Is a random draw a fair way to split the weekends?
Twelve weekend shifts drawn at random across six people, with a seed so the draw can be repeated in front of anyone. One person gets three and one gets one, which is what random actually looks like and why a rota is not a lottery.
Operations Starter Random Number Generation free
After you install, this is the model to open.
Assign the Shifts Without Arguing
- In your spreadsheet, click the Sortia icon in the strip of icons down the right-hand edge. No strip? Click the arrow at the bottom-right to open it. You can also use Extensions, then Sortia, then Open Sortia.
- Click Start from a template and put that name in the search box.
- Pick the card with that name and click Load this template. It arrives on a new tab with real numbers already in it.
The answer
- The odds
- 1 in 6 for every name on every one of the 12 draws
- The outcome
- 4 to 0 Dara draws four weekends, Bea and Eli draw none
- Nobody relitigates it
- seed 7 the same draw comes back on every rerun
Six people, twelve weekend shifts, and the awkward conversation about who takes them. The distribution is already set to Discrete, the value and probability range already points at the Number and Probability columns of the team block, and the count is 12 with a seed of 7. Click Run. The draw comes back 6, 6, 4, 1, 1, 1, 4, 4, 4, 3, 3, 6. Paste those twelve numbers into the drawn number column and the name column turns them into people.
The shifts drawn tally then reads 3, 0, 2, 4, 0, 3. An even split would have been two each. Dara drew four and Bea and Eli drew none at all, from a process that gave all six of them exactly the same chance on every single draw. That is not a flaw in the tool, it is what random looks like at twelve draws, and it is the most useful thing this template has to teach.
Random is fair in the sense that nobody was favored, and it is not fair in the sense that everyone ends up even, and those two meanings of the word are what the argument in the break room is actually about. Try a seed of 11 and the unevenness simply moves: the draw is 3, 6, 1, 1, 5, 1, 2, 3, 5, 3, 3, 4, which gives Cai four of the twelve shifts and leaves Bea, Dara and Fen on one each.
Every one of those draws was fair and the rota is indefensible. So use this to break a tie, not to build a rota. The defensible way to run it is to draw, read the tally, and rebalance by hand until nobody is more than one shift off the even split, with the draw deciding who gets the odd one. Announce the seed before you draw. That is the second half of the point: a seed makes the lottery repeatable in front of the people affected by it, so anyone can rerun it and get the same twelve numbers, and what makes a random allocation acceptable is not the randomness, it is that nobody could have chosen the outcome.
If you want a strict rotation rather than a lottery, use the Patterned distribution running from 1 to 6 in steps of 1 with the sequence repeated twice, which produces each person exactly twice in a fixed order. To use it for your own team, change the names, keep the probabilities summing to 1, and set the count to the number of shifts.
The model
It arrives on a tab called Template: Assign the Shifts Fairly, carrying these columns:
- Number
- Probability
- Name
- Shift
- Date
- Name
- Shifts drawn (count)
with the model computed beside the data:
| Ade | 0 |
| Bea | 0 |
| Cai | 0 |
| Dara | 0 |
| Eli | 0 |
| Fen | 0 |
| An even split would be (shifts) | 2 |
Once it is in your sheet
- The model arrives with real numbers in it and runs as it stands, so you can press the button first and understand it second.
- Change the numbers to yours. The sheet marks which cells are inputs and which hold formulas, and most labels carry a note explaining the row.
- Press the run button at the bottom of the panel. It is labeled for the tool you are in, and the result lands on its own tab, with a written reading of it beside the figures.
Never used Google Sheets? Start here goes the whole way, in seven steps, and assumes nothing.
Next question
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Every model like this one, and the method behind them: Statistics in Google Sheets.