Making the right decision, in business and in life, is the most important thing you can do. Wrong decisions can haunt you your entire life while the right decision can mean making your company worth billions, years of happiness, etc. Imagine if Travis Kalanick, CEO of Uber, had decided to focus on connecting buses with passengers and not taxis, or if Trip Hawkins would have focused 3DO on creating software and not a hardware platform. Understanding Bayes’ Theorem (also known as Bayes’ Rule, two terms I will use interchangeably) increases the chance you use data the right way to make your decisions.
This post is the first in a series I will be writing on Bayes’ Rule. This post and most of the background I discuss is based on the best book I have found about Bayes’ Rule, A Tutorial to Bayesian Analysis by James Stone. Last year, I wrote several posts on Lifetime Value (LTV), given how crucial it is to the success of any business, from the newest technology to the oldest brick and mortar enterprise. This year, we will be tackling Bayes’ Theorem. As you will see in the next few posts, by understanding Bayes’ Theorem you can then make optimal decisions about what games or projects to green light, how to staff your company, what to invest in, which technology to use, who to sell your company to, what areas of your company need to be fixed/improved, etc. Bayes’ Theorem is the single most important rule for good decision-making, both in your professional and business life.
What is Bayes’ Theorem?
Bayes’ Theorem is a rigorous method for interpreting evidence in the context of previous experience or knowledge. Bayes’ Theorem transforms the probabilities that look useful (but are often not), into probabilities that are useful. It is important to note that it is not a matter of conjecture; by definition a theorem is a mathematical statement has been proven true. Denying Bayes’ Theorem is like denying the theory of relativity.
Some examples of Bayes’ Rule
The best way to understand Bayes’ Rule is by example (I will touch on the math later). Again, much of this is based on Stone’s tutorial on Bayesian analysis. First, look at probability as the informal notion based on the frequency with which particular events occur. If a bag has 100 M&Ms, and 60 are green and 40 are red, the probability of reaching into the bag and grabbing a green M&M is the same proportion as green M&Ms in the bag (i.e., 60/100=0.6). From this, it follows that any event can adopt a value between zero and one, with zero meaning it definitely will not occur and one that it definitely will occur. Thus, given a series of mutually exclusive events, such as the outcome of choosing an M&M, the probabilities of those events must add up to one. Continue reading