# Probability of Backtest Overfitting (PBO) — CSCV Engine for MQL5

Source code for the article **"Measuring the Probability of Backtest Overfitting of Your MT5
Optimization (Part 1): The CSCV Engine in MQL5"** (mql5.com article 24095), by Astralys LLC.

The engine implements the Probability of Backtest Overfitting of Bailey, Borwein, Lopez de Prado
and Zhu (2015), computed through Combinatorially Symmetric Cross-Validation. You feed it a matrix
of per-bar returns, one column per parameter combination, and it returns one number: how likely
your optimization picked noise rather than signal. All 12,870 splits of 16 partitions run in about
0.2 seconds on 1,300 combinations and 3,610 bars.

## Files

| File | What it is |
|---|---|
| `Include/PBO/CSCVEngine.mqh` | The engine. Depends on nothing but the standard library. |
| `Include/PBO/MACDp.mqh` | MACD on price: distance of the close to its own SMA, optionally as a percentage. |
| `Include/PBO/BearsPower.mqh` | Bears Power: distance of the low to an EMA of the close, optionally as a percentage. |
| `Scripts/PBO/RunPBO.mq5` | Builds the 1,300-column returns matrix on the chart symbol, runs the engine, runs the control experiments, exports CSVs. |
| `Scripts/PBO/TestCSCVEngine.mq5` | Two known-answer validation cases: pure noise (PBO must be near 50%) and one planted winner (PBO must be 0, logit exactly ln(200)). |
| `Scripts/PBO/ExportBars.mq5` | Exports the bar history of the chart it is dropped on to CSV, used to draw the article figures. |

## Install

Copy `Include/PBO/` into `MQL5\Include\` and `Scripts/PBO/` into `MQL5\Scripts\` of your terminal
data folder, then compile the scripts in MetaEditor (F7).

## Minimal use on your own optimization

```cpp
#include <PBO/CSCVEngine.mqh>

CCSCVEngine engine;
engine.SetPartitions(16);
engine.SetReturns(retMatrix, bars, sets);   // bars x sets, log returns, row-major
engine.Run();
PrintFormat("PBO = %.2f%%", engine.PBO());
```

Two constraints carry over from the article: the returns must be logarithmic, because the engine
rests on them being additive, and the signal that decides the position on bar `t` must be read on
bar `t - 1`.

## Reference

Bailey, D., Borwein, J., Lopez de Prado, M., Zhu, Q. (2015), *The Probability of Backtest
Overfitting*, Journal of Computational Finance.

The validation study behind the article: Bergerat, J. (2020), *On the Relevance of Optimizing
Technical Indicators on U.S. Stock Markets*, University of Lausanne. SSRN abstract 5212650.