How Many of 8 Staff Can Be Off at Once?
Two of eight can be off at once, and that second slot is the difference between about 18.1 short days a year and the 57 a team of seven faces.
Two of a team of eight can be on leave at the same time before the operation drops below its assumed minimum of six on shift. On those assumptions the model expects the team to be short on about 18.1 working days a year, and at a peak leave rate that works out at about 54.3. That 18.1 is lower than every smaller team in this library and lower than teams of nine, ten, and eleven as well.
How often that many are actually away
The average is 1.01 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 8 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 6, and those add up to about 18.1 days a year.
What is hard about 8
Eight sits immediately above a whole-person boundary, and that is the whole story of this page. A team of seven and a team of eight both need six people on shift; the difference is that seven has one spare body and eight has two. The eighth person does not raise the floor, they raise the ceiling, and the expected count of short days falls from about 57 to about 18.1. No other single hire in this library moves the number that far, because it is not buying capacity so much as buying a second slot in the approval queue.
The flip side is that eight is at the bottom of its band, and the next three hires make the roster worse rather than better. Headroom stays at two through nine, ten, and eleven, while each added person carries the same 12.6 percent chance of being away on any working day, so there are more ways for three to be out at the same time. The model puts nine at 24.7 short days, ten at 32, and eleven at 40.1. Not until twelve, where headroom becomes three, does the figure drop back to 14.3 and finally beat what eight already had. A team of eight is better protected than a team of fourteen, which the model puts at 23.6.
None of this is comfortable in a peak period. On an average day the model expects 1.01 of the eight to be away, well inside the two slots, but in a peak leave period that rises to 1.62, which consumes most of the allowance before anyone requests anything unusual. The team also has to absorb 200 person-days of planned annual leave into two seats a day across 261 working days. And the model assumes people choose their dates 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. Treat 18.1 as a floor on the 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 |
|---|---|---|
| 7 | 1 | 70 |
| 6assumed | 2 | 18.1 |
| 5 | 3 | 3.1 |
| 4 | 4 | 0.3 |
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 1.01 to 1.62. Held across a full year, that rate would imply about 54.3 short days rather than 18.1. 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 leave at two and treat the third overlapping request as a staffing decision rather than a routine approval, because two is the entire headroom a team of eight has.
Defend the eighth head before defending anything else, since the same operation run by seven people carries about 57 expected short days a year against 18.1 at eight.
Test the minimum on shift before you test the headcount: holding five instead of six takes expected short days from 18.1 to 3.1, while adding a ninth person raises them to 24.7.
Common questions
- How many of a team of 8 can be on leave at once?
- Two, assuming six people have to be on shift. Once a third is away the team is short, and the model expects that on about 18.1 working days a year, rising to about 54.3 if a peak leave rate held all year.
- Why does a team of 8 come out safer than a team of 10 or 11?
- All three carry the same headroom of two, so the extra people add absence risk without adding an approval slot. The model puts eight at about 18.1 short days a year, ten at 32, and eleven at 40.1.
- How much confidence should I put in 18.1 short days?
- Treat it as a floor. It assumes each person's absence is independent, which real leave never is, and the same math run at a peak leave rate gives about 54.3 short days a year with 1.62 of the eight away on an average peak day.
Your next schedule could take 2 minutes.
Import your team, set your rules, hit auto-fill. Most teams are live the same day.
30 days free ยท No credit card required
Already have an account?Sign in
