If you were at a party, and wanted to shake hands with everyone, how many handshakes would it take?

Simple: it would be the total number of people at the party, minus one (yourself).

That grows with the total number of people involved.

But how many total handshakes take place, and how long would it take for everyone to shake hands?

This can teach us much about why companies and teams slow down as they grow larger.

So how many handshakes would it take in total:

  • If there are only 2 people, there would only be one handshake
  • If there are instead 9 people, it would take 36 handshakes
  • And if there are 100 people, it would take 4,950 handshakes
  • And if there are 1,000 people, it would take 499,500 handshakes (nearly half a million)

There is in fact a formula for this, sometimes called the “Handshake Overhead”, and if “n” is the number of people involved, the number of interactions or handshakes required is n*(n – 1)/2.

This shows one of the problems which companies have staying efficient as they grow.

When startups first begin, with small teams, everyone can still interact with everyone else, without too much time being taken up with interactions between team members. In fact, often the entire company can sit in a single meeting together and then be productive for the rest of the day.

However, as more employees join, more and more time is required for everyone to interact with one another. This slows down the speed of work. At some point, there are too many people in total to interact with one another directly, so individual teams are formed. This might reduce the total number of people that need to interact with one another, but necessitates new types of meetings where these individual teams now share updates, and team leaders then share these updates with other teams.

Beyond a certain size, in order for every team to be aware of each others’ work to facilitate collaboration and coordination, the time required for administration and bureaucracy will naturally increase.

This is one of the reasons why often, the pace of change and innovation slows down as the number of people involved increases.

Many thanks to Seth Godin for inspiring this post.

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Creativity & Innovation expert: I help individuals and companies build their creativity and innovation capabilities, so you can develop the next breakthrough idea which customers love. Chief Editor of Ideatovalue.com and Founder / CEO of Improvides Innovation Consulting. Coach / Speaker / Author / TEDx Speaker / Voted as one of the most influential innovation bloggers.