How Many of 18 Staff Can Be Off at Once?
Eighteen carries the same headroom of four as a team of 16, so the two extra people buy nothing: 17.6 expected short days a year against 11.1.
Four. With 14 people required on shift, a team of 18 can have four away at once and still run, and the fifth absence is the one that breaks it. Across 261 working days the model expects about 2.28 people away on an average day and expects the team to fall short on about 17.6 days a year.
How often that many are actually away
The average is 2.28 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 18 people each away on 12.6 percent of working days, this is how a year of 261 days is expected to distribute.
Everything below 5 away fits inside the roster. Everything from 5 up is a day the operation runs under its minimum of 14, and those add up to about 17.6 days a year.
What is hard about 18
Headroom moves in whole people, and 18 sits at the top of a step rather than the bottom of the next one. A team of 16 carries a headroom of four, and so does a team of 18. The fifth place does not arrive until the team reaches 20. That is why the expected short days run backwards across this stretch of the library: 11.1 a year at 16, 17.6 at 18, then 8.6 at 20. The two people added between 16 and 18 brought their own leave and their own sickness, and no extra slack to absorb either. The comparison that should sting most is further down: a team of 12, with a headroom of three, expects 14.3 short days a year. Eighteen people expect more trouble than twelve.
So the useful question at this size is not how to schedule better inside a headroom of four. It is what a fifth place would cost, and the headroom matrix answers that twice over. Hire to 20 and the expected short days fall from 17.6 to 8.6. Leave the team at 18 and drop the minimum on shift from 14 to 13, and the same figure falls to 5.1, which beats the hire outright, because a smaller team holding the same slack has less absence to absorb in the first place. The reverse holds with equal force. Hold the floor at 15 instead and these same 18 people are expected to be short on 48.3 days a year. What the operation declares as its minimum moves this number far more than the headcount does.
Every figure here assumes people take leave independently of one another, which is the assumption most generous to the roster. Real leave clusters on school holidays and the last two weeks of December, so 17.6 is a floor on the risk rather than a forecast of it. Apply the peak rate to 18 people and the average number away moves from 2.28 to 3.64, which sits just under the headroom of four rather than safely below it, and the short-day rate implied by that period works out at about 76.3 a year. The 450 person-days of leave this team is owed have to land somewhere in the calendar, and at a headroom of four the only real defense is deciding where before the requests arrive.
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 |
|---|---|---|
| 17 | 1 | 178.4 |
| 16 | 2 | 105 |
| 15 | 3 | 48.3 |
| 14assumed | 4 | 17.6 |
| 13 | 5 | 5.1 |
| 12 | 6 | 1.2 |
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 2.28 to 3.64. Held across a full year, that rate would imply about 76.3 short days rather than 17.6. 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
Approve up to four absences on the same day and hold the fifth, because the fifth is the one that takes the team below 14 on shift.
Price the floor before you price the hire: dropping the required minimum from 14 to 13 moves the expected short days from 17.6 to 5.1, while hiring up to 20 only moves it to 8.6.
Cap concurrent leave below four through peak weeks, when the expected number away rises from 2.28 to 3.64 and the implied short-day rate reaches 76.3 a year.
Common questions
- How many of a team of 18 can be on leave at the same time?
- Four, on the assumption that 14 must be on shift. A fifth absence on the same day breaks the minimum, and the model expects that to happen on about 17.6 of the 261 working days in a year.
- Is a team of 18 safer than a smaller team?
- Not reliably. A team of 16 carries the same headroom of four and expects 11.1 short days a year, and a team of 12, with a headroom of three, expects 14.3. A team of 18 expects 17.6, because it added people without crossing the boundary that would have added a place to put them.
- What is one more place of headroom worth at this size?
- More than any rota tweak inside the current headroom. Raising the floor from 14 to 15 on shift pushes the expected short days from 17.6 to 48.3; lowering it from 14 to 13 pulls them down to 5.1. Growing the team to 20, which is where the fifth place of headroom arrives, gives 8.6.
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