The luck bar for 10, 50, 500 and 4,096 tries, at the spread of the 4,096-strategy test
Our own calculation, 8 November 2026 (UTC), for the article "4,096 trading strategies, 20 years of the S&P 500: none told from luck". The 4,096-strategy test (https://hypothesess.com/lab/4096-strategies) gives a luck bar of 1.198: the annual Sharpe ratio the best of 4,096 no-edge strategies is expected to reach in its 2006-2017 sample. That bar is the spread of the strategies' Sharpe ratios times the expected best of 4,096 standard normal draws. Keeping the same spread, we compute the bar for fewer tries, two ways.
What we found
- The expected best of 4,096 normal draws is 3.64 standard deviations by the Bailey and López de Prado approximation and 3.63 exactly (numerical integration), so the test's bar of 1.198 implies a spread of 0.329 in annual Sharpe ratio.
- At that spread, the luck bar is 0.52 for 10 tries, 0.75 for 50 tries, 1.01 for 500 tries and 1.20 for 4,096 tries (approximation); the exact values are 0.51, 0.74, 1.00 and 1.19.
- The best strategy's in-sample Sharpe ratio of 0.89 is above the bar for 50 tries (about 0.75) and below the bar for 4,096 tries (about 1.20).
What this cannot tell you: the bars for fewer tries assume the same spread of Sharpe ratios as the 4,096 tried; a smaller, different set of rules would have its own spread.