You will be able to calculate the expected value of a choice and compare options.
Siti, from lesson 7.1, is weighing up a professional HR certification. It costs S$3,000 after any subsidy she can get, and takes most of her Saturdays for six months. Her manager has hinted that people with the certification tend to move up a grade, which would mean a raise. A colleague did the same course and nothing changed for her. Siti keeps thinking "it might pay off", which does not help her decide.
Lesson 7.1, Decisions are bets, gave her a way to say how sure she is. This lesson puts those probabilities to work. All the figures here are examples, and every calculation has been checked.
Expected value is the average result you would get from a choice if you could make it many times over. You calculate it by taking each possible outcome, multiplying its value by its probability, and adding the results together.
A simple example first. A made-up office charity raffle sells 1,000 tickets at S$2 each and gives one prize worth S$1,000. If you buy one ticket, there is a 1 in 1,000 chance you win S$1,000, which is worth S$1 on average. You paid S$2. So the expected value of a ticket is S$1 minus S$2, which is minus S$1. On average, every ticket loses a dollar. With a charity raffle nobody minds, since the lost dollar is really a donation.
Commercial lotteries and casino games work on the same principle. They have negative expected value for players by design, because the operator pays out less in prizes than it takes in from tickets and bets. That is how the operator covers its costs and makes money or funds its causes. Any one player can win, but the average player cannot, and the more you play, the closer your results get to the average.
Siti thinks about what could happen after the certification. To keep it simple, she uses two outcomes. Either she moves up a grade with a raise she estimates at S$300 a month, or nothing changes. She puts the chance of the raise at about 50 percent, because her manager's hint was encouraging, but her colleague's experience reminds her it is not automatic.
The question then is: over what period? If she looks only at the first year, the raise is worth S$300 times 12, or S$3,600. Half of that is S$1,800. Subtract the S$3,000 cost and the expected value is minus S$1,200. On a one-year view, the course does not pay.
But a raise usually lasts. Over three years, the raise is worth S$300 times 36, or S$10,800. Half of that is S$5,400. Subtract S$3,000 and the expected value is S$2,400. On a three-year view, the course is worth it on average.
The horizon you choose matters as much as the probability. Choose it honestly, based on how long you would realistically stay in a role where the raise applies, not on whichever answer you were hoping for.
Siti also considers a cheaper alternative: a S$800 short course that she thinks has about a 30 percent chance of leading to a S$200 a month raise. Over three years, the raise would be worth S$7,200. Thirty percent of that is S$2,160, and subtracting S$800 leaves S$1,360. The full certification has the higher expected value, S$2,400 against S$1,360.
Siti does not know that her chance is 50 percent. Nobody gave her that figure. It is her best estimate from what she knows. Some people refuse to calculate expected value because the inputs are uncertain. That is a mistake. A rough estimate, stated openly, is far more useful than a vague feeling, because you can see it, question it and change it.
It also helps to test how much the answer depends on the estimate. If Siti's chance were 40 percent rather than 50, the three-year expected value would be S$1,320. At 60 percent it would be S$3,480. The course comes out ahead in all three cases. In fact, for the three-year expected value to fall below zero, her chance of a raise would have to be under about 28 percent. That is useful to know. Her decision does not hang on getting the probability exactly right.
When you lack data, you can get better estimates from the outside view in lesson 5.3, Vivid stories and the planning fallacy. How many people in Siti's company who took this certification moved up within a year? Her manager or HR records may know. One colleague's experience is a single story, as lesson 1.2, Not all evidence weighs the same, warned.
Expected value lets you compare options on one scale. But an average hides the range of outcomes, and you never live the average. You live one outcome.
So after comparing expected values, look at the worst case of each option separately. For Siti, the worst case of the full certification is losing S$3,000 and six months of Saturdays with nothing to show on her payslip. The worst case of the short course is losing S$800. Both are setbacks she could recover from, so the higher expected value of the certification is a fair guide. If the worst case were something she could not recover from, the calculation would need a different kind of thinking, which is the subject of lesson 7.3, When the average is not enough.
Siti decides to ask HR how many past course-takers moved up, and to enrol if the answer is anywhere near half.
You probably have a choice like hers in front of you, whether it is a course, a certification, a side project or a change of role. Keep it in mind for the activity below, and be honest with yourself about the horizon.
Calculate the expected value of a real choice, such as taking a course to qualify for a pay rise, using your own estimates of cost, probability and gain.
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