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

Across 650 nights of a single body, nighttime respiratory rate has to move more than 3.07% away from your own median in a 28-night window before it stops being background noise. Widen the window to 56 nights and that threshold drops to 2.17%. Below those lines, the jump your sleep app just flagged isn't a signal — it's the ordinary variation of an ordinary night.

Why most respiratory rate alerts are noise

Any wearable that reports nightly respiratory rate produces a series of numbers that rises and falls from one night to the next with nothing underlying it. The metric itself isn't the problem. The problem is that almost nobody measures how much that number moves on its own, with no event behind it, before deciding which jump deserves attention.

That's the work behind this figure: 650 consecutive nights of a single body, recorded without intervention, to build a background-noise map across 31 physiological variables — respiratory rate among them. This isn't a lab sample or a population average. It's the natural variation signature of one person, night after night, across close to two years of data.

What "threshold" means here

The threshold is the point where a change stops being explainable by ordinary night-to-night variation and starts being, statistically, a real movement. It's derived from the coefficient of variation (CV) of the full series, and from how that CV compresses as the observation window grows.

For respiratory rate, the CV of the complete 650-night series is 3.2%. That already tells you something: night to night, respiratory rate moves, on average, by 3.2% around its own center — with no event behind it at all. Any alert that fires below that margin is, almost certainly, flagging noise, not signal.

The table: the threshold by how many nights you look at

The threshold isn't fixed — it depends on how many nights you use to build your baseline. More nights average out the noise, so the movement needed to count as a real change shrinks.

Window (nights)	Threshold for real change
28	3.07%
56	2.17%
84	1.77%
168	1.25%

With 28 nights of history, you need to see a shift of at least 3.07% before the data stops being noise. With 56 nights banked, that bar drops to 2.17%. At 84 nights, it's 1.77%. And at 168 nights — roughly half a year of near-daily tracking — the threshold falls to 1.25%, the finest reading this body allows before the signal gets lost in ordinary variation.

Why does the threshold drop as more nights accumulate

Because a baseline built from a handful of nights still carries its own noise: a short run of restless or unusually deep nights can shift the median without any real change happening underneath. With more nights, that median stabilizes, and a smaller movement becomes information instead of coincidence. It's the same logic behind a poll with a larger sample shrinking its margin of error — the question doesn't change, but the confidence in the answer does.

How predictable is respiratory rate from one night to the next

Another number from this same data row: the series' autocorrelation (rho) is 0.541. That means one night's respiratory rate carries a moderate relationship to the night before it — neither fully random, nor fully repetitive. It's a variable with partial memory: it tends to resemble the previous night somewhat, but not enough to predict it with any certainty.

The relative-variation ratio (rcv) for this row is 8.86, and the median respiratory rate logged across the 650 nights is 14.3. Together, CV, rho, and rcv form the specific noise signature of this variable within the set of 31 metrics measured on this body.

Does this threshold apply to anyone else

Not directly — and that's the most important caveat in this file. The threshold above describes the background noise of one nervous system, with its own circadian rhythm, its own baseline breathing pattern, and its own sleep history. A different body will carry a different CV, a different rho, and a different threshold — it could be wider or narrower than 3.07%.

What does generalize is the method: before reacting to a number that moved, find out how much that number moves when nothing is happening at all. That's the principle underneath this entire measurement project.

The limit

This figure describes background noise, not a diagnosis. A change that exceeds the 3.07% threshold (at 28 nights) or 2.17% (at 56 nights) is, statistically, distinguishable from this body's ordinary variation — but that says nothing about what caused it, whether it carries clinical relevance, or whether it applies to a different person with a different baseline breathing pattern.

This threshold comes from 650 nights of a single body, measured with a consumer device outside any controlled laboratory setting. It doesn't substitute for a medical evaluation of respiratory function, doesn't diagnose sleep apnea or any other sleep disorder, and doesn't establish causation between any daytime event and the nighttime change observed. It's a statistical baseline, not a clinical reading.

The 14.3 median and the 3.2% CV also belong to this specific 650-night period: if living conditions, the device, or the time window change, the threshold can shift with them.

Keep exploring the dataset

• Mental Work — all protocols
• Related file: magnesium-for-sleep
• Open science — the dataset