Late night thoughts on Football Betting

This is the essay that kick started my gambling spree. In a way it was not a gambling spree but rather my attempt to test this theory. So far the theory is proving to be moderately but not spectacularly successful. This was also sent to some ppl in my department who regularly bet on 4D / Toto, games with negative expected takings. I never play those games.

In summary, the bad news is that if the bookies price their odds in a certain way, and if they don't make mistakes, you will never win money from football betting in the long run. But the thesis here is that not only do they often make mistakes, they make deliberate mistakes, because the people who bet against them are not rational maximisers of money (since when could that description ever be pinned on gamblers?) but have a higher preference for risk. The betting odds are designed to maximise profits against punters with this profile.

The modest profit that I have made from making 40 bets suggests that the theory is sound. But it is quite a bit of work for quite a little bit of money. If I want to really roll in the cash, I will have to be a big big punter, and I don't know if I have the stomach for this.

Anyway, here it is, for those of you who want to milk the Singapore Pools cow.

Some people have asked me why I bet on football and do not bet on 4D / Toto. After some experimentation I have tried to make sense of it all:

Betting


Before we get into the main topic of what a good betting strategy is, let us go into the mind of the bookie. One of the first things is to realise that to be a bookie you need some objectives, some of which are fairly contradictory to each other.


Probability based pricing


The standard way of setting odds is based on probability. That is to set odds that prevent statistical arbitrage. What is this? Let us go into some maths.


Suppose there is an experiment with 2 possible outcomes, A and A’. Event A takes place with probability p. If somebody bets on A, then you should sell it to him at odds X(A), where X(A) is less than 1/p. I write X(A) the way Singapore Pools does it here. If you buy a betting ticket at X(A), it means that if you bet $1 and lose, you will lose that $1. Otherwise you will win X(A). Obviously X(A) is more than 1.


As for why you, as a bookie, should sell the odds at X(A), let’s go to the law of large numbers. Suppose this experiment were to be performed many times. Then the number of times you get outcome A is close to pn. Suppose the gambler were to bet $1 on A every time. Then he would win close to pn times, and your payout is around np(X(A) - 1). At the same time the gambler loses n(1-p) times, and he pays you n(1-p). So the amount of money you have is n(1-p) - np(X(A) -1). Rearranging the terms, that means X(A) is less than 1/p.


At the same time, X(A’) should also be less than 1/(1-p). That way, you will get a profit either way. Don’t worry too much about the numbers. Just try to understand the idea of what p is. p is the actual probability of A taking place.


The question is, what is p? Nobody really knows what p is. It is just the perception. But the "rational" buyer will have his own conception of what p is. I say "rational" because your customers are all gamblers and gamblers are not generally rational.


If bookies always set their odds on this principle, then football gambling would be like toto or 4d: the odds are always against you, every ticket gives you a negative expected return. Fortunately for us, there are a few reasons why bookies will sometimes deviate from this principle.


Why bookies deviate from probability based pricing.


First, there is also the market to consider. Suppose everybody were to bet on A. That would be bad for you if A actually did happen. Fortunately there is a pricing mechanism that can influence more gamblers to bet on A’ instead. So you adjust X(A) and X(A’) accordingly. But now you have shifted the balance away from the ideal, which is to set things based on p.


Suppose p were, say 0.95. Then by right you should price X(A) at less than 1.052. The thing is - who the hell would want to buy a bet from you at 1.052? You can’t balance the odds. Everybody will bet on A’, and in the event that A’ takes place, you will lose on A’ more than what you gained from the people who bet on A and lost to you.


In order to induce more people to bet on A, you price it at X(A) = 1.1, or 1.2 instead. But that means that the rare person who buys it from you at 1.1 will get a free ride. Understand that what is going on here is essentially the bookie is buying insurance from the punter who bets on a likely outcome. If you are buying insurance, chances are you are making a loss.


This criterion – loss minimisation is often contradictory to probability based pricing schemes. This contradicts the efficient markets hypothesis. If people are rational and have a cold hard look at the value of p, they would not be betting the way they are betting.


This is why you must realise that the punter is not only betting against Singapore Pools. He is also betting against the market, and the market is other punters, many of whom do not have "O" levels in Maths.


Gamblers are generally not very good at calculating stuff. That’s why you, the bookie, are making so much money. Suppose the probability p is 0.95. Then 1-p is 0.05. What would X(A’) have to be under the probability based pricing scheme? 19. A big fat 19! Is anything ever priced at 19? You will never find it. But you could price something at, say, 7 or 8 and people would think that it’s hell of a bargain. They’re not going to demand that you set your odds at 19, even though that is the fair price. They will be happy with 8. They will feel lucky and bet on 8, and chances are, they will lose their clothes, the poor suckers.


The other reason why you don’t want to set X(A) at 1.05 is this: by doing so, you will be telling the whole world that you, the knowledgeable bookie thinks that it is almost impossible that A’ is going to happen. Who would want to bet on A’? Nobody, because you are announcing to the whole world that A’ will never happen. Who will want to bet on A? Nobody, because the odds are too low.


The 90% rule


So my strategy is, find outcomes that have p = 0.9. Chances are, whatever the odds are, they’re better than 1.1. You will win more than you lose. You may think that it’s not worth it to bet on low odds, but that would be making the classic mistake.


So the question is: is there such a thing as a 90% event? Yes. If you look at football and the league table, the league winners will win around 65-70% of their matches. Last season Man U won 25 out of 38, which is around 65%. When Chelsea won their first EPL, they were so dominant they won 29 matches, which is 75%. Last season, at the other end of the table, Derby County lost 29 matches, which is also 75%.


So that is already a 70% chance of winning, playing the average middle table team. If you have a big 4 team playing a whipping boy, the chance that the big 4 team will beat it could go up to more than 90%.


The other thing is that the form of both teams is non-stationary. This means that Man U winning 65% of the matches includes all the matches where they have just returned from Europe, had key players injured, gone through a bad patch. Yes, Virginia, there is such a thing as form. Team dynamics is a very ephemeral thing. Shift a few parameters out of line, and the whole teamwork disappears, heads drop, etc etc.


So there are such things as 90% events. It is simple. Just bet on them. So how do you identify 90% events? Well there’s not enough space here to talk about it. Obviously your skill is important. I am writing a non-constructive proof here so I only have to show that something exists without necessarily telling you how to attain it.


Risk


Maybe you think that a 10% return is meagre? The average investor would think that 10% a week is fantastic. Even 5%. You are in this thing to win money. You don’t ask for higher returns unless you really want to be a gambler. Well you are not a gambler. You are a probabilist. You must pick your fights.


Here’s the thing: there is asymmetry of power in this game. Yes, the bookie sets the odds and if he had his way, he will set the odds against you every time. That’s why you should stay on the segment of the spectrum where it is difficult for the bookie to price the odds against you. Think of yourself as a winger. The right back / left back will find it difficult to tackle you because he has to stay inside you, and because if he tackles, chances are you’ll get a throw in anyway. This method of punting is similar to playing on the wing.


You can see this in what Singapore pools have done. They are sick and fed up of losing money all the time because they always expose their asses wide open for bad people like me to take advantage of the system. So in order to steer people away from betting on 90% events, they have introduced the first half – final results combi. Combis are bad bad things because they are not in the 90% range, so don’t fall for it.


Maybe you think that gambling is not safe? Compared to what? Lehman minibonds? When you buy a structured product there’s not much you know except that your relationship manager has a tight skirt and a fantastic ass. There is not much useful information out there. At the same time, when you put your money in for the long run, there is always a case that something really bad would go wrong, and your investment will blow up.


When hedge funds blow up, it is because of the unknown unknowns. Think about LTCM. Who knew that the Russians were going to default? Who knows the way that interest rates / oil prices / the weather is going to go? Who knows if your bank is going to collapse? Who knows the insides of companies, and how well they are really run? Who knows how the iPod is going to fare in the market?


In contrast, in football, the information is there. Who is on fire, who is not playing well, who is injured, who is the good tactician, who is a good acquisition. Your risk manager is Alex Ferguson / Arsene Wenger / Rafael Benitez. They are the best in the business and your interests are perfectly aligned with them, if they want to win. Even better are internationals, where you know that if Italy were to lose or draw against Luxembourg they will have shit thrown at them in the airport when they come back. When you invest in a company, do you ever get to see first hand how it is being managed?


Make no mistake, though, gambling is not safe. This is still gambling. At the most you can call it speculation. I have tested this theory with $200 of my own money: 16 bets, and got my money back every time. But I still feel the trepidation and dread every time I go down and punt. Your judgement has to be good. I do not have the temperament of a gambler. I suppose this is what trading is like, but it has worked for me so far.


You need to have discipline to stick to the 90% rule. I once bet on Argentina or Brazil to win the 2006 World Cup. Bad move. I once bet on a World Cup semi-finals where both teams were strong. Also bad move. In general, the more exciting a match (exciting meaning a see saw match, just like Aston Villa- Everton last night) the less you should bet on it. One sided massacres like Liverpool ass raping Blackburn is OK, except that I didn’t know if Liverpool are tired from Europe.


I would not have believed I had found a winning formula until I have had a chance to test it. I will lose a bet sooner or later but in the long run I will be ahead. You know the law of large numbers – if a person is consistently lucky, it is not luck.


Why don’t people know about this?


Well I don’t think that hedge funds would use this strategy. It is illegal. I don’t think people who found a way to consistently win money from Singapore Pools would crow to others about this. Might get into trouble with the authorities. I know 1 or 2 people who regularly bet money on football and claim to be ahead. I think it is possible. This concept was explained to me by a character in Graham Swift’s excellent novel, "Last Orders". He claims that through a careful study of the books, you can choose which ones to bet and you can land up ahead. Perhaps Graham Swift is relating the real life experience of a person who did the same.


Furthermore, there is a bias against gambling. Many people believe that all gambling is bad. True, it has the stigma of wrecking lives. True, it is addictive – and the chances that you will get hooked and all your discipline goes out the window is a very real possibility. But the same is true for anybody who trades in the financial markets for a living!


The last objection has to do with whether this is ethical, because every dollar you win is taken out of a community service project or some other expensive government project. Everybody who wants to win at Singapore pools is guilty of this, but yes you are more guilty because you know that in the long run you are ahead. This is not an essay about ethics, the choice is up to you.