A data gap is not a rest day

What you will learn

• Why zero, in load monitoring, is a number with a precise meaning: no work.
• How a single day counted as zero moves the total, monotony, strain and the ACWR, with the calculations worked out.
• When to declare the gap and when to estimate it, and how to write an honest estimate.

The problem

A typical scene. On Wednesday the session goes ahead, but the GPS units come back flat from the pitch and the file never arrives; or half the squad forget to send their RPE. On Thursday morning the weekly report says load has dropped, monotony is lower and the acute:chronic ratio is calm. None of that happened: what happened is that a value is missing.

Data gaps happen to everyone: a GPS unit with a flat battery, a file that never got uploaded, a player who forgets to send their RPE, a session at a ground with no signal. The gap is not the problem. The problem is that most spreadsheets and most software quietly turn it into a zero, because an empty cell counts as zero in a sum.

And in load monitoring, zero is a number with a precise meaning: no work.

A worked example

One player's week, internal session load (sRPE = duration × RPE, in arbitrary units). On Wednesday the session took place, but the data never arrived. Demo data.

If the real Wednesday had been 600, this is what happens when you count it as zero:

One missing day and the week loses 20% of its load, monotony drops as if the week had been far more varied, and strain is almost halved (−44%). None of these numbers is wrong because of a calculation error. What is wrong is the data we fed them.

The calculations, step by step

Foster's monotony is the mean of the seven days divided by their standard deviation (here the sample one, with n − 1), with rest days at zero.

With zero on Wednesday. Seven values: 420, 560, 0, 380, 250, 720, 0.

mean = 2,330 ÷ 7 = 332.9 · standard deviation = 270.7

monotony = 332.9 ÷ 270.7 = 1.2295 → 1.23 · strain = 2,330 × 1.2295 = 2,865

With the real value. Seven values: 420, 560, 600, 380, 250, 720, 0.

mean = 2,930 ÷ 7 = 418.6 · standard deviation = 241.1

monotony = 418.6 ÷ 241.1 = 1.7358 → 1.74 · strain = 2,930 × 1.7358 = 5,086

Strain is worked out with the unrounded monotony: with 1.74 it would come to 5,098.

The zero does two kinds of damage at once: it lowers the mean (the numerator) and widens the standard deviation (the denominator), because it adds a value far from all the others. That is why monotony falls so far, and why strain, which multiplies both by the total, is almost halved.

The same thing happens to rolling windows: one day short in the 7-day acute load pulls the acute:chronic ratio down for a whole week, until that day drops out of the window.

What the science says

Chapter 8 of the NSCA textbook (Data Hygiene) starts from a rule of method: missing values should always be marked the same way, with an explicit convention (such as N/A or NULL), rather than left as empty cells that each tool reads in its own way. That is the foundation: before you can decide how to handle a gap, you have to know it is a gap.

Chapter 17, on perception of effort, describes Foster's monotony (1998) and points out that rest days enter the calculation as zero. Quite right: a rest day is a day with no work. That is exactly why a training day with no measurement cannot enter it the same way.

Two recent papers looked at what to do next. Benson and colleagues (2021) simulated missing data in a season of monitoring and compared ten ways of estimating (imputing) it: the estimates that use the context of the session (what the squad did that day) and of the player work better than crude fixes. Griffin and colleagues (2021) propose a practical approach for team sports. The shared message is that a gap has to be recognised and handled with a declared method, not filled with zero by default.

Fill it in or declare it?

Estimating the missing value (the squad's mean for that session, the player's usual value for that type of day) is possible and sometimes useful. But an estimate is an estimate: if it goes into the calculations, whoever reads them needs to know.

When there is a single gap, the simplest and most honest route is to declare it: it was a training day, the measurement is missing, and the numbers that depend on that day are reported as "not available" or calculated only where the gap doesn't matter. Better an "n/a" with the reason next to it than a clean, false number.

Estimating makes more sense when the gap keeps recurring, or when that day weighs on numbers that last for weeks, such as the acute:chronic windows. Then the estimate should be made with a written method (for example the player's usual value for that type of session), marked as an estimate next to the number and kept apart from measured values, so it can be removed if the real value turns up later.

The most common mistakes

• Leaving the cell empty. In a sum it counts as zero, and from then on nobody will know it was a gap.
• Typing zero "to close the week". The worst case: the gap becomes a rest day that never happened.
• Comparing a week with a gap against the others. That week's total, monotony and strain are not comparable until coverage is complete.
• Estimating without saying so. A hidden estimate looks like a measured value six weeks later.