow the food scene is genuinely varied; where it is purple it leans on one cuisine.
Why we chose cuisines
Variety only makes sense for a set of kinds, and cuisines are a set everyone understands. London's place data lists every restaurant under its cuisine, so picking six well-known ones gives a question a café owner, a landlord or a curious resident can all read: is the food scene here varied, or is it one thing?
The same map works for any set - kinds of shop on a high street, kinds of bar in a nightlife neighborhood, kinds of building along a street. Cuisines are just the example that needs no explaining.
Switching it on
Variety is its own row in the Map type picker. Choose the map first and then fill it: an empty Variety map simply waits for the kinds you want it to compare.
Where to click
Map type
Variety
Tick 6 cuisines
Measure as: How mixed
Variety selected in the picker. It sits under 'How much' rather than 'Compared with', because a variety index is a number in its own right - nothing is being compared with an average. The picker holds nine map types in five groups; the list goes on below this crop to Put together, with Your formula.
Arriving with exactly one measure already chosen is the interesting case. Variety is a question about a set, and one kind is not a set - so instead of refusing the row, the map opens empty and asks: “Pick two or more kinds: variety is the mix between them”. The measure picker opens on the category you came from, so the neighboring kinds are one click away, with nothing ticked for you. Tick one and it counts what is still missing; tick a second and the map draws.
Six cuisines on the Variety map, measured as 'How mixed'. There is no 'Count as' row at all here: a variety index is already a share of the set, so there is nothing left to divide it by. 17,222 of London's 40,253 hexes have an answer, and the highest value is 0.82.'Measure as' set to How mixed. It offers three readings of a set: How mixed, How even and How many kinds. Adding the kinds together is not one of them - that is the Amount map, one row up in the picker.
The third reading, How many kinds, asks a simpler question: how many of the kinds are here at all, from none of them to all of them. Thirty Italian restaurants and one Thai make a street that is barely mixed, but it has 2 of the 6 cuisines either way. The How many kinds post works it through with the ready-made question Everyday needs.
We read the set within a 10-minute walk because a single hex - one hexagon on the map, about 350 m across (roughly 0.1 km²) - rarely holds more than a restaurant or two, and two restaurants cannot be very mixed. Over a hex and the hexes around it the index has enough places to say something. The walk post explains that setting.
Reading the map
The legend deliberately shows words at its ends rather than 0 and 1. A value of 0.14 is true and meaningless; “One kind of place” is what it means.
The ramp runs from 'One kind of place' to 'Very mixed'. Hexes with none of the six cuisines within reach show as no data, because there is nothing to be mixed.Hovering a hex near Greenwich gives the index for the walk around it: 0.70. The closer to 1, the more evenly the six cuisines share the restaurants within a 10-minute walk.
The math, honestly
Take each kind's share of the total, square it, add the squares up, and subtract from 1. Squaring is what makes a dominant kind weigh so heavily: 92.5% squared is 0.856, while four shares of 25% squared add up to just 0.25.
Two streets, forty restaurants each
Street A - 37 Italian, 1 Indian, 1 Chinese, 1 Thaisum of squared shares = 0.857
0.925² + 3 × 0.025²
Street A - How mixed
1 − 0.857 = 0.14
Street B - 10 each of four cuisinessum of squared shares = 0.25
4 × 0.25²
Street B - How mixed
1 − 0.25 = 0.75
0.75 is the maximum four evenly-split kinds can reach, which is why the app says '1 is as mixed as this set can be' rather than promising a 1 for every set.
Same formula, two industries
Competition regulators use the Herfindahl index (HHI) to decide whether a market is concentrated. It is exactly 1 − Simpson, scaled to 10 000. Two disciplines invented the same sum independently.
Already in the census data
MapBees' nationality diversity measures are Simpson indices computed the same way, so 'How mixed' on cuisines and 'nationality diversity' from the census are one definition, not two.
How mixed versus How even
Both rise with variety, but they answer slightly different questions. How mixed (Simpson) asks how likely two random picks differ and is forgiving of a few rare kinds. How even (Shannon) asks whether every kind gets a fair slice and punishes a dominant kind harder. The How even post runs the same six cuisines through that formula.
How mixed = the chance two things picked at random here are different kinds. That is the Simpson index: 1 − Σ share².
It needs a set: tick two or more kinds and the 'Measure as' row appears.
Forty Italian restaurants score near 0; forty split across six cuisines score near 1. A count cannot tell them apart.
The legend speaks in words - 'One kind of place' to 'Very mixed' - because 0.14 on its own means nothing.
Read it within a 10-minute walk so each hex has enough places for the index to mean something.
Quick questions
What does the Simpson index measure?
The chance that two things picked at random from a hex are different kinds. 0 means only one kind is present; the closer to 1, the more evenly the kinds are mixed. MapBees calls it 'How mixed'.
How do I map cuisine variety in MapBees?
Open the Map type picker and choose 'Variety', tick two or more kinds in the measure picker (for example six cuisines), then set 'Measure as' to 'How mixed'. The map colors each hex from 'One kind of place' to 'Very mixed'.
What happens if I pick Variety with only one kind chosen?
Variety is never grayed out in the picker. With fewer than two kinds it opens empty and asks you to pick two or more kinds, because variety is the mix between them; tick a second kind and the map draws.
What else can 'Measure as' do on the Variety map?
It offers three readings: How mixed (the Simpson index), How even (Shannon evenness) and How many kinds, which counts how many of the kinds are present at all, as in the ready-made question Everyday needs.
What is the difference between 'How mixed' and 'How even'?
Both rise with variety. 'How mixed' (Simpson) asks how likely two random picks differ, and is forgiving of a few rare kinds. 'How even' (Shannon) asks whether the kinds are spread evenly, and punishes one dominant kind harder.
Can I divide a variety index per resident?
No. A variety index is already a 0-1 proportion, not a count, so dividing it again would be meaningless. The Variety map therefore has no 'Count as' row at all.
See it on a real map
The best way to understand the score is to play with it. The full app is on a Free Tier, with no sales call.
Builds MapBees's location-intelligence pipeline end to end — census and Overture Maps ingestion, H3 hex scoring, and the map interface — and writes the methodology behind every number on the site.
