Why Dependence of Productivity on Group Size Is Log-Normal

Empirical analysis shows that, on average, the productivity of a group log-normally depends on its size. The current explanations for this empirical fact are based on reasonably complex assumptions about the human behavior. In this paper, we show that the same conclusion can be made in effect, from first principles, without making these complex assumptions. 1 Formulation of the Problem How productivity changes with group size: a qualitative description. Productivity of a group depends on its size. Usually, if first a single person has been working on a project, and then a second person arrives to help, the project speeds up. Addition of the third helper also increases the productivity, etc. However, this is only true until a certain threshold is reached. After that, too many people just confuse each other – whether it is too many people trying to help wash the dishes after a meal, or too many programmers trying to work on a joint software project. How productivity changes with group size: a quantitative description. Several studies analyzed how exactly productivity c changes with the group size n; see, e.g., [1, 4], and concluded that this dependence can be well described by the log-normal formula c(n) = const · exp ( − (ln(n)− μ) 2 2σ2 ) (1) for appropriate values μ and σ. Why this is interesting. If we know how the productivity depends on the group size, we will be able to select the group size that leads to the optimal productivity.