How Many of 30 Staff Can Be Off at Once?
A team of 30 can have 7 away at once and still expects more short days a year than a team of 24, which can only spare 6.
A team of 30 can have 7 people on leave at once before it drops below its minimum of 23 on shift. The model expects 3.79 away on an average working day, and about 7.6 working days a year when more than 7 are away at the same time. In a peak leave period the expected number away rises to 6.07, and that rate works out at about 65.1 short days a year.
How often that many are actually away
The average is 3.79 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 30 people each away on 12.6 percent of working days, this is how a year of 261 days is expected to distribute.
Everything below 8 away fits inside the roster. Everything from 8 up is a day the operation runs under its minimum of 23, and those add up to about 7.6 days a year.
What is hard about 30
Hiring is supposed to buy resilience, and between 20 people and 30 it mostly does not. A team of 20 carries headroom of 5 and about 8.6 short days a year. A team of 24 carries 6 and about 6.6. A team of 30 carries 7 and about 7.6, which is worse than the smaller team manages. Ten hires barely moved the expected shortfall, and across the last stretch of that growth it moved the wrong way.
The mechanism is that headroom only changes in whole people. The minimum on shift scales with the team, so each new hire is both another source of absence and only a fraction of a new slot in the margin. Put the two sizes side by side: 30 people with 7 slots against 24 people with 6. The extra slot is real, but so are the six extra people who can use it, and at a 12.6 percent chance that any one person is away on any one of the 261 working days, the model already expects 3.79 of the 30 to be out on an ordinary day. The plateau only breaks at 40, where headroom reaches 10 and the expected shortfall falls to 2.4 days a year.
The annual averages also hide the shape of the year. In a peak leave period the model expects 6.07 of the 30 away on a normal day, which still fits inside the 7 the roster can carry but leaves almost nothing for a sick call, and at that rate the shortfall runs at about 65.1 days against 261 working days. The model also assumes people book leave independently of each other, which is the assumption most generous to the roster. Real leave clusters on school holidays and the last two weeks of December, and 750 person-days of annual demand have to land somewhere. Read 7.6 as a floor on the real risk rather than a forecast of it.
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 |
|---|---|---|
| 29 | 1 | 236.8 |
| 28 | 2 | 195.6 |
| 27 | 3 | 139.9 |
| 26 | 4 | 85.5 |
| 25 | 5 | 44.6 |
| 24 | 6 | 19.9 |
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 3.79 to 6.07. Held across a full year, that rate would imply about 65.1 short days rather than 7.6. 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
Cap concurrent approvals at 7 and hold a slot back during the peak weeks, because the model already expects 6.07 of the 30 to be away before you approve anything.
Defend the minimum of 23 whenever someone proposes running leaner, since a floor of 24 cuts headroom to 6 and moves the expected shortfall from about 7.6 days a year to about 19.9.
Place the 750 person-days of leave demand across the 261 working days deliberately rather than first come first served, because the 7.6 figure assumes independent booking and real requests arrive in clumps.
Common questions
- How many of a team of 30 can be on leave at once?
- Seven, assuming the operation needs a minimum of 23 on shift. With 25 days of paid annual leave and 8 days of average sickness each, any one person is away on about 12.6 percent of the 261 working days, which puts 3.79 away on an average day and leaves the team short on about 7.6 days a year.
- How many days a year does the model expect a team of 30 to be short?
- About 7.6 working days a year at the average absence rate. In a peak leave period the expected number away rises from 3.79 to 6.07 against headroom of 7, and that rate implies about 65.1 short days across 261 working days, so almost all of the exposure sits in the peaks rather than in the ordinary weeks.
- What happens to a team of 30 if the minimum on shift is 24 instead of 23?
- Headroom falls from 7 to 6 and the expected shortfall rises from about 7.6 days a year to about 19.9. The ladder steepens fast from there: a minimum of 25 gives about 44.6 short days, 26 gives 85.5, 27 gives 139.9, 28 gives 195.6, and 29 gives 236.8. At this size, one person of headroom is worth more than any single hire.
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