The Betfair Prof / Leighton Vaughan Williams / 03 March 2008 /

The Betfair Prof, Leighton Vaughan Williams, tells us why the best way of predicting the outcome of Tuesday's primaries between Hillary Clinton and Barack Obama is to leave a drunken man in a field and see what happens...

In 1905 two English scientists, Karl Pearson and Lord Rayleigh used the pages of the leading scientific journal 'Nature' to discuss the concept of what has come to be known as a "random walk," with Pearson noting, "In an open country the most probable place to find a drunken man ... is somewhere near his starting point." This is not because he is too incapable to move at all but simply because he is equally likely to have moved in any direction. Since you can't tell which, your best guess as to his current location is where he started out. Hence the riddle - Question: "If you leave a drunk in a field where are you most likely to find him?" Answer: "Where you left him!"

All sorts of naturally occurring phenomena follow a so-called 'random walk', historically the best documented being pollen seeds in a liquid solution. Scientists call this haphazard journey 'Brownian motion' after the nineteenth-century botanist, Robert Brown, who first spotted its existence. Random walk theory has wider implications than being able to find your drunken friend in a field, however, or being able to explain the movements of little pollen seeds. It tells us about patterns of movement in all sorts of vital areas, and that includes financial, betting and prediction markets.

The idea of a random walk in the movements of share prices has been with us since Louis Bachelier first noticed that you couldn't predict the movements of prices tomorrow and beyond on the Bourse (the Paris Stock Exchange) from movements in past prices. The reason was quite simple. At any point in time, share prices should reflect all available information. At least, that's the theory. If so, there is no way to predict how the share price will move in the future until and unless new information becomes available. Any movements before then will be purely random and as such unpredictable.

On Tuesday, March 4, Barack Obama takes on Hillary Clinton for the Democratic Party's nomination for President of the USA in the showdown states of Ohio and Texas. The Betfair markets, as I write 40 hours before the opening of polling, indicate that Senator Clinton has roughly a 55% chance of winning Ohio, while Senator Obama has about a 3 in 4 chance of winning Texas. And so our best guess, if the 'random walk' theory is correct, of what the markets will tell us about their respective chances when the polls open is what they are saying now.

That's our best guess, though as new information becomes available the odds are in fact very likely to change and it is in truth very unlikely indeed that the markets will be telling us exactly the same story almost two days later as two days before. The real point, however, is that we are unable to tell in what direction they will change and by how much and so our best estimate statistically is that we will find them exactly where we left them a full 40 hours earlier.

It seems, indeed, that not much has changed since we left that drunken man in that open field in 1905!

Professor Leighton Vaughan Williams is the Director of the Political Forecasting Unit and Betting Research Unit of Nottingham Business School, Nottingham Trent University

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