In the investing world, your financial success will be determined by your ability to make decisions. What you choose to invest in and when you choose to invest in it can have a massive impact on your eventual profitability. There are many potential approaches to making an investment decision, but one of the best is expected value (EV), the sum of all possible values of all possible outcomes for a given decision.

Expected value is an ideal way to make decisions because it allows you to quantify and incorporate risk into your decision making, as well as balance potentially good and bad outcomes in the same equation—since good and bad outcomes are both possible. Unfortunately, trying to calculate it outright is a nightmare for non-statisticians.

## A Basic Example

The easiest way to think about expected value is through an example given by Billy Murphy of Forever Jobless. Imagine you’re playing a coin-flipping game with a friend, and you wager $1. If the coin comes up heads, you win $2, but if the coin comes up tails, you lose your original $1 investment. There’s a 50 percent chance you’ll gain $1 and a 50 percent chance you’ll lose $1. The expected value of the scenario, then, is $0, making it a neutral investment.

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Let’s say you get $3 if heads comes up, however. In that case, you’ll have a 50 percent chance of gaining $2 and a 50 percent chance of losing $1, so the EV of your scenario is $1, making it worth the risk, on average.

## Simplifying the Calculation

You don’t have to fully understand every possible variable in the equation to utilize EV in your decision making. You simply have to use the information you do have—and some educated guesses—to ballpark the EV of a given situation. For example, let’s say you’re playing poker, and the pot stands at $30. You don’t have anything in your hand, but your opponent checks to you. Imagine you’re considering betting $15. In that case, you can make an assumption about your opponent’s chances of folding—let’s say you estimate it to be two-thirds, based on their folding behavior in the past. In two-thirds of cases, you’ll win $30, and in one-third of cases, you’ll lose $15. That makes the EV of your decision $45 ($30 + $30 – $15).

This decision-making style is somewhat predicated on your ability to estimate the percentages of various outcomes. For example, when applied to investing, you’ll need to guess at the likelihood that a stock price will drop—and how far it may drop in that scenario. Once you have an estimate, you can reasonably estimate the EV of your investment decision. Though you’ll inevitably lose some of these approaches, if you consistently make net-positive EV decisions, it’s almost mathematically impossible for you to lose in the long-term.

## Estimating By Example

The biggest problem with EV is that it relies on estimations—and unless you’re a skilled and experienced statistician, you won’t be able to forecast accurate numbers. Fortunately, there’s a simplified way around brute-force calculations; you can monitor the examples of others. Look at historical data to see how this scenario has played out in the past. Look at competitors to see how they’ve done in similar situations. Figure out what’s different in this scenario, and update the numbers accordingly. You should be able to ballpark the probability of a given event just by studying the landscape and getting a “feel” for how it’s played out in other applications.

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## Using Expected Value

Expected value is meant to help you quantify and better understand the nature of your potential risks and rewards when making a decision. In theory, always opting for decisions with a positive EV will eventually work out in your favor; however, EV shouldn’t be used as a sole factor in your decision making. You also need to consider your risk tolerance, non-quantifiable variables, and even your gut feeling on your decision (especially if you’re an experienced investor).

Use EV as a tool to help you come to the right decision; the more you use it, the more natural it will seem.

*How do you go through the decision-making process when it comes to investments?*

**Let me know with a comment!**

## 3 Comments

Hey Larry,

Thanks for posting. However, I believe you are forgetting some important steps to using EV.

For one; Isn’t EV the sum of all values MULTIPLIED BY THE PROBABILITY OF IT OCCURING?

For instance, using the example you provided where there’s a 2/3 (66%) chance of winning $30 and 1/3 (33%) chance of losing $15, EV should be:

30 x .66 = 20

-15 x .33 = -5

20-5 = an Expected Value of 15.

Or in the example with a 50% chance of winning $2 and a 50% chance of losing $1.

2 x .5 = 1

-1 x .5 = -.5

1-.5= am expected value of .5

Yeah, I was hella confused lol! EV is x1*P1 + x2*P2+…+xn*Pn, where x is an outcome and P is the probability of getting that value.

“In two-thirds of cases, you’ll win $30, and in one-third of cases, you’ll lose $15. That makes the EV of your decision $45 ($30 + $30 – $15).”

Might want to check that math… I find an EV of $15 there. You need a 3 in the denominator because you’re looking at three cases.