You will be able to work through a full expected value analysis of a real decision you face.
A decision you are stuck on usually gets easier once each option has numbers beside it and you know which number matters most. With about thirty-five minutes and the tools from this module, you can build that sheet for a real choice of your own.
Siti, the person in the example, is made up, and so are all her figures; the arithmetic has been checked. A competitor has offered her a job with higher pay. The company is younger, she would be joining a new team, and the reports she has heard about the director are mixed. At her present company there has been a hint of a promotion next year, but nothing has been promised. Her friends weigh in, and her parents weigh in harder. She must answer the offer within a week, and three days of that have already gone on circling the same thoughts.
Before anything else, write down what you could actually do. It is easy to frame an offer as take it or leave it, and Lesson 6.3, "Widen your options before you choose", helps you look past that. Siti finds three: accept, stay, or take the offer to her manager and use it to press for a clearer promotion path. She puts only accept and stay on the sheet and keeps the third to try afterwards.
Under each option, note what could realistically happen. Most options need only two or three outcomes. Past four, each one is harder to put a number on, and the extra detail rarely helps.
Make the sheet a simple grid with a row for each outcome. Give it six columns: the option, the outcome, its probability, its value, probability multiplied by value, and a short note on how confident you are.
Value here means how much an outcome is worth to you, measured against a baseline. Siti measures everything against staying put with nothing changing. She looks two years ahead, since that is roughly how long she expects to remain in either job before taking stock again.
If she accepts and it goes well, she earns about S$800 a month more for 24 months, which comes to S$19,200. If she accepts and it goes badly, she expects to be gone within a year, and between a lost bonus and a few months looking for work she puts that at minus S$6,000. If she stays and gets the promotion, she gains about S$500 a month for 24 months, or S$12,000. If she stays and is not promoted, the value is S$0, because nothing has moved from the baseline.
Within one option, the probabilities have to total 100 percent. Draw on any evidence you have. Where you can, begin from a base rate and adjust from there, the approach Lesson 7.4, "Update your beliefs with new evidence", recommends.
Siti spent a long time talking with someone who used to work at the new company. On the strength of that, she gives the move a 70 percent chance of working out and a 30 percent chance of failing. For the promotion she settles on 40 percent, so no promotion takes the remaining 60 percent. She keeps it low because the hint was vague and because the last two people promised a promotion at her company each waited two years for it.
Beside every estimate, jot down how sure you are, then mark the shakiest one. Siti flags the 40 percent promotion figure as her weakest estimate and notes that minus S$6,000 is only a rough guess.
For each outcome, multiply probability by value, then add up the results for each option. The total is that option's expected value. Accepting gives 70 percent of S$19,200, which is S$13,440, plus 30 percent of minus S$6,000, which is minus S$1,800, for a total of S$11,640. Staying gives 40 percent of S$12,000, which is S$4,800, plus zero, so S$4,800. Accepting comes out S$6,840 higher.
An average can hide a bad outcome, so check the worst case under each option on its own, following Lesson 7.3, "When the average is not enough". Siti's worst case if she accepts is a loss of about S$6,000 and a hard year. Her worst case if she stays is no change at all, which costs her no money, though her motivation may suffer. She could get through either, since she has an emergency fund and nobody relies on her income alone.
Where every worst case is something you could recover from, it is reasonable to let expected value guide you. Where an option could leave you unable to recover, halt at this point and rethink the choice, however good its average looks.
Of all the steps, this one is the most useful. Pick out the single estimate that would reverse your decision if it changed, and work out how far it would need to move. That estimate, together with its break-even point, is the number that would flip it.
For Siti, the uncertain figure with the most influence is the chance that the move works out. Staying only comes out ahead if that chance falls below about 43 percent. She has it at 70 percent, a long way above.
Next, push your weakest estimates in the unfavourable direction and see whether the answer changes. With the promotion chance at 60 percent instead of 40, staying is worth S$7,200, still far short of S$11,640. With the cost of leaving at S$15,000 instead of S$6,000, accepting is worth S$8,940 and still comes first.
Siti can now see that her choice holds up without any one of her guesses being exactly right. The same test points her to what to check before she commits. Only evidence that the new company is far riskier than she believes would change her mind, so before accepting she asks to talk with one more member of the team.
Your sheet is complete when it shows at least two options, each with two to four outcomes; a probability and a value for every outcome; an expected value and a worst case for each option; and a note naming your weakest estimate. Along the bottom, record what you decided and the one number that would change it, plus how far it would have to move. Then put the sheet in your decision journal from Module 8, so that later you can set it against what really happened.
For the activity below, pick a decision you face now with at least two options and real money or time at stake, so the numbers mean something to you.
Fill in the expected value worksheet for one real decision, then write down the one number that would change your choice.
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