Groups v Individuals in Betting
Whether we’re talking raffles, sports odds, stock prices, economies, societies or nations, when it comes to predictions, the ‘many’ should judge better than the ‘one’. A group’s collective analysis will almost always be more accurate or perform better than the individual; even an expert individual.
A trial by jury could be understood as a ‘wisdom of the crowd’ example. The jury are from a diverse background and not experts in the law or the case material and yet are trusted to come to a more just decision than a ‘trial by judge’ scenario, with just the single expert.
In nature too, the ‘advantages’ of the group, are everywhere to be seen. The Golden Shiner is a fish that likes a shady environment. A lone Shiner would have a tough time finding shady regions in a stretch of water, whereas a large group is much more efficient at finding shade. Similarly, the pack mentality of many predators give them a distinct advantage. Although in nature these phenomenon are generally ‘instinctive’ as opposed too deliberate, we should sit up and take note, because nature’s ‘wisdom’ is ubiquitous!
In 1906, the renowned statistician Francis Galton observed a competition at a country fair, where the public had to guess the weight of a slaughtered ox. Around eight hundred people entered. Galton ran statistical tests on the numbers. He discovered that the average guess of 1,208 lbs, was extremely close to the actual weight of 1,198 lbs. A mere 9 lbs difference. It highlighted the idea that observations of large groups of people are more accurate than the observations of the elite few.
(see The Wisdom of Crowds, by James Surowiecki)
This was an early, fascinating and widely publicised contribution to the theory in cognitive science, that a crowd’s individual assessments can be modeled as a probability distribution of responses, with the median centered near the true value of the quantity to be estimated.
It isn’t, however, as simple as it sounds. The wisdom of the crowd can fail. Social influences can cause the average of the crowd’s answers to become inaccurate. Too many people from a similar background, or a situation where individuals in the crowd can hear the guesses of other members of the crowd (and so be influenced) can undermine the effect.
For the wisdom of crowds effect to work at its best, individual judgments need to be kept independent from each other and the crowd needs to be made up of people with diverse opinions and ideologies.
Scott E. Page came up with the diversity prediction theorem:
“The squared error of the collective prediction equals the average squared error minus the predictive diversity”.
Therefore, when the diversity in a group is large, the error of the crowd is small.
The Wisdom of Crowd in Betting
One of the best examples of the wisdom of the crowd at work, that I see virtually every day, is on the betting exchanges. Here, individuals set there own prices for sports events and because of the sheer number of customers and the diverse backgrounds of those customers, prices are very accurate across many markets and many sports.
If you take a live football match. Let’s say we are in the 67th minute, one team is 2-1 up but a man down due to a red card. The losing team is on the attack, close the winning team’s penalty area, the price will be pretty much spot on. Or simply put, whatever the match situation, the price will be right.
Of course there are deviations from the ‘true price’, especially as a market fluctuates, after a goal is scored for instance, but in a settled market the prices are accurate. If you needed more proof, just know that in the early days of Betfair (the first big exchange) the customers on the exchange were few and set their prices in line with bookmaker prices. Today, in many liquid markets, bookmakers set their prices in line with Betfair prices – on a betting platform used by tens of thousands of customers from hugely diverse backgrounds.
So bookmakers are forced to ‘listen’ to the wisdom of the crowd, but in essence that has always been the case. If a bookmaker posts a bad line, odds or price, the betting public will soon let them know by taking advantage of their error, generally forcing the bookmaker to correct their price.
I hope this has given you a basic understanding of the ‘wisdom of the crowd’ effect.. – the ‘many’ v ‘the one’!