How much does deep sleep have to change before it stops being noise? The threshold from 650 nights

Case zero's deep sleep has a coefficient of variation (CV) of 22.11% across 650 nights. From that series, the threshold for calling one night's number "real change" instead of ordinary noise is 13.52%, measured in windows of 28 nights. That threshold drops to 9.56% with windows of 56 nights. Below those numbers, one night differing from another still sits inside what this body normally produces.

What the data is

sleep_deep_min is deep sleep, in minutes, from a single person: Black Swan's case zero. The median of the series is 84 minutes per night. That median is the reference point; the 22.11% CV describes how much the full series moves around it, night after night, across 650 nights.

This is not a population average or a lab figure. It is one body's own record, tracked night by night for close to two years. No one else appears in this number.

How it was measured

650 nights of data, one body, one device. Every night enters the series with its deep-sleep value in minutes. Five numbers come out of that series:

• CV — how much the whole series moves: 22.11%.
• rho — the correlation between one night and the next: 0.154. It's low: what happened last night predicts little of what happens tonight.
• RCV — the variability of the raw night-to-night change: 61.28%.
• Window thresholds — the CV a change has to clear to count as real, computed across windows of different sizes: 28, 56, 84, and 168 nights.

The table

Metric	Value
Nights measured	650
Median (min)	84
CV	22.11%
rho (night to night)	0.154
RCV (raw change)	61.28%
Threshold at 28 nights	13.52%
Threshold at 56 nights	9.56%
Threshold at 84 nights	7.81%
Threshold at 168 nights	5.52%

Why the threshold falls as the window grows

The threshold isn't fixed: it drops from 13.52% to 9.56%, then to 7.81%, then to 5.52% as the window moves from 28 to 56, 84, and 168 nights. With more nights inside the same window, night-to-night noise spreads across more data points, and the margin separating "real change" from "normal variation" narrows. At 28 nights, a bigger move is needed before you can trust it. At 168, the bar sits lower because more accumulated evidence sits behind the number.

That has a direct practical consequence: someone comparing a single week or a single month of deep sleep against another is working with a wide "this doesn't mean anything yet" margin — 13.52%, the widest of the four windows here. Comparing two single nights, or even two single weeks, almost never clears that threshold by chance alone.

CV versus RCV: two different questions

The 22.11% CV describes the whole series: how far each night sits from the 84-minute median, summed across 650 nights. The 61.28% RCV asks something else: how much deep sleep changes from one night to the very next, in raw terms, night against immediate night.

Both numbers are high, for different reasons. A high CV says deep sleep, as a series, moves a lot relative to its own center. A high RCV says that movement doesn't arrive smoothed out: the jump between two consecutive nights is, proportionally, larger than what lower-RCV variables show in records of this kind. Neither number, on its own, says whether that movement matters for anything outside this series.

How to read this in practice

If someone compares one night's deep sleep against another, and the difference is below 13.52% within a short window of data, that change still sits inside the normal noise of this record. It takes either a bigger change, or more accumulated nights — 56, 84, or 168 — before the same relative movement starts to fall outside the expected range.

That doesn't turn the threshold into an alarm or a target. It's a measuring stick, built from 650 specific nights, that separates "this moves on its own" from "this moved more than it moves on its own."

The limit

This data comes from one body — case zero, 650 nights, one device. It is not a population figure or a "normal" range that applies to anyone else. The 22.11% describes the variability of this record, not deep sleep variability in general.

The threshold (13.52%, 9.56%, 7.81%, 5.52%) is a statistical definition of the instrument: the point at which a change stops sitting inside the noise expected from this series itself. It is not a sleep-quality verdict, and it does not say whether one night's deep sleep is "good" or "bad." Nor does it certify what caused a given change even when that change does clear the threshold: the number marks that something moved more than expected, not why it moved.

A rho of 0.154 means one night predicts little of the next inside this record; it does not mean nights are independent in any broader sense, nor does it rule out unmeasured factors explaining part of that low correlation.

This is a method file, not a verdict on any product or practice. The question this number doesn't answer — what pushes deep sleep past the threshold on a given night — is left for another piece.

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Mental Work — all protocols · related file: magnesium-for-sleep · open science — the dataset