---
title: "Z-score"
description: "What is a Z-score in trading? In systematic trading, the Z-score is a runs test that tells you whether a strategy's sequence of wins and losses is genuinely random or streaky. A Z-score beyond ±1.96 m..."
url: https://quantmonitor.net/z-score/
date: 2023-01-06
modified: 2026-07-21
author: "Kornel"
image: https://quantmonitor.net/wp-content/uploads/2023/01/z_score-jpg.webp
categories: ["Trading encyclopedia"]
type: post
lang: en
---

# Z-score

## What is a Z-score in trading?

**In systematic trading, the Z-score is a runs test that tells you whether a strategy’s sequence of wins and losses is genuinely random or streaky.** A Z-score beyond ±1.96 means consecutive trades are dependent at the 95% confidence level; a Z-score near 0 means winning and losing streaks are just random noise.

*(In general statistics, the Z-score measures how many standard deviations a value sits from the mean. In trading we apply that same idea to the run of wins and losses, using the runs test below.)*

| Z-score | Confidence of dependency | Streak meaning | Money-management implication |
| --- | --- | --- | --- |
| 0 to ±1.0 | Below 68% | Random noise | Trade normally; don’t chase streaks |
| Around ±1.65 | ~90% | Weak dependency | Monitor only |
| Below −1.96 | 95%+ | Clustering — wins follow wins, losses follow losses | Consider cutting size or pausing during a losing run |
| Above +1.96 | 95%+ | Alternating — a loss tends to follow a win | Can add size after a loss |

*You need roughly 30–50 closed trades before the ±1.96 (normal-approximation) reading is reliable.*

## The Z-score (runs test) formula

Z = ( N × (R − 0.5) − X ) / √[ X × (X − N) / (N − 1) ], where X = 2 × W × L.

Here **N** = total number of trades, **R** = the number of runs (unbroken streaks of wins or losses), **W** = number of winning trades and **L** = number of losing trades. A negative Z-score means fewer runs than random (clustering); a positive Z-score means more runs than random (alternating).

## Why the Z-score matters for a trading system

The Z-score does not measure whether a strategy is profitable — it measures whether its wins and losses are *dependent*. If losses cluster (Z below −1.96), a losing trade makes the next loss more likely, so reducing size during drawdowns can help. If results alternate (Z above +1.96), a loss tends to be followed by a win, which can justify a different money-management rule. Between −1.96 and +1.96, streaks are statistically just luck and should not drive sizing decisions.

## Frequently asked questions

### What is a good Z-score for a trading strategy?

There is no “good” or “bad” Z-score in the profit sense — it measures dependency, not quality. A Z-score between −1.96 and +1.96 means your winning and losing streaks are random; readings beyond that reveal exploitable structure you can manage with position sizing.

### Does a high Z-score mean my strategy is better?

No. A high absolute Z-score only means the sequence of wins and losses is non-random (streaky or alternating). Profitability is measured by other metrics such as [R-expectancy](https://quantmonitor.net/r-expectancy/) and [profit factor](https://quantmonitor.net/profit-factor/).

### How many trades do I need for a reliable Z-score?

Around 30–50 closed trades at minimum. Below that, the normal approximation behind the ±1.96 threshold is unreliable and a Z-score reading is mostly noise.

### What is the difference between Z-score and serial correlation?

The trading Z-score looks only at the sequence of win/loss outcomes (a runs test), while serial correlation looks at the sizes of consecutive trade results. The Z-score answers “are my streaks random?”; serial correlation answers “does a big result tend to follow another big result?”

### How do I use the Z-score for position sizing?

If losses cluster (significantly negative Z), reduce risk during a losing run and restore it afterwards. If results alternate (significantly positive Z), you can lean the other way. With a non-significant Z-score, keep sizing constant — the streaks are random.

The Z-score is one of several strategy-robustness metrics. Read it alongside [the Sharpe ratio](https://quantmonitor.net/sharpe-ratio-understanding-using-investing-decisions/), [R-expectancy](https://quantmonitor.net/r-expectancy/) and [profit factor](https://quantmonitor.net/profit-factor/) and the [System Quality Number (SQN)](https://quantmonitor.net/system-quality-number-sqn/), and see how we apply them in our [live trading portfolio](https://quantmonitor.net/blog/).