Welcome, and in this session we're going to look at betting odds and how to convert betting odds into probabilities. And we're also going to look at different types of bets that people place in order to understand better how this market works. So first, I want to talk about some of the different types of odds that you'll see, and there are basically three basic ways, three commonly used ways of representing the odds. The first is what is called either traditional or British odds. The second is called decimal or European odds, and the third or what are called moneyline or American odds. And if you visit an online betting site, you'll often find that the bookmaker, the betting site, will allow you to view the odds in any of these formats, depending on which you prefer. So here's an example. So I've taken this data from a website called Odds Portal and what I've got here are some of the games from the 2018, 2019 basketball season. And you can see here the list of the games on particular days. You can see the score of the games because this was loaded after after the games took place and then you can see what the betting odds were. And of course, these were the betting odds before the game was actually played. And you can see two columns there, one labeled one and one label two. And one represents the betting odds on the first name team winning and two represents the betting odds on the second named team winning. And so one thing you might ask yourself is, why do betting sites provide this kind of information? And if you go, you can find betting odds data for games going back for many years. In fact, on some of these websites, lots of information that is provided. And in fact, one thing the bookmakers actually want punters to be is informed about betting markets. They actually like you to know something. The way they view it, the more informed you are, the more likely you are to think that you know what you're doing. The more likely you are to think you're going to win, and therefore the more likely you are to bet. So and always be aware a little bit of knowledge can be a dangerous thing. But it is very useful for us at least to be able to go back and look at some of these betting odds and use them in our analysis of probabilities, which is what we're going to do. So first, now let's look at the traditional British odds and see how they work. So here in the first game, the game in the first row, the game between the heat and the 76ers, you can see that the odds on the Heat winning were 39 to 100 that slashes usually read as two. And what that means is that if you bet $100, you would get back 39 if they won. If the Heat one plus, of course, you get back your 100 dollars initial stake, so you get 100 and $39 back in total. And that can then be converted into a probability. And the way you convert the probability is to take the second number, the number of the slash the 100 and then divide that by the sum of the two numbers 39 plus 100. And that gives you the probability, the implied probability. And that's 79.1% in this example. And in fact, you can see from the game the Heat won pretty easily 122 to 99. So the bookmaker's odds really reflected that fact that they were red hot favorites to win that game. Now here's the same set of games, but here now it's written in the decimal or European odds format. So bear in mind that these odds mean exactly the same thing as the odds we just looked at. It's just a different way of expressing exactly the same thing. And often people like this presentation format because it gives you a very easy interpretation of what you're going to get back. So if you bet $100, your return is going to be 139 or 1.39. In other words, you get 139%. That 100% is just, of course, your original stake. So really, the rate of return on your investment is 39%. That's the amount above and beyond the $100 that you state. And these are very easy to turn into probabilities. To turn them into probability, you just divide one by the betting odds. So here, if you divide one by 1.39, you get 71.9, which of course is exactly the same as the probability we have with the British odds because these are not different odds. These are the same odds expressed in a different way. And to convince yourself at this, you should go through and calculate some of the other odds. So one thing that's going to be fairly obvious if the Heat were the favorites to win the game with the probability being very high, then the probability of the 76ers was going to be very low. And a low probability is going to be reflected in a very high rate of return. So you get a lot of money back because if you bet on the 76ers because their chances of winning were pretty low. And of course, in this particular case, if you bet you would have lost your money anyway. And then, so finally, we come to the moneyline, the American odds format. So moneyline odds are expressed either as a positive number or a negative number. And that has, that means that you have to think a little bit about what it means in each case. So if the moneyline odds are a positive, that means, they state the amount of money you're going to get returned if you stake a $100. And if they're negative, they state the amount of money you have to stake in order to win $100. So here you can see the Heat as the red hot favorites. You have to put up $256 just for the chance of making $100 on your bet. So to convert moneyline odds into probabilities depends on whether they're positive or negative. If they're positive, 100 is divided by the moneyline number plus 100. And if the moneyline odds are negative, then you do the same calculation, but only in the numerator you have the moneyline value. If you think about the Heat example, you would put 256 on the top, and then you divide that by 100 plus 256. So note that you take away the negative signs there. So you measure these in terms of absolute values if they're negative. So it's slightly more fiddly than the other two versions of the odds. But again, it adds up to the same thing here. In the case of Miami, we get 256 divided by 256 plus 100, which is 71.9%, which is the same as the amount that we had in the previous two cases. And of course, as I say, they must be because these are exactly the same odds just presented in a different format. So now what I want to do is talk a little bit about some some of the different types of bet. We've talked so far mostly in terms of winning the game or winning the race as being the type of bet that we're thinking about. And in fact, as we go on in this weekend, the following two three weeks, we are going to focus primarily on winning games, betting on who's going to win the game. But there are other kinds of bets, and in fact, some of these other kinds of bets are often more popular. Now I just want to mention those briefly, even though we're not going to analyze them in this course in more detail. So I'm going to talk about spread bets, over under bets, and prop bets. So spread bets come from the US and are very popular in sports gambling. So instead of offering odds on the outcome of the game, what the bookmaker does is offer a number representing the difference in the points scored by the two teams in the game. Or by the individual athletes, if we're talking about individualistic sports. So, for example, if you had a value of plus ten, the implication of that would be that the favorite wins by ten points or more in the game. And you can bet on either side of the spread. So you could give the points or take the points. So if you give the points, it means you bet on the favorite. So what you're going to say is, favorite will win by more than ten points. And if you take the points, what you're betting is that the favorite will either win but win by less than ten points or that the underdog will win. In which case the points would be net in favor of the underdog. So you can choose which side of the spread you're going to bet on. And again, you can imagine that the bookmaker can balance their books by setting the spread. So they can fix the spread in such a way that they make as much money. Or they pay out as much money in the event of the favorite winning or as if the spread is beaten or if the outcome comes in under the spread. One thing to say about this is that spread betting is particularly suitable for sports like football in America or basketball, where the scores tend to be high. And so the spread has quite a lot of possible outcomes either side of the spread. In games like hockey and soccer, the less well suited to spread betting since the games are relatively low scoring and so there's not a lot of variation either side of the spread. So an over/under bit is also suited to high scoring games. And in this type of bet, you don't bet on one side score or the difference in the scores, you want your betting is the total score in the entire game. So what you're betting on is whether the actual score is going to end up being higher or lower than the total offered. So it will work in exactly the same way the spread bets work. The bookmaker can offer an over/under, and they can balance their book in with the way that they choose the over/under. And then you can decide as a punter which side of the over/under you want to put yourself. Finally, I just want to say a few words about prop bets. Prop bets are something that's become more and more popular in recent times, particularly associated with sports. And a prop bet is based on something related to the game, but typically not nothing to do with who wins or loses the games, but betting on certain types of events in these games. And these events can be very significant or they could be very trivial. So a prop bet, for example, might be on the number of corner kicks in a game of soccer, which would be a pretty important indicator of which team was dominating a game. For example, in basketball you might have the number of blocked shots, for example. Or in cricket, you might have the number of scoring shots in the game. In baseball, you might think of the number of runs, the plus hits plus errors so you could make it in some accumulative, but often a prop bet can have, be something completely trivial. So for example, in soccer, you can think of something like a throw in, which is not a very significant event in the game. But you could bet on the number of throwings in the game. You can also bet on how long it will be before the first throwing happens in a game. And so these bets are often quite popular. Again, these bets you might think there's much less skill involved in these kind of bits. These are more like lottery tickets, rather than relying on the skill of the gambler. And prop bets have in some cases been seen as being somewhat problematic because they can lead to match fixing as well. If it's not that hard to see how you could persuade players that they could say decide to make sure that there was only a certain number of throwings in the game. Or to make sure there was a higher than normal number of throwings in the game without the players think that they were doing anything particularly corrupt. But of course it would be corrupt. It would be interfering with the outcome of the game. And some people think that that's a small step from that to actually fixing the whole game in the end. So related to prop bets is the idea of in- play betting, which has become increasingly popular in recent years. In-play betting refers to betting on events taking place as a game is progressing. And so you can see how this would be particularly well suited to prop bets. So, for example, you could think of a game was betting on how long before a team takes a time out in a game. How long is it going to be before that happens. You can think of an over/under bet based on that as a kind of a prop bet. So you can see that there's an enormous scope for in-play betting and where people can now watch a game on their phone or watch the game on TV and then bet on their phone as they're watching. And sometimes even people in the stadium can be betting using their smartphone at the same time that you can see that these forms of betting have become increasingly popular. And by and large, you might think that this is harmless. As long as it doesn't turn into an addiction, that can just be a bit of fun. But obviously there are risks as well because gambling ultimately can lead people to become financially distressed, okay? Okay so what we've looked at in this session are some basics of gambling and betting odds and shown how the different formats for betting odds relate to the underlying probabilities of the outcomes. We've shown how to derive those probabilities in the three different popular formats. And to familiarize yourself it would be no harm to go and look on some online gambling sites and look at some of the betting odds and how they're presented. And think about how you can calculate probabilities from those odds. We're going to use that in the next couple of sessions where we're actually going to start looking at betting odds in relation to particular games. And look at probabilities and see how successful bookmakers odds are in terms of predicting game outcomes. So we've also looked here at some of the different types of bets, and we've seen that there are a number of different popularized bet. Although this has been very brief, there's no, it's by no means an exhaustive list, but useful to give you some idea of the sorts of possibilities. So the next session we're going to look at the concept of efficiency in terms of the bookmaker's odds and seeing whether how reliable, how reliable bookmakers odds are in terms of predicting outcomes.