|
Best Value Bets
Professor Leighton V Williams
June 2003
Professor Leighton V Williams is Professor of Economics and Finance at Nottingham Trent University and Director of the Betting Research Unit there. Here he lays out the conundrum of the betting market – the favourite-longshot bias. Favourites turn out to be the better bet on average and longshots are rather poor value. This is an unexpected finding given that bookies set odds so that average gains and losses are the same across all the odds levels. Professor Vaughan Williams explains why.
Placing a bet is a classic example of decision-making under uncertainty. From an economist's point of view, a betting market is an example of a simple financial market – one which possesses the advantage that each bet or transaction is characterized by knowing exactly what you stand to win or lose. This is true whether you are bookie or punter. For the punter, a £10 bet on a horse at 3-1 has an end point of £10 lost if the horse loses, or £30 gained if the horse wins. There are no other possibilities.
For these reasons, there has developed a rapidly growing economics literature, which has focused on the nature and behaviour of betting markets. This literature has been published in some of the foremost international academic journals, and it has increasingly influenced mainstream economic enquiry.
The efficiency of the betting market
A particular concern for economists is the idea of 'market efficiency'. If the stock market was completely efficient, then buying any particular share would give the same return, on average, as any other share in the market. In an efficient market no individual can know more than the market. But, markets are never fully efficient. For example, in the stock market, if some 'market insiders' are privy to 'market sensitive information', for instance, that a wealthy company is about to launch a takeover offer, they will expect to make a killing by using their information to buy shares in the takeover company. In other words they hold key information that is not widely known in the market. Because some individuals know more than others, the stock market is not efficient, or to put an economist's spin on it, the market is not informationally efficient.
To clarify the point further, think of the market in washing machines. This market is probably fairly efficient. There is a range of prices that presumably reflects the quality of the goods. There are cheap machines, which may be less reliable and not so good at the job, and expensive ones that will last longer and wash better. If you buy a machine that costs £1000 perhaps it will last you 15 years. But a machine that costs £300 might only last you five years. So in the long run, you will spend about the same whether you go for the cheap or the expensive option (especially if you factor in the extra money you'll spend on clothes because the cheap machine doesn't do the job so well). In this case, the market is efficient because, on average, a cheap machine is neither better nor worse value than an expensive one.
Turning to betting then, if the betting market is efficient, the average return of a bet at any given odds level will be the same as that at any other odds level. What is meant by odds level is the net amount gained by a winning bet to a given stake. For example, odds of 5-1 against would imply that a £1 bet on a horse would, if successful, return a net amount of £5, ie £5 and the £1 back. A losing bet would lose the stake. In fact, there is significant published evidence to suggest that the expected return differs quite a lot at different odds levels. This phenomenon has come to be known as the 'favourite-longshot bias', and can be traced to a seminal piece of work published in 1949 by Richard M Griffith, a psychologist based at the Veterans Administration Hospital, Lexington, USA.
|
Setting the odds
Why is the expected average return on all odds levels the same? Well, suppose bookies expect to make 20p in every £1 for every horse. Then a horse whose chance of winning is 1 in 5 (a 20% chance) would be offered at a price of 3-1. The maths here works like this. On average over five races, it will win once and lose four times (winning chance of 1 in 5). So if you bet £1 on each of the five races, you lose four times (= £4 loss) and win once (= £3 profit). A net loss of £1 over five races is an average loss of 20p per bet. Fair odds for this horse would be 4-1, as on the one occasion in five that your horse wins, you win £4, which exactly matches the £4 you lost on the other four races. But, bookies have to make a profit!
Suppose another horse in the same race is priced at 9-1. Then, in order for the average return to be the same for the bookies (20p in every £1), the horse must have a winning chance of 8%. Why? Consider 100 races in which you bet £1 every time on this horse. On average, the horse wins eight times. You will win 8 x £9 = £72. You will have lost on 92 of the races – so £92 lost, and £72 won, giving you a net loss of £20. A net loss of £20 over 100 bets of £1 is, of course, the same as a net loss of 20p to every £1 bet. The bookies have kept their return and so have you.
|
Next: Part 2 >
top ^
|
