Question

A. Explain the Law of Small Numbers.
B. Explain how the Law of Small Numbers is relevant for investing.
C. Explain how the law of small numbers impacts other aspects of life.

Answer 1

A.

The law of small numbers is the name economists give to a very common mistake people make when it comes to making predictions or gauging probability. Judgmental bias which occurs when it is assumed that the characteristics of a sample population can be estimated from a small number of observations or data points. It is a cognitive bias where people show a tendency to believe that a relatively small number of observations will closely reflect the general population.
The simplest example of it is when we toss a coin. Every time we toss a coin there is a 50% chance that it will land on a head, and a 50% chance it will land on a tail. However, if we get a run of, say, five straight heads, we might start to feel as if the next time we toss the coin there will be a higher probability of it being a tail. This would be wrong because the outcome of each toss of the coin has no bearing on the next one, so the odds of each toss are still 50/50.

B.

There are a number of ways in which the law of small numbers can bias our investing decisions.

The Gambler’s Fallacy

The gambler’s fallacy describes how gamblers might expect, for instance, a number that hasn’t come up on the lottery or on a roulette wheel for a while to be ‘due’. These people are effectively making the same mistake that’s highlighted by the coin-toss example, but on a larger scale: their brain is telling them that they’re dealing with a finite pot of numbers that aren’t replaced once they’re picked. But actually, all numbers are available with every spin of the roulette wheel.

As with other biases, an interesting theory of why our brains do this looks to our evolutionary past. It might have been beneficial to expect that a series of common outcomes would be broken at some point: for example, the hunter who believes their luck will turn around after a series of failures is much more likely to eat than the hunter who gives up.

The Hot-Hand Effect

While in some cases the law of small numbers causes people to underestimate the chances of a particular outcome (as with the likelihood of seeing a run of five heads in the coin toss example), in others, it causes them to overestimate. Economists call this the ‘hot-hand effect’. The name comes from basketball and the mistaken belief among fans and players that the chance of a player hitting a shot is greater following a hit on the previous shot, than a miss. It’s as if they believe the player is ‘on a roll’ or ‘in the zone’ and that success will breed more success.

So how do these phenomena translate to the everyday way that we approach investing? The gambler’s fallacy and the hot hand effect can be spotted regularly by financial advisers in the behavior of their clients.

For example, if stock markets go up for a period, as they have done recently, some investors fear that at any minute everything is going to go into reverse. They announce they are not investing anymore as the market is sure to plummet any day now. This could be seen as an example of the gambler’s fallacy – if the stock market has gone up for a while, a fall must be due. If we compare the rising stock market example to how we think about house prices, we get a totally different reaction. When house prices go up, people say they are going to invest in property as it’s a safe bet because prices always go up and they see no reason why this won’t continue – this is the hot-hand effect.

C.

Law of small numbers is an erroneous belief that people have in daily life that if something happens regularly for over a period of time, something opposite will happen soon in the near future.

As every parent knows only too well, newborn infants specialize in what psychologists refer to as “magical thinking”. In other words, we magically expect that a mummy or a daddy will automatically bring us milk and biscuits, or will cuddle us, or change our nappies, just as they did yesterday, and the day before that. Great parents will gratify this magical thinking in infants and will respond to the baby’s needs in the most desirous way.