Welcome to week 2 of this course and we're going to look today at the relationship between gambling and betting markets. One of the objects of this course is to assess how well we can predict the outcomes of games. Use it by comparing performance to the performance of betting odds. We're going to look at betting odds in some detail. In order to get into that, we need to think a little bit about how gambling markets work and discuss what's involved in the setting of odds. What is gambling? Well, we usually define it as a game of chance that involves some monetary value, and you're very familiar with all ways in which people can gamble and sports is just one of those types. Now, one distinction that people often like to make is between gambling that involves pure chance, such as a lottery, and gambling that involves skill. That tends to be sports betting where people think that they can use sub-rational schemes in order to predict what's going to happen, what the outcome is going to be. If you buy lottery tickets. There's no rhyme or reason to which lottery ticket you buy and a lottery ticket is as good as any other. There's no real skill involved in buying lottery tickets. Gambling in sports is typically regulated and taxed and is often illegal in the United States, for example, has long been illegal. It's being legalized in lots of states now. There are many parts of the world where it's still illegal though India, China are places that come to mind. In that sense, it's a somewhat controversial area. We will talk later in this course about ways in which that affects gambling and sports in general. One point to make is that betting on sports is a little bit like investing in the stock market in the sense that the skills involved are not too dissimilar making a judgment about what's likely to go up, what's likely to go down. One thing that I think many economists have concluded looking at gambling and the stock market is that stock markets are generally not controversial. Sports gambling is quite controversial. A lot of this seems to have to do with social norms rather than with any particular fundamental issue. But we'll come back to that at a later stage. In this presentation, I'm going to talk about three ways of betting. Pari-mutual betting, bookmaking, and betting exchanges. All these are different in some fundamental ways, they are all fundamentally the same in the sense that the same logic is going to apply. It just plays out in somewhat different ways. I'm going to start off with pari-mutual betting, which is in some ways the easiest way to grasp what is at stake and how sports gambling really works. The idea here is that the people who make bets and I'm going to cool them, punters. That's a phrase that is often used to describe people who make bets. The punters put their money into a pool, and then the people who back the winning, who's team, whatever it is they're betting on. They share out the pool, and they share it out in proportion to the money that they put in. Pari-mutuel has been very popular form of gambling in horse racing, as you can maybe tell from the name it originated in France. But it's actually widely used around the world with horse racing. It's a particularly good way to understand some of the principles involved here and particularly understand the probabilities evolve with the outcomes. I want to set up a simple example here to illustrate the way in which the amount that people stake of the outcome relates to the probabilities of each outcome. I've set up a hypothetical example here. Suppose this a horse race with one host is called the White Queen, the other horse is called the Red Queen. Then there are five punters, and I've just labeled them A, B, C, D, and E and each puts money into the pool based on what they think the outcome is going to be. Punter A puts $10 on the White Queen. Punter B puts $50 on the White Queen. Punter C puts a $100 on the White Queen, and then punters D and E, bet on the Red Queen. D puts in $30 and E puts in $60. In total, the pool adds up to $250. The first thing to notice that the probabilities that the outcome should be related to the proportion of money bet on each horse. Out of the $250, $160 went on the White Queen, that's 64 percent of all the money bet and that represents or should represent the probability that the White Queen wins. The way to think about that is if you took, the White Queen was more likely, had a better than 64 percent chance of winning. You should be willing to put money into betting on the White Queen because you get more out than you put in. But if you do so likewise, if you think it's less likely, you should put money onto the Red Queen. One of the principles here is that if punters are free to keep laying bets until they are confident that they are getting the best possible outcome, then we should see ultimately the probabilities are proportional to the amount staked on each horse. What I've done here is drawn up a little table to show how the money that is laid on the bets, how that relates to the winnings under each circumstance and the rates of return that you get on your bets. Firstly, I've reproduced the figures for the amount laid on the bets and then the pay-out is in proportion to the amount that you put in. It shows there the proportion of the money that is paid out to each punter based on who wins if the White Queen wins or the Red Queen wins. Then given that percentage, we can say what is the amount that will actually be one, so that's in the column that's colored blue. You can see what's paid out in terms of money terms to the punters if the White Queen wins or if the Red Queen wins. Of course, if you back those that loses, then you get nothing back, you lose everything. Then convert that into a rate of return. The rates of return being the amount by which the percentage of your winnings exceeds your steak. For example, if you bet $10 of the White Queen and the White Queen wins, you get six percent of the pot. That adds up to $15.63 and that also adds up to a 56 percent rate of return on your original $10, so that's the first row there in green. Of course, if the Red Queen wins, you lose a 100 percent of the money you put in, so your return is 56 percent if you win and minus a 100 percent if you lose. The point here is that actually that's true for each of the punters of the White Queen, regardless of the size of their state, those are their rates of return and then if you think about working out what's the expected value? The expected value means the rate of return times the probability of that outcome. If you do the math, then 64 percent times 56 percent plus 36 percent times minus a 100 percent actually equals 0. Your expected rate of return on your gamble in this story is 0 and that's true whether you're punter A, B, or C and though punters D and E only get a return if the Red Queen wins not if the White Queen wins and the rates of return are different, the rates of return if the Red Queen wins are higher because the Red Queen has a lower chance of winning. The overall return weighted by their probabilities is also zero for the backers of the Red Queen. This is an example of what you would call a fair gamble. On average, you're not going to win or lose. You have a chance. You have a probability of winning something and you have a probability of losing something but if you weigh up these probabilities together, the overall return is zero. That's what is defined to be a fair gamble. Now in practice, betting on sports is all overs never a fair gamble in the sense that there is usually tax to be paid on gambling. That means that once you've paid the tax, your expected return is negative. It is usually less than one in gambling. Gambling is not on average a money-making proposition. Most people seem to understand that, that in fact they're gambling for fun, they're not necessarily gambling to get rich. The only punters who think that they can make money are those who believe that they are better able to identify the true probabilities than everybody else. In other words, the probability is implied by what everybody else thinks are the probabilities derived from the payout of the pool in our mutual example. You will only make money from gambling if you think you know those probabilities better than the pool. In a sense, to win a gambling you'll pity yourself against everybody else. What you're saying is, I understand, everybody else doesn't understand, which is quite a bold claim of hole. That's pairing mutual betting, which is the simplest, purest and there's no intermediary between that in some sense it's an arrangement amongst all of the punters. Most people actually bet with bookmakers. A bookmaker is someone who takes bets from punters in order to make a profit. The way they do that is by offering odds to the punters probabilities and those odds imply rates of return on a bet. What a bookmaker could do, can actually reproduce what the pari-mutuel set-up produces, which is by adjusting the odds so that if the Red Queen wins, you pay out just as much money as if the White Queen wins. In that situation, you get a balanced book and why would you do that? You pay out the same amount of money. Where's your profit? Well, the profit is going to come because you charge money to take their bets. In that sense, a bookmaker can act like a parimutuel betting but needs also to make a profit. Where does the profit come from? Well, the odds that the bookmaker offers add up to probabilities greater than 100 percent. The excess over the 100 percent applied for the probabilities is what's called the overround, or in America, it's known as the vig or the vigorish. Again, to restate that if you add up the probability that the white queen wins or the red queen wins in our example, the combined probabilities offered by the bookmaker will be greater than 100 percent. The bookmaker will profit by that excess or overround, remembering that they are only paying out in the event of one horse winning not both. A bookmaker operating a balanced book is guaranteed a profit equal to the vague. In some sense, sometimes some say "Bookmaking is an easier way to make money there's just guaranteed profit in bookmaking." Now, it turns out, and it's quite interesting that in reality, most bookmakers actually take a position which means they may win more money or lose money on a particular outcome. That has to do with competition in the bookmaking market. But a lot of the time, it will be convenient for us to think of bookmakers working on the basis of a balanced book. Again, in order for the punter to make a profit against a bookmaker, the punter needs to believe that the gap between the troupe of probability and the probability implied by the bookmaker's odds is larger than the vig, the overround. Also, remember it's also going to be better than the tax. In reality, the gap will generally need to be quite large. For example, could be as large as 20 percent, that's quite a large gap in probability which you have to believe exists in order for you to make money. Again, hopefully, you're seeing as you think about this, that it's actually pretty hard to beat the bookmakers. The third way in which people often gamble nowadays is through something called a betting exchange. These are something that developed out of the Internet era where the idea is a little bit similar to parimutuel betting. Where instead of there being a bookmaker who makes prices and punters buy or sell at the prices which are being offered, here punters actually get in touch with each other and one side offers a bet and the other side accepts. It's different from pirate mutual in the sense that it's not pooling, it's based on individual choices. But it's like parimutuel in the sense that there's no bookmaker intermediary. This can work with pretty much any sport, any activity. One punter just goes online and says "They're willing to offer such and such a bet." And another punter says, "Yes, okay, I'll, I'll take that bet and their way." The betting exchange just takes a commission for matching the two punters with each other. These betting exchanges offer a lot more flexibility to punters and give them many more opportunities to be creative in the way that they gamble. Well, given that in general, gambling is usually a way to lose money, not to make money a betting exchange can be a particularly risky way in which to lose money. It would certainly be good advice to anybody, even if they're thinking of starting sports gambling definitely not to start on a betting exchange, but to start with a conventional bookmaker. But certainly, people who are experienced to know what they're doing get a lot of fun out of the betting exchanges. In this section, we have looked at different gambling markets and thought about different ways that people stake money in these markets and the meaning of odds, and how they represent probabilities. We worked through a particular example of parimutuel betting, Which is a good way to understand the fundamentals of sports betting. The example that I used in the slideshow, you can work through that example, I've written it up in the text which accompanies the slides and you can see there how it fits together. If you would like to see a slightly more detailed explanation. The one thing I'd like you to take away from this is that although there are different ways of gambling and different modes and formats, ultimately, it comes down to the same thing as to staking money on probabilities and odds reflect probabilities and from our perspective in terms of thinking or forecasting, we want to know how to derive our own probabilities of outcomes based on our own models and compare our probabilities. with those probabilities implied by the bookmakers.
