1. Expected value calculations
Welcome back! In this chapter, we'll look at techniques you can use to interpret and manage uncertainty. First up: expected value calculations.
2. What is expected value?
The expected value is an average you estimate by weighting each scenario by its probability. It gives you a realistic expectation of what might happen over time.
Suppose you're working at a restaurant. Some customers might tip $10, some $5, and some might not tip at all. By calculating the average amount per customer based on past data, you get an 'expected' tip amount per table. That's the expected value; it gives a weighted estimate of what to expect over time rather than relying on just one outcome.
3. How expected value calculations work
Here's how it works:
The first step in expected value calculation is to identify and list possible outcomes, like winning a lottery price or losing the ticket money.
The next step is to estimate how likely each outcome is so we can assign probabilities to each outcome. These probabilities need to add up to 1, or 100%.
We can calculate the expected value now that we have our outcomes and their probabilities. This is done by multiplying each outcome by its probability and then summing up the results.
Once we have the expected value, we can use it to help guide decisions.
4. Expected value calculations in practice
Expected value calculations help businesses and investors make smarter decisions by considering the bigger picture rather than focusing on a single outcome. Instead of relying on intuition or best-case scenarios, expected value incorporates multiple possibilities and their probabilities, allowing for a more balanced approach to risk and reward.
For example, companies use expected value to set optimal product prices, ensuring they maximize revenue while remaining competitive. Marketers apply expected value to assess the financial impact of different promotional strategies, such as discounts or ad campaigns. Investors leverage expected value to evaluate stock options or new ventures, weighing potential returns against associated risks.
5. How are probabilities for expected values determined?
Probabilities for expected value calculations are typically determined based on data or expert judgment. One approach is to analyze historical data, where past trends provide insight into how frequently specific events occur.
Another method involves market research and surveys. Businesses often conduct customer surveys or analyze competitor strategies to estimate how likely certain outcomes are.
In cases where data is limited, companies rely on expert judgment, where industry professionals use experience and insights to make probability estimates.
6. Example: pricing decisions
Suppose a company is launching a new product and estimates demand based on different market conditions. If demand is high, they expect to sell 1,000 units, which has a 30% probability of happening. If demand is moderate, they expect to sell 700 units, with a 50% probability. If demand is low, they expect to sell only 400 units, with a 20% probability.
If they price the product at $50 per unit, they can estimate expected revenue. This would be $50,000 in a high-demand scenario, $35,000 in a moderate one, and $20,000 if demand is low. By taking into account the probabilities, total expected value would be $36,500.
The company can then compare this to their break-even point to determine whether the new product is likely to be profitable. If not, they may need to reconsider their pricing strategy, for example by increasing the price per unit.
7. Let's practice!
Time to put expected value into practice!