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The Birthday Paradox

Answer this: How many people do you think need to be in the same room before two of them have the same birthday? We have a tendency to think of this question in a linear way and so most people approach this by thinking about the 365 days in a year. Meaning that having around 180 people in the room would give you a near certainty of meeting one other person with the same birthday. And having over 90 people would give you a good (over 50%) chance.

However if we think of a group of people as a network, then every additional person increases the number of connections between people exponentially. For every additional person added you’re effectively adding a potential birthday match not just to one other person but to every person already in the group. So the number of people you need for a 50% chance of two people having the same birthday is actually 23. And the number that you need for a near certainty is closer to 60 – much less than we tend to think. The Birthday Paradox is properly counterintuitive, and is a good example of how thinking can be skewed by an overly linear approach.

The implications of this are quite significant when we think about things that are connected. As the diagram above shows, when we consider the size of a project team (or indeed any team) we also need to take into consideration that the communication overhead increases exponentially for every additional person we put in the team. When we think about taking more responsibilities or tasks on we need to consider not only the additional burden of those individual tasks but also how they interrelate with all the other responsibilities and things that we already need to do. And when we think about new technologies we need to think about all the connected possibilities that they create. AI, for example, will have a profusion of different applications which in turn will cascade into many more new potential applications.

We tend to think about exponentiality only in the context of rapid change or technology adoption but this underplays the significance of one of the key aspects in which exponentiality reveals itself – in connections.

HT @davidkadavy for the inspiration

2 responses to “The Birthday Paradox”

  1. Conor McNicholas Avatar
    Conor McNicholas

    This challenge also occurs when you have multiple agencies working for the same brand client. Coordinating becomes a full-time job. One way to address this is to put a ‘network node’ in the middle of the diagram so it becomes hub and spoke. Then, no matter how many elements you have outside you can traffic the communication to make sure the right people know the right stuff. We built this system as the (award-winning) Barclays Editorial Board back in 2012. Was very successful as a way to orientate everyone’s work around genuine audience (consumer) challenges rather than the business sitting on broadcast-mode all the time.

    1. neilperkin Avatar

      Thanks Conor. That makes complete sense that multi-agency working would generate the same effect – and a good approach that you mention there for mitigating it

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