Free tool
Deflated Sharpe ratio calculator
The best of many backtests always looks better than it is. Enter the Sharpe ratio of your best variant and how many variants you tried, and see the Sharpe ratio noise alone would have produced, and the probability yours beats it.
Annualised, as your backtest reports it.
Every parameter set, market, filter and timeframe you looked at, the discarded ones included.
Annualised, as your backtest reports it. Every parameter set, market, filter and timeframe you looked at, the discarded ones included.
Shape of the returns and spread of the trials
0 if symmetric or unknown.
Raw, not excess: 3 is normal.
Their standard deviation, annualised. Blank assumes pure noise.
Deflated Sharpe ratio 92.6%. More likely real than not, but short of a 95% bar once the trials are counted.
Bailey and López de Prado's deflated Sharpe ratio (2014). It treats the trials as independent. Correlated variants are worth fewer independent tries, so counting every one of them makes the correction conservative, not lenient.
The best of many backtests always looks good
Run one backtest of a strategy with no edge and its Sharpe ratio scatters around zero. Run twenty variants and keep the best, and the best is no longer around zero: it is the top of twenty draws, and it looks like skill. Nothing in the winning backtest itself says how many losers it was chosen from.
The table shows how large that effect is. Each figure is the annualised Sharpe ratio you should expect from the best of that many backtests of pure noise, on daily returns. None of these strategies has an edge.
| Variants tried | 1 year | 5 years | 10 years |
|---|---|---|---|
| 2 | 0.52 | 0.23 | 0.16 |
| 5 | 1.19 | 0.53 | 0.38 |
| 10 | 1.58 | 0.70 | 0.50 |
| 20 | 1.90 | 0.85 | 0.60 |
| 50 | 2.28 | 1.02 | 0.72 |
| 100 | 2.54 | 1.13 | 0.80 |
| 1,000 | 3.26 | 1.46 | 1.03 |
| 10,000 | 3.87 | 1.73 | 1.22 |
With one year of daily returns, 5 noise backtests are enough for the best of them to be expected above a Sharpe ratio of 1.0. With five years it takes 50; with ten, 1,000. Longer samples shrink the effect, because each estimate is less noisy, but they never remove it, and more tries always push it back up.
What the deflated Sharpe ratio measures
David Bailey and Marcos López de Prado built the correction in two steps. The probabilistic Sharpe ratio (PSR) asks how likely it is that a strategy’s true Sharpe ratio exceeds a benchmark, given how many returns it was measured on and how skewed and fat-tailed they were. The deflated Sharpe ratio (DSR) sets that benchmark at the best Sharpe ratio N tries of noise are expected to produce.
PSR(SR*) = Φ( (SR − SR*) × √(T − 1) / √(1 − γ3·SR + (γ4 − 1)/4 · SR²) )
SR0 = √V[SR] × ( (1 − γ)·Φ⁻¹(1 − 1/N) + γ·Φ⁻¹(1 − 1/(N·e)) )
DSR = PSR(SR0)V[SR] is the variance of the Sharpe ratios across the trials. When it is unknown the calculator uses the variance noise alone would give, which is what a set of trials with no edge among them would scatter by. If you have the Sharpe ratios of every variant, enter their spread instead.
With the calculator’s starting values, a Sharpe ratio of 1.5 over 5 years of daily returns is comfortably significant as a single test, at a PSR of more than 99.9%. Chosen as the best of 20 variants, its DSR is 92.6%, short of the 95% bar, because 20 tries of noise are expected to reach 0.85 on their own. It would have cleared 95% only if no more than 13 variants had been tried.
Counting the trials honestly
The correction is only as good as N, and N is the number people most often get wrong, because the variants that were looked at and dropped leave no trace in the final backtest. Every parameter set, market, timeframe, filter, exit and session window that was evaluated is a trial, whether or not it was kept.
That is why the research here runs on a ledger. Every specification screened is recorded whatever its verdict, and the multiple-testing correction runs against the full count. As of 28 October 2026 the ledger holds 105,204 screened specifications, of which 562 cleared every gate: 1 in 187. The method page sets out the rest of the gate stack.
What the deflated Sharpe ratio cannot tell you
It corrects for selection, and only for selection. A backtest can clear it and still be wrong for reasons it cannot see: costs that were never charged, a contract roll traded as if it were a price move, a feature that looked ahead, or a long-only strategy whose Sharpe ratio is mostly the market’s own drift. The research record keeps a separate test for each, a drift null for the last of them.
It also assumes the returns come from one process. A strategy whose profit sits almost entirely in its last few years can post a strong Sharpe ratio that is the property of one era, which is why every result on the ledger is split by era before it is believed.
Bailey, D. H. and López de Prado, M. (2012), “The Sharpe Ratio Efficient Frontier”, Journal of Risk 15(2). Bailey, D. H. and López de Prado, M. (2014), “The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting, and Non-Normality”, Journal of Portfolio Management 40(5).
Questions
- What is a good deflated Sharpe ratio?
- It is a probability, so read it like one: 95% is the usual bar, the equivalent of a 5% significance level. A DSR of 95% says there is a 95% chance the strategy's true Sharpe ratio beats the best that the same number of pure-noise trials would have produced.
- What is the difference between the probabilistic and the deflated Sharpe ratio?
- The probabilistic Sharpe ratio asks whether a Sharpe ratio beats zero, allowing for sample length, skew and fat tails. The deflated Sharpe ratio asks the same question against a higher bar: the best Sharpe ratio expected from N tries of noise. With one trial they are the same number.
- How do I count the number of trials?
- Count every variant you evaluated and could have kept: each parameter set, market, timeframe, filter and exit you looked at, including the ones you threw away. If you do not know, the number is larger than you think, and a guess on the high side is the honest one.
- Can I use per-trade returns instead of daily returns?
- The formula works on any return series whose observations are roughly independent. Daily returns are the usual choice for intraday strategies because trades on the same day are not independent of each other. Choose the frequency your Sharpe ratio was calculated from.
- Is 1 minus the deflated Sharpe ratio a p-value?
- Approximately: it is the probability of seeing a Sharpe ratio this high if the true one were no better than the best of N noise trials. It carries the same caveats as any p-value, including the assumption that you counted the trials honestly.
Every trial counted, including yours.
The screener records every specification it runs, whatever the verdict, and corrects for the true count. A pass means something because nothing was left out of the denominator.