The Weekly Shape
The day-of-week pattern is the largest and most stable thing in most demand series. How to estimate it, how it drifts, and what breaks it.
One team's weekday profile, as ratios to the weekly mean
Monday
1.31
±0.06
Weekend backlog; the largest and steadiest day.
Tuesday
1.08
±0.05
Still elevated after a bank holiday Monday.
Wednesday
0.97
±0.04
The quietest ordinary day.
Thursday
0.98
±0.05
Indistinguishable from Wednesday.
Friday
0.81
±0.07
Lowest, and the most variable.
Saturday
0.85
±0.11
Its own series; does not move with the weekdays.
The spread across six days is half the weekly mean, and the bands are widest on the two days furthest from the middle. Estimated from ten clean weeks, excluding holidays. One employer's own profile, not a benchmark.
The day-of-week pattern is the largest regular movement in most workforce demand series and the most stable. In a typical operation Monday runs twenty to forty per cent above the weekly mean and Friday twenty below, and those figures hold for years.
The method in “The Weekly Shape” is only as useful as the definitions and source records behind it. A team exploring read the platform explanation here for how to detect mouse jigglers can add timely work and project context, with transparent settings, limited access and a documented correction route around every consequential use.
It is also the cheapest thing to get right, which is why it is worth getting right first.
For an independent reference relevant to “The Weekly Shape”, consult OECD Employment Outlook. Compare the general material with the organisation’s actual horizon, data definitions and decision process.
Estimating it
Take the last eight to twelve complete weeks, exclude weeks containing public holidays or known events, express each day as a ratio to its week's mean, and average the ratios by weekday.
- Take the last eight to twelve complete weeks.
- Drop any week containing a holiday or a known event.
- Express each day as a ratio to its own week's mean.
- Average the ratios by weekday.
Twenty minutes. The result is usually better than whatever the system is using.
Why ratios rather than averages
Because the level moves and the shape does not. Averaging Mondays over twelve weeks mixes a shape with a trend; averaging Monday-to-mean ratios isolates the shape.
This is the single most common technical error in weekly profiles and it costs a few per cent of accuracy quietly.
Why eight to twelve weeks
Long enough to average out noise, short enough to track drift. Under six and the estimate is unstable; over twenty and it lags real changes by months.
Where the series is very noisy, a longer window with a weighting toward recent weeks is a reasonable compromise.
Excluding the holiday weeks
Essential. A week with a bank holiday has four working days and a redistributed shape, and including it drags the whole profile.
Those weeks get their own treatment as events, and the profile is estimated from clean weeks only.
How it drifts
Slowly, and in response to channel changes. As self-service takes the simple Monday queries, the Monday peak flattens. As opening hours change, the shape shifts.
Quarterly re-estimation catches this. Annual re-estimation catches it about nine months late.
What breaks it
A change in opening hours. A new channel. A change to when communications are sent. A merger that joins two operations with different shapes.
Each produces a step in the profile rather than a drift, and each is announced before it appears.
The shape by category
Often different: complaints peak differently from sales, which peak differently from technical support. Where the mix is changing, an overall profile drifts even though no individual profile has moved.
Estimating by category and recombining is more work and it is the right answer where the mix is moving.
The shape within the day
The same exercise one level down, and it is where staffing is actually decided. The intraday profile is usually estimated from a shorter window still — four to six weeks — because it moves faster.
It also differs by weekday, which means the honest object is a profile per weekday rather than one profile.
Saturdays and Sundays
Treated as part of the weekly profile where the operation runs seven days, and as separate series where weekend demand has a different character.
The test is whether the weekend ratio moves with the weekday level. If it does not, the weekend is its own thing.
Using the profile
Two ways: to split a weekly forecast into days, and to convert a day's partial actuals into an expected total for the rest of the day. The second is what makes intraday management possible.
Both depend on the same profile being right, which is a good reason to keep one and maintain it.
Checking it
Plot the last four weeks' actual ratios against the profile. Four lines, one profile, and any drift is immediately visible.
This chart takes a minute to make and is worth having on the wall.
The profile after a holiday
Not the ordinary profile. The day after a bank holiday carries the holiday's deferred demand plus its own, and the following day is often still elevated.
These are events with a known shape, estimable from the last several occurrences, and treating them as ordinary days is a reliable source of Tuesday understaffing.
The shape that staff create
Worth naming: part of the apparent arrival pattern is produced by the operation itself — when it answers, when it calls back, when it sends.
That part is controllable, and separating it out occasionally shows that a peak everybody treats as customer behaviour is a dispatch schedule.
Why the profile repays attention
In most operations more than any modelling improvement, because the weekly shape drives the staffing split and because an out-of-date profile is wrong every single week in a repeating pattern.
A profile two years old in an operation whose channel mix has moved is a standing error nobody has attributed to anything.