Risk and Expected Value in Decision-Making
The part of our choices that scares us and that which we ignore (Part 1 of 2 on managing odds for career success)
Hello 👋 and welcome to another Friday edition of this newsletter. This week is about a framework that will teach you to repeatedly make decisions that maximize how much value you end up with over time.
Highlights of this issue:
Risk is your tolerance for the worst outcome. The expected value of an action is the sum of the value of each of its possible outcomes multiplied by their probability of occurrence.
When making a decision, people tend to think too much of risk and not enough about the expected value.
Even when calculating the expected value precisely is not possible, putting yourself through the process forces you to assess both the upside and downside potential of your action before taking it.
Two common mistakes people make in estimating probability of success/failure is picking the wrong reference class and ignoring the base rate.
The reference class indicates the closest decision category to your situation (what else is most like this?) while the base rate offers the median probability of success and failure.
When making a decision, people tend to think too much of risk and not enough about the expected value.
👉Risk is your tolerance for the worst outcome. More often than not, the worst outcome isn’t going broke or losing a limb. It is much more salvageable in modern life (no war or famines).
👉The expected value for an act is the sum of the value of each of its possible outcomes multiplied by their probability of occurrence.
Consider this gamble: Heads, win 200$, Tails, lose 100$. There’s an even likelihood of heads or tails.
Potential outcome X Probability = Potential gain/loss
200$ X 50% = Gain of $100
100$ X 50% = Loss of $50
Expected value of the coin flip = Gain of $50
In real life, the value of an outcome to you may be in terms of money, time, reputation, and/or any other currency that matters to you. The action you’re thinking of taking could be anything from moving to a new city to hiring a candidate to buying a house.
Let’s imagine a situation where you’re thinking between starting a company AND staying at your current job.
Scenario 1
As you weigh your options, think of this as an internal narrative running in your head.
It is much more likely that my startup will fail than that I won’t find another job. Failure of my startup would mean all/most of my money is gone. But I can survive without a job for much longer. I can do side projects, freelance, et cetera and make some bucks on the side while I continue to look for a job. Okay—it’s too risky to start up, not with the kinda money I have anyway.
What has happened is that you’ve looked at the risk first. You’ve evaluated your exposure to the downside and concluded that it’s beyond your tolerance. The worst outcome for this decision to start a company is unacceptable to you. It is beyond the edge of the cliff. So, no startup! I want to live! Job it is.
At the point of making this decision, you have looked at your downside and concluded that it is too dark for your liking. If you put a pin here and ask people to judge you, you will appear to most as a reasonable person.
But you haven’t even looked at the other side of your outcome, which is the potential upside. Remember there are two parts to your decision: risk and expected value. The expected value for a decision option is the aggregate of its upside and downside potential. A net positive value suggests there’s more opportunity than risk; a negative value points to more risk than opportunity.
You’ve only looked at the risk and ignored expected value. Because you’ve done this, you’ve not thought about two other scenarios.
Scenario 2
Picking up from Scenario 1 calculations, you don’t like your risk. But you’re curious. What if, you ask yourself, I get it right with this startup thing? What if it takes off?
You reckon there’s a 10% chance of success, and the payoff in that case would be, say, 100 million dollars.
Upside potential = Size of payoff X Probability of success = $100mn X 10% = $10mn
You give yourself the chance to pocket a cool $10mn (upside potential) while living with the doomsday possibility of bleeding $0.5mn (all your savings, basically).
Wait a minute! Suddenly, it starts to look a little different. You start thinking differently. Instead of concluding that the entrepreneurial route is not for you, you start asking some questions.
Scenario 3
You’ve now seen a glimpse of the future. It has blue skies, green grass, and an apple tree that grows apples many times over what you can consume. You want to see if you can beat a path to this future. So, you start exploring.
What if I bet half my savings? By how much will the odds of success reduce?
In probability science, ‘the Kelly Criterion is a formula to determine how big one should wager on a given proposition when given the opportunity.’ The Kelly bet is perfect for our situation. We have a simple bet (start up OR not?) with two potential outcomes (failure OR success). One involves losing the entire amount bet (your life savings), and the other has you securing gains orders of magnitude more than your investment (10 million dollars).
So, you wonder to yourself: What if I go half Kelly (meaning put half my savings in the pot)? And along those lines…
What if I bet half my savings and borrow the other half from others?
What if I bet a third of my savings and set myself a tripwire? If I hit a milestone by such and such time, I’ll double down. If I miss it, I’ll pull out, two-thirds of my hard-earned wealth intact.
What if I aim for a slightly different market category? How will the odds of my success change?
In what areas should I put my money first such that my odds of success improve the most?
By not putting a full stop on your thinking like you were tempted to in Scenario 1, you’re now actively working to improve your odds of success without giving up any more than you can afford. This is possible only because you’re willing to consider the expected value of your decision.
💡Insight: When you have a choice to make, work out the expected value of your options first. If it is positive for any of the options, look at the risk and figure out ways to mitigate it. Do this often enough, you’ll have learned to mitigate risk through diversification. You’ll have learned to hold 10,000 coin flips in your portfolio in a way that is net positive, so that a few bad flips don’t kill you.
🎩Hat tip: A numerical probability is a sharp instrument. It’s possible that you may not be comfortable coming up with a probability for a potential outcome with such precision. Or it may be hard to do so anyway. In such a case, and this is more common, you can make yourself some blunt instruments. Use a spectrum of natural language terms (from real possibility to extremely unlikely) to make the probability specific. Or you can use a range to define the limits of your confidence (between 20 and 30%, for example).
This post serves to alert readers to a rather common but avoidable mistake, which is getting unduly swayed by risk. At the same time, it’s rare to be able to precisely predict potential benefits/losses or the likelihood that they occur. But instead of throwing the baby with the bathwater, you can make rough informed guesses and still evaluate your upside and downside than make a decision with no evaluation at all. That is the second point this post makes.
Mistakes people make in calculating expected value
Going back to your career decision. You considered reasonable a 10% probability for the success of your new business venture. In other words, you believed a failure rate of 90% makes sense. But not all business ventures are the same. Starting a car company has different odds than launching rockets into space. The base rate is different.
In arriving at this probability for success—or base rate—there are two common mistakes people make.
1️⃣Picking the wrong reference class
In a recent interview, Daniel Kahneman expounds on common errors in picking whom to compare their situation with.
The more novel the thing is, the less the experience, then it’s harder to find a good reference class. And that’s where people will focus on the unique aspect of their project and go drastically wrong.
If you’re starting a rocket company you’re less likely to find a reliable comparison set. Your problem is relatively unique and the number of people who have tried to solve it is not statistically significant. When you find yourself in such unknown territory, you may be tempted to quantify this uncertainty with what you know—your awesome entrepreneurial chops!
Most of the time, though, you’re not doing things as rare as launching a rocket company. S, it is important to spend time and effort finding that Goldilocks point—a category of situations that is big enough to be statistically meaningful while also sharing high resonance with your situation.
2️⃣Ignoring the base rate
Say you’re starting a car company, not a rocket company. You’re pretty likely to find yourself a good reference class. You may find, however, that there have been very few new successful car companies in the last 50 years. The base rate—median probability of success—is not up to scratch. When confronted with such sobering reality, you may pump yourself up with the ‘The rules don’t apply to me’ talk.
The talk may go something like this: ‘So what if previous car ventures have tanked? They didn’t have our vision. We’re doing something truly revolutionary that customers will see.’
Your self-talk may just have some substance and as long as you know it, that’s fine. You may actually have a non-obvious insight. Which in the case of this particular example may go something like this:
Car companies historically have had zero margins on new car sales. They make all their money off car parts sales for used cars. Incumbent car companies have a big advantage because they have all these used cars on the road that need maintenance. A new car company, in the absence of a fleet, therefore cannot compete on price with the incumbents. It will have to offer a product that is far ahead of the incumbents.
Now this is compelling grounds to look beyond the base rate. Once you have such an insight, you can work with it to craft your competitive advantage. That advantage, in the case of Tesla, is a combination of having autonomous driving and being an electric vehicle.
But most of us are guilty of base-rate neglect. We think our restaurant will be a roaring success when seven others in the same block have closed down in the last year. Or we can complete our project in three months when others like it have taken double that time on average. Oh, the optimism in the little voice in our heads!
Conclusion
We saw that there are two parts to making a decision: calculating the expected value and assessing the risk. We then learned that being waylaid by risk is common. Our biological instincts lay siege to our thinking machinery and we forget all about the upside potential. That can be a big mistake.
For most types of decisions, the risk can be managed if the upside potential is appropriate. Hence, bring the expected value math out from the shadows. Do that first. Then assess risk.
As you use the expected-value framework, tighten up your predictions by avoiding two mistakes: ignoring the base rate (likelihood of success) and picking the wrong reference class (most similar kind of situations to compare with).
Yet, you’ll find that sometimes your odds of success are not high enough. The proposition is too risky. What do you do? Do you abandon your aspirations?
At other times, the worst outcome is not financial ruin. It is living a life without doing the thing that gives it meaning.
Next week, we’ll delve into how to improve your odds of success and how to approach decision-making in cases where the worst outcome is not going broke but something worse.
Until then… 👋