How can decision trees help with expected value calculations?

1 What is expected value?

Expected value is a concept that measures the average result of a decision that involves uncertainty or randomness. For example, if you flip a fair coin, the expected value of getting heads is 0.5, because you would get heads half of the time in the long run. Expected value is useful for comparing different options and choosing the one that maximizes your benefit or minimizes your cost.

2 How to build a decision tree?

Building a decision tree requires following a few steps. First, identify the decision you want to analyze and draw a square node to represent it. Then, draw branches from the node to show the different alternatives you can choose from. Next, identify the uncertain events that can affect the outcome and draw circle nodes to represent them. Subsequently, draw branches from the circle nodes to show the possible outcomes of the uncertain events and their probabilities, which can be indicated using fractions, decimals, or percentages. Finally, assign a value to each outcome and label the nodes and branches with relevant information.

3 How to calculate expected value using a decision tree?

To calculate the expected value of each alternative, you need to multiply the value of each outcome by its probability and add them up. This will give you the expected value of each branch. Then, you need to compare the expected values of the branches that originate from the same decision node and choose the one that is highest or lowest, depending on your goal. You can also calculate the expected value of the whole decision tree by adding up the expected values of the final branches.

4 How to simplify a decision tree using folding back?

Folding back is a technique that can help you simplify a decision tree by working backwards from the end. To do so, start from the rightmost nodes and calculate the expected value of each branch. Then, replace the circle nodes with their expected values and delete the branches and values that are no longer needed. Repeat this process until you reach the leftmost node, which will give you the expected value of the whole decision tree. By following these steps, you can easily fold back a decision tree and make complex decisions simpler.

5 How to use a decision tree in research?

A decision tree can be a valuable tool for research, enabling you to explore different scenarios and hypotheses, as well as quantify the uncertainty and risk associated with your decisions. Additionally, it can help you evaluate the trade-offs and sensitivity of your decisions, while also providing a visual representation of your decisions that can be communicated and justified clearly.

6 Example of a decision tree for expected value calculation

Suppose you are a researcher who wants to decide whether to conduct a survey or an experiment to test a hypothesis. With a budget of $10,000 and the potential of receiving a grant of $20,000 if the hypothesis is confirmed, you need to weigh the costs and probabilities. The probability of confirming your hypothesis with a survey is 0.6 and the cost is $5,000; with an experiment, the probability is 0.8 and the cost is $8,000. The probability of getting the grant if your hypothesis is confirmed is 0.9. A decision tree can be used to calculate the expected value of each option and choose the one that maximizes your net benefit. For example, the expected value of the survey branch is $8,500 while that of the experiment branch is $7,600; therefore, you should choose the survey option. Moreover, you can fold back the decision tree to simplify it and get the same result. The decision tree can help you calculate the expected value of your decisions and choose the best option for your research.

7 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?