Decision trees

Welcome to the World of Decision Trees!

Ever had to make a tough choice where you weren't quite sure what the outcome would be? Maybe you were deciding whether to study for an extra hour or get some sleep, weighing up the chance of a better grade against the risk of being tired. Managers in business do this every single day!

In this chapter, we are going to learn about Decision Trees. These are clever diagrams that help businesses take the guesswork out of big decisions by using math to figure out the most likely "winning" path. Don't worry if you aren't a math whiz—we'll break it down step-by-step!

What exactly is a Decision Tree?

A Decision Tree is a mathematical model used by managers to help them make decisions where there are several choices and uncertain outcomes. It’s basically a map of all possible "what ifs."

The Three Basic Parts

To read or draw a tree, you only need to know three symbols:

1. The Square (Decision Node): This represents a point where a decision needs to be made. Think of it as a "fork in the road" where you are in control.
2. The Circle (Chance Node): This represents a point where an uncertain outcome occurs. This is where "luck" or the market takes over.
3. The Lines (Branches): these show the different paths you can take or the different things that might happen (like "Success" or "Failure").

Quick Tip: Think of the Square as "I choose" and the Circle as "The world decides."

Step-by-Step: Constructing a Decision Tree

Let's say a business is deciding whether to launch a New Product or Update an Old Product. Here is how we build the tree:

1. Start with a Square on the left.
2. Draw two branches (lines) coming out of the square: one for "Launch New" and one for "Update Old."
3. At the end of those branches, draw a Circle. This is because once you choose, the outcome is up to the market.
4. From each circle, draw branches for possible outcomes, like "High Sales" and "Low Sales."
5. Write the Probability (the chance of it happening) and the Financial Payoff (the money made) on these branches.

Example: High Sales might have a 0.6 probability (60% chance) and a payoff of £100,000.

Key Takeaway: Decision trees move from left to right when you draw them, but we do the math from right to left!

The Math: Calculating Expected Value

This is the part that sometimes scares students, but it’s actually just a simple "multiply and add" game. We want to find the Expected Value (EV).

The Formula

For each outcome, you multiply the probability by the payoff, then add them together:

\( \text{Expected Value (EV)} = (\text{Probability 1} \times \text{Payoff 1}) + (\text{Probability 2} \times \text{Payoff 2}) \)

Finding the Net Gain

The EV tells you how much money the branch is worth on average, but it doesn't account for how much it costs to take that path. To find the real winner, we calculate the Net Gain:

\( \text{Net Gain} = \text{Expected Value} - \text{Cost of the Decision} \)

Analogy: If you play a game where you have a 50% chance to win £10 and a 50% chance to win £0, the EV is £5. If it costs £3 to play the game, your Net Gain is £2. Easy, right?

How to Interpret the Figures

Once you have calculated the Net Gain for every option, the rule is simple: Choose the option with the highest Net Gain.

If "Launch New Product" has a Net Gain of £40,000 and "Update Old Product" has a Net Gain of £25,000, the tree suggests the business should launch the new product.

Quick Review Box:
- Probabilities must always add up to 1.0 (which is 100%) for each chance node.
- Expected Value is the average reward.
- Net Gain is the average reward minus the costs.

Common Mistakes to Avoid

- Forgetting the Cost: Many students calculate the Expected Value but forget to subtract the initial cost of the project. Always check for a cost!
- Mixing up Squares and Circles: Remember, the Square is your choice; the Circle is the chance event.
- Adding Probabilities: Make sure you multiply the probability by the payoff, don't add them!

Limitations of Using Decision Trees

While decision trees are great, they aren't perfect. Managers shouldn't rely on them 100%. Here’s why:

1. Estimates are just "Guesstimates": The probabilities (e.g., 0.6 chance of success) are often based on past data or even just a manager’s "gut feeling." If the estimates are wrong, the whole tree is wrong! (This is often called "Garbage In, Garbage Out").
2. Ignores Qualitative Factors: A decision tree only looks at money. It doesn't consider things like how a decision might hurt the brand image, affect employee morale, or how competitors might react.
3. Static Model: Markets change fast. By the time the tree is drawn, a new law or a change in the economy might have made the data out of date.
4. Complexity: In the real world, decisions have hundreds of possible outcomes. A simple tree might oversimplify a very complicated situation.

Key Takeaway: Decision trees are a quantitative tool. They should be used alongside qualitative (non-numerical) information to make a final decision.

Summary Checklist

- Can you identify the Square and Circle nodes?
- Do you know how to calculate Expected Value?
- Did you remember to subtract the Cost to find the Net Gain?
- Can you list two reasons why a manager might not trust a decision tree?

Don't worry if this seems tricky at first! The more you practice drawing and calculating them, the more natural it becomes. You've got this!