Derren Brown and the lottery prediction

On 9th September, Derren Brown appeared to predict the results of the UK National Lottery on Channel 4 television. Two days later, he purported to explain this in terms of the "wisdom of crowds". He referred to a study reported by Francis Galton in 1907, in which many people attempted to guess the weight of an ox at a country fair. Although many different estimates were made, the average of these was staggeringly close to the true weight. Brown claimed to have averaged the guesses of a panel of people in order to produce the lottery prediction (the explanation was also mixed up with some stuff about automatic writing and group bonding).

On the blog site of the Guardian newspaper, some people expressed their doubts about the whole wisdom of crowds concept, including the Galton study. I posted the following response (I've corrected a small error in this reprinting):

Regarding the wisdom of the crowds argument, which some people have doubted, aggregating imperfect judgments can improve accuracy but it doesn't apply to the case of lottery numbers. Let's take Galton's example of people guessing the weight of an ox, mentioned in the programme (Galton's paper was published in Nature). In reality, the ox weighed 1198 lbs. If person A guesses the weight to be 1178 lbs then s/he is inaccurate by 20 lbs. Person B guesses the weight to be 1208 lbs and is inaccurate by 10 lbs. Thus, the average level of inaccuracy is 15 lbs. But suppose we average their two guesses; this gives an estimate of 1193 lbs, which is inaccurate by only 5 lbs. Thus, the level of error obtained by averaging the estimates is less than the average error of each individual estimate.


There are a couple of things to note here. First, the two estimates in the example fell either side of the actual weight, a phenomenon called 'bracketing'. With multiple estimates, at least one instance of bracketing is necessary in order that averaging estimates will improve overall reliability. When making estimates about something where knowledge can be applied, even imperfectly, multiple estimates are likely to cluster either side of the true answer. In the case of the lottery, knowledge cannot be applied. Because numbers are randomly determined, there is nothing "real" for guesses to cluster around. Indeed, the numbers 1 and 49 cannot even be bracketed, as guesses can only fall to one side of them.


Second, even where bracketing can occur, thus leading to greater reliability of the averaged estimates, greater reliability does not mean pinpoint accuracy. Rather, it simply means a reduced level of error. In the case reported by Galton, 787 people guessed the weight of the ox and the average of their estimates fell 1 lb short of the correct weight. Thus, even if it were possible to apply the wisdom of crowds to the National Lottery, the notion that this would lead to seven correct answers is risible.


I don't know how Brown did it, but having viewed the video of the "jumping ball" I'm inclined to agree that there was something along the lines of the split screen trickery that many have suggested.


As someone who teaches the psychology of judgment, it does concern me a little that mixing up genuine science with a barrel-load of hokum could damage people's understanding of, or trust in, the former.