Base rates refer to the underlying probability of an event or category. For example, if 1% of the population has a particular disease, then the base rate of having the disease is 1%. When making predictions or judgements about individual cases, we often neglect base rates and instead focus on specific information about the case, even if that information is unreliable or uninformative. This can lead to significant errors, as we fail to consider the underlying probability of the event.

Section: 2, Chapter: 14

Author: Daniel Kahneman

There are two types of base rate information, and they are treated differently by our minds:

Statistical Base Rates: These are facts about the overall population or category, such as the percentage of people who have a college degree. We tend to underweight or ignore statistical base rates when specific information about an individual case is available.

Causal Base Rates: These are facts that have a direct causal bearing on the individual case. For example, if you learn that a student attends a highly selective university, this information has a causal influence on your judgement of the student's academic abilities. Causal base rates are treated as information about the individual case and are readily combined with other case-specific information

Section: 2, Chapter: 16

Author: Daniel Kahneman

Pascal introduced the concept of mathematical expectation, which calculates the average outcome of a random process if it were repeated many times. This idea is crucial in decision theory and game theory. Pascal applied it to his famous "wager" about belief in God, arguing that the potential infinite gain of believing outweighs any finite cost. In modern times, expectation is used in various fields, from insurance to gambling, to quantify the likely outcome of uncertain events. Understanding expectation can help in making rational decisions under uncertainty.

Section: 1, Chapter: 4

Author: Leonard Mlodinow

Chapter 3 presents a method for empirically placing activities on the skill-luck continuum, using three statistics:

1. Demonstrated consistency of outcomes across repeated trials (e.g. year-to-year correlation of batting averages)
2. The distribution of success among the population of participants (e.g. number of players hitting above .300)
3. The ability of a measure to predict future performance (e.g. correlation of on-base percentage to future runs scored) Using these measures, we can estimate the relative contribution of skill and luck in different domains.

Section: 1, Chapter: 3

Author: Michael Mauboussin

• Basketball statistics show high year-to-year correlations, a dispersed distribution of success, and strong predictive power - indicating a strong role for skill
• Hockey statistics show lower consistency, a more concentrated success distribution, and less predictive power - indicating a larger role for luck These statistical tools give us an objective way to assess the skill-luck balance in different domains and make better predictions.

Section: 1, Chapter: 3

Author: Michael Mauboussin

Mauboussin examines the surprising statistical regularities that show up across many domains of human performance. The key finding is that many performance metrics follow a power law distribution, wherein:

• A small number of top performers account for a disproportionate share of the total output
• The gap between the best and the rest is much larger than a normal distribution would predict.

For Example:

• City sizes (a few mega-cities, many small towns)
• Wealth distribution (a few billionaires, many people of modest means)
• Bestseller lists (a few blockbuster hits, many low-selling titles)
• Scientific citations (a few papers with massive impact, many rarely-cited papers)

The power law pattern arises from the complex social dynamics that shape success in these domains - in particular, the rich-get-richer effects of cumulative advantage.

Section: 1, Chapter: 6

Author: Michael Mauboussin

Imagine you're considering two slot machines to play at a casino. For machine A, you watch a dozen people play and 4 of them win. For machine B, you have no information. Which should you choose?

Most people avoid uncertainty and pick machine A. But rationally, machine B is more likely to pay off. Even though you have no data, the chances it pays off more than 33% are better than the chances it pays off less.

This is a direct implication of Laplace's Law: if you have no prior information, the probability of a positive outcome is (k+1)/(n+2) where k is the number of positive outcomes observed out of n attempts. For machine A, that's (4+1)/(12+2) = 36%. For machine B it's (0+1)/(0+2) = 50%.

Human attention, and media coverage, is drawn to the vivid and available, not the representative. This selective attention means that more media coverage of an event indicates that it's more rare, not necessarily more common. To be a good Bayesian, look for the silent evidence as much as the headline grabbing stories. Often what you haven't seen is as informative as what you have.

Section: 1, Chapter: 6

Author: Brian Christian

Suppose you arrive in a new city and see a long line outside a restaurant. Knowing nothing else, what does that tell you about the restaurant's quality?

According to Bayes's Rule, long lines are more likely to form for good restaurants than bad ones. Even with no other information, the line is evidence of quality. The longer the line, the better the restaurant is likely to be.

But now imagine you go into the restaurant and have a terrible meal. What should you believe now - your own experience or the line of people waiting? Again, Bayes's Rule says to weigh the evidence based on sample size. A single bad meal is a small sample. The long line reflects dozens of people's opinions. It should still dominate your judgment.

The same idea applies to product reviews, survey results, or any wisdom of the crowd. If your own experience contradicts the majority, trust the majority. Your own sample size is too small to outweigh the group. First impressions can lead you astray.

Section: 1, Chapter: 6

Author: Brian Christian