What a team is
Why eight people need twenty-eight pairs
Adding one person to a team of seven adds seven new pairs, not one. This is why a team that felt connected at five stops feeling connected at nine.
The people this page is about, and which of them have ever worked together
- 01The team's managerFive of this person's six pairs are with people not in this grid
- 02The senior engineerThe one working pair on the whole team that does not involve the manager
- 03The second engineer
- 04The engineer who joined in MarchNo pair with anybody
four people · 6 possible pairs · 2 of them have worked on something together · 4 have never done either
Four of the eight, and only the pairs that run between those four.
Where projects cross several roles, teams can see the official overview to make hours and handoffs visible enough for a useful capacity discussion.
An independent source worth comparing with this example is Yale School of Management.
Eight people, and which of them have ever worked on anything together
- 01The team's managerFive of the six working pairs run through this one person
- 02The senior engineerThe only working pair that does not involve the manager
- 03The second engineerJoined eleven months ago
- 04The engineer who joined in MarchHas worked with nobody else on this team
- 05The designerShared with two other teams
- 06The data analyst
- 07The product managerWrites the brief everybody reads, and works with none of them
- 08The QA engineer
eight people · 28 possible pairs · 6 of them have worked on something together · 4 have only been in the same meeting · 18 have never done either
One team, one quarter, counted from the work itself. Roles are named here and people are not.
A team of two has one pair. A team of three has three. A team of four has six, a team of five has ten, a team of eight has twenty-eight, and a team of twelve has sixty-six. The number of people grows in a line and the number of relationships grows in a curve, which is the whole reason this subject is difficult and the reason nobody notices it happening.
The formula is the handshake one: for a group of size n, the number of distinct pairs is n times n minus one, divided by two. The panel above draws all twenty-eight of them for one team of eight, as a triangle with one cell per pair, and fills in the cells where the two people have actually worked on something together.
The arithmetic nobody does
What makes this counterintuitive is that hiring feels linear. You add a ninth person to a team of eight. One desk, one laptop, one onboarding plan, one line in the budget. Everybody's mental model of the change is "one more person".
What actually arrived is eight new pairs. The team went from twenty-eight possible relationships to thirty-six, an increase of nearly thirty per cent, and nobody budgeted a minute for any of them. The ninth person will form a working relationship with their manager in the first fortnight because the process requires it, and may form one or two more by accident. The other five or six pairs will not happen unless something causes them to.
Do that four times in a year and the team has doubled its possible relationships while the number of real ones has grown by whatever happened to occur. This is the mechanism by which a team that genuinely felt like a team at five stops feeling like one at nine, with nobody having done anything wrong.
Why you cannot have all of them
It is worth saying plainly: twenty-eight is not a target. Nobody has twenty-eight working relationships inside an eight-person team, and a team where everybody had worked with everybody on everything would be a team that had serialised all its work and shipped very little.
The useful readings are not the total but the shape:
- How many pairs exist at all. Six out of twenty-eight is sparse. Twelve would be ordinary. Eighteen would be unusual and probably means the team is smaller than its chart says.
- How many of them run through one person. Five of the six here do. Remove that person and the network is a single pair plus six isolated individuals. That is a fact about resilience, not about the manager, who is probably doing exactly what they were asked to do.
- How many people have no pair at all. One, in this case: the engineer who joined in March. They have been present at every ritual the team has and have produced nothing jointly with anybody in it.
Reading the triangle
The grid is a triangle rather than a square for a reason worth a sentence. A pair has no direction — if two people have worked together then both of them have — so a square would state every pair twice and carry a useless diagonal of people working with themselves. The lower left triangle holds each pair exactly once and nothing else.
Rows and columns are numbered, and the numbers match the roster beside the grid. The cell where row five meets column three is the pair made of the fifth and third people on that list. Filled means they have worked on something together. Ringed means they have been in the same meeting and nothing more. Empty means neither.
Where the curve bites
The practical effect is that advice about teams does not transfer across sizes, and it is given as though it did.
Everything people recommend for a team of four — talk often, keep everybody in the loop, make decisions together — works there because six pairs is a number a group can maintain by having conversations. The same advice at nine people asks for thirty-six relationships and produces a calendar instead of a team.
This is also why a team that grew from five to nine remembers being better and cannot say what changed. Nothing was taken away. The same behaviours now cover a quarter of the ground they used to.
What to do with the number
Count it once and write it down with the date. That is the entire first step, and it is worth doing before any attempt to improve anything, because the count is the only thing that will tell you later whether what you tried worked.
Then look at the empty rows rather than the total. A person with no filled cell is the most actionable thing on the grid: there are seven candidate pairs available and arranging one of them is a week's work at most. A total of six is hard to move by a quarter of itself. One isolated person becoming connected is a change you can cause on purpose, and it shows up in the count immediately.
The next part of this site is about how to do the counting without it turning into surveillance, and what the number means once you have it.