Z-score
A z-score expresses a value as a number of standard deviations away from the mean of a reference window; in trading it turns price, delta or volume into a unit-free reading that says how unusual the current bar is compared with the recent ones.
Senzoukria · Glossary · Updated September 2026
Formula
z = (x − μ) / σ, where μ is the mean and σ the standard deviation of the last N observations. A z-score of 2 means the value sits two standard deviations above the window mean; −1 means one standard deviation below. The number has no unit, which is the point: a z-score of 2 on MNQ delta and a z-score of 2 on 6E volume describe the same degree of departure from their own recent behaviour.
- Senzoukria uses the population standard deviation (division by N), the same convention as its Bollinger Bands, so the three z-score indicators and the bands agree with each other.
- When σ is zero the window is flat and z is undefined. The indicator reports a missing value, never 0, because 0 would claim that the bar is exactly average.
- Before N bars are available there is no reference, and the output is missing during that warm-up.
Three subjects, one method
The volume version excludes the current bar from its reference on purpose. A single very large bar would otherwise inflate its own σ and shrink its own z-score. Price and delta keep the current bar in the window, matching the Bollinger convention. The default window is 20 bars for all three, and none of them reset at the session boundary.
| Indicator | Subject | Reference window |
|---|---|---|
| Price Z-Score | Bar close | Last N bars, including the current one |
| Delta Z-Score | Bar delta (ask volume − bid volume) | Last N bars, including the current one |
| Volume Z-Score | Bar volume | The N bars strictly before the current one |
How to read it
- Price z-score far from zero: the close is stretched relative to its own recent mean. Whether that stretch tends to revert depends on the regime, which is why the Hurst guide pairs it with a regime filter.
- Delta z-score: a bar whose aggressor imbalance is unusual for the recent tape. It flags an abnormal bar, not a direction for the next one.
- Volume z-score: participation that is out of line with the preceding bars. Combine it with where the volume printed in the footprint before interpreting it.
- Thresholds such as 2 or 3 are conventions inherited from the normal distribution; return and volume distributions have heavier tails, so extreme z-scores occur more often than the textbook suggests.
In Senzoukria
The catalogue lists Price Z-Score (Momentum group), Delta Z-Score (Delta group) and Volume Z-Score (Tape & flow group), each drawn in a separate pane with a Period parameter. The Hurst MR (signals) overlay uses a price z-score internally: its Z lookback and Entry K (σ) settings define the window and the number of standard deviations at which a candidate entry is marked. The Python template Mean reversion under regime (HMM + Hurst) in the Scripts editor uses the z-score to decide when to enter and toward which price.
Common mistakes
- Comparing a z-score from a 20-bar window with one from a 200-bar window as if they measured the same thing.
- Assuming symmetry: a −2 on delta after a long run of selling is not the mirror image of a +2 after a quiet stretch.
- Reading a missing value during warm-up or on a flat window as a zero.
- Using a z-score threshold as a complete rule without stating the exit, the invalidation and the costs.
Related
This page in other languages
Frequently asked questions
- Which standard deviation does the z-score use, population or sample?
- The three z-score indicators use the population form, dividing by N. This is the same choice as the Bollinger Bands in the catalogue and matches the common charting convention. The Realized Vol indicator uses the sample form instead, because that is the historical-volatility convention; the difference is documented per indicator.
- Why does the volume z-score exclude the current bar?
- So that an unusual bar is measured against bars that did not include it. If the current bar were part of its own reference, a large spike would raise the window's mean and standard deviation and partly hide itself. Price and delta include the current bar to stay consistent with Bollinger-style bands.
- Is a z-score of 2 a signal?
- It is a measurement that the current value is two standard deviations from its recent mean. Turning it into a signal requires a hypothesis about what tends to follow, a test on data with costs, and a check on a later period that took no part in choosing the threshold.