Mathematics
Power Law
A mathematical relationship where one quantity varies as a power of another: y = x^k. Power laws appear as straight lines on log-log plots and produce highly skewed distributions with many small values and few large ones.
Biological Context
Species abundance, body size, metabolic rate, and extinction frequency all follow power laws. Power law distributions have 'fat tails'—extreme events are more common than normal distributions predict. Power laws often arise from multiplicative processes or preferential attachment.
Business Application
Business outcomes follow power laws: a small fraction of products generate most revenue, a few employees drive most value, and rare events dominate long-term results. Averages mislead.