Expected Value: The True Currency of Life
In this article, I will be outlining a simple and elementary model for evaluating the overall productivity and value our lives, but before that, I will define some elementary statistics concepts.
A Quick Lesson On Statistics:
If you graduated high school, at some point you’ve come across the concept of expected value (EV). EV is the probability of an event happening multiplied by the sample size. What does this measure? In short: the payoff of an event given a specific number of trials. For example, if I roll a fair dice, wanting to land a 6, given 6 trials I should get at least 1 six. Of course this isn’t guaranteed to happen but as sample sizes increase (1/6) of my dice rolls will likely be 6’s.
If you roll a dice 100 times, you won’t always get exactly 17 sixes, but luckily, across well defined experiments we can predict the range in which our results will vary. This is what statisticians refer to as confidence intervals.
As we can see in this graph, the red line presents the actual performance of a result and the gray shadows exhibits the range of the predicted result. So expected value will tell us how an action performs in the ideal world, but variance will tell us where performance fluctuation might occur along the way.
An action that might have an extremely large payout in terms of expected value but, also comes with a large variance is high risk and high reward. This acton pays off extremely well but only across a large number of attempts. An action that might have a small payout in terms of expected value but has low variance is a safe and profitable decision. Now that we’ve defined these concepts. Let’s look at some real world examples. We can classify events and actions into four buckets: High EV High Variance, Low EV High Variance, Low EV Low Variance, and High EV Low Variance.
Low Reward High Risk:
When I was 16, for a brief period I dreamed of being a world famous EDM DJ. I idolized my role model Afrojack, who I would closely follow on the internet watching him perform on huge festival stages all around the world. In numerous interviews he would say “If you have passion for something and you follow that passion you will have success.” We hear this sort of stuff from massively successful people all the time. It sounds so great to hear, but their confirmation bias blinds them from seeing that they are a statistical anomaly in an event with extremely low expected value, but massive variance.
Most electronic music producers in the world spend hundreds of hours studying the technical aspects of music while churning out many tracks. The bulk of these artists scarcely make a salary that matches up to an average engineer. Even the moderatlely popular artists who are signing tours around the world and perform at world famous clubs often barely break even. Yes, world famous DJ’s will go on tours around the world and not even make money! The hope is that they can break into the high paying music festivals. Running their own tours is merely in investment into reaching that goal.
Similar concepts apply to wanting to be a famous actor, model, etc. The expected result of these careers is tiny but once every few million trials there is a massive payout due to high variance. This is a low reward high risk option. The expected value of these careers is essentially nothing, but every once in a while someone in the sample size gets launched to the top. Math can’t tell you whether you will succeed in these careers or not, that is up to a variety of factors but it is important for anyone who wants to pursue these paths to know the sort of risk they are taking on. I myself, have a few friends who variance has been very kind to.
Low Risk High Reward:
I come from a mixed race family. I’m half Indian and half white. There is a saying about Indian families. Parents look at their chldren at birth and wonder to themselves “Will he be a doctor, lawyer, or engineer?” This is a common string among immigrant families in foreign countries. This is because any one of those career paths are extremely low risk with high reward. The mean pay for an engineer is $101,790 with a 66% confidence interval that ranges from $77,000 to $130,000.
Successful lawyers on average will make six figures and the top performers make millions. So if you pursue any of these paths, put a considerable effort into achieving them, you safely have a comfortable livelihood even at the middle to bottom tiers of these careers. The expected value is massive and the variance is relatively low.
High Risk High Reward:
Careers with high expected payoff but large variance involve sales based careers, entrepreneurship, and investing. Across large sample sizes the payoff for these careers is generally good. Furthermore, terrible investors can experience insane upswings in their portfolios and stupid entrepreneurs can have insane business success (think about all the shitty products out there with market success). On the other side, the downswings for the top entrepreneurs, salesman and investors can be crushing.
The top performers can have years of loss despite being the best in their field. The difficult thing about High EV High Variance career paths is that variance masks skill. Idiots who bought bitcoin for fun years ago and made millions can suddenly get thrown in with the pioneers who saw a future in the currency. Timid individuals who sold off their crypto portfolio before the crash can seem far superior to smart people who stayed in the market but ran into bad luck. Only long term performance actually differentiates skill in these fields. The man who runs a moderatly successful business for 40 years is far more skilled than the man who runs into millions in 3 years but then goes bankrupt after 10. Why? Because only skill can normalize variance over time. Only skill can beat probability in the long run.
Thinking About Life in Terms of EV:
I like to think about life as a portfolio of activities, hobbies, and habits all of which have their own EV and variance. I like to hit the gym but regularly eat burgers and fries. The net outcome on my physique is a positive EV but there’s definitely some negative EV thrown in there from all that saturated fat. It’s perfectly fine to make a negative EV decision, we all do. But when we do, we should be careful to make negative EV choices with low variance.
We want to largely have positive EV components in our life. We want to mix up the variance to maximize reward. A balance of high EV low variance choices with some high EV high variance choices is ideal. Example: Having a stable career while investing intelligently.
The Drugs Example and Negative EV:
We all know that drinking alcohol and smoking pot brings a negative EV but the variance of these activities is pretty small. Everyone knows exactly what will happen when they do these drugs. Contrast that with crack, coke, meth, or LSD. You can range from having a high and a headache afterwards to literally dying.
Control Variables and Normalization:
Control variables change the game. If your father owns a multi-million dollar law firm and you choose to study law, you will out perform the expected value of your career. If you want to be a world famous musician and already have connections, you will quickly rise to the top.
Good Choices, Bad Results:
Sometimes making good choices in life will yield less than expected results. This is just variance. Sometimes you study like crazy for an exam and don’t ace it. Sometimes you don’t study and still ace it.
Sometimes making bad choices will be inconsequential. But eventually variance normalizes and EV is realized.