How Many of 6 Staff Can Be Off at Once?
A team of 6 can spare exactly one person at a time, and the model still expects about 44.3 short days a year.
One. With 5 people required on shift, a team of 6 has headroom of 1, so a single absence is absorbed and the second one on the same day leaves the operation short. On these assumptions the model expects the team to fall below its minimum on about 44.3 of the 261 working days in a year, and in a peak leave period the same math implies a rate of 91.4.
How often that many are actually away
The average is 0.76 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 6 people each away on 12.6 percent of working days, this is how a year of 261 days is expected to distribute.
Everything below 2 away fits inside the roster. Everything from 2 up is a day the operation runs under its minimum of 5, and those add up to about 44.3 days a year.
What is hard about 6
Expected short days do not fall smoothly as a team grows. Headroom only moves when the team crosses a whole-person boundary, so sizes 4, 5, 6 and 7 all sit in the same band with headroom of 1, and inside that band the expected count of short days climbs with every hire: about 21 at 4, 32.1 at 5, 44.3 at 6, and 57 at 7. A team of 6 is the third of four rungs on that stretch, one rung below the exit.
That makes the seventh person the worst value on the chart for this team. Another hire raises the number of people who can be absent without raising what the roster can absorb, because the minimum on shift rises alongside the headcount, so the model's expectation moves the wrong way, from 44.3 short days to 57. Headroom only reaches 2 at a team of 8, where the expectation drops to 18.1. The honest budget request at this size is two people or none, because one buys a worse roster than the one you already have. Before either, argue about the minimum instead: holding the team at 6 and getting the minimum on shift from 5 down to 4 takes the expectation from 44.3 to 7.8, which beats what two hires would buy, and a minimum of 3 takes it to 0.8.
Every figure here is a floor. Each person is assumed to take 25 days of paid annual leave and 8 days of sickness, which works out at a 12.6 percent chance that any one of them is away on any one working day, and the model treats those absences as independent of each other. That is the assumption most generous to the roster. Real leave clusters on school holidays and the last fortnight of December, and the 150 person-days of annual leave this team is owed each year have to land in a calendar that only ever has one seat open. On an average day the model puts 0.76 people away, comfortably inside headroom of 1. In a peak period it puts 1.21 away, which is already over the line before a single unplanned sickness is counted, and that rate implies 91.4 short days a year rather than 44.3.
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 |
|---|---|---|
| 5assumed | 1 | 44.3 |
| 4 | 2 | 7.8 |
| 3 | 3 | 0.8 |
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 0.76 to 1.21. Held across a full year, that rate would imply about 91.4 short days rather than 44.3. 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 one absence per day and treat any second request for the same day as an exception that needs a named backfill, because headroom at this size is exactly 1.
Refuse to fund a single hire, and price either the move to 8 people, which takes the expectation from 44.3 short days to 18.1, or a minimum on shift of 4, which takes it to 7.8 for no extra salary.
Close peak periods to second approvals early, since the model already expects 1.21 people away then against headroom of 1, a rate that implies 91.4 short days a year.
Common questions
- How many of a team of 6 can be on leave at the same time?
- One. With 5 required on shift, headroom is 1, so a single absence is absorbed and a second one leaves the team short. The model expects that on about 44.3 of the 261 working days in a year, and because it assumes people take leave independently of each other, 44.3 is a floor rather than a forecast.
- Would hiring one more person fix a team of 6?
- No, it makes the number worse. At 7 people the minimum on shift rises with the team, headroom stays at 1, and the model's expectation goes from about 44.3 short days a year to 57. Headroom only reaches 2 at a team of 8, where the expectation falls to 18.1, so the useful comparison is two hires against none.
- What does lowering the minimum on shift do for a team of 6?
- More than hiring does. Dropping the minimum from 5 to 4 raises headroom to 2 and cuts the expectation from 44.3 short days a year to 7.8, and a minimum of 3 raises headroom to 3 and cuts it to 0.8. Two extra bodies only get the same team to 18.1, so the minimum is the stronger lever at this size.
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