In most aspects of the world, we are trying to improve our expected value (E.V) of love, happiness, money, time, and etcetera. Companies operate on this principle. They always try to increase expected value of their business, customers, or employees. Yet, we don’t frame our personal lives or careers as maximization of E.V. I recently have reframed my decision making to include a sort of E.V analysis, and it’s a helpful heuristic.
So, what is the expected value of any decision?
At first, a naïve approach would be to take the weighted average of success and failure, where failure is always a negative.
E.V = (Probability of Success x Reward) - (Probability of Failure x Cost)
But even in the event of failure, there is always some reward. It might be more skills, insights, decision making prowess, relationship. There is always something. So, E.V looks something more like this. The cost of failure is not as great as it seems. Even in success, there is some cost of energy, and sacrifices.
E.V = [Probability of Success x (Reward - Energy)] – [Probability of Failure x (Cost – Learning)]
There is one key component missing. How do you figure out all the unknowns? What is success, probability of success, reward of success, and cost of failure. How you determine what is a reward? It depends on what you value—love, happiness, money, etc. No one truly knows the probability of success, so it’s a guess based on how risk taking or averse you are. I can’t answer any of those questions for you because it’s a personal choice.
This is how I think about it.
Let me illustrate a difficult decision that I had to make last year. I had two options. First, I could take a PhD offer at several top 5 universities and becoming an academic. Or I leave academia and start a career in technology. At that time, I didn’t break down the decision in a sort of E.V analysis, but I wish I did. It would have saved me a lot of sleep.
So, let’s calculate the E.V of if I did do a PhD. Up till that point, I developed some considerable skill in research, so my probability of success is high. Let’s say it would have been 90% (failure is then 10%). Now, we measure reward, cost, and learning the following scales.
Notably, I derive a lot of happiness by making an impact in both the world, my career, and personal life, so I measure reward by the happiness I get from it. It doesn’t take much for me to be happy
Reward
1- Sad- Not making any impact in personal life, company, and world
2- Happy- making impact in personal life
3- Super Happy– making impact in personal life, career
4- Extremely Happy– making impact in personal life, career, world
5- Enlightenment- allowing others to achieve their potential in life, career, and world
For me, I measure most cost in time, as opportunity cost of learning and impact elsewhere. This is my personal scale. I value growth and learning a lot (different strokes for different folks).
Cost
0- Time spent but I’m gaining skills and making the most impact I can.
1- Time spent but I’m gaining skills, but I can make most impact elsewhere
2- Time spent where I did not grow
3- Time spent where my skills wane
I see energy spent in success and learning in failure as binary. I’m either gaining energy from what I am doing or losing it. Similarly, I’m either learning what I want or not. It is that simple.
Internal Energy Cost
0- My work is giving me energy
1- My work is draining energy
Learning
0- I’m learning but not what I want
2- I’m learning what I want
Back to calculation, there is 90% chance of success and 10% chance of failure. The reward of PhD to me is the ability to research, which I gain some personal pleasure and the lifestyle is relaxing, giving me a lot of personal time. However, I don’t want to be an academic regardless of how good I was. So, the reward would have been a 2 and my energy would be draining, a 2. The cost meanwhile would have been a 1 because I would have been learning but I would always be looking outward, thinking I could have done more. Although I enjoyed learning Biophysics at Penn, I became bored of it. Personally, it was application of computers, which I always had lifelong interest in. So, learning, for me, would have been 0.
Thus, the EV = [.9 x (2 – 1)] – [.1 x (2-0)] = .7.
Now let’s compute this for starting a career in technology, specifically startups. The chance of success for any random technology startup is roughly 5% at the founder stage. An early employee with a good eye can choose to work at a great startup. This likely increases the probability of success to 25%. If a startup is successful, it will birth a new product or service to world providing immense value, while I personally be growing my career there. At a startup, I would be making that impact and growing personally and professionally, so it would be a 4. The executives of company can reach a 5 because they help others achieve their potential. I’m motivated to learn about technology, so my work will give me energy. I’m doing it anyways—the internal energy cost is 0. The cost is either a 0 or 1 because it’s very company dependent, so let say 1 to be conservative. I would be learning what I want so that’s a 2.
Thus, the EV = [.9 x (4 – 0)] – [.1 x (2-1)] = 3.5!