The two numbers
A deficit is energy taken in minus energy used. Intake comes from what you ate and what the food composition data says about it. Expenditure comes from a formula, a wearable, or both. Neither is measured directly outside a metabolic ward.
Every estimate on either side carries an error bar, and the deficit is the small difference between two large numbers, which is exactly the arithmetic that makes small errors look big.
How large the intake error gets
The most cited work here is a 1992 study in the New England Journal of Medicine, which compared self-reported intake against doubly labelled water in people who described themselves as diet-resistant. Reported intake was substantially below measured intake, and reported activity above measured activity. Later reviews found under-reporting to be a general pattern in dietary self-report rather than a quirk of that group.
Under-reporting is not usually lying. It is forgotten oil, an unlogged handful, a portion estimated by eye. It concentrates in exactly the foods that are hardest to log, which makes it a measurement problem rather than a character one.
Why the scale disagrees with the maths
Body mass moves with water, glycogen and gut contents on a scale of a kilogram or more, day to day. Over a week those swings are larger than the change a moderate deficit produces, so a single weigh-in cannot confirm or refute a deficit. Trends over weeks can.
This is why tracking systems that only show a daily number tend to feel wrong on any given day even when they are right over a month.
What actually improves the estimate
Self-monitoring itself is one of the more consistently reported correlates of weight change in behavioural research. Reviews of weight-loss programmes repeatedly find that the people who record more, do better, with adherence as the main moderator.
That points at a specific conclusion for anyone building or choosing a tracking tool: the accuracy that matters is the accuracy you keep using. A perfectly precise method you abandon after nine days measures nothing.