The Wayward Axolotl

There is a lot of confusion over the concept of regression to the mean, so I thought I would try to explain what it is, and what it isn't. Let's start with a very simple example. Suppose you have 10 6-sided dice. Assume that these dice are all fair, so that the expected value on any given roll is 3.5. You roll each die once. Then you select the 5 dice that rolled the highest and set them aside. Probably the average of the top 5 dice is higher than 3.5, simply because you selected the highest rollers. Now roll those 5 dice a second time. Probably the average of the second roll is lower than the first: something closer to 3.5. That is regression to the mean. If you select a sample based on the measurement of a random variable X, the value of X within the sample is a biased estimator of X. Future measurements of X will tend to "regress" to the mean of X. No physical process is involved in this. It is simply the removal of sample bias by a second measurement or experime

This is an excerpt from a book that I am writing. I am sitting in a coffee shop in Seattle, Washington. A few minutes ago, something amazing happened. I walked up to the counter, made eye contact with the pretty girl behind it, and said “Medium drip coffee, please”. She took my money, said “Thank you”, and gave me back some change. Then she asked me “Do you want room for cream?”. I said “Yes”. She poured coffee into a cup and handed it to me. I said “Thank you”. Then I found a table, sat down, and began to write. As I have just described it, the event was not remarkable at all. It was just a little slice of ordinary life. Behind that simple description, however, there lies an enormous amount of complexity. Once you start unraveling that complexity, it seems amazing that such an event could take place. For some reason, my brain generated the intention to buy a cup of coffee. That intention was selected from an almost infinite number of possibilities. Somehow, I knew that I coul