Do the decision rules agree on what to build?
Every decision analysis course opens with the same exercise: score a payoff table under each rule and say which one you would use. The reason it is worth doing is that the rules disagree, and the disagreement is the lesson rather than an inconvenience on the way to an answer.
Words on this sheet
- Expected value: The average payoff you would get if you faced this same choice many times, with each outcome weighted by its chance.
School Intermediate Data Table free
After you install, this is the model to open.
Which Option Wins, and at What Odds?
- 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
Five rules, three different answers, and only one of them uses your probabilities:
- Worst case
- Build small guarantees $40,000
- Best case
- Build large reaches $160,000
- Expected value
- Build medium $67,000
- Answer flips at
- 34.7% chance of strong demand
Worst case picks Build small, best case picks Build large, and equal likelihood, smallest biggest regret and expected value all pick Build medium. Three different answers off one table, which is why the rule you choose has to be defended rather than assumed. Expected value gives 49, 67 and 62.75 in thousands, so medium leads, but only until the odds move: at a 30% chance of strong demand medium is ahead 67.00 to 62.75, and by 35% large has taken over at 68.00 to 67.75. Solving the two lines exactly puts the crossover at 34.7%, so the recommendation turns on a probability that is itself a guess, and saying so is part of the answer. The sheet also prices the uncertainty: the best expected value available is $67,000, a perfect forecast would be worth $94,000, so perfect information is worth $27,000. That is the ceiling on what any market study is worth here, and it is worth knowing before one is commissioned.
The model
Three options, three demand scenarios, one payoff for each combination. The sheet scores every row under worst case, best case, equal likelihood, biggest regret and expected value, builds the regret table underneath, and then prices what a perfect forecast would be worth.
| Options | build small, medium or large |
| Scenarios | weak, steady or strong demand |
| Payoffs | -$40,000 up to $160,000 |
| Probabilities | 25% weak, 45% steady, 30% strong |
| Rules scored | worst case, best case, equal likelihood, biggest regret, expected value |
| Swept | the chance of strong demand, 0 to 0.6 |
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
- Three averages differ. Is that more than chance?Which Study Method Actually Works?
- Should you switch doors or stay?Switch or Stay? The Monty Hall Problem, Simulated
- Why does splitting the money cut the risk?Why Diversification Works
- Drill blind or pay to learn the odds first?Is the Test Worth Paying For?
- Why is the textbook schedule too optimistic?The Classic Project Network, Simulated
- Does discounting to fill the room ever work?What Does the Course Have to Charge?
Every model like this one, and the method behind them: What-if analysis in Google Sheets.