4 Lessons from The Signal and The Noise | Nate Silver

How to Think Like a Statistician and Make Better Predictions

Jack Yang
5 min readOct 18, 2020
The Signal and the Noise: Why So Many Predictions Fail-but Some Don’t


I picked up this book because I heard about the author, Nate Silver, from his website FiveThirtyEight.com. It is a website that makes predictions on sports, science, politics, etc. I learned about this website as the election season is coming up and I was looking for some reliable insights on how it could turn out. After reading some of the factors and mindsets that are taken into account in making such a prediction, I was intrigued by Silver’s mental models and eventually landed on this book. The book talks about common mistakes that people make, how to make better predictions, as well as some case studies on how the theories can be applied. Overall, I enjoyed this book since it allows me to see my flaws when it comes to predicting and it offers insights on some areas I am very interested in, such as stocks and weather forecasts.

Score: 4.5/5

Who Should Read It: People are want to make more rational and reliable predictions in life


1. Think Probabilistic

Think probabilistic means to think in terms of probability, but how exactly can you do that? The author offers a well-known formula called Bayes Theorem as the ultimate guide to making probabilities guesses.

Bayes Theorem

The formula itself may seem very daunting at first, but it can be broken down into several key components. The left side of the function is the probability of an event happening given another event. The right side is the calculation of that probability. Two pieces really stand out here: the probability of this event happens before and the amount of evidence.

We can take three examples to illustrate this case. The first one is when the probability of an event happening before is too high. For example, the sun has risen every day for the past millions of years, as far as humans can document, since the prior probability so high, we can be near certain that the sun will rise tomorrow as well. The second case is when there is a fair amount of evidence as well as a prior probability. Let’s say you are not sure if you are lactose intolerant. You only drank milk a hundred times in your life and your stomach is sick after drinking about half of the time. There isn’t a piece of overwhelming evidence as to whether you are lactose intolerant. You can predict the probability your stomach will be upset after drinking your next cup of milk is the same as flipping a coin. The third example is when the evidence is too strong. Let’s go back to the milk problem. If your doctor has performed a series of testing and determined you are lactose intolerant. Even though you have not taken a single sip of milk in your life, you can be very sure that the next sip you take will cause a stomach.

To summarize, even though it is nearly impossible to make every decision in your day to day life with Bayes Theorem, you should consider the important ones in such a manner to help you have a better understanding of the potential outcomes.

2. Constantly Update Your Prediction

This is another important factor when it comes to making better predictions. This is also where the magic of Bayes Theorem lies. As new information comes in, such as an update on prior probability or a new piece of evidence, you should go back to the formula and adjust the parameters accordingly so that the output is better informed and more reliable. Let’s use an absurd example to illustrate this point. Since I have been living in Wisconsin for a while, it is only right to use my milk example again. Say you have not drunk milk before nor have you been tested by a doctor on your lactose tolerance, you decide to give the milk a try one day. For now, you have a zero percent chance of getting sick because there is no sample to draw from, but when you drink your first sip of milk, your stomach suddenly gets very sick. If you update your prediction, the probability suddenly rises to 100%. You are not truly convinced yet, so you over the next few days you drank some more, and every time it resulted in a stomach. Therefore, you updated the probability, your likelihood of being lactose intolerant is 100%. However, if you do not update your prediction since the beginning, you still believe you have 0% chance of getting sick and therefore keep drinking milk, you will most likely get yourself into big trouble. In another word, it is critically important to constantly update your worldview and your prediction with the influx of new knowledge.

3. Humans And Computers are Better Predictors When Working Together

Computers have been a powerful component of prediction-making thanks to its capability to process a large amount of information at a speed that humans cannot fathom. However, it is just a tool when it comes to making such predictions because humans control the input information as well as understand the lessons from the data. Computers are incredible at finding solutions and would sometimes find relationships that are purely caused by luck. On the other hand, humans are more visual and seeing the whole picture. It is therefore important for humans to take results generated by computers with a grain of salt instead of treating them as definitive answers.

4. Mistakes That People Make When Making Predictions

  • Quantify Uncertainty: Risk can be calculated but uncertainty is risks that cannot be calculated. It is important to be able to differentiate the two, or it will lead to disastrous consequences (ex. people try to quantify uncertainty and eventually caused 2008 Financial Crash)
  • Out of Sample Problem: When an event has never occurred before, and you cannot create a reliable prediction. Sometimes people draw prediction from similar scenarios, but they are not usually the same thing (ex. you never drink and drive before, so you think you will before since you drove consciously before and never had an accident)
  • Categorize Probabilities: People like to categorize things into smaller sections because it helps to get a more organized view. However, people overlook cases or outliers that do not particularly fit the current categories well.
  • Overfitting: This is when people treat noise as signals. However, it is a difficult problem to address especially if there is only a small amount of data available.
  • Overconfidence: People, especially stock analysts, tend to be very proud of complicated formulas because it makes them seem intelligent and sophisticated. However, many of the elaborate models are better at predicting history, meaning to fit past data well, then at predicting future events.
  • Self-cancellation: The opposite of self-fulfilling prophecy. For example, when everyone is using the route with the least traffic, the route becomes the most traffic instead.
  • Mistaken Relationships Between Data: there are many potential relationships between data, sometimes the relationship might just be purely random.
  • Treat Improbable as Impossible: People often treat the unthinkable (9/11) as impossible when it comes to prediction. It is important to consider all potential aspects of an event.