A Drunkard’s Walk - Winning Streaks and Randomness

I am doing some work on probability and randomness for a entrance test later on in 2011 and have been re-reading some puzzles in this area. Here is a reprise of a book review from 2008 - this book still stands as one of the best on probability that I have read. A super book for ambitious students.

Statistical significance, random errors, laws of sample space, hot hand fallacies, bell curves, regressions towards the mean and the Baye’s theorem about conditional probability - hardly the stuff to get the pulse racing during a relaxing summer break. But when the risks of having a life-threatening disease when your test comes back positive turn out to be much lower than you thought. When your local sports club has been on a losing streak for seven or eight games against evenly matched opposition and you cannot understand why. Or when the local paper goes overboard about the existence of cancer hotspots / clusters or an abnormal rate of suicides in certain towns - that is when a good grounding in the laws of probability come in handy in appreciating what might lie behind what are intuitively unlikely occurrences.

“The Drunkard’s Walk - The Mathematics of Randomness” by physicist and one-time Star Trek writer Leonard Mlodinow provides an entertaining and thought-provoking read on probability, randomness and how it affects our day to day lives. This fast-flowing work packed with anecdotes takes us through the history of mathematics and how the discipline eventually came to find the tools necessary to understand statistics and probability in particular. The core premise of the Mlodinow book is that we often misinterpret the effects of randomness. People are affected by uncontrollable and unpredictable events - we get pushed here and there in myriad different ways - but regardless of this, we are on a journey and it will take us somewhere even if we suffer from the illusion of having some degree of control.

Illusions - a tag in many of the new genre of behavioural economics books that have been published in recent years and which are attracting the interest of politicians on both sides of the Atlantic. Mlodinow focuses on several of these illusions - the Illusion of causality, the illusion of small numbers - random errors from using small sample sizes. And the illusion of control - the unconscious or gut feeling that we have some control over random events.

Mlodinow looks at the real chances of what appear to be very unlikely occurrences such as winning streaks for sports teams, authors whose books are rejected by a succession of publishers and fund managers beating the stock market average for a number of years in succession. Rare events are often more probable than we think and the secret to understanding this is to apreciate the laws of probability - something that many of us - this blogger included - have rarely come to terms with!

Here is one nugget from the book

(1) Suppose that a family has two children. What is the probability that both are girls?
(2) What is the probability of having two girls if at least one of the children is a girl?
(3) What is the probability of a family having two girls if one of the children is a girl named Florida?

Mlodinow encourages us to take as many opportunities as we possibly can - one of the potential joys of randomness is that we never quite know who we will bump into when we take that early morning walk with a dog, or head to the gym for a work out instead of staying home. Or spend some time looking for innovative ways of improving our business even though the chances of success are low! In the words of one of the founders of IBM, if you want to succeed, double your failure rate.

I really enjoyed this book and I have added it to my student reading list. And when the new school year starts I must remember not to judge the essays that my students hand in on the basis of my previous evaluation of their intellectual prowess. (A confirmation bias) And I can also now tell my tallest students with reasonable confidence that their children are likely to be smaller than they are! (Regression towards the mean). Mlodinow makes probability fun…. he deserves the place in the best seller rankings - or maybe he is just at the start of a long lucky streak!

Here is his recent presentation to authors at Google