Svenkat

A fun thought experiment on survivorship bias and selecting the best strategy: Imagine two entrepreneurs, Alice and Bob. They each open a business with an initial capital of $100,000. Alice takes more risks and, as a result, has a high growth rate of 10%. However, because of those risks, she also has a high failure rate of 5%. Conversely, Bob takes less risks. As a result, his growth rate is lower, 8%, but so is his failure rate, 1%. Who do we expect to make the most money: Alice or Bob? The answer is counterintuitive: Alice is more likely to be wealthier than Bob, yet we expect Bob to end up wealthier. Let me explain. If we consider periods of a single year, Alice is expected to be wealthier than Bob 95% of the time. Yet, if you compare the expected wealth, Alice’s is 95% times $100,000 times 110% = $104,500, whereas Bob’s is 99% times $100,000 times 108% = $106,920. Bob’s expected wealth is higher than Alice’s despite him being less likely to be wealthier than her. Here is another way to see it. Given a hundred Alices and a hundred Bobs, the top 95 wealthiest entrepreneurs would all be Alices. Yet, on aggregate, Bobs would have more wealth. Survivorship bias makes us think that Alice’s strategy is better because all the winners are Alices, but her strategy is not better. Alice’s strategy has higher potential but is less reproducible; therefore, she ends up worse, at the net of survivorship bias.