Expected value (EV) is a useful tool. I first discovered EV while learning how to be a better poker player. In poker, you use EV calculations all the time. An easy example is a flush draw. In a game like Texas Hold’em, if you have a flush draw at the start of the hand, your odds of hitting that flush by the end of the hand are roughly 2-to-1 against. You’ll hit the flush about 35% of the time. Let’s say you’re playing against a single player that goes all-in for $20 on the flop, making the pot $100. You can call or fold. Because you know the odds (2-to-1 against hitting your flush), you can use EV to make a better decision. If you think your flush will be the best hand, over the long run (if you played out this same scenario over and over again) you know on average for every three hands played you’ll lose $20 twice, and win $100 once. Therefore, the EV of this call is +$60. In poker, you’re trying to make bets, calls, and raises with positive EV. If you do that over the long term you’ll be a winner.
When making an investment decision, you’re usually trying to accurately predict the future cash flows of the business. Predicting cash flows with precision isn’t easy. There are multiple versions of a possible future that depend on how various uncertain interconnected events unfold. Betting on a single scenario would be ignoring this uncertainty. For a more accurate representation of future cash flows, use EV with simple probability weighted scenarios. Here’s a real example I used in January 2016 while deciding whether or not to increase my investment in Apple Inc. (AAPL) when the stock price was around $100.
|2018 earnings scenarios||Probability||Probability weighted|
| Best case: $12.23||20%||$2.45|
| Base case: $10.11||70%||$7.08|
| Worst case: $5.68||10%||$.57|
|Total (expected value)||-||$10.10|
- Scenarios predicting calendar 2018, not fiscal 2018.
- All scenarios assume 4.75B shares outstanding at the end of 2018.
-  Best case: $264B in revenue, 22% net income margin.
-  Base case: $240B in revenue, 20% net income margin.
-  Worst case: $150B in revenue, 18% net income margin.
When estimating I try to be roughly right instead of exactly wrong. So, instead of building a complex model, I reduced the owner earnings calculation to two key factors: revenue and net income margin. Then, I assigned probability estimates to each scenario based on my best estimate of the likelihood of each possible future. The result was an EV for 2018 owner earnings of $10.10 per share. A 10% return looked like a no brainer for such a great business in the interest rate environment, so I made the investment.
I still use a similar format for all new investments and find it helpful. The key factors change depending on the business, but the core format remains the same. I now use four possible scenarios (best, good, base, worst) instead of three to account for more possibilities. Of course, it’s important to spend time studying the business to ensure your probability scenarios are well informed, and to update them when things change.
When you’re building software, you’re using EV all the time. Most product teams have limited resources and long lists of feature ideas. Keeping proper balance between sustaining product improvements and high impact new initiatives is important. Sustaining improvements help your product deliver incremental value, while new initiatives have the potential to open up new markets or lines of business.
In the new initiatives case, you’re behaving more like a seed stage investor, spreading many smaller bets in the hopes one will payoff big. When it does, you’ll pour more investment into that initiative. But again, you’re limited by resources, so you want to focus on the ideas with the highest EV. First, decide what you are optimizing for. In this case, you want to optimize for impact (higher is better) and time to ship (lower is better). Assign each initiative an impact score and a time to ship score of 1 to 5. For example, Initiative X has a high potential impact (4 out of 5), but will take longer to ship (2 out of 5). Score 6. The highest score is 10. EV rankings help ensure you’re staying objective and sticking with your strategy.
When ranking a list by EV, be sure to score each variable independently. For example, work through your entire list of initiatives and score each initiative on impact, then move on to scoring each initiative on time to ship. To avoid bias, don’t score an entire initiative all at once.
EV isn’t just useful in business. For example, you’re planning a family holiday. As part of the trip, you’d like to expose your children to a different culture while keeping them safe. You’re optimizing for cultural differences and safety. Compile your list of potential destinations, score them, rank them, and make a more informed decision.
When analyzing any decision, first outline the variables you’re optimizing for. Some variables lend themselves to math focused probability based EV calculations (like an earnings estimate) while others work better with a crude scoring system (like a feature list or a family vacation). In either case, EV can help you make better decisions.