How many of a team of 9 can be on leave at once?

Two, if the operation needs seven people on shift. That leaves headroom of two, and the model expects a third person to be away often enough to put the team below its minimum on about 24.7 of 261 working days a year.

How often will a team of nine be short?

The model expects about 24.7 short working days a year out of 261, and at the absence rate of a peak leave period that same calculation implies 69.9. Both are floors rather than forecasts, because the model treats each person's absence as independent, and real leave clusters on school holidays and the last two weeks of December.

Would hiring a tenth person fix it?

Not on its own. A team of ten carries the same headroom of two and works out at about 32 expected short days a year, which is worse than the 24.7 a team of nine carries, because the minimum on shift usually rises with the team. Headroom only reaches three at a team of twelve, where expected short days fall to about 14.3.

How Many of 9 Staff Can Be Off at Once?

Two can be off at once, and the model expects about 24.7 short days a year, less than half what a team of seven carries.

Can be away at once2

Short days a year24.7

Two. On a team of nine holding a minimum of seven on shift, two people can be away at the same time, and the third absence is the one that breaks coverage. With 25 days of annual leave and 8 days of average sickness each, which puts any one person away on 12.6 percent of working days, the model expects the team to fall below its minimum on about 24.7 of the year's 261 working days.

How often that many are actually away

The average is 1.14 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 9 people each away on 12.6 percent of working days, this is how a year of 261 days is expected to distribute.

0 away

77.3 days

1 away

100.7 days

2 away

58.3 days

3 away

19.7 daysshort

4 away

4.3 daysshort

5 away

0.6 daysshort

6 away

0.1 daysshort

7 away

0 daysshort

Everything below 3 away fits inside the roster. Everything from 3 up is a day the operation runs under its minimum of 7, and those add up to about 24.7 days a year.

What is hard about 9

Nine sits second in a band of four. Teams of eight, nine, ten, and eleven all carry the same headroom of two, because headroom only moves when the team crosses a whole-person boundary, and inside the band the cost climbs steadily: about 18.1 expected short days at eight, 24.7 at nine, 32 at ten, and 40.1 at eleven. Nine is near the cheap end of that band, which is the useful thing to know about it. On an average working day 1.14 of the nine are away, and in a peak leave period the average rises to 1.82, which sits just under the two the roster can absorb before it breaks.

The reason nine is affordable at all is the boundary just behind it. A team of seven carries headroom of one and works out at about 57 short days a year, more than twice what nine carries while being two people smaller. Those two extra bodies did not buy relief in proportion to their cost. The second unit of headroom did, and it arrived at eight. Nine inherits that unit and adds a little slack on top of it, which is why the jump from seven to nine looks so much better than the jump from nine to eleven.

Ahead of nine, the arithmetic gets worse before it gets better. The next real step up is a team of twelve, where headroom reaches three and expected short days fall to about 14.3, while ten and eleven cost 32 and 40.1 because the minimum on shift rises along with the team. A tenth hire therefore only helps if the work arriving with that person does not lift the minimum above seven. The cheaper lever is the minimum itself: hold nine against a minimum of six and expected short days drop from 24.7 to about 5, while letting the minimum drift up to eight pushes them to about 83. All of these figures assume people book leave independently of each other, which is the assumption most generous to the roster, so read 24.7 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
8	1	83
7assumed	2	24.7
6	3	5
5	4	0.7
4	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 1.14 to 1.82. Held across a full year, that rate would imply about 69.9 short days rather than 24.7. 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 the first two absences on any given day as routine, and treat the third request as a coverage decision rather than a leave decision, because that is the one that drops nine below seven.
Test the minimum on shift before you test the headcount, since holding nine against a minimum of six instead of seven cuts expected short days from 24.7 to about 5, and letting it rise to eight raises them to about 83.
Spread the team's 225 person-days of leave demand across the calendar on purpose, because the 24.7 figure assumes no clustering and the peak rate already implies 69.9.

Common questions

How many of a team of 9 can be on leave at once?: Two, if the operation needs seven people on shift. That leaves headroom of two, and the model expects a third person to be away often enough to put the team below its minimum on about 24.7 of 261 working days a year.
How often will a team of nine be short?: The model expects about 24.7 short working days a year out of 261, and at the absence rate of a peak leave period that same calculation implies 69.9. Both are floors rather than forecasts, because the model treats each person's absence as independent, and real leave clusters on school holidays and the last two weeks of December.
Would hiring a tenth person fix it?: Not on its own. A team of ten carries the same headroom of two and works out at about 32 expected short days a year, which is worse than the 24.7 a team of nine carries, because the minimum on shift usually rises with the team. Headroom only reaches three at a team of twelve, where expected short days fall to about 14.3.