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

A sleep score shift needs to clear at least 5.25% to exit noise at a 28-night window. At 56 nights, that threshold drops to 3.71%. These are not model estimates: they come from 650 nights of one body, with a baseline coefficient of variation of 9.5%.

The finding

The variable sleep_score was tracked across 650 nights as part of a 31-metric dataset. Its natural variability — measured as coefficient of variation (CV) — is 9.5%. The median score across the full record is 85.

The autocorrelation rho is 0.052. A value near zero means yesterday's score does not predict today's with any meaningful force. Each night is nearly independent from the previous one.

From that CV and an RCV of 26.34, the change thresholds by observation window are:

Window (nights)	Minimum change threshold
28	5.25%
56	3.71%
84	3.03%
168	2.14%

Source: ruido.medido.json#sleep_score · 650 nights · 18,483 measurements · one body

A CV of 9.5% in baseline conditions means the score moves by that margin naturally — night to night, with no intervention, with no change in protocol. The score varies. That is not instrument failure: that is the instrument showing what it measures.

An RCV of 26.34 confirms this swing is substantial. Separating signal from noise requires a window wide enough to distinguish the two.

The gap

Published research shows that sleep affects cognition, recovery, and metabolic function. That is measured in groups. What does not appear systematically in the reviewed literature is the individual change threshold: how much the number on the screen needs to shift, for a specific device used by a specific body, before that shift clears the noise floor.

Without that individual threshold, every point gained or lost can look like a signal when it is ordinary variation. The gap is not in the evidence about sleep — that evidence is solid. The gap is in the calibration of the marker: what counts as a real change for this body, with this device, at this baseline.

Group averages establish that sleep matters. They do not tell you whether last night's score was different from the prior week in a way that means something for you specifically.

The translation

Your app shows a number every morning. Say your score sits near the record median — 85 — and tonight it reads 4 points higher. Does that matter?

With 28 nights of data, the threshold calculated from this dataset is 5.25%. A 4-point shift on a score around 85 falls short of that line. It sits inside the expected noise band. There is no signal to read yet.

With 56 nights of data, the threshold drops to 3.71%. That same 4-point shift begins to cross it. Something happened worth noting — not necessarily worth concluding anything about.

The difference between 28 and 56 nights is not arbitrary. More nights allow a more precise estimate of individual variability. The threshold does not fall because the body changed. It falls because the noise estimate is sharper. At 84 nights, the threshold is 3.03%. At 168 nights, it reaches 2.14%.

This follows directly from the autocorrelation of 0.052. Because each night is nearly independent of the previous one, averaging over more nights converges quickly toward the true variability of that body. More data tightens the threshold. A tighter threshold makes the signal easier to distinguish from the background.

No different device required. Time in the record is the instrument.

The instrument

The data comes from the Black Swan open dataset: 650 nights of one body, 31 metrics, 18,483 individual measurements. The CV of 9.5% and the RCV of 26.34 are the parameters that produce the four thresholds in the table.

The calculation does not require a laboratory or an external service. It requires enough nights of personal data for the individual noise estimate to become more precise than a group average. At 28 nights, the threshold already has a statistical basis. At 56 nights, it is substantially tighter.

The limit

The published threshold belongs to one body. It is not the universal sleep score threshold. It is not the threshold for your device.

The CV of 9.5% describes the baseline variability of this subject during this period. A person with more stable sleep will have a lower CV and a lower change threshold. More nocturnal variation produces the opposite.

The source row certifies: nights, median, CV, rho, RCV, and the four thresholds. It does not certify the conditions that governed those 650 nights — seasonal shifts, protocol changes, health events, or work cycles. It does not confirm whether the record was continuous or contained gaps.

The score is a composite proxy. What drives it — sleep architecture, latency, interruptions, physiological signals captured by the sensor — is not broken out in this source row. The threshold says when the proxy shifts beyond its own noise. It does not say which part of the underlying state moved, or by how much.

Reporting the limit before anyone asks is part of the method.

The inherited gap

This piece answers when a sleep score change exits noise. It does not answer what moves it reproducibly.

That question is in the related file: related file: magnesium-for-sleep, which tracks an intervention with a measurable signal on sleep variables. Other metrics from the same dataset — with narrower thresholds — appear in Mental Work — all protocols.

The full dataset, with provenance hash, is at open science — the dataset.