Expected value, a fundamental concept in probability theory, represents the weighted average of possible outcomes, each weighted by its probability of occurrence. In Excel, a versatile spreadsheet application, finding the expected value is a valuable technique for making informed decisions. By utilizing Excel’s functions, users can easily calculate expected values for various scenarios, such as investments, game theory, and decision-making under uncertainty. This article will provide a comprehensive guide on how to determine expected value in Excel, leveraging functions like SUMPRODUCT and AVERAGEIFS to simplify the calculations.
How to Find Expected Value in Excel
Let’s get straight into the steps:
1. First, create a table that lists all the possible outcomes and their associated probabilities. Something like this:
| Outcome | Probability |
|—|—|
| A | 0.2 |
| B | 0.5 |
| C | 0.3 |
2. Next, you’ll need to find the value of each outcome. So, if the outcomes are monetary amounts, you’ll simply use those amounts.
3. Now, multiply each outcome by its probability. So, for example, if Outcome A has a value of $1 and a probability of 0.2, you’ll calculate 1 x 0.2 = $0.2.
4. After that, add up the products you calculated in the previous step. This result is what we call the expected value.
5. So, to find the expected value in Excel, you can use the SUMPRODUCT function:
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=SUMPRODUCT(Range of Values, Range of Probabilities)
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For instance, if the values are in cells B2:B4 and the probabilities are in cells C2:C4, you’d use:
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=SUMPRODUCT(B2:B4,C2:C4)
“`
Expected Value in Excel
Expected value (EV) is a statistical measure of the average value of a random variable. It is calculated by multiplying each possible outcome by its probability and then summing the results. EV can be used to make decisions about outcomes that are uncertain and to assess the risk of a particular course of action.
Here are 7 different ways to find EV in Excel:
Example 1: Calculating the EV of a Simple Gamble
A simple gamble involves paying $1 to flip a coin. If the coin lands on heads, you win $2. If the coin lands on tails, you win nothing. The EV of this gamble is $0.50, which is calculated as follows:
- Probability of winning: 0.5
- Payoff if winning: $2
- Probability of losing: 0.5
- Payoff if losing: $0
- EV = (0.5 * $2) + (0.5 * $0) = $0.50
Example 2: Calculating the EV of a Lottery
A lottery involves buying a ticket for $1. The prize pool is $1 million. The probability of winning the jackpot is 1 in 175,711,536. The EV of this lottery is $0.0057, which is calculated as follows:
- Probability of winning the jackpot: 1 / 175,711,536
- Payoff if winning the jackpot: $1,000,000
- Probability of not winning the jackpot: 1 – 1 / 175,711,536
- Payoff if not winning the jackpot: $0
- EV = (1 / 175,711,536 * $1,000,000) + (1 – 1 / 175,711,536 * $0) = $0.0057
Example 3: Calculating the EV of a Slot Machine
A slot machine has three reels, each with 10 symbols. The probability of getting a winning combination is 1 in 1,000. The payout for a winning combination is $10. The EV of this slot machine is $0.01, which is calculated as follows:
- Probability of winning: 1 / 1,000
- Payoff if winning: $10
- Probability of losing: 1 – 1 / 1,000
- Payoff if losing: $0
- EV = (1 / 1,000 * $10) + (1 – 1 / 1,000 * $0) = $0.01
Example 4: Calculating the EV of a Business Investment
A business investment involves investing $10,000. The expected return on the investment is 10%. The probability of success is 70%. The probability of failure is 30%. The EV of this investment is $7,000, which is calculated as follows:
- Probability of success: 0.7
- Payoff if success: $10,000 * 1.10 = $11,000
- Probability of failure: 0.3
- Payoff if failure: $10,000 * 0 = $0
- EV = (0.7 * $11,000) + (0.3 * $0) = $7,000
Example 5: Calculating the EV of a Job Offer
A job offer involves a salary of $50,000 per year. The probability of getting the job is 50%. The probability of not getting the job is 50%. The EV of this job offer is $25,000, which is calculated as follows:
- Probability of getting the job: 0.5
- Payoff if getting the job: $50,000
- Probability of not getting the job: 0.5
- Payoff if not getting the job: $0
- EV = (0.5 * $50,000) + (0.5 * $0) = $25,000
Example 6: Calculating the EV of a Retirement Plan
A retirement plan involves investing $1,000 per year for 30 years. The expected return on the investment is 8%. The EV of this retirement plan is $50,730, which is calculated using the FV function in Excel:
- Rate: 8%
- Nper: 30
- Pmt: -$1,000
- Type: 0
- FV = $50,730
Example 7: Calculating the EV of a Tax Refund
A tax refund involves receiving a refund of $1,000 from the government. The probability of receiving the refund is 90%. The probability of not receiving the refund is 10%. The EV of this tax refund is $900, which is calculated as follows:
- Probability of receiving the refund: 0.9
- Payoff if receiving the refund: $1,000
- Probability of not receiving the refund: 0.1
- Payoff if not receiving the refund: $0
- EV = (0.9 * $1,000) + (0.1 * $0) = $900
Well, that’s a wrap on our crash course in finding expected value in Excel! Whether you’re a seasoned spreadsheet wizard or just starting to dip your toes in the world of probability, I hope you’ve found this guide helpful. Remember, expected value is a powerful tool that can help you make better decisions in all walks of life. So, go forth and conquer the realm of uncertainty with your newfound Excel skills. Thanks for stopping by, and be sure to visit again for more spreadsheets goodness!