The law of small numbers

In my previous post I shared a few thoughts on probabilities and statistics.  I wrote about disregarding probabilities in decision making, ignoring small probabilities and not over-weighting small probabilities.

A tough act to follow.  I am totally guilty of failing at it.

Especially in view of all those solid statistics media, ‘advisors’, and the internet are presenting to me on a silver platter. on a silver platter

The only positive aspect here being the silver platter itself. That one is getting much more valuable in recent times.  Just check out the Silver Price Chart. But careful, a chart is just a form of a statistic where the message depends on its time frame.  But I am totally digressing.

What I want to share with you, is to become more sensitive to the way information is presented and represented to us.

You see, in the case of many so-called cognitive illusions, our problems result from difficulties that arise from getting along with probabilities.

Don’t be so insensitive

Take for example our insensitivity to sample sizes.  We have the tendency to under-expect variation in small samples.

The smaller the sample used (or the shorter the record), the more likely the findings are to be chance rather than meaningful.

probably we desire the impossible

probably we desire the impossible

Are you always aware of the number of samples making up a statistic or a report when you take it into account for your decision making?

Could that be the reason why investors regularly flock into unit trusts that are better performing for a year or few years?  Even though financial researchers have shown that the “hot” funds in one time period are often the poorest performers in another?

Chasing the hot hand ends in disaster more times than not.

It all looks so similar

Or take our tendency to use representativeness as a proxy for probabilistic thinking.  We draw analogies and see identical situations – where none exist.  It causes us to give too much emphasis to the similarities between events and does not take into account the actual probability that an even t will occur.

We assume when something is assigned to represent something, it really is what it is supposed to represent.  We judge something by what it “looks like” as opposed to what its probability rate is.

This can lead to base-rate neglect, the tendency to insufficiently take into account the overall frequency (= base rate) of an event in a population.  We often just look at the case rate – being more recent and short-term – without considering other important factors that may result in a vastly different outcome in the long term.  The case rate in most instances does not last and reverts back to the base rate.  Recency frequently convinces us that the case rate is now the new base rate.

That means for the stock market, the greater the complexity and uncertainty in the market, the less emphasis we should place on the case rate.

We need to keep in mind that the representation is just a shortcut for presenting a lot of information, or even worse, a distortion of that information.

Look beyond obvious similarities between a current investment situation and one that appears similar in the past.  A stock or market chart, unlike a picture, is not always worth a thousand words; sometimes they are downright misleading.

More active thinking is called for

Rational consideration of contingencies and probabilities is the only sound basis for good decisions.

More Rational ThinkingLet’s pledge to not use lazy mental shortcuts to make important investing decisions.  Just because something reminds us of something else doesn’t make it more than superficially similar.  Bats aren’t birds and most fish aren’t fish any more than an elephant is a koala bear.

Because whether we should take a risky decision depends not only on the probability that we are right, but also on the consequences if we are wrong.

So, it’s best to balance and take healthy risks – as the greatest risk is that we’ll get to the end of our lives having never risked them on anything.


“You’ve got a complex system and it spews out a lot of wonderful numbers that enable you to measure some factors.  But there are other factors that are terribly important, yet there’s no precise numbering you can put to these factors.  You know they’re important, but you don’t have the numbers.  Practically everybody overweighs the stuff that can be numbered, because it yields to the statistical techniques they’re taught in academia, and doesn’t mix in the hard-to-measure stuff that may be more important.” – Charlie Munger

“There are two kinds of statistics: the kind you look up and the kind you make up.” – Rex Stout Statistics

“There are three kinds of lies: lies, damned lies, and statistics.” – Mark Twain

“Statistics are like bikinis. What they reveal is suggestive, but what they conceal is vital.” – Aaron Levenstein

“An unbiased appreciation of uncertainty is a cornerstone of rationality.” – Daniel Kahneman

“In our society, we teach most citizens reading and writing from the time they are children, but not statistical thinking.  A phenomenon called innumeracy.” – John Alan Paulos

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