The Graičiūnas formula in practice
You have the number. What is left is what to do with it, and the answer is almost never "work faster" — it is "group them".
Why two people is six relationships
Almost everyone counts three: you and Rūta, you and Tomas, Rūta and Tomas. Graičiūnas is not counting the same thing. He is counting the conversations you have to hold in your head, and there are three kinds of them.
- Direct single2
- You and Rūta
- You and Tomas
You and one person. Nobody else is present.
- Direct group2
- You and Rūta, while listening: Tomas
- You and Tomas, while listening: Rūta
You and one person while another is listening. That is a different conversation from the private one — who is in the room changes what gets said.
- Cross2
- Rūta → Tomas
- Tomas → Rūta
The two of them, without you. Counted both ways: Rūta leaning on Tomas is not the same event as Tomas leaning on Rūta.
Move the number. People go up one at a time. Relationships do not.
Person number 2 added 5 relationships.
| The formula | n = 2 |
|---|---|
| Direct single · n | 2 |
| Direct group · n(2n−1−1) | 2 |
| Cross · n(n−1) | 2 |
| C = n(2n−1 + n − 1) | 6 |
Graičiūnas never said how many people is too many. He said what one more costs. The decision is yours.
Write everyone who comes to you on one sheet and sort them into three piles by who already talks to whom daily. Put one name against each pile and tell that person directly what they now decide without you.
Why this number is your problem, not Graičiūnas's
Count the conversations you have to keep in your head, not the people. Two people is six relationships. Four people is forty-four. Five is a hundred. One more person is never just one more.
That is why the day ends and your own work has not moved. Not because you are slow or disorganised. Because you took on more relationships than fit in one head, and no weekly planning system fixes that.
Clubs do not fall apart because the people are bad. They fall apart because somebody asked you something and you did not get back to them. That person did not ask a second time, quietly stopped turning up, and you found out two months later. Staying inside your span is not controlling less. It is the first time you are actually in control: everyone who comes to you gets an answer.
And this is the thing that will later separate a good leader from a bad one. The bad one keeps everything and calls it responsibility, because giving work away feels like losing grip. The good one notices they have stopped keeping up and splits the work while there is still something left to split. Noticing that you are overloaded is a skill, and you can start learning it today.
The honest exception, and it is his own: if your people's work does not touch — each doing their own thing, with nothing to coordinate — you can carry more of them. This is a question to ask yourself, not a rule somebody will come and audit.
| Reporting to you | Relationships to hold |
|---|---|
| 2 | 6 |
| 3 | 18 |
| 4 | 44 |
| 5 | 100 |
| 6 | 222 |
| 12 | 24 708 |
Going from four people to five: a fifth more hands, and two and a half times the complexity. His own figures: +20% capacity for +127% complexity.
The whole story is in the text below. This is only its spine.
- 1898Chicago
Born to a Lithuanian emigrant family. American from day one.
- 1923–1925Chicago, New York
Finished his engineering degree and advised Chicago and New York companies on management.
- 1926Kaunas
Came to Lithuania and became technical director of the Metalas factory.
- 1929Paris
Met Lyndall Urwick at the management congress and asked for help putting the argument into English — his own English, he felt, was not good enough.
- 1933Geneva
'Relationship in Organization' — four pages in the institute's bulletin. Reprinted in Gulick and Urwick's collection in 1937, which is how a Lithuanian's paper ended up in the American management canon.
- 1938Kaunas
Gathered the Lithuanian Scientific Management Society and became its first chairman.
- 1944Kaunas
As the front moved west, he chose not to leave.
- 1945–1948Kaunas University
Taught construction management. His students remembered a lecturer who showed processes with movement, gesture and a shift of voice. Dismissed in 1948 as the campaign against 'cosmopolitanism' began.
- 1948Moscow
Renounced his US citizenship. The embassy told him he could leave alone; his wife, the actress and director Unė Babickaitė, had no citizenship. He stayed.
- 1951Lefortovo, Moscow
Both arrested. Charged with espionage for the United States and anti-Soviet agitation, sentenced to ten years; she to five.
- 1952Olžeras, Kemerovo oblast
Died in the Kamyšas camp, less than three months after the sentence. His burial place is unknown and the circumstances are disputed to this day.
- 1988
Rehabilitated.
The full biography is on the public version →
Photograph held by the club. Held by the club; its own namesake.
These screens carry out this specific work. Every published work in the library also has at least an exercise — it is at the foot of this page.
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These works are related to the one you just read — and not by accident:
same author
shared competencies: Span and structure, Continuity
shared competencies: Span and structure, Continuity
same competency: Continuity
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The same work written at length: what it claims and what its evidence is worth.
Links to publishers and libraries. There are no links to unauthorised copies here, and there will not be.
- H. A. Simon (1946), The Proverbs of Administration — the classic attack on the span-of-control principle
- Studijų ir polėkių metai (2000) — his own students on his teaching in Kaunas, 1945–1948
- The V. A. Graičiūnas Nomination — Lithuania's annual management award and its laureates
- How the Kaunas university's name changed, 1920–1990 — why 'VDU' in 1945 needs explaining
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