I’ve been wanting to write this post for a long time, because it’s the kind of post that will allow me to write more posts, linking this one as background. Because it’s so important, I’ve been waiting for the right time to write it. Sometime like now, when I’m fed, tea-caffeinated, motivated, and have a few hours with no anticipated distractions.
Expected Value, or EV, is the fundamental building block of decision-making. If you don’t understand it, whether by name or not, you are not making optimal decisions. If you do understand it, at least you stand a chance.
EV is a term that describes the mathematically predicted outcome of an action. The EV of you finding a dollar on the ground is one dollar. Whenever you find a dollar on the ground, you gain one dollar, so that’s the value of that event.
Let’s say that you and I are going to flip a coin. If it’s heads, nothing happens. If it’s tails, you give me a dollar. The expected value for you is negative fifty cents because half the time nothing will happen, and half the time you’ll lose a dollar.
It’s important to note that the expected value may never actually be possible to realize in a single event. Even though the EV to you is negative fifty cents, you’ll never actually lose fifty cents.
Deciding the EV of mathematical events is pretty easy. The EV of buying a $1 lottery ticket is roughly negative fifty cents (because the state keeps 50% and distributes the rest to winners). If you’re playing basketball and have a 2/3 chance of hitting a three-pointer, your EV is plus two points.
It’s easy to see how comparing these numbers could be used to make decisions. If you could go for a two pointer, and have a 99% chance of getting it, that EV (.99 x 2 = 1.98) is still less than going for the three pointer (.667 * 3 = 2), even though you might miss.
However, sometimes the EV can be abstracted. Let’s say you’re down to the buzzer and have one shot left. You’re down by one point. Now the EV could be expressed as 99% chance of winning with the two-point shot and 66.6% with the three-point. So even though the EV, when expressed in points, is lower for the two-pointer, it’s better when measured in what actually matters: winning the game.
Calculating EV for abstract outcomes is a lot more difficult, but equally important. To some degree, we all do it all the time. Let’s say you could hang out with Adam or Barbara. You consistently have a better time with Adam, so your EV is higher hanging out with him.
That’s a simple example, but life is full of more complex ones. Here’s a real-life example I went through last week:
I had purchased a $500 ticket that would bring me to Dubai and Delhi. After a nine-week twice-around-the-globe trip, I was burnt out on seeing new places and was starting to feel like I was just going through the motions. If I stayed in San Francisco I could spend more time with my friends, who I had missed, and take a weekend trip to the Northeast to see family.
If I canceled the Dubai/Delhi trip, I would get $160 of my fare back, plus I wouldn’t have to spend approximately $350 in taxis and hotels. I would buy plane tickets and use points ti visit family for a total value of $400. So, financially, my EV is +$110 for staying back.
You’ll notice that I disregard entirely the non-refundable $340 that I spent on the plane ticket. Most people would feel as thought they have to go on the trip because they spent that money, but it’s actually irrelevant to the calculation of EV. That money is spent now whether I go or not.
So financially it’s a small gain to stay back. So if I thought my enjoyment/productivity would be even across both trips, I should just stay back. But is it even?
I can be fairly sure that staying back and going on a short family trip is about an 8/10. That is to say that I will be happy, productive, and spend time with people I love, but that it’s unlikely to be a “Top 5” moment of my life.
I thought going on the trip was most likely to be a 7/10 with about a 15% chance of being a 10/10. That’s because I know that when I travel alone, especially when I’m behind on work, I tend to hole up in my hostel or hotel. I’d seen so many incredible things in the past weeks (Petra, Great Pyramids, Hong Kong), that even seeing the Burj, life in India, and the Taj Mahal was unlikely to impact me in a huge way.
But there’s still that fifteen percent to account for me not really knowing what would happen if I went. Maybe I’d meet great people, have an unexpected adventure, or be brought to tears by the majesty of the Taj Mahal.
Roughly averaging, I put the value of each course about even. Coupled with the $110, the scales tipped towards staying back. So I canceled my ticket and made new plans. And, of course, the end-of-game basketball scenario affected my decision as well. I needed to get work done and catch up, and didn’t really need to see more amazing things. So maybe the EV in those terms was even more in favor of staying.
The practice of thinking in terms of EV is extraordinarily valuable. It makes some otherwise murky decisions very black and white. It helps overcome fear. It allows you to discuss decisions with others and figure out why you disagree. Often it boils down to valuing certain factors differently, which is a productive conversation to have.
Sometimes it feels like comparing apples to oranges. What’s the EV of eating a meal at home vs skipping dinner and picking a friend up at the airport? That’s hard to calculate, but going through the motions and trying is worth doing. Eventually you get pretty good at knowing what various outcomes are worth to you, and this helps you understand what you really value in life. Using EV to make decisions helps you get more of whatever that happens to be.
Photo is a monkey in Japan who has obviously calculated the EV on eating some wires.