You will work through a full expected value analysis of a real decision you face.
Siti gets a job offer from a competitor. The new role pays more, but it is at a younger company, the team is new and she has heard mixed things about the director. Her current employer has hinted at a promotion next year, though nothing is promised. Friends have opinions. Her parents have stronger ones. She has a week to reply and has spent three days going round in circles.
This exercise takes the tools from this module and applies them to one real decision of your own, in about thirty-five minutes. Siti's numbers below are a worked example. They are made up, and every calculation has been checked.
Start with the options. Use lesson 6.3, Widen your options before you choose, to make sure you are not stuck on yes or no. For Siti, the options are to accept the offer, to stay, or to use the offer to ask her current employer for a clearer promotion path. To keep the example short, she works through the first two and treats the third as a follow-up.
For each option, list the realistic outcomes. Two or three per option is usually enough. More than four gets hard to estimate and adds little.
Set up a sheet with a row for each outcome and these columns: option, outcome, probability, value, probability times value, and a note on how confident you are in the estimates. Value means what the outcome is worth to you compared with a baseline, here staying where she is with no change.
Siti's outcomes over the next two years, which is how long she expects to stay in either role before reassessing:
Accept, and it works out: about S$800 a month more for 24 months, worth S$19,200. Accept, and it does not work out: she leaves within a year and loses a bonus and a few months of job search, which she estimates at minus S$6,000. Stay, and she is promoted: about S$500 a month more for 24 months, worth S$12,000. Stay, and no promotion comes: no change, worth S$0.
Now give each outcome a probability, so that the outcomes for each option add up to 100 percent. Use whatever evidence you have, and start from a base rate where you can, as lesson 7.4, Update your beliefs with new evidence, recommended.
Siti puts a 70 percent chance on the move working out, based on a long conversation with someone who left that company, and 30 percent on it not working. She puts the promotion at 40 percent, because the hint was vague and the last two people promised a promotion waited two years.
In the confidence column she notes that the promotion probability is her weakest estimate, and the minus S$6,000 is a rough guess.
Then multiply each probability by its value and add them up for each option. Accepting: 70 percent of S$19,200 is S$13,440, and 30 percent of minus S$6,000 is minus S$1,800, so the expected value is S$11,640. Staying: 40 percent of S$12,000 is S$4,800, plus zero, so S$4,800. On expected value, accepting is ahead by S$6,840.
Lesson 7.3, When the average is not enough, said to look at the worst case of each option separately. For Siti, the worst case of accepting is losing about S$6,000 and a difficult year. The worst case of staying is no change, which costs nothing in money but might cost her some motivation. Neither is ruinous. She has an emergency fund and no one depends on her income alone. So expected value is a fair guide here.
If one option had a worst case you could not recover from, this is where you would stop and rethink, whatever the averages say.
The last step is the most useful. Ask which single estimate, if it changed, would flip your decision, and how far it would have to move.
For Siti, the most uncertain number that could change the outcome is the chance the move works out. She asks: at what probability would accepting and staying be equal? The answer is about 43 percent. Below that, staying wins. Her estimate of 70 percent is well above it, so even if she is quite wrong about the new company, accepting still comes out ahead.
She also checks her weakest estimate. If the chance of promotion were 60 percent instead of 40, staying would be worth S$7,200, still well below S$11,640. If leaving went worse than she thought, costing S$15,000 rather than S$6,000, accepting would be worth S$8,940, still ahead.
That gives Siti something she did not have before: confidence that the decision does not depend on getting any one guess exactly right. It also tells her what to find out. The one thing that could change her mind is evidence that the new company is much riskier than she thinks, so she asks to speak to one more person on the team before accepting.
A finished sheet lists at least two options with two to four outcomes each, a probability and value for every outcome, the expected value of each option, the worst case of each, and a note on your weakest estimate. At the bottom, write your decision and the single number that would change it, with how far it would have to move. File it in your decision journal from Module 8 so you can compare it with what happens.
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.
Complete the expected value worksheet for one real decision and write the one number that would change your choice.
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