# Power laws In most systems that grow by accumulation or connection, a small number of items carry most of the weight. The concentration is structural, not random, and it makes averages meaningless. --- ## The mechanism A bell curve describes outcomes driven by many independent additive factors: height, IQ, daily temperature. Power laws describe outcomes driven by preferential attachment, where the well-connected attract more connections, or multiplicative reinforcement, where early advantage compounds. The resulting distribution has no meaningful average. Median and mean can differ by orders of magnitude, and the tail never thins out the way a bell curve does. [[Lognormal Distribution]] is the adjacent case. Multiplicative noise produces a skewed distribution with a long right tail, but it thins out eventually. Whether a real-world distribution follows a strict power law or a very wide lognormal is often hard to tell from finite data. The practical consequence is the same: extreme concentration, where a single outlier can outweigh the rest of the distribution combined. --- ## Where this shows up You have 200 customers. Average annual revenue per customer is £50k. But the top five accounts generate 40% of total revenue, and the bottom hundred generate 8%. The "average customer" exists nowhere in your base. [[Variance]] teaches you to check whether a baseline is meaningful before reacting to a movement. In power-law domains, the baseline itself is suspect. An average deal size, an average customer lifetime, an average employee contribution: if the underlying distribution is this concentrated, the average describes nobody. [[The Formula]] traces how this works in careers and networks. Performance follows a bell curve: bounded, clustered, modest variation. Success follows a power law: unbounded, concentrated, driven by network position as much as ability. The same fractional improvement near the top produces wildly different outcomes depending on timing and visibility. [[Linked]] explains the generating mechanism: growth plus preferential attachment produces scale-free networks where a few hubs carry exponentially more connections than the rest. --- ## Why "80/20" misleads People invoke "80/20" without understanding what generates the ratio. It isn't a fixed rule. It's a consequence of structure, and changing the structure changes the concentration. A sales team that relies on inbound leads will see revenue dominated by a few large accounts that found them. A team that actively prospects mid-market will see a flatter distribution. Same product, different structure, different concentration. The question worth asking is whether you're in a domain where the tail dominates the average. If yes, optimising for the average is optimising for nobody. [[Scale]] works precisely because it deals in orders of magnitude rather than precision. In power-law domains, that instinct is the right one: being in the right neighbourhood matters more than being exactly right.