How Many of 40 Staff Can Be Off at Once?
Ten can be away before a team of 40 drops below 30 on shift, and the model expects that line to be crossed about 2.4 days a year.
With 30 required on shift, 10 of a team of 40 can be away at once. On an average working day the model puts 5.06 people away, about half the available headroom, and it expects the team to fall short on roughly 2.4 working days a year. That is the lowest short-day rate anywhere in this library, and it comes from the ratio between 40 and 30, not from the team being large.
How often that many are actually away
The average is 5.06 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 40 people each away on 12.6 percent of working days, this is how a year of 261 days is expected to distribute.
Everything below 11 away fits inside the roster. Everything from 11 up is a day the operation runs under its minimum of 30, and those add up to about 2.4 days a year.
What is hard about 40
Headroom only moves when a team crosses a whole-person boundary, so the expected short days do not fall smoothly as teams grow, they saw-tooth. A team of 24 carries headroom 6 and about 6.6 short days a year. A team of 30 carries headroom 7 and about 7.6, slightly worse despite having six more people, because one extra person of slack did not keep pace with the extra variance six more bodies introduce. At 40 the boundary lands cleanly. Thirty on shift out of 40 leaves headroom 10, and the model falls to about 2.4 short days a year. This is the first size in the library where the buffer clearly outruns the spread, and the gain arrived at the boundary rather than accumulating on the way there.
The comfort here belongs to the 30, not to the 40. Hold the team at 40 and raise the minimum on shift and the picture collapses quickly: 34 on shift leaves headroom 6 and about 61.7 short days a year, and 35 on shift leaves headroom 5 and about 103. Set that against a team of 20, which also carries headroom 5 and sits at about 8.6 short days. Same absolute buffer, twice the people, and far worse exposure, because the spread of outcomes widens with the size of the group while a fixed buffer does not. Scale does not buy safety on its own. The ratio does, and at 40 the ratio is doing all the work.
At this size the individual approval stops being the control point. Any one request is almost always safe against headroom 10, so a manager working request by request will say yes nearly every time and can still end the year short. The binding problem is placement: 1000 person-days of annual leave have to land somewhere across 261 working days, and the model assumes they land independently of one another, which is the assumption most generous to the roster. Real leave clusters on school holidays and the last fortnight of December. Run the same team at peak concentration and the average away count rises to 8.09, close enough to the 10 line that the implied rate becomes 44.4 short days a year. The 2.4 is a floor on the risk, not 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 |
|---|---|---|
| 39 | 1 | 253.1 |
| 38 | 2 | 233.9 |
| 37 | 3 | 198.9 |
| 36 | 4 | 151.9 |
| 35 | 5 | 103 |
| 34 | 6 | 61.7 |
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 5.06 to 8.09. Held across a full year, that rate would imply about 44.4 short days rather than 2.4. 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
Publish the headroom figure of 10 rather than the team size of 40, because 10 is the number that actually binds an approval decision.
Cap concurrent leave below 10 during school holidays and the last fortnight of December, since the peak model already puts 8.09 people away before a single unlucky sickness day lands on top.
Re-run the math before agreeing to any rise in the minimum on shift, because moving it from 30 to 34 takes the expected short days from about 2.4 a year to about 61.7.
Common questions
- How many of a team of 40 can be on leave at the same time?
- Ten, if the operation needs 30 people on shift. That leaves headroom 10, with 5.06 people away on an average working day, and the model expects the team to drop below 30 on about 2.4 working days a year.
- Is a team of 40 really safer than a team of 30?
- On these assumptions, yes, and by more than the size difference suggests. A team of 30 carries headroom 7 and about 7.6 short days a year, while a team of 40 carries headroom 10 and about 2.4. The jump happens because 40 crosses a whole-person headroom boundary that 30 sits below.
- What happens if we need more than 30 people on shift?
- Each person added to the minimum costs more than the last. At 34 on shift the headroom is 6 and the model expects about 61.7 short days a year, at 36 the headroom is 4 and about 151.9, and at 38 the headroom is 2 and about 233.9, which is most of the 261 working days in the year.
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