Solace for England

Jun 21 2010

The World Cup Football 2010 has started. England fans and the British media are extremely unhappy with performance of their team. Two draws into the tournament and fans are booing the players off the pitch, newspapers are suggesting the coach must go, WaGs (Wives and Girlfriends) are being flown out to ‘boost the boy’s morale’. As the final group game approaches next week, a Sky News presenter offered a ray of hope, “England tend to perform better with their backs against the wall”. I noted the same media driven feeding frenzy happening at the recent congressional hearing for BP CEO Tony Hayward.

Luckily though, whilst watching these media stories unfold on TV, I also happened to be reading, Leonard Mlodinow’s book, The Drunkard’s Walk – How Randomness Rules Our Lives. It made me realize that a dose of sanity was required to interpret the stories we see each day on the news.  Whilst the science of probability may not make for exciting headlines, it casts a needed sober tone on the way the World works and how we should react to things.  Mlodinow points out that human beings habitually underestimate the effects of randomness.  Our broker recommends a mutual fund based on a five year up trend. Football fans call for a coach to resign after two football games. CEOs tender resignation after a quarter of bad sales. Most are likely to be short-term overreactions to the effects of randomness.

As an example, many of these situations overlook a well-established aspect of randomness called “regression to the mean”. Francis Galton, discovered the phenomenon in 1840, where if one measurement is far from its mean, then another will be closer to the mean. The effect applies to a variety of things including for example the height of our siblings (there is a good chance my son could be taller than me..). Eminent scientists such as Stephan Jay Gould have shown that coin-tossing models can closely match the performance of players and teams, including their so called hot and cold streaks.  Could it be that England’s next performance will be better, by chance alone?

Extraordinary events can happen without extraordinary circumstances. From a statistical perspective, coincidences are inevitable and often less remarkable than they may appear intuitively. An example is the birthday problem, where the probability of two individuals sharing a birthday already exceeds 50% with a group of only 23. I recall being surprised when two people at work shared my birthday; in fact it seems quite probable.

Human beings tend to be very good at linking facts together even when the probability of combined events is lower. Is it more likely that your company will increase sales next year or that it will increase sales because the overall economy has had a banner year? As psychologist turned economist, Daniel Kahneman says, “A good story is often less probable than a less satisfactory explanation”. The ability to evaluate meaningful connections among different phenomena maybe so important it is worth seeing a few mirages. Don’t forget in our caveman past survival was a lot less a given than it is for our modern day office worker.

Psychologists have identified another heuristic mistake called “availability bias”, where we give unwarranted importance to memories that are most vivid and hence available for retrieval.  Stark illustrations of the effect of this have been given in jury trials, where more ‘vivid’ forms of evidence one way or the other can swing the vote.

Mlodinow shows that probability theory itself has been used in legal situations, but is easy for even learned experts to get it wrong. “The prosecutors fallacy” for example is where prosecutors employ fallacious arguments to lead juries to convicting suspects on thin evidence.

In Britain, Sally Clark was convicted of smothering her two children who died of sudden infant death syndrome. An expert pediatrician testified on the rarity of SIDS (the chances of two siblings dying of SIDS were estimated at 2.75million to 1. But it is not the probability that two children will die of SIDS we seek; it is the probability that two children who died, died of SIDS. A mathematician later concluded that two infants are 9 times more likely to be SIDS victims than murder victims. Next time you see a positive drugs test on an athlete, or you get a result from a medical test, beware of false positives, most doctors don’t even understand the probabilities.

“Our brains are just not wired to do probability problems very well”. They are made to assimilate data, fill in gaps, and look for patterns. In World War II, newspapers started publishing maps of the impact sites of V2 rockets landing in London. Much speculation was given to the apparent targeting of the rockets. In  1946, just after the war, a mathematical analysis of the bombing data showed that the overall pattern was consistent with a random distribution.

Over time we can easily be fooled by the apparent patterns in random sequences. We put research data into graphs so we can see the meaningful relationships, we may have otherwise missed. But in doing so we can also easily fall into the trap of the ‘Tinkerbell effect’ of things seeming to exist only because we believe in them (named after Tinker Bell, the fairy in the play Peter Pan who is revived from near death by the belief of the audience).

In terms of applications in research, it is clear that we need to be very careful in how we read data. We should spend, as much time looking for evidence that we are wrong as we spend searching for reasons we are correct. Moreover, by turning the lens on ourselves to understand errors of bias and brain heuristics we may find insights to guide our marketing:


The Drunkard’s Walk, How Randomness Rules Our Lives – Leonard Mlodinow

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