How Many of 24 Staff Can Be Off at Once?
A team of 24 splits into 18 on shift and 6 off with nothing left over, which is why it beats a team of 30 on expected short days.
Six of a team of 24 can be on leave at once. With 18 required on shift, the model expects the team to fall short on about 6.6 working days a year, the lowest figure in this library for any team under 40. That number is low because a quarter of 24 is a whole 6 people, so nothing is lost when the minimum on shift is rounded up.
How often that many are actually away
The average is 3.03 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 24 people each away on 12.6 percent of working days, this is how a year of 261 days is expected to distribute.
Everything below 7 away fits inside the roster. Everything from 7 up is a day the operation runs under its minimum of 18, and those add up to about 6.6 days a year.
What is hard about 24
Headroom moves in whole people, so the expected short days across this library saw-tooth rather than fall smoothly with team size. Hold back a quarter of the team and round the minimum on shift upward, and a team of 7 ends up with 1 person of headroom and about 57 short days a year, while a team of 8 gets 2 and drops to about 18.1. A team of 24 lands on the good side of that pattern. Eighteen on shift and 6 off divides with no remainder, so no fraction of a person is surrendered to rounding, and the whole of the reserve counts.
That puts 24 on the crest of the sawtooth rather than just under a boundary, and the crest carries a cost of its own: the next several hires buy nothing at the line. The library makes this plain. A team of 30 is a quarter larger than 24 and still carries only 7 of headroom, which works out at about 7.6 short days a year, worse than the 6.6 that a team of 24 gets from 6. A team of 20 sits at 8.6 with headroom of 5. The improvement waiting at 40, where headroom reaches 10 and short days fall to 2.4, is real, but it does not arrive gradually on the way there, so a manager of 24 who is arguing for one more head should argue for capability or cover quality, not for this number.
The annual figure also hides the shape of the year. On an average working day the model puts 3.03 of the 24 away, comfortably half the headroom of 6. In a peak leave period that rises to 4.86, which leaves only just over 1 person of slack, and if a whole year ran at the peak rate the model would expect 51.4 short days instead of 6.6. The 600 person-days of leave the team is owed have to land somewhere inside 261 working days, and the model assumes each person picks dates independently of everyone else, which is the assumption most generous to the roster. Real leave clusters on school holidays and the last fortnight of December, so treat every figure here 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 |
|---|---|---|
| 23 | 1 | 215.5 |
| 22 | 2 | 156.6 |
| 21 | 3 | 94.1 |
| 20 | 4 | 46.7 |
| 19 | 5 | 19.2 |
| 18assumed | 6 | 6.6 |
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 3.03 to 4.86. Held across a full year, that rate would imply about 51.4 short days rather than 6.6. 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 absence at 6 and treat the 7th request as an escalation rather than a queue item, because 6 is where a team of 24 still holds 18 on shift.
Defend the minimum of 18 before you defend anything else, since moving it to 19 takes the model from about 6.6 short days a year to 19.2, and 20 on shift takes it to 46.7.
Plan the peak weeks on their own numbers, because the model puts 4.86 away on an average peak day against headroom of 6 and a peak-rate year would run at 51.4 short days.
Common questions
- How many of a team of 24 can be on leave at the same time?
- Six, given a minimum of 18 on shift. At 25 days of annual leave and 8 days of average sickness each, any one person is away on about 12.6 percent of the 261 working days, and the model expects the team of 24 to be short on about 6.6 working days a year.
- Would a bigger team be safer than 24?
- Not immediately. A team of 30 carries headroom of 7 and about 7.6 expected short days a year, which is worse than the 6.6 a team of 24 gets from headroom of 6, because a quarter of 30 is not a whole person and the minimum on shift rounds up against the roster.
- What happens if the operation needs 19 on shift instead of 18?
- Expected short days rise from about 6.6 a year to about 19.2. Each further person added to the minimum costs more than the last: 20 on shift works out at 46.7 days, 21 at 94.1, and 22 at 156.6.
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