Test 100 no-edge strategies on two years of data and the best backtest typically shows a Sharpe ratio of 1.7: luck alone

Our own calculation, 7 November 2026 (UTC), for the article "The best of many". A strategy with no edge has a two-year Sharpe ratio that is noise around zero with a spread of 1 / sqrt(2) = 0.707 per year (Lo, 2002). Way 1, exact: the q-quantile of the best of k such strategies is 0.707 x the standard normal quantile of q to the power 1/k. Way 2: 1,500 simulated batches of 100 coin-flip strategies, each trading 500 days of +1% or -1% at random (fixed seed 20261108), Sharpe = daily mean / daily spread x sqrt(250). The two agree.

What we found

Best of 100 no-edge strategies: the typical (median) best two-year Sharpe ratio is 1.74, about 1.7 (simulated 1.78); the luckiest batch in ten reaches 2.17, about 2.2 (simulated 2.23).
The same for other batch sizes, typical and luckiest in ten: 1 strategy 0.0 and 0.9; 10 strategies 1.1 and 1.6; 20 strategies 1.3 and 1.8; 300 strategies 2.0 and 2.4; 500 strategies 2.1 and 2.5; the best of 50 is typically 1.6.
With 10 tries luck clears a Sharpe of 1 56% of the time (56%); with 100 tries 99.97% of the time (99.97%), and a Sharpe above 2 in 21% of batches (one in five).
The rough rule sqrt(2 ln k) spreads gives 2.15 for k = 100 (2.15) against the exact median of 1.74.
The typical best of 100 gains about 71% over the two years compounded (simulated median), roughly two thirds; one year of a single no-edge strategy wanders with a spread of 15.8 percentage points (about 16; simulated 15.7).

Check it yourself

Strategies tested	Typical best Sharpe (exact)	Luckiest batch in ten (exact)	As the article rounds
1	0.00	0.91	0.0	0.9
10	1.06	1.63	1.1	1.6
20	1.29	1.81	1.3	1.8
50	1.56	2.02	1.6	2.0
100	1.74	2.17	1.7	2.2
300	2.00	2.40	2.0	2.4
500	2.12	2.49	2.1	2.5

What this cannot tell you: the luck line for strategies that are correlated with each other (it is lower), or for daily returns that are not symmetric; whether any real strategy has an edge.