Reversion to the mean

Learning Goal: I’m working on a political science question and need an explanation and answer to help me learn.

Read the chapter 8, and answer the exercise after the chapter, which is exercise 81, 8.2, 8.3.

1. Early on in every baseball season, someone appears to be on pace to break the home-run record, but they almost never do. Let’s think about why.Suppose you hit a phenomenal number of home runs in the first 20 games of theseason, and you’re on pace to break the record.
   1. (a) In the next 20 games, are you more likely to hit an above average or belowaverage number of home runs? Why?
   2. (b) In the next 20 games, are you likely to hit fewer home runs, the same number ofhome runs, or more home runs than you hit in the first 20 games? Why?
   3. (c) A commentator notices that players on pace after the first 20 games almost neverbreak the record. The commentator argues that this shows that players lose theirnerve when they start thinking about setting the record. What data might youwant to collect, and how might you want to analyze it in order to see if thisinterpretation is right?
2. Anthony once took a course from a famous econometrician who made the followingargument: Paul’s son John has a genius-level IQ. Therefore, because of mean reversion,Paul himself must have had a super-genius-level IQ.
   1. (a) What’s wrong with the econometrician’s reasoning? If you had to guess, is Paul’sIQ lower or higher than average? Is it lower or higher than John’s?
   2. (b) How would your answer change if we told you that the Paul in this exampleis Paul Samuelson, a Nobel Prize winner considered by many to the foremostacademic economist of the 20th century?
3. At the time of this writing, the stock price of Zoom (a company specializing in onlinevideo conferencing with which many of us became all too familiar in the year 2020) hasjust fallen by about 18% in response to Joe Biden winning the 2020 U.S. presidentialelection and the release of promising results on COVID-19 vaccines. Because of meanreversion, your friend argues that now would be a great time to buy Zoom stock.
   1. (a) Explain to your friend, in layman’s terms, what’s wrong with their reasoning.
   2. (b) Without knowing any additional details except that Zoom stock recently fell,would you expect your friend to make money, lose money, or break even on thisinvestment?