What Is Survivorship Bias?
Survivorship bias is one of the most insidious forms of selection bias. It occurs whenever we draw conclusions from a dataset that only includes entities that 'survived' some process — companies that didn't go bankrupt, funds that weren't closed, people who succeeded — while ignoring the far larger number that failed and became invisible.
The Wald Aircraft Problem
The most famous illustration comes from World War II. The U.S. military examined returning bombers and found bullet holes concentrated in certain areas. The intuitive recommendation was to reinforce those areas. But statistician Abraham Wald recognized the critical flaw: the data only represented planes that survived. The areas without bullet holes were where planes were being hit and not coming back. Wald recommended armoring the undamaged areas — a brilliant inversion that saved lives and became the canonical example of survivorship bias thinking.
How the Simulation Works
This simulator creates a cohort of companies, each starting at a value of 100. Each year, every surviving company earns a random return drawn from a normal distribution, and faces a probability of failure. Companies that fail stop being tracked in 'survivor only' statistics but remain in the full population data. The fan chart shows all trajectories: survivors are highlighted in cyan, while failures fade into darkness — mirroring how failed companies disappear from real-world databases and media coverage.
The Bias Gap
The bottom bar chart reveals the key insight: the average return of survivors is substantially higher than the true average return of all companies. This gap — the survivorship bias — arises because companies with unlucky return sequences are more likely to fail. When you study only the winners, you systematically overestimate how good the typical outcome is. This same logic applies to studying successful entrepreneurs, profitable trading strategies, or star fund managers.