Sir Francis Galton, a British polymath, did pioneering work on Regression or Reversion to the Mean in Statistical Research in the late 19th Century. According to his analysis of human characteristics, he applied statistical methods to the study of human differences and inheritance of intelligence and pioneered the work on Eugenics. He also contributed to the field of psychology by founding psychometrics with personality mapping.
He was a versatile genius and being the half-cousin to Charles Darwin, his works in many ways drew sufficient inspiration from Darwin's studies. But his most outstanding contribution is Regression to the Mean in Statistical analysis. He is also considered to have developed a central limit theorem showing that with sufficient sample size the binomial distribution approximates a Normal Distribution and the practical demonstration of it is called Galton Board or Quincunx or Bean machine
Regression to the Mean is in simple terms that if there is volatility observed over the mean, over a while the values will show Regression to the Mean/Average and Francis Galton termed it as Regression to the Mediocrity in terms of inherited human characteristics. This led to modern statistical modeling based on linear regression analysis.
Regression to the Mean is also important to understand the stock market behaviour. Stock market behaviour is considered to be a Random walk and the financial world which considers a normal world will always look for stable returns. Jeremy Siegel said that "return to the mean" may show that returns may be unstable in the short term but stable in the long run. In such a situation the returns can be easily quantified and not a Random walk. But the stock market exhibits typical Random Walk characteristics. A Random Walk is one in which future steps or directions cannot be predicted based on past actions or performance. But Dalal street would hate to call its three-piece suit executives , who carry an air of super cat financial strategists, as "Random Walkers"!!(link). The central hypothesis of Random walk is that one cannot consistently outperform the market averages. In other words, even the best of financial strategies would eventually start regressing to the mean.
The law of averages which is a law of large numbers gives false belief and therefore it is called "Gamblers' fallacy". It leads to the misconception that the probability of an outcome occurs with a small number of consecutive experiments so they will have to "average out" sooner rather than later. This is the fallacy that rules the mind of every gambler and that is why it is called "gambler's fallacy". Stock market ups and downs can also lead to this kind of fallacy in the short term.
Dalal Street is a minefield for the uninitiated and a good playground for those who have an appetite for a long walk or for those lethargists who buy indexed bonds, sleepover them and don't go for a walk!!
