Regression To The Mean

Regression to the mean is not some magical force that forces everyone to become mediocre over time. It’s simply the observation that where luck is a component of outcomes, extreme results tend to have a high luck component. Stephen Hsu has a good post on this. Here’s my attempt to rephrase what he said:

Suppose you have a trait that is the sum of 2 random variables with the exact same distribution e.g X = A + B where A and B are both normal distribution with std=15, mean=100.

Suppose X = 230. Then it’s much more likely that A and B were both 115, than that either A=130, B=100 or A=100, B=130, since in a normal distribution there are way more people in the 115 range than in the 130 range. EDIT: Actually the argument is that ON AVERAGE the figures will be 115, 115 since we have a range of values from 100,130 to 130,100.

Now, let’s call A the stable factor and call B luck. Luck averages at 100 and is not heritable, but A is. A does not change over the generations, whereas B fluctuates. (A could also be skill in certain games where both luck and skill are involved).

If we had gotten a bunch of these X=130 people, we would expect that most of them had pretty good luck as well as good A. So we’d expect their A to be centered around 115. Now over the generations, luck has a mean of 100 but A has a mean of 115, so we have an average X of 115+100 = 215.

Now, I’m not saying I know how height works, but we see regression to the mean there. A pair of abnormally tall parents will tend to have children who are shorter than themselves since a portion of what made them so tall was just abnormally good luck, which is not heritable. ALSO works in the reverse direction, so if you take a person who is abnormally tall, it is likely that his parents were less tall than he is, since he is most likely tall due to extremely good luck which his parents are unlikely to also have.

Since height is partly heritable, if you grabbed a bunch of very tall people from the general population and formed a new population, it’s likely that the new population would have a much higher average genetic height potential than the general population. Reversion to the mean would happen only for the first generation as the “luck” contribution to the first generation’s extreme height disappears in the 2nd generation, but the population retains the genetic height potential so the population height average remains the same from the 2nd generation onwards, at a new average which is higher than the general population.

Did I get something wrong? Please leave a comment.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s