How Many of 20 Staff Can Be Off at Once?
Five of 20 can be away before coverage breaks, and that fifth slot is what separates 8.6 short days a year from the 17.6 a team of 18 faces.
Five. With 15 people required on shift, a team of 20 can have five away at once and still run, and the model expects the sixth simultaneous absence on about 8.6 working days a year out of 261. The same model gives a team of 18, which has room for only four, about 17.6 short days, so 20 is one of the sizes that has just bought its way onto a better step.
How often that many are actually away
The average is 2.53 people away, and averages do not break rosters. What breaks a roster is the tail: the days when more people than usual are off at the same time. With 20 people each away on 12.6 percent of working days, this is how a year of 261 days is expected to distribute.
Everything below 6 away fits inside the roster. Everything from 6 up is a day the operation runs under its minimum of 15, and those add up to about 8.6 days a year.
What is hard about 20
Twenty sits immediately above a step rather than in the middle of one. Expected short days do not fall smoothly as a team grows, because headroom only moves when the team crosses a whole person, and everything between two boundaries gets steadily worse rather than better. A team of 18 carries room for four and about 17.6 short days a year. A team of 20 carries room for five and about 8.6. The step from 18 to 20 is where that improvement gets paid for, and it is the largest single gain anywhere in this part of the range.
The consequence is that size stops being the useful lever almost as soon as you reach 20. A team of 30 is expected short on about 7.6 days a year, which is barely better than the 8.6 a team of 20 already has, and a team of 24 beats both at 6.6 because it has just crossed the next boundary of its own. Growing past 20 buys close to nothing until that next whole-person step arrives, so a manager at this size arguing for headcount on coverage grounds is arguing for the wrong thing, and will get a thin result even if the argument is won.
The lever that does move is the minimum on shift. Hold the same 20 people and change only that line: at a minimum of 16 the model expects 25.8 short days a year, at 15 it expects 8.6, and at 14 it expects 2.3. A minimum of 16 would leave 20 people worse off than a team of 18 is today. None of this is a measurement, either. The model treats each absence as independent, which is the most generous assumption a roster can be handed, so 8.6 is a floor rather than a forecast. In a peak leave period the expected number away climbs from 2.53 to 4.05, near enough to the headroom of five that the same rate works out at about 53.1 short days a year.
Move the minimum, move the answer
The team size is usually fixed. The minimum on shift often is not, and it is the faster lever: making one role coverable for a day changes the arithmetic more than a hire does.
| Minimum on shift | Can be away | Short days a year |
|---|---|---|
| 19 | 1 | 192.9 |
| 18 | 2 | 123.3 |
| 17 | 3 | 62.9 |
| 16 | 4 | 25.8 |
| 15assumed | 5 | 8.6 |
| 14 | 6 | 2.3 |
What this assumes, and where it is generous
These figures treat each person as independently likely to be away, which is the assumption most favourable to the roster. Real leave clusters: school holidays, the last fortnight of December, and the local summer shutdown pull requests onto the same dates. Treat every number here as the best case, and the peak column as a reminder of how far the real case sits from it.
Run the same team at a peak concentration of 1.6 times the ordinary rate, which is a stated planning assumption rather than a measured figure, and the expected count away rises from 2.53 to 4.05. Held across a full year, that rate would imply about 53.1 short days rather than 8.6. Real years are neither, but the gap between the two is the size of the scheduling problem that leave clustering creates.
The inputs are 25 days of paid annual leave and 8 days of average sickness per person. Both vary by country, and the relief factor library carries sourced figures for 17 of them, from zero statutory leave in the United States to 28 days in the United Kingdom. Swap your own numbers in and the shape of the distribution holds even as the counts move.
What to do with this
Write the minimum of 15 into the operating standard and defend it, because moving it to 16 turns 8.6 expected short days into 25.8 without changing a single person on the payroll.
Approve up to five overlapping absences and hold the line at the sixth, and tighten below five in the peak weeks where the model already puts 4.05 people away on an average day.
Place the 500 person-days of leave this team books across the 261 working days deliberately rather than first come first served, since the 8.6 figure assumes absences fall independently and real ones do not.
Common questions
- How many of a team of 20 can be on leave at once?
- Five, against a minimum of 15 on shift. With 25 days of annual leave and 8 days of average sickness each, any one person is away on about 12.6 percent of working days, which puts 2.53 people away on an average day and leaves the team short on about 8.6 days a year.
- Would hiring more people fix the short days?
- Not at this size. A team of 20 is expected short on about 8.6 days a year and a team of 30 on about 7.6, so growth barely moves the number until the next whole-person boundary. Lowering the minimum on shift from 15 to 14 moves it much further, to about 2.3 days a year, with the same 20 people.
- Can I plan against 8.6 short days as the real figure?
- Treat it as a floor. The model assumes people take leave independently of each other, which is the assumption most favorable to the roster, while real leave clusters on school holidays and the last fortnight of December. In a peak period the model expects 4.05 away on an average day, and that rate works out at about 53.1 short days a year.
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