How can you compare decision options using expected value?

1 What is expected value?

Expected value is the sum of the possible outcomes of a decision or experiment, weighted by their probabilities. For example, if you flip a fair coin, the expected value of the number of heads is 0.5, because there are two possible outcomes (heads or tails), each with a probability of 0.5, and the value of heads is 1. If you flip the coin 100 times, you would expect to get 50 heads on average, but the actual result may vary. Expected value is not a prediction, but a measure of the long-term average.

2 How to calculate expected value?

To calculate the expected value of a decision or experiment, you need to identify the possible outcomes, assign values to each outcome, and estimate the probabilities of each outcome. Then, you multiply each value by its probability and add them up. For example, suppose you have a choice between two lottery tickets: A and B. Ticket A costs $10 and has a 1% chance of winning $1,000. Ticket B costs $5 and has a 5% chance of winning $100. The expected value of ticket A is (0.01 x 1,000) - 10 = $0. The expected value of ticket B is (0.05 x 100) - 5 = $0. Both tickets have the same expected value, but ticket B has a higher probability of winning.

3 How to compare decision options using expected value?

To compare decision options using expected value, you simply compare the expected values of each option and choose the one that is higher (if you are maximizing) or lower (if you are minimizing). For example, suppose you have to choose between two investment options: C and D. Option C has a 50% chance of returning 10% and a 50% chance of losing 10%. Option D has a 25% chance of returning 20% and a 75% chance of losing 5%. The expected value of option C is (0.5 x 0.1) - (0.5 x 0.1) = 0. The expected value of option D is (0.25 x 0.2) - (0.75 x 0.05) = 0.0125. Option D has a higher expected value than option C, so it is a better choice.

4 What are the limitations of expected value?

Expected value is a useful tool for comparing decision options under uncertainty, but it has some limitations that you should be aware of. First, expected value does not account for the variability or risk of the outcomes. For example, option C and option D have the same expected value, but option C has a higher standard deviation, which means it is more volatile and risky. Some people may prefer a lower expected value with less risk, while others may prefer a higher expected value with more risk. Second, expected value does not account for the utility or preference of the decision-maker. For example, suppose you have to choose between two options: E and F. Option E gives you a 100% chance of winning $100. Option F gives you a 50% chance of winning $200 and a 50% chance of winning nothing. Both options have the same expected value of $100, but option E is more certain and option F is more exciting. Some people may prefer option E because they value certainty, while others may prefer option F because they enjoy gambling. Third, expected value relies on the accuracy and availability of the probabilities and values of the outcomes. Sometimes, these may be difficult to estimate or obtain, or they may change over time. For example, suppose you have to choose between two options: G and H. Option G gives you a 90% chance of winning $100 and a 10% chance of losing $1,000. Option H gives you a 10% chance of winning $1,000 and a 90% chance of losing $100. The expected value of option G is (0.9 x 100) - (0.1 x 1,000) = -10. The expected value of option H is (0.1 x 1,000) - (0.9 x 100) = -10. Both options have the same expected value, but option G is more risky and option H is more conservative. However, suppose that the probabilities of option G change over time, and become 80% and 20% respectively. Then, the expected value of option G becomes (0.8 x 100) - (0.2 x 1,000) = -120, which is lower than option H.

5 How to improve your decision-making using expected value?

Expected value is a powerful and simple way to compare decision options under uncertainty, but it is not the only way. You should also consider other factors, such as the variability, utility, and reliability of the outcomes, as well as your own goals, values, and constraints. You should also use other tools and methods, such as decision trees, sensitivity analysis, scenario planning, and intuition, to complement and validate your expected value calculations. By doing so, you can improve your decision-making skills and make better choices in uncertain situations.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?