The Lab

Where it comes from

• The best-known story is from the Second World War. The statistician Abraham Wald, at Columbia University's Statistical Research Group, worked on where to add armour to bombers. The planes that came back showed where a plane can be hit and still fly. The ones that didn't come back, hit elsewhere, were missing from the data. His memoranda (1943) were reprinted in 1980. The popular retelling is simpler than his actual maths.
• In finance, the problem was measured in investment funds. Funds that do badly close or merge, and drop out of the records. Studies that only see the funds still running see the winners.
  • Stephen Brown, William Goetzmann, Roger Ibbotson and Stephen Ross (1992) showed how this makes past performance look more persistent than it is.
  • Burton Malkiel (1995) and Edwin Elton, Martin Gruber and Christopher Blake (1996) measured how much it flatters fund returns.
  • Brown, Goetzmann and Ross (1995) showed that survival alone can make a market's history look better than its future.
  • Tyler Shumway (1997) found that stock databases left out much of the final fall of companies that were delisted.

The maths, step by step

1. The stark case. Ten coins start equal. Five double and five go to zero.

• The true average: (5 × +100% + 5 × −100%) ÷ 10 = 0%.
• The survivors' average: +100%.

2. A gentler case. Ten coins end at +200%, +80%, +50%, +20%, 0%, −10%, −30%, −50%, −80% and −100%.

• All ten: +8%.
• Leave out the dead one: +20%.
• Keep the five biggest at the end, as a list made today would: +70%.

The third is the hindsight version, and it's the biggest error.

3. Two coins. Both start equal. One triples, one halves.

• Holding both: +75% on average.
• "The biggest coin," picked at the end: +200%.

What we tested and found

This section is ours. It measures a known effect on crypto.

• Picked at the end against picked at the start. For 23 quarters from 2021 to 2026, we took the 30 most-traded futures coins twice: ranked on the quarter's first day, and ranked the day after it ended. The list made at the end did better in all 23 quarters (by the average coin; 21 of 23 by the median coin). Its median coin was 15 points ahead in a typical quarter, and 126 points ahead over a year.
• Our own live studies' 32 coins, picked in October 2026, rose a median 60% over the 90 days before, against 36% for a list picked at the start of those 90 days.
• Over a quarter, hindsight was the bigger part, as in step 2. No coin in either list stopped trading inside a quarter. Picking the risers mattered more than dropping the dead.
• Re-running with the dead coins put back:
  • picking carry coins by their funding lost 29% to 42% a year, against −1% to −3% on today's list;
  • buying sharp drops made +0.61% a trade instead of +0.73%, and still failed.
• Steady buying, run on the top 20 coins picked at the start of 2022: most lost money over four years however they were bought.

Credits

• Abraham Wald, "A Method of Estimating Plane Vulnerability Based on Damage of Survivors", Statistical Research Group memoranda, 1943, reprinted by the Center for Naval Analyses, 1980.
• Stephen J. Brown, William Goetzmann, Roger G. Ibbotson and Stephen A. Ross, "Survivorship Bias in Performance Studies", Review of Financial Studies, 1992.
• Stephen J. Brown, William N. Goetzmann and Stephen A. Ross, "Survival", Journal of Finance, 1995.
• Burton G. Malkiel, "Returns from Investing in Equity Mutual Funds 1971 to 1991", Journal of Finance, 1995.
• Edwin J. Elton, Martin J. Gruber and Christopher R. Blake, "Survivorship Bias and Mutual Fund Performance", Review of Financial Studies, 1996.
• Tyler Shumway, "The Delisting Bias in CRSP Data", Journal of Finance, 1997.
• Our tests: "Survivorship: how the coins were picked, and what it does", "Buying a sharp drop: does the market bounce the next day?" and "Buying steadily, or all at once?". Binance's public data archive.
• PerpGremlin and Claude, Survivorship bias: the coins you can't see, TerminalGremlin, 2026: the tests, the code and the words.