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Football: Win, Lose or Draw?

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You can barely watch a football match these days without being reminded that you can bet on the result. Gambling on sports is big business. So is it possible to beat the market? And if so, how easy is it? In a world of number-crunchingly powerful computers in our pockets surely someone could write a program that could beat the odds (and make them rich)! As it happens, Anthony Constantinou, while a student at Queen Mary, University of London has developed software that has beaten the bookies.

Computers are far better than humans at some kinds of decision-making. They are great in situations where there is no randomness and the computer can be given perfect information to work on. Chess is a classic example: there is no chance involved and both players can see all the pieces on the board at all times. Clever algorithmic techniques are enough to provide an outstanding chess-playing decision-maker. They basically work by checking vast numbers of possibilities quickly and then picking the one that leads to the best result. Deep Blue, the chess supercomputer developed by IBM, beat Garry Kasparov, the best human player on the planet this way back in 1997. Even personal computers can be as powerful nowadays as the supercomputer that beat Kasparov back then!

Real-life isn't a game of chess, though. There are other kinds of situations where we make decisions. They involve uncertainty and taking risks. Then supercomputers alone are not the answer. You need something more than just number-crunching power.

Football is an ideal test-bed for researchers trying to come up with computer decision-makers that can deal with real-life uncertainties. Making predictions about football matches is now both massively important and a real challenge. It's the world's most popular sport and as a result has the fastest growing international gambling market. There are vastly many things that can influence the final result of a game making it just too complex to number-crunch. Risk and uncertainty play a huge role in coming up with accurate predictions.

sports gambling markets publish odds that are biased towards giving the bookies' the most profits

As a result, researchers are taking more and more interest in football. Models of the gambling market are built by economists, while statisticians and computer scientists test their worth with sophisticated models based on probabilities for predicting results. It's not just academics mining historical football match results either, bookmakers live and breathe football prediction models. It's not as easy as many football fans think though. Clearly most football gamblers are not winning money against the bookmakers. After all, bookmakers make millions of pounds profit every year.

The first thing to realise is that for a football forecast model to make a profit, given the bookmakers' in-built profit margin, you must be able to predict probabilities that are noticeably more accurate from their published odds. That is what Anthony Constantinou aimed to do for his Ph.D. His research was based on the idea that sports gambling markets, and particularly football, publish odds that are biased towards giving the bookies' the most profits. That means the publicised odds suffer from a certain amount of built-in inaccuracy. For any large-scale gambling market it's 'efficiency' that matters. Essentially a gambling market is inefficient if there's a way to consistently generate profit against published market odds. But that is what the bookie's odds build in. Their intended inefficiency can potentially be exploited for profit with a good enough model. A simple way to try would be to collect historical data about teams' results and use that to give a probability for each result this time. If Spurs have always beaten Norwich in the past, for example, then they probably will this time.

To beat the bookie's odds you need to be more sophisticated than that though. Anthony's approach involves using what are called 'Bayesian networks'. They are probabilistic models but ones that can take account of more than just hard facts like historical data. You can include all those vague, subjective things that a match might turn on as well - like availability of key players, team fatigue, team motivation, and so on. They give a way for an expert to include their best guesses about things that there are no hard facts about. That extra data is then taken into account appropriately in the model's predictions.

Anthony, jointly with Norman Fenton and Martin Neil, used their system to make predictions, giving probabilities for wins, losses and draws about premiership matches. To keep them honest, all their predictions were published online at www.pi-football.com before the kick-offs. Did it work? Yes - they made a profit against the published market odds over a long period of time. No other published work has successfully done that. That suggests the importance of the novel part of Anthony's approach: Bayesian networks.

Having demonstrated the approach works for football, it's now worth trying it on other markets too: both other kinds of sports gambling and the financial markets. In the meantime if you want to beat the bookies you can follow the tips of pi-football. If you want to write your own program (with vast riches on your mind) you need to learn some computer science first (and reading Anthony's PhD dissertation would help too).