Sleep Debt

Sleep Debt#

What the number means#

Sleep Debt answers one question: after the recent nights, how many hours short of your need are you, and how many are banked? It is a running balance, not the shortfall of last night alone. Seven hours of sleep against a need of 7h 30m costs half an hour, and a few such nights in a row add up.

The balance is built from your last 30 days of nights, oldest first. A night that is not in your records is skipped, and it changes nothing. Debt older than the window is not counted. The model is based on sleep-restriction studies that found cognitive costs adding up over days (Van Dongen 2003) and recovery taking several nights, not one (Banks 2010, Belenky 2003, Kitamura 2016). The hour limits and the exact rates below are our own calibration, not published constants.

How one night changes the balance#

Each night does three things, in this order.

Exact calculationThe three steps of one night

1. The old balance fades a little. How much depends on how much you slept, as a share of your need (naps counted, see naps):

Slept, as a share of your need	The old balance keeps
100% or more	75%
90% to under 100%	85%
80% to under 90%	90%
70% to under 80%	95%
60% to under 70%	98%
Under 60%	100% (nothing fades)

A night under 60% of the need (about 4h 30m at a need of 7h 30m) lets your debt keep every hour. A night that is long enough lets a quarter of it go.

2. The night's shortfall or surplus is worked out. The shortfall is your need minus the hours slept (naps credited), plus the quality penalty and minus the deep-sleep allowance described below.

3. The shortfall is added, or the surplus is subtracted.

• A shortfall is added to the debt. The nearer the debt is to its ceiling of 15 hours, the less of a new shortfall is added: the share added is 1 minus the debt divided by 15. At a debt of 3 hours, 80% of a new shortfall is added.
• A surplus (a night longer than your need) pays the debt down, but at most 1.5 hours per night count, and the payment is the surplus times the larger of two shares: the debt divided by 15, or 15%. A long night pays more when the debt is large and never less than 15% of its surplus.

The balance never goes above 15 hours of debt or above 3 hours of reserve. Every night is also capped at 12 hours of sleep, because a longer record is more likely a sensor error.

Quality and deep sleep#

Exact calculationPenalties for a poor night and the deep-sleep allowance

Not every hour counts the same, so a night's shortfall is adjusted:

• A poor sleep score adds a penalty. When the night's sleep score is under 50, the penalty is (50 minus the score) divided by 100 hours, at most 0.5 h. The score is your device's, or the estimate we make from the night when the device sends none.
• Time awake adds a penalty. When more than 15% of your time in bed was awake (an efficiency under 85%), the penalty is (the awake share minus 0.15) times 2 hours, at most 0.2 h. The efficiency is the same one shown on the Sleep tab (efficiency). When efficiency cannot be measured for the night, no penalty is added, because a missing measurement is not a bad night.
• The two penalties together are at most 0.5 h per night. They also shrink the surplus of a long night: a long night with a poor score or a lot of waking pays the debt back less.
• Strong deep sleep takes a little off a short night. When more than 20% of your measured sleep was deep sleep, the shortfall is reduced by (the deep share minus 0.20) times 3 hours, at most 0.4 h. This applies only to a night that fell short of the need, never below zero, and never to the quality penalty. The idea is that the brain makes up some lost sleep depth when it sleeps short. Nights whose stages are physically implausible (a device that over-reports deep sleep) get no allowance.

How fast extra sleep pays it back#

Debt clears slowly on purpose. The research behind the model found that one long night does not erase a week of short ones (Banks 2010: a single 10-hour night after five nights of 4 hours was not enough). In practice:

• a night at your need keeps 75% of the debt, so about a quarter fades every day you sleep enough;
• a night 1 hour over the need pays at least 0.15 h on top of that;
• a night between 60% and 100% of the need lets only 2% to 15% fade, and adds its own shortfall;
• a night under 60% of the need lets nothing fade.

Naps#

Daytime sleep that your device records as a nap counts toward the day's sleep, because the recommended hours are stated per 24 hours. The rules:

• A nap is credited for at most 2 hours a day.
• Nothing is credited on a day whose naps are longer than its night. That looks like one sleep period that the device split in two (a shift worker's day, for example), not like a nap.
• Nothing is credited on a day with no measured night.

The Naps card ("Naps" / "Šlofíky") shows the total, how many naps, their average length and a strip of the last days. It hides itself when your device reports none (naps and Sleep Quality). On the Overview, a line such as "and a 2h 25m nap, 2h 00m of which counts toward the debt" says how much of a long nap was credited.

A night that is not recorded#

• A night that has not arrived yet. Data reaches us late as a matter of routine. For the day being lived and the day before it, a night that is missing whole can be scored as your usual night, so that a delivery delay does not raise your debt. The day is then marked provisional until the real night comes (a night that has not arrived).
• A night with no record, but a worn watch. If your Garmin watch with Body Battery was worn (it has steps, stress or a resting rate) and the overnight recharge was under 40% of your own usual recharge, and the battery did not climb from the evening to the morning by that much either, we count the night as an all-nighter: one full night of need is added to the debt, with no fade. The usual recharge is the median over your nights with sleep (at least 3). Any other night with no record is skipped, because "no data" is not "no sleep".
• When a worn watch has no night, the Sleep tab says "Last night’s sleep was not recorded" and shows the last night that was recorded. If the watch also showed no overnight recovery, it adds "No overnight recovery was detected. Below is your last recorded night, not today."

A reserve#

When the debt is cleared and you keep sleeping more than you need, the surplus is banked as a reserve of up to 3 hours, with the bank filling more slowly as it nears the cap. It fades the way a debt does and cushions the next short night before any debt appears. A reserve is shown with a plus: "+1h 30m". It is a buffer, not a stronger kind of good, so on the 0 to 100 gauge a reserve counts as 100, the same as no debt.

The gauge and the words#

Besides the hours, the debt has a 0 to 100 gauge (higher is better) that drives its color and its word. Hours map to the gauge along fixed steps, and every step ends where a word changes, so a number, a color and a word always describe the same amount of sleep.

Exact calculationHours, gauge and word

Debt	Gauge	Word (Czech)
up to 15 min (0.25 h)	100 to 91	Cleared (Vyrovnaný)
to 1 h	91 to 81	Very low (Velmi nízký)
to 2 h	81 to 71	Low (Nízký)
to 3 h	71 to 61	Mild (Mírný)
to 4 h	61 to 51	Mild to moderate (Středně mírný)
to 5.5 h	51 to 41	Moderate (Středně silný)
to 7 h	41 to 31	Elevated (Zvýšený)
to 9 h	31 to 21	High (Vysoký)
to 11 h	21 to 11	Very high (Velmi vysoký)
over 11 h	11 to 0, reached at 15 h	Critical (Kritický)

The gauge is only a rendering of the hours. Where the app needs a higher-is-better 0 to 100 figure for the debt, it is called "Sleep balance" ("Spánková bilance").

How the hours are printed: in the app's own sign, minus is debt, plus is reserve. Hours are rounded to the nearest ten minutes, and anything under 5 minutes either way prints as a bare "0". The card under the number says one of: "A run of earlier bedtimes pays it down." (over 1 hour), "Aim for longer, consistent sleep." (over 5.5 hours), "You hold a healthy sleep balance." (up to 1 hour), or "Need more nights to compute."

A worked example#

Your need is 7h 30m and the balance is 0 before night 1. You then sleep like this.

On the screen, night 3 reads "−2h 40m" and the word "Mild"; night 7 reads "−1h" and "Very low". Two nights of 8h 30m did not clear a debt of 2.7 hours. Most of the way back came from the fade, not from the surplus.

A second example shows the penalties. Your need is 7h 30m, you sleep 6h 00m with a device score of 40 and 1h 30m awake in bed. The shortfall is 1.5 h. The score of 40 adds (50 − 40) / 100 = 0.1 h. The awake share is 1.5 / 7.5 = 20%, so the awake penalty is (0.20 − 0.15) × 2 = 0.1 h. The night adds 1.7 h to the debt.

When Sleep Debt is not shown#

• It needs sleep length on at least 3 days in your records. Until then the card says "Need more nights to compute." and the pill says "not worked out yet".
• The newest night must be fresh, which means dated today or yesterday (within 36 hours). If it is older but you have at least 3 nights in the last 7 days, the debt is shown as an assessment of the week with lower confidence. With fewer, it is withheld.
• The strip of bars needs at least two scored nights in the last seven days. Without them the card shows the number alone.

What the debt changes#

• Body Status: 3 hours or more is listed as a thing to watch on a Steady day and keeps the day from Strong, under 1 hour is needed for Peak Day, and over 6 hours makes the day Recovering (Recovering, Strong, Peak Day).
• Training Readiness: debt above 2 hours takes 3 points per extra hour, at most 15 (readiness).
• Tonight's goal and bedtime: see Tonight's sleep goal and bedtime.
• Daily goals: a debt above 3 hours nudges the automatic movement goals down a little (daily coach).
• The bedtime mission: the night counts as on plan when you fall asleep within 30 minutes either side of the planned bedtime, and only a bedtime we trust (when we show a bedtime) is a plan (Progress).

Frequently asked questions#

Why does my Sleep Debt not clear after two long nights?#

It is meant to be slow. A night at your need lets about a quarter of the old debt fade, and a surplus pays at least 15% of its hours, at most 1.5 hours count per night. Studies of sleep restriction found that recovery takes several nights (Banks 2010, Kitamura 2016). The worked example above goes from 2.7 hours to 1.0 hour in three nights, two of them long.

Why is my debt larger than the shortfall of last night?#

Because it is a running balance over 30 days, and because a poor sleep score or a lot of time awake adds up to half an hour to a night's shortfall. Open the Sleep Debt card and read the seven bars: the last bar is the number above it.

Why did my debt go up on a night I slept enough?#

Usually one of three reasons. The sleep score was under 50, or you were awake more than 15% of your time in bed, and the penalty outweighed a small surplus. Or the night has not arrived, and we scored the day with your usual night (the day is marked provisional). Or your watch had no overnight recharge and no sleep was recorded, so we counted it as a night without sleep.

Does a nap count toward my debt?#

Yes, up to 2 hours a day, and not on a day when your naps are longer than your night. A nap is not part of the night's length on the Sleep tab. It is a separate record on the Naps card (naps and Sleep Quality).