(Intro Music Starts) SH: Hello everyone, I’m Sam Hansen SW: And I’m Sadie Witkowski. SH: And you’re listening to Carry the Two, a podcast from the Institute for Mathematical and Statistical Innovation aka IMSI. SW: This is the podcast where Sam and I talk about the real world applications of mathematical and statistical research. (Intro music ends) SW: So, we’ve visited the land of lotteries and spent two episodes touring around casinos. Where is our guide leading us next? SH: Well, do you remember what prompted us to investigate the math and stats of gambling in the first place? SW: Ummm, it was a podcast ad about sports betting right? SH: Right. And that is where our guide, the mathematician, Assistant Vice President at SUNY Erie, and author of the book Mathematics of Gambling and Games, an Introduction to Mathematics David Taylor will lead us next SW: Does this mean I will finally learn what a money line is? SH: In fact you will. But first we need to dig into where the mathematical edge that a sports bettor is trying to exploit exists. Because like we discussed with poker and blackjack last episode, while there is randomness involved sports. Sports betting definitely falls under the games of skill umbrella DT: You know, there’s randomness involved in playing, say, an American football game or a basketball game, but you're relying on the skill of players and any sort of sports better that's making a lot of money is knowing enough about the betting and the players to try to find some sort of advantage. SW: Interesting, so unlike fully random games of chance sports betting is more of an information game? SH: Exactly. The sports book will be trying to gather a ton of information about the games. This includes recent results, injuries, and historic performance, not to mention how the bets coming in on the games look. While the sports bettors are trying to find out the same stuff even faster so that they can place their bets before the sports book can adjust their odds to include the new information DT: That's where I think the people who follow the sports and do a lot of sports betting try to make money is by doing a sense of arbitrage. They have information or they believe they have information that the sports book does not, or they have information that will affect the outcome of the game other than what other people are not thinking. SW: Wow that almost sounds like day trading in the stock markets SH: Honestly it is not that far off, which is why we’re seeing sports being one the main uses of those new prediction markets like Kalshi and Polymarket. There is “technically” a difference as instead of placing bets with odds you buy futures contracts, but they are “functionally” the same thing SW: Fascinating, but since we are discussing gambling I am guessing that we’re going to be swerving a deeper dive into prediction markets? SH: That we will, though I am sure they will become of more and more interest to mathematical and statistical focused researchers as time goes on. So a future episode might dig deeper into them SW: No doubt. So, with all that said, let’s dig into what exactly all those sports bets mean SH: Great idea. Let’s start with the names of the standard one DT: The base ones that have existed for a long time are usually your over under that's very common. There's also the spread and there's also the money line. SH: Of those three, David first guided me through the over under. Small note, I spoke with David during the regular season of the NFL DT: The Bills and the Eagles play at the end of the month up here in Buffalo. So you might say maybe the odds maker says it's 46.5 is the over under, in which case you're betting money. If you're taking the over, you're saying, hey, the odds maker has some reason to think that 46.5 points a summer are going to be about even money. That's their bet. They're going to charge you $110, and if you win, you're going to get $100. If you lose, they keep your money. SW: Just a second, if the sports book is setting the expected combined score of the two teams at 46.5 then why does a bettor have to pay $110 to get a win of $100? SH: Ok, to be clear the $100 win that David is talking about means that you get $100 of winning and $100 back from your initial bet it is just that the sports book keeps $10 so really you get $200 back total while the sports book keeps $10, after all sports books do have to make their money DT: That's how they're going to make some of their money, and they make of their money for people who lose too. You know the hope is if the odds maker is doing their job they're setting the spread at enough so that there are equal number of people betting over as they're under and the house is getting its money from that small little fee to you know what somebody pays and they pay out not quite as much as they win SW: I never realized that. I always thought that a sports book made its money off of people losing their bets, not on what is essentially a poker ante SH: I had no idea either, but it makes sense. Sports books know that they will have to pay out, they have bettors on both sides. They also know that even with all the information they can gather they will sometimes have to pay out big when something really unexpected happens like when Leicester won the Premier League in England. So, collecting a small fee is a much more reliable source of income SW: Oh yeah, of course. Now what about those other common bets that David mentioned, the spread and the money line? SH: We will get to those, but first let’s hear about another podcast from the University of Chicago Podcast Network that our listeners might enjoy (ad music starts) SH: Have you ever wondered what goes on inside a black hole or why time only moves in one direction? Or what is really so weird about quantum mechanics? Well, you should listen to why this universe. On this podcast, you'll hear about the strangest and most interesting ideas in physics broken down by physicists Dan Hooper and Shama Waksman. If you want to learn about our universe from the quantum to the cosmic, you won't want to miss. Why this universe? Part of the University of Chicago Podcast Network. (ad music ends) SH: Welcome back Sadie, would you like to hear about a spread bet? SW: Why yes, yes I would! DT: So spread is kind of similar, but it's saying that one of the teams is better than the other. And in order to make it an even money wager, which is the goal, they want to give points or take away points from the team. SH: And to explain this David used the same Buffalo Philadelphia game he mentioned for over under DT: Let's say the Bills are a five-point favorite. This means rather than just betting on the Bills to win, you would bet on the Bills to win and cover that five points. SH: Which is just another way to say that the Bills have to win by at least 5 points. Which means the Bills can win but you could still lose if you bet on them covering the spread and they only win by a field goal, or three points DT: From the betting perspective, they didn't cover their spread. The Eagles did better than expected. In that case, the Eagles win because they covered their five-point spread loss. SW: What? Buffalo could win but if I bet on them I could still lose? SH: Yeah, that’s sort of rough isn’t it, but the Eagles won from the point-spread perspective as Buffalo only won by 3 instead of 5 or more. Though as they say, a W is still a W in the standings. But as David mentioned this is how the sports books help make a bet on a game between two unequal teams an even money wager. DT: Even money wagers, so you bet $110 on the Eagles to win and cover their spread. Bills still technically win the game, don't cover the spread, so the Eagles win and the sportsbook gives you $100. SW: Mmmm, still feels wrong. SH: Well then maybe the money line will feel a bit better to you DT: In other sports, baseball is probably the most common where instead of seeing the spread, you usually see a money line. SW: Whoa, whoa, wait. Why would the money line be more common in baseball and the spread more common in American Football? SH: Really it comes down to how many points are scored. In lower scoring sports like baseball, soccer, and hockey there are fewer points to play with. For example the most common scores in baseball are 3-2, 4-3, and 2-1 SW: All of which have a spread of only 1, and you can’t really have less of a spread as ties at the end of 9 innings keep going… So soccer would also fall into the money line camp. SH: Even with ties that is exactly true, so it’s much better to have a gambling method that determines payouts based on how likely it is that a team is expected to win. Which is exactly what money lines are DT: So you'll see something like one team is negative 135, the other team is plus 116. Instantly, this says to me, the team with the negative is favored to win. Because the negative 135 means I need to wager $135 on this team. And if they win, I get $100 back. SH: And this means when you have a highly favored team, so in the last season let’s say a game last year between the LA Dodgers and the Colorado Rockies, the top and bottom baseball teams in the National League West last season, you will see some rather bonkers money lines DT: You might see something like negative 350, in which case, yes, you are literally giving the casino $350 with the hopes that you win 100. SH: And just as a reminder what David is saying is that if you win you would get back $450, for your original $350 bet and the $100 for the win. Of course there is the other side to that. For example if the Dodgers were -350 and the Rockies were plus 480. Which means if the Rockies win, and you bet $100 then DT: They'll give you your money back plus the 480. So that's where you can really get a lot of money if you have inside information. But this is, you know, all the casinos put their odds on websites. They see them. You can find websites where it has the odds for multiple casinos. You won't find places where the MGM has odds that are way different than Caesars down the the Las Vegas Strip. SW: Or in other words while it might seem like a great chance to win a huge payout by betting on the underdog, there’s probably a reason that all of the sports books have them as an underdog SH: Yeah, and the sports books are offering you the chance to win those huge payouts because they still want people to bet on those underdogs. After all it is those bets which allow them to cover the winnings of all the people who took the smaller payout bets on the favorites SW: Right, all while making their money on the fees SH: Exactly, and just wait until you hear about some of the other types of bets sports books are raking in fees on by offering in the next episode SW: (Fearfully) I can’t wait (outro music) SH: If you or someone you know is struggling with a gambling problem, help is available. The National Council on Problem Gambling provides a range of resources, including the National Problem Gaming Helpline™ you can reach at (1-800-MY-RESET) and they will help connect you with local resources. SH: Don’t forget to check out our show notes in the podcast description for more about David’s work and a link to his book SW: And if you like the show, give us a review on apple podcast or spotify or wherever you listen. By rating and reviewing the show, you really help us spread the word about Carry the Two so that other listeners can discover us. SH: And for more on the math research being shared at IMSI, be sure to check us out online at our homepage: IMSI dot institute. We’re also on Bluesky at IMSI dot institute, as well as instagram at, you guessed it, IMSI dot institute! That’s IMSI, spelled I M S I. SW: And do you have a burning math question? Maybe you have an idea for a story on how mathematics and statistics connect with the world around us. Send us an email with your idea! SH: You can send your feedback, ideas, and more to sam AT IMSI dot institute. That’s S A M at I M S I dot institute. SW: We’d also like to thank Blue Dot Sessions for the music we use in Carry the Two. SH: Lastly, Carry the Two is made possible by the Institute for Mathematical and Statistical Innovation, located on the gorgeous campus of the University of Chicago. We are supported by the US National Science Foundation and the University of Chicago. SW: Yes, I’m a new person and it’s a new day. I’m going to ignore that I’m tired, it’s fine SH: (laughs) SH: But it makes spense SW: It makes spense? I make good spense SW: I refuse to let that stand (laughs) SW: Podcast Podcast Podcast SH: Podcast Podcast Podcast Podcast Podcast Podcast SW: Podcast SH: Vocalizing