How Many of 10 Staff Can Be Off at Once?
A team of 10 carries headroom 2 and about 32 short days a year, which is worse than a team of 8 and only really fixed by reaching 12.
Two people can be off at once. A team of 10 that must keep 8 on shift has headroom 2, and with 25 days of paid leave and 8 days of average sickness each, the model expects the team to fall below that minimum on about 32 of 261 working days a year. Run the same rate through a peak leave period and it works out at about 85.9.
How often that many are actually away
The average is 1.26 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 10 people each away on 12.6 percent of working days, this is how a year of 261 days is expected to distribute.
Everything below 3 away fits inside the roster. Everything from 3 up is a day the operation runs under its minimum of 8, and those add up to about 32 days a year.
What is hard about 10
Expected short days do not fall smoothly as a team grows, because tolerance only increases when the team crosses a whole-person boundary. Sizes 8, 9, 10 and 11 all carry headroom 2, and across that band the expected short days climb from 18.1 to 24.7 to 32 to 40.1. A team of 10 is the third rung of that climb. It is larger than a team of 8 and measurably worse off, because the two extra people brought their own 25 days of leave and 8 days of average sickness with them without buying a third slot of tolerance. The whole team is now spreading 250 person-days of leave across the same 261 working days, and only 2 of those days can land on any one date.
That makes the hiring question at this size unusually blunt. One more person does not help: a team of 11 still holds headroom 2, and the model expects about 40.1 short days, worse than the 32 you started with. Two more crosses the boundary: a team of 12 carries headroom 3 and about 14.3 expected short days, which is below even the 18.1 of a team of 8. If the plan is to grow one head at a time, the coverage benefit arrives only on the second hire, and the first hire is spent making the roster tighter than it already is.
The cheaper lever at this size is the minimum, not the headcount. Keep the same 10 people and drop the required minimum on shift from 8 to 7, and headroom rises to 3 while expected short days fall from 32 to 7.4, which is better than what hiring two people would buy. Moving the minimum the other way is punishing: at a minimum of 9 the headroom is 1 and the model expects 95.7 of 261 working days to be short. Every figure here also assumes people take leave independently of each other, which is the assumption most generous to the roster, since real leave clusters on school holidays and the last fortnight of December. Treat each number as a floor on the real risk rather than a forecast.
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 |
|---|---|---|
| 9 | 1 | 95.7 |
| 8assumed | 2 | 32 |
| 7 | 3 | 7.4 |
| 6 | 4 | 1.2 |
| 5 | 5 | 0.1 |
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 1.26 to 2.02. Held across a full year, that rate would imply about 85.9 short days rather than 32. 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
Set the concurrent approval cap at 2 and hold it, because the model already expects about 32 short days a year with that cap in place.
Do not add a single head to fix coverage at 10, since 11 pushes expected short days to 40.1 while 12 brings them down to 14.3.
Test whether the operation can genuinely run on 7 rather than 8 before you spend on hiring, because that one change moves expected short days from 32 to 7.4.
Common questions
- How many of a team of 10 can be on leave at once?
- Two. With a minimum of 8 on shift the headroom is 2, and holding to that cap the model still expects the team to be short on about 32 of 261 working days a year.
- Why does a team of 10 look worse than a team of 8?
- Both sizes carry headroom 2, so the extra people add leave demand without adding tolerance. Expected short days run 18.1 at a team of 8, 24.7 at 9, 32 at 10 and 40.1 at 11, and the rate only drops once the team reaches 12, where headroom 3 brings it to 14.3.
- What happens to a team of 10 in a peak leave period?
- The number away on an average day rises from 1.26 to 2.02, which is already at the headroom limit of 2, and that rate works out at about 85.9 short days if it held for a full year. Since the model treats each absence as independent while real leave clusters on school holidays and the last fortnight of December, 85.9 is a floor rather than a forecast.
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