## What the Luck? : The Surprising Role of Chance in Our Everyday Lives – Gary Smith

**Thoughts:** A book about regression to the mean. Generally enjoyable, and I have a better understanding now of what regression to the mean is, why it happens, and where and when it is important. It was a bit repetitive at times: “And here’s a graph illustrating an example from a *different* sport!” *Right, the points don’t lie along the x=y line… looks like another example of regression to the mean…* “…and watch closely now as I switch the axes…” *Cool, you printed another graph of the same data, that* still *looks like regression to the mean…*

If you’re not familiar with regression to the mean, it’s an important concept, and this book is a fun and approachable introduction to the idea. Just maybe skim the second half.

(The notes below are not a summary of the book, but rather raw notes - whatever I thought, at the time, might be worth remembering.)

Smith, Gary. 2016. *What the Luck? : The Surprising Role of Chance in Our Everyday Lives*. Overlook Press.

### Epigraph

“There are a few statistical fact more interesting than regression to the mean for two reasons. First, people encounter it almost every day of their lives. Second, almost nobody understands it. The coupling of these two reasons makes regression to the mean one of the most fundamental sources of error in human judgment.” -Anonymous

## I. Overreaction

### 1: The Law of Small Numbers

## II. Inherited Traits

### 2: The Father of Regression

### 3: Choose Your Parents Carefully

## III. Education

### 4: Testing 1, 2, 3

- 35: “The score on any single test is an imperfect measure of ability.… Luck is endemic whenever a test is used to measure a persons aptitude. ¶ We observe scores, not ability.”

### 5: The Beatings Will Continue Until Morale Improves

- 50: Kelley’s equation, which can be used to correct for regression:
- estimated ability = R(performance) + (1 - R)(average group performance)
- where R is the reliability of a test, i.e. the degree to which scores on repeated tests are correlated

- 51: or, stated in Bayesian terms:
- posterior estimate of ability = R(score) + (1 - R)(prior estimate of ability)

- estimated ability = R(performance) + (1 - R)(average group performance)

### 6: Money for Nothing

### 7: Learning and Unlearning

- 74: For a while, there was a proposed program of affirmative action called Strivers, where a college applicant’s SAT score would be compared to their “expected” SAT score based on a bunch of metrics related to poverty during their childhood, other indicators of socioeconomic status, and so on. The argument was that a student with an expected score of 800 who actually scored 1000 should have their score adjusted to 1200, and we should thus expect them to be more likely to succeed than a student who scored 1000 when they were predicted to score 1000. Smith points out that, due to regression to the mean, a student who exceeded their expected score is likely to have
*lower*ability than other students who achieved the same score (and if they were admitted, would be consigned to struggle through their studies, surrounded by a group of more-able peers).

## IV. Games of Chance

### 8: Hopes and Excuses

## V. Sports

### 9: Champions Choke

### 10: Jinxes, Slumps, and Superstitions

### 11: Being Smart About It

## VI. Health

### 12: Take Two Aspirin

### 13: The Tin Standard

## VII. Business

### 14: The Triumph of Mediocrity

### 15: From Bad to Better and Great to Good

- 197: “the real lesson from the enduring popularity of such advice [that we should emulate the practices of businesses that improve over time and eschew those practices used by businesses that become less successful] is that the authors who write these books and the people who buy them do not realize that the books are fundamentally flawed. This problem plagues the entire genre of books on formulas/secrets/recipes for a successful business, a lasting marriage, living to be 100, so on, and so forth, that are based on backward-looking studies of successful businesses, marriages, and lives.”
- i.e. since the very best businesses/marriages/lives at a given moment tend to be those that are doing the right things but also have a bit of luck on their side, these will be the ones which are likely to get worse over time. The inverse is true of the very worst, which are likely to see their prospects improve in spite of doing things that tend not to lead to success, as their transitory bad luck passes.

### 16: Draft Picks, CEOs, and Soul Mates

- 224: “[The fact that people who initially seem to be excellent are likely to regress to the mean] should not mean that we shouldn’t choose those who appear to be the best. What it does mean is that we should be prepared for the likelihood that they are not as great as they initially appear to be.”
- “the general principle is that things that seem to be far above or below average probably
*are*above or below average, but not as far from average as they seem.”

- “the general principle is that things that seem to be far above or below average probably

## VIII. Forecasting

### 17: A Better Crystal Ball

## IX. Investing

### 18: $100 Bills on the Sidewalk

## X: Conclusion

### 19: Living With Regression

Posted: Jul 24, 2022. Last updated: Jul 24, 2022.