Many people were shocked after Donald Trump won the United States presidential elections of 2016. They were fooled by false sense of security, supported by many mainstream poll and prediction sites forecasting Hillary Clinton to win. But how could the pollsters be so wrong? And how is it possible to improve future predictions? These are some of the questions, the book The Signal and the Noise wants to answer.

The book is written by Nate Silver, an American statistician and blogger. His repertoire consists of the analysis and prediction of events from different topics, foremost sports and politics. His younger self was bored from his consultant job at KPMG and much more interested in sports and online poker. He created PECOTA, a statistical system that projects the future performance of baseball players. Additionally, he won a lot of money through playing online poker, enough to quit his consultant job and start his own website, which later evolved into the famous FiveThirtyEight.com.

For Silver, the reason why so many predictions fail is because people confuse the signal (what is the truth or what we actually want to predict) with the noise (what distracts us from the truth). By eliminating as much noise as possible while finding the true signal, our predictions about the future will become better. This can improve our overall well-being because predictions influence our everyday lives.

A classic example of the signal vs. noise dilemma is the confusion between correlation and causality. From the first modern Super Bowl in 1967 to the 31^{st} in 1997, the stock market gained an average of 14% for the rest of the year when a team from the National Football League (NFL) won the game. Moreover, it lost 10% whenever a team from the American Football League (AFL) won. Does this correlation imply a causality between the trend of the stock market and the league, the winning team was from? Not really, it was just a coincidence and the indicator began to form badly since 1998.

Nate Silver argues that an analysis of Bayes’s theorem (and also his way of thinking) can improve one’s ability to predict events. Thomas Bayes was an English minister that lived in the 18^{th} century. In his view, humans learn about the universe (and everything in it) through approximations, which get us closer and closer to the truth. To do so, humans have to admit that they are imperfect. Bayes’s theorem was actually established by French mathematician Pierre-Simon Laplace, who expressed Bayes’s thoughts in a mathematical formula. At its core, the theorem deals with conditional probability. It can tell us the probability that a prediction (or hypothesis) is true if some event has happened. It needs a prior probability (x), a new event with the probability that this supports (y) and denies (z) the initial prediction and a formula (xy/xy+z(1-x)) to calculate the posterior probability. Bayes’s theorem implies two core things. First, one should not think deterministic (yes/no) about an event to happen but in a probabilistic way. Second, if an event somehow related to the prediction happens, this does not automatically prove or deny the hypothesis, but increases or decreases its forecasting potential. Over time and with more evidence to evaluate, this method should guarantee that different beliefs converge towards the truth.

In the authors view, this way of thinking helps us to be less subjective, less irrational and less wrong. People should be more willingly to question their own beliefs and ideas. To do so, there is no way around testing a lot of hypotheses and making a lot of predictions. Furthermore, the theorem should help becoming disciplined about how to weigh new information and not to “overhype” it.

The Signal and the Noise is easy to read and well written. Nate Silver is able to explain complex matters in a simple way. The book includes some graphs and formulas, which might be too much for readers with a fear of mathematics. A lot of topics are discussed, ranging from politics to economics, natural disasters, online poker and sports. Although this is a great variety, it can also be overwhelming at times.

Silver, Nate (2012): The Signal and the Noise: Why Most Predictions Fail – But Some Don’t, Penguin, New York.