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256 Biases in probability assessment
3. Expecting chance to be self-correcting
If a fair coin is tossed and a long sequence of heads appears, many
people will think that the occurrence of a tail on the next throw is highly
probable because the tail is overdue. In a random process, after all, one
would expect the occurrences of heads and tails to be equally frequent.
The phenomenon can also be seen in newspaper articles about lotteries
which advise readers to identify cold numbers, that is, numbers which
have not been drawn for a long period and therefore must have a higher
probability of appearing in the next draw. Of course, coins and lotteries
have no memories so there is no reason at all why they should correct
for earlier sequences of results. This bias is another consequence of the
belief that random sequences of events should be representative of what
a random process is perceived to look like.
Test your judgment: answers to questions 6 and 7
Q6. This thinking is false. At the start of his driving career there may
have been a high probability of the driver having an accident at
some time during the 45-year period. But given that 40 of these
years are now in the past, there is no reason why an accident should
become more likely in order to ‘correct’ for the 40 accident-free
years. You may argue that the driver’s chances of an accident have
increased because 40 accident-free years have bred complacency, or
because he is losing his faculties as he grows older, but this was not
the basis for the argument given in the question.
Q7. No.
4. Ignoring regression to the mean
In the nineteenth century the British scientist Sir Francis Galton found
that relatively tall fathers tended to have sons who were shorter than
them. Short fathers, on the other hand, had sons taller than them. In
both cases the sons tended to be closer than their fathers to the mean
height of adult males. Galton referred to this phenomenon, whereby
events which are above or below average tend to be followed by events
closer to average, as regression to the mean. The phenomenon can be
widely observed in many situations. If you give somebody an intelligence
test and they perform exceptionally well, it is likely that they
will perform less well if you retest them. A month of exceptionally