Distribution Metrics
Distribution metrics describe the statistical shape of your trade P&L data. They reveal whether returns follow a "normal" bell curve or have unusual characteristics like fat tails or asymmetry.
Quick Reference
| Metric | Formula | Unit |
|---|---|---|
| Standard Deviation | StdDev of daily equity returns | ratio |
| Downside Deviation | StdDev of negative daily returns only | ratio |
| Skewness | Distribution asymmetry of trade P&Ls | score |
| Kurtosis | Distribution tail heaviness | score |
| Z-Score | Runs test: (Runs - Expected) / StdDev of Runs | score |
| Z-Probability | Statistical significance of Z-Score | % |
| Avg Trade StdDev | Standard deviation of individual trade P&Ls | $ |
| Trade Coef. of Variation | StdDev / |Avg Trade| | ratio |
Key Metrics Explained
Skewness
Measures whether returns lean left (negative) or right (positive):
| Category | Meaning |
|---|---|
| Loss-heavy | Occasional large losses dominate |
| Symmetric | Balanced wins and losses |
| Win-heavy | Occasional large wins |
| Jackpot | Rare, very large wins |
Positive skewness is preferred — it means your outlier trades tend to be winners, not losers.
Kurtosis
Measures how extreme the tails of your distribution are:
| Category | Meaning |
|---|---|
| Predictable | Few extreme outliers |
| Normal | Standard tail behavior |
| Volatile | Occasional extreme trades |
| Extreme | Very heavy tails — rare but huge outliers |
High kurtosis means your strategy occasionally produces very large wins or losses. This makes results less predictable.
The 16 Distribution Profiles
AlgoChef combines skewness and kurtosis to classify your strategy into one of 16 profiles.
The following 16 distribution profiles are proprietary to AlgoChef and protected by copyright.
| Predictable | Normal | Volatile | Extreme | |
|---|---|---|---|---|
| Loss-heavy | Steady Bleeder | Asymmetric Grind | Tail-Risk Trap | Black Swan Magnet |
| Symmetric | Predictable Grinder | Standard Trader | Fat-Tail Balanced | Chaos Balanced |
| Win-heavy | Positive Edge | Skew Advantage | Volatile Winner | Jackpot Mix |
| Jackpot | Rare Win System | Outlier Dependent | High-Variance Jackpot | Extreme Jackpot |
Tip
The ideal profiles are in the top-left area: Predictable Grinder (symmetric, no outliers) or Positive Edge (slightly win-heavy, predictable). Bottom-right profiles (extreme kurtosis + jackpot skew) are the hardest to trade consistently.
Understanding your distribution profile helps you select the most appropriate Monte Carlo simulation method for stress-testing.
Z-Score
The Z-Score from a "runs test" measures whether wins and losses are randomly distributed or clustered:
- Z-Score near 0 — Random sequence (no pattern)
- Negative Z-Score — Streaks (wins follow wins, losses follow losses)
- Positive Z-Score — Alternating (win-loss-win-loss patterns)
The Z-Probability tells you how statistically significant this pattern is. Above 95% means the pattern is likely real and not due to chance.
Tail Analysis
These metrics go beyond standard skewness/kurtosis to examine the specific behavior of extreme trades.
| Metric | Description | Unit |
|---|---|---|
| Negative Tail Kurtosis | Kurtosis of losing trades only — measures how extreme your worst losses are | score |
| PnL Tail Ratio | Ratio of right-tail magnitude to left-tail magnitude | ratio |
| Tail Direction | Whether extreme trades skew toward wins or losses | label |
| Tail Ratio | 95th percentile gain / abs(5th percentile loss) | ratio |
Tail Ratio is particularly useful: a value above 1.0 means your best trades are larger than your worst trades. Below 1.0 means extreme losses outsize extreme wins — a warning sign for strategies that look profitable on average but carry hidden tail risk.
Robust Statistics (Winsorized Metrics)
Standard metrics can be distorted by a few extreme outliers. Winsorized metrics trim the most extreme values before calculating, giving a more stable view of "typical" strategy behavior.
| Metric | Description | Unit |
|---|---|---|
| Winsorized Skewness | Skewness after trimming extreme outliers | score |
| Winsorized Kurtosis | Kurtosis after trimming extreme outliers | score |
| Winsorized Neg Tail Kurtosis | Tail heaviness of losses after trimming | score |
| Winsorized Mean PnL | Average trade P&L after trimming outliers | $ |
| Winsorized Profitable | Whether the strategy is profitable after removing best/worst trades | yes/no |
| Core Edge Robust | Whether the strategy's edge survives after outlier removal | yes/no |
Core Edge Robust is the key metric here. If your strategy is profitable overall but not profitable after removing outlier trades, your edge depends on rare events rather than a repeatable process. This is critical for assessing long-term viability.
Tip
Compare your standard skewness/kurtosis to winsorized versions. If they diverge significantly, a small number of trades are dominating your results — investigate whether those trades are repeatable.
Tip
Want to understand your strategy's distribution profile in depth? The Strategy Analyzer shows your full distribution analysis with visual histograms.
Tip
Ready to analyze your own strategy? Start your free trial — no credit card required.