How many staff can be off at once?
Not the average, which never broke a roster. The tail: how often more people are away at the same time than the shift can carry. It does not improve smoothly as a team grows, because slack only arrives one whole person at a time.
16 team sizes · 261 working days · 25 days leave and 8 days sickness assumed
Bigger teams are not reliably safer
A team of 7 is expected to run short on about 57 days a year. A team of 40 manages 2.4. In between, the line saw-tooths rather than falling, because the minimum on shift rises with the team while slack only increases when the team crosses a whole person. Adding people inside a band makes things worse, and crossing a boundary makes them abruptly better.
How this is worked out
Each person is treated as away on some share of the year: 25 days of paid annual leave plus 8 days of average sickness, across 261 working days. That gives the chance any one person is out on any one day. A binomial across the team then gives the chance that more are out than the roster can carry, and multiplying by the working year turns that into a count of days.
Every page assumes a minimum on shift of roughly three quarters of the team, which is a stated assumption rather than a finding, and each page carries a table showing what the answer becomes at other minimums. That table is usually the more useful one, because team size is fixed far more often than the minimum is.
The model treats absences as independent, which is the assumption most generous to the roster. Real leave clusters on school holidays and the last fortnight of December, so every figure here is a floor on the real risk. The country figures behind the leave and sickness inputs live in the relief factor library, where they are sourced per country rather than assumed.
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